Note: Descriptions are shown in the official language in which they were submitted.
- 219S925
TITLE OF INVENTION
FMCW RADAR WITH ANGULAR POSITION DETECTION
R~ K~hO~r_~- OF INVENTION
This Invention relates to frequency modulated continuous wave
(FMCW) radar, and in particular to short range FMCW radar which can
provide the angular position of targets.
Frequency modulated continuous wave (FMCW) radars have been used in many
applications. These such as navigation radars [1], altimeters, and various automot*e radar
applications including station keeping, obstacle avoidance, and collision war~ing [2-4].
- Recent advances in microwave technology and signal processing capabilities are making
automot*e applications a practical technical and commercial proposition.
For short range applications, FMCW~radar systems have- rnany advantages over
other radar systems. These include simple solid state transce*ers, resistance to
- interception and interference, good range resolution, and compatibility with inexpens*e
and accurate signal processing techniques (namely digital signal processors performing
FFTs). FMCW radars have been designed to detect the range and velocity of multiple
targets[5] ,as in U.S. patent No. 5,268,692 issued December 7, 1993,
to Grosch et al, which is lncorporated herein by reference.
The ability to provide angular resolution is critical for many applications. Standard
beam-steering techniques can be applied to FMCW radar systems. Digitally controlled
phase shifters can be incorporated into the RF transce*er, electronically steering the radar
beam in space. Ferrite phase shifters can be used for the same purpose. Both of these
methods change the relati~e phase of the RF signal from various elements in the antenna
2195925
_ 2
array to change the main beam position. However, these standard techniques are
expensive and increase the size, weight, and complexity of the hardware.
1.2 Research Obiectives and Summar~ of Results
The research in this thesis describes a new method for implementing beam-steering
in F~ICW radar systems. A unique radar prototype was designed, built, and tested to
prove the concept. Testing procedures were developed to verify the beam-forming
capabilities of the radar prototype. The VCO linearity, a critical pelroll~lance parameter of
the radar, was greatly improved in the prototype by implem~nting a novel linearizing
algorithm.
The F~ICW radar with digital beam-forming represents an advancement in the art
of radar technology. lt has several advantages over traditional RF-based beam-forming
techniques. First, the hardware costs are lower and the reliability is higher. Second, the
target detection time is reduced. Third, sophisticated signal processing techniques can be
applied to further improve the accuracy of the radar.
The first advantage of the digital beam-forming technique is that the hardware
costs are lower than those of an RF-based system. The digital beam-forming system uses
standard audio frequency components (such as analog to digital converters and op-amps).
These components are inexpensive and are very reliable. In contrast, R~-based beam-
2195925
forming networks use PIN diodes and ferrite material, which are more expensive, lessefficient, and less reliable for long-term operation.
The second advantage of the digital beam-foring technique is that the target
acquisition time is reduced. Only one modulation cycle is required, since the phase shifting
is performed in software. In RF systems, on the other hand, one modulation cycle is
required for each of the RF beam positions. This has the disadvantage of increasing the
target acquisition time by a multiple of the number of switched beams.
The third advantage of the digital beam-forming technique is that sophisticated
signal processing techniques can be applied to the return signals to further improve the
radar accuracy. Sidelobes can be reduced by applying, in software, phase and magnitllde
tapers across the receive array. Windowing functions can be also used to decrease the
range ambiguity in the return signals, and im~ging techniques can be applied to provide a
three dimensional output of targets (in range, angular position, and velocity).
A unique contribution of the FMCW radar prototype is its angular resolution
capabilities. The results, presented in Chapter 4, show that the IF signals from different
receive channels were digitized, phase shi~[ed, and combined in software to provide
angular resolution. Radiation patterns from a single receive channel were measured and
compared to the theoretical patterns. The returns from all receive channels were combined
- 2195925 4
in software, yielding several synthesized patterns with different main beam locations. The
results from the prototype were within the experimental error of the theoretical patterns.
Two additional tests indicate that the radar prototype can determine the range and
angular position of multiple targets, as discussed in Chapter 4. The first test result
indicates that the radar can identify two targets at different ranges and di~erent angular
positions. The second test result shows that the radar can identify two targets at the same
range but di~elen~ angles. This ability to identify range and angular position using digital
beam-steering is a unique and significant conl~ilJulion to the radar capabilities reported in
the literature.
1.3 FMCW Radar Principles
This section describes the basic operation of an FMCW radar system. First, the
general operation of a linearly modulated FMCW radar isillustrated. Next, a detailed
analysis of the FMCW signal is presented. Then, the various types of signal processors are
discussed. The section concludes with a general discussion of the non-ideal effects of an
FMCW radar.
An FMCW radar is shown in Figure I [6]. The radar consists of a modulated
continuous-wave source~ a transmit antenna. a receive ~n~nn~j a mixer, and an IF amplifier
and f~ter stage. A portion of the transmit signal is coupled into the mixer as the local oscillator
(LO). The radar uses the time delay between the transmitted wave and the received wave to
2195925 5
deterrnine target range. This time delay results in a frequency difference between the two
signals. A plot of the tr~ncmtted and received signals for a stationary target are shown in
Figure 2.
VCO
~3 -10 dB \ Trarlsrmt
Filter LNA / AMP LO Receive
IF Output < ~) RF <
~~ Figure 1 FMCW Radar System
The FMCW radar operates as follows. The VCO is linearly rarnped. A portion of the
VCO output power is tr~ncmitte-~, and this wave travels to a fixed target at a distance R in a
tirne t=R/c, where c is the speed of light. The wave is then reflected back to the receive antenna
in time t=R/c, giving the total transit time T=2R/c. This received signal is then mixed with the
.;..g VCO signal. However, since the VCO is linearly modulated, the two frequencies are
slightly offset. The resultant IF signal is thus the difference between these two frequencies.
2195925 6
11 . 3 0 ~,, T rAnsm it
1 1.2~ Receive
-26-~
, 11.24--
.22 -/ -' - - \,
.20 ' ' , , .
o ~ ~ v ~ ~coO~ O
o o g o o o ~o o ~O ~
o o o o o o o o o o o o
Time (sec)
Figure 2 Plot of FMCW Transmit and Receive Signals for St~ nqry Target
A detailed analysis of a linearhy modulated FMCW signal, inrhl~ling Doppler and
second order terms follows [7], This derivation is for a single target, but the effect of multiple
targets can easily be included since the system is linear with respect to the received signals,
The in~t~nt~neous transmit frequency,f, is given in Equation 1,1:
f =fio+ fm t, (1.1)
wherefm is the modulation rate (Hz/sec) ofthe VCO, andfO is the tran~er frequency at t=O,
and t is the time since the start of the sweep. The phase of the transmitted signal is shown in
Equation 1 2:
~ = 2~ J fr dr = 2~r[fOt + 1/ 2fmt2], ( 1.2)
assuming that ~=0 at t=(7.
~19~925
In the following portions of the analysis, aO, bo, and cO are constants that determine the
absolute amplitude of the signals, but have no effect on the derivations. The in.ct~nt~neous
amplitude ofthe transmitted signal is given in Equation 1.3:
a(t) = aO sin 2ir~fOt + (1/2)fm t-]. ( 1.3)
The received signal re~ected back from the target is delayed and ~ n-~te~, as shown in
Equation 1.4:
b(t) = bosill 2ir~fO(t-r) + (1/2)fm (t-r)~] (1.4)
where ris the tirne delay between the tr~n.cm;~ted and received signal; and the IF signal is
c(t) = cO cos 2~foT + fm t r- (1/2)fm ~]. (1.5)
If the target is moving, then
r(t) = r~ + vt (1.6)
where r~ is the range of the target at t=O and v is the radial velocity of the target and r =
2r(t)/c c is the velocity of propagation. Manipulating Equation 1.5 with Equation 1.6 yields the
following:
-c(t) = cO cos 2~T[2rl t(l - 2v/c)/c + 2fo vt/c + 2fm vt- (1-2v/c)/c + 2(fo - fm r~ /c)r~ /c]. ( 1. 7)
The terms in Equation 1.7 can be rewritten as
c(t) = cO cos 27~[ 2fo r, /c - 2fm r,~ /c~ (phase terms) ( ! 8)
+ 2fo l t/c + 2f n vt- /c - 2fm vt- /c~ (radial velocity terms) ( 1.9)
+ 2f r, t,'c (range terrn) ( 1.10)
- 4r~ f h/C ~ (mixed range/velocity term) ( I . I l )
2195925
Equation 1.8 contains phase terrns which do not vary with time. The radial velocity
terrns, contained in Equation 1.9, are dorninated by the Doppler shi~, ~fo Vt/c. The range term
is shown in Equation 1.10, which is proportional to the range of the target. It is generally
represented as
f,~ = 2fr~ rO /c- ( 1.12)
This relationship maps range to an audio, frequency-domain signal, from DC to fs~ where f~ is
the highest IF frequency, norrnally in KHz. The final frequency term, shown in Equation 1.11,
can be interpreted in two ways: first, as the chirp on the range beat due to the l~h~n~ing range,
or, alternatively, as the chirp on the Doppler due to the ~ nging transmit firequency.
For the ~ ;llg portions ofthis thesis, all analysis and data will assume a f~ed target
with a radial velocity of zero. This greatly simphfies the irnpl~ nt~tion of the radar system
under question. However, all analysis and appl;~ ~tion~ (li~lcced in this thesis can be extended
to moving targets. With this assumption, Equation 1.12 becomes the basis of our target
analysis.
The audio signal given by Equation 1.12 must be analyzed in an IF signal processor.
This can take many forrns. Traditionally, the IF signal processors consist of a number of f~ters
which are linked to form a spectrum ana~zer [8]. The IF filter bandwidth det~nnles the range
resolution. For an IF filter bandwidth offB~,; the range resolution is g~en by Equation 1.13 [9]:
R = 2~"f ( 1.13)
219592~ - 9
Furthermore, the number of filters required isfc /fs~
There are several non-ideal effects that can degrade the pe-rul~ce of an FMCW
radar. The linearity of the frequency modulation must be m~int~ined. Any non-linearity's will
result in the spreading and cmP~nng of the IF signaL System noise can also deteriorate
pe-rul~ce. System noise levels are determined by the purity of the VCO, and are therefore
dependent on the ramp rate and phase noise. Other factors in determining system noise are the
receiver noise figure and system bandwidth, and qll~nti7~ti~n errors. These non-ideal effects
will be discussed in Section 3. 5.
1.4 Di~ital Si~nal Processin~
IF signals can also be analyzed using digital signal processors (DSPs) via FFTs [10].
The IF signal is ~ ;iti7Pd using AID converters, and the spectral components of the signal are
determined in so~are, providing phase and mqgnitllde information. The accuracy ofthe signal
processing is determined by the A/D sampling rate (fs) the modulation bandwidth, and the
number of samples [11]. The frequency resolution (and therefore the range resolution) of the
~~1 is given by Equation 1.14:
f M*~T' (1.14)
where M is the total nurnber of samples and ~T is the sampling period, ~T=I/fs . Today, DSPs
are fast and accurate enough to provide target determination in several milliseconds. which is
ecsPnti~lly real time for many applications.
2195925 lo
The analysis presented above can be extended to moving targets, as well as multiple
targets, by utihzing several modulation schemes [5]. For example, for a single target, the
modul~tion can ramp positive, then reverse and ramp negative, as shown in Figure 2. By
con~qnn~ the IF signals dunng these t~,vo periods, the Doppler shift in the RF signaL and thus
velocity of the target, can be determined. Sirnilarly, multiple targets with Doppler shifts can be
detecte~l by rh~nging the modulation rate,fm, ofthe transmit signaL
There are several non-ideal effects that can degrade the pelro,~ce of a DSP. These
effects include qll~nti7~tion and round-off errors. In ~ liti-n, this system uses a digital
fee~ba~l~ system (discussed in Section 3.4) to lineari7e the VCO. This D/A based system
increases linearity of the VCO ramp, but is limited by the hardware components. The analysis
ofthese non-ideal effects will be ~iccllc~e(l in Section 3.5.
1.5 Thesis Outline
Chapter 2 provides a general overview of antenna theory and beam-steering
techniques. Antenna array theory is presented in Section 2.2 to show the effect of applying
a progressive phase shift across the antenna. In Section 2.2, Microstrip antennas are
discussed and the theoretical radiation pattenns of several antennas used in the prototype
are calculated. Section 2.3 discusses various beam-forming techniques, including post-
processing beam-forming techniques and phase shifter hardware. In Section 2.4, an
adaptive beam-forming technique is presented. This chapter is concluded by introducing
the new FMCW beam-steering technique.
- 219S925 11
In Chapter 3, a unique FMCW radar prototype is described. The first section
contains a detailed description of the radar hardware. The software used to control the
radar is discussed in Section 3.2. The data processing and beam-forming algorithms are
discussed in Section 3.3. The novel VCO linearization technique is discussed in Section
3.4. The chapter concludes with a system noise analysis.
The expenmPnt~l results presented in Chapter 4 show the angular resolution
capabilities of the radar system. Section 4.1 describes the test setup used to measure the
radiation pattern of a single radar channel. The pattern is generated by measuring the
Channel I retum from a target at a range of 16 m, as the target is moved from 0~ to 180~
in 1~ steps. In Section 4.2, the returns from all eight channels were combined in software
to synthesize very narrow main beams at 90~, 92~, and 94~. These results show the beam-
forming capabilities of the prototype, and are compared to the theoretical patterns. The
results in Section 4.3 show that the radar can discriminate between two targets, one at 20
m and 88~, the other at 26 m and 90~. Section 4.4 shows that ~he radar can discriminate
two targets located at a range of 30 m, but at two dilrelelll angular positions: 90~ and 94~.
Chapter 5 concludes that the FMCW radar discussed in this thesis provides angular
resolution capabilities. Furthermore~ the thesis concludes that this method of beam-
forming increases the capabilities reported in the literature, thus advancing the art of radar
technology. A summary of the research from this thesis is provided in Section 5.1. Future
work to further improve this technology is discussed in Section 5.2.
2195925
Chapter 2
ANTENNA TEEORY AND BEAM-STEERING TEC~INIQUES
This chapter discusses various beam-steering and im~ging techniques used in radar
systems. Section 2.1 contains classical antenna array theory. Section 2.2 discusses the
microstrip antennas and presents theoretical radiation patterns of the microstrip antenna
arrays used in this thesis. Electrically steered arrays using ferrite and switched phase
shifters, as well as other beam-forming techniques, are discussed in Section 2.3. Adaptive
beam-forming is reviewed in Section 2.4. This chapter concludes with a section on the
theory of the F~ICW radar digital beam-forming technique presented in this thesis.
2.1 Antenna Array Theory
In many radar applications, the target range and velocity are the only quantities desired.
However, for a large class of radar systems, angular resolution is also needed. Several
techniques can provide this information. Radar bearns can be swept across a volurne of space
to providing angular resolution [8]. The antenna can also be mech~nir.~lly rotated. Monopulse
radars are available, providing angular position inforrnation by comp~ring ma~i~lde and phase
in two (or more) separate receiving antennas [12]. In phased array antennas, the radar bearn
can be electrically swept by varying the relative phase of each radiating element [13]. This
section will discuss basic antenna array theory.
2195925 13
An antenna array is a group of two or more radiators geometrically aligned so that the
radiation from the individual elements combine or cancel (depending on the angle offboresight)
at large distances to provide a desired radiation pattern. A linear array is a group of elem-Pnts
aligned along a common axis. If the array has N number of PlP.mPntci equal spacing d between
PlPmPntc, relative current levels L" and relative progressive phase shif't az across the array, then
the array factor is given by [ 14]:
AF((9) = ~ n e~ dcos~-e~ (2. 1)
n=l O
where k=27~/~, and ~ = 90~ is normal to the plane of the array. Furthermore, if each of the
array PIP.rnPntC has a radiation pattem E(~), then the total array pattem is given by:
Aa(~) = E(~J) AF(O). - (2.2)
The quantity Aa(~) represents the phasor addition of N PIPrnPntc at a large distance
from the individu~l PlemPnt~ The relative phase shift, az, of each element can be varied,
~h~n ing the location of the main beam. The relative current levels, I " can be varied to control
sidelobe levels and shape the beam. Similar analysis can be apphed to two (or more)
~imPncinnal arrays [15].
Any radar system providing angular resolution uses the phase and magnitl1de
tion to determine target location. In phased arrays, the phase is changed to steer the
rnain beam location. In irnaging radars, the receive signal from many different channels is
combined in rnatrix forrn to ~ield a two or three ~imPncinnal image [16]. These systems will be
(licc1lcc~P(l in detail in Sections 2.3 and 2.4.
2195~25
'-- 14
2.2 Microstriu Antenna Arrays
Microstrip patch qnt~nnqc have been well docllm~nted in the literature [17-22]. They
have rnany adv ntages, in that they are inexpensive and easy to mqmlfqctllre, they are
physically thin and conr~ ,, they have relatively high gain and efficiency, and they can be
easily incorporated into an array with an integrated feed structure. There are numerous
disadvantages as well: They are inherently narrow band, they have high cross po!qri7qtinn, and
they are sensitive to en~ onlllelllal vqri~tion~ Feed network losses also lin~it the practical size
ofthe array, and therefore the upper limit on gain.
The most basic microstrip antenna element is the rect~n~ r patch radiator. The input
irnpedance of this structure is several hundred ohrns, thus requiring an irnpedance m~tching
network. Using a quarter-wave microstrip transformer can result in 1.5:1 VSWR bandwidths
on ~he order of 1.5%, sufficient for many apphcations. The efficiency of microstrip patches is
generally between 25% and 85%. The gain of a single rect~ng~ r patch is on the order of +4
to +8 dBi and the radiation pattern is broad in both azimuth and elevation, with 3dB
beamwidths of approximately 60~ [23]. The radiation pattern in the ~7irnllth~1 plane is
approximated by Equation 2. 3:
sin(2~Ta- cos(~))
E(~) ~ (2 a cos(~) (2.~)
where a is the patch width and ~90 ~ is norrnal to the plane of the microstrip patch.
--- 219S92~ 15
Individual microstrip patch PlPmPntc can be combined to form array ~nt~nn~c A
corporate feed structure uses ~1-l power splitters to sequential~r split (or combine) the power
and feed n indin,idual elements [24]. Series feed structures use n-l tran~ro~ el~ between the
individual elements [25]. Both of these feed methods have their advantages and disadvantages.
and some feed structures use a hybrid ofthese two feeds [5].
The radar descnbed in this thesis utihzes microstrip patch ~ntPnn~c as the primciple
ra&tion element. The basic building block is a lx4 array PlPmPnt, shown in Figure 3, using a
series feed structure. This element has an elevation 3 dB bearnwidth of approximately 16~, and
an ~7imllth~1 pattem given by Equation 2.3. The transmit antenna is constructed of two of
these lx4 arrays, and is shown im Figure 4. The receive ~nt~nn~ are constructed of four of
these lx4 arrays, shown im Figure 5. Eight ofthese receive nt~nn~c are used in the radar, one
for each channeL
The calculated :17imllth~1 ra&tion pattern of the 4x4 array is shown in Figure 6. All of
the elements in this array are fed in phase, resultimg m a main beam at 90~ and a symmetrical
response on both sides of the main beam The 3 dB bearnwidth is approximately 16~. The first
sidelobe level is approximately -14 dB, and the secondary sidelobe level is below -22 dB. Nulls
m the pattern occur at 90~ + 22~ and 90~ + 45~.
219592~ 16
300 mils x
330 mils
Microstri:p
Inter Patch
Impedance
W ~/4 Transformer
L~
50Q Input Line ~
Figure 3 lx4 Microstrip Antenna Array
2195925 17
~0.750"~
300 mils x
330 mils
Microstrip
lnter-Patch
Transformer
~/4 Transformer
J
50Q Input Line ~
Fi~ure 4 2~4 Microstrip Antenna Array
2195925 18
~0.750" ~11 0.750" ~11 0.750"~
~ 300milsx
330 mils
Microstrip ~ter-Patch
Transformer
50Q Input Line ' ¦~
Figure 5 4x4 Microstrip Anterma Array
- 2195925 19
o
~ ~ I Theoretical Pattern
_ -20 -
~-40
-50
-60 : , .
ooooooooooooooooooo
~ ~ oo ~ o -- ~ ~ ~t ~ ~o _ _
Angle (degrees)
Figure 6 Calculated A7imllth~l Radiation Pattem of a 4x4 Microstrip Antenna Array
Eight ofthese 4x4 arrays are used as the receive ~ntrnn~ in the radar. The c~lrlll~ted
radiation pattem for the 8x(4x4) array, with all rl~mrnt.s fed in phase, is shown in Figure 7. The
pattem has a 3 dB beamwidth of 2~ centered at 90~. The first sidelobes are approximately -14
dB, and further sidelobes decrease as the angle increases away from the main beam.
This main beam is '~steered" by varying the relative phase ~ across the array. Equation
2.4 was modified into the following form:
)= E(H) ~ ~e~ cOs~-c~v~ ) (2.4)
C'.V=I ~1
~,vhere n varies from 4*(CN- I ) to 4*CN for the second s~mm~tion. The phase is progressively
increased (or decreased) from channel-to-channel across the array. For a progressive phase
shift of c~ = -35.7~, the main beam position changes to 92~. The calculated pattem for this case
- 2195925 20
is shown in Figure 8. This pattern also has a 3 dB bearnwidth of 2~, and first sidelobes at
approximately-14 dB. However, grating lobes appear at several angles. These gratmg lobes
are present because ofthe l~rge spacing between the 4x4 arrays.
Theorehcal Pattern
- 1 0 - - -
-20
-60
ooooooooooooooooooo
x G~ O -- ~ ~ ~ _ _ _ _
Angle (degrees)
Figllre 7 Calculated A7im..th~1 Radiation Pattern of an 8x(4x4)
Microstrip Antenna Array with a 90~ Main Beam
~ I Theoreocal Pattern
-10
O O O O O O O O O O O O O O O O O O O
~ ~ ~ ~, ~ ~ 00 ~ O = ~ ~ ~ ~ ~ ~ 0~
Angle (degrees)
Figure 8 Calculated A~mllth:ll Radiation Pattern of an 8x(4x4)
Microstrip Antenna Array with a 92~ Main Beam
- 21959~5 21
By increasing the progressive phase shift between channels to -71.4~, the main beam
position was moved to 94~, as shown in Figure 9. This pattem also has a 3 dB beamwidth of
2~. The grating lobes are quite high, at -12 dB, but the close sidelobes are still appro~mately
-13 dB.
Theore~ical Pattem ¦
-20
3~ -30
-50- ~ ~ t
-60
o o o o O O O O O o o o O o o o o O o
~ ~ ~ I~ CO ~ O ~ ~ ~ ~ ~ I' X
Argle ~de~rees)
Figure 9 Calculated A7iml-th~1 Radiation Pattern of an 8x(4x4)
Microstrip Antenna Array with a 94~ Main Beam
These calculated pattems show that the main beam ofthe 8x(4x4) array can be tilted by
applying a progressive phase shift between the channels. The main beam location was changed
from 90~ to 92~ and 94~. However, the sidelobe and grating lobe levels in the radiation pattems
increased with increasing phase shift. The beam can also be shifted to 88~ and 86~ by apply~g
a +35.7~ and +71.4~ progressive phase shiflc (respectively) across the array. In Chapter 4, these
calculated radiation pattems ~ill be cornparedto the synthesized pattems derived from the
radar return data.
- 219592S 22
2.3 Beam-Formin~ Techniques
All radar systerns providing angular resolution manipulate the phase and m~itllde of
the receive signals to locate targets. In phased array systerns, the phase delay in each channel is
switched between two or more di~ values, and the receive beam is formed by s..mmnlg
these delayed signals. In other systems, the received signal is amplified and then split into
paths, each path with a dia~le.l~ phase delay, and the signals are then recornbined to
form ~imllh~neous bearns. This section reviews these two types of beam-forming techniques.
A phased array antenna is an electrically steerable ant~nn~, where the relative phase of
each element or group of elem~nts is controlled digitally [6]. By varying the relative phase
shifts, the main beam position can scan a wide area of space very quickly. The relative phase
differences can be achieved by diode switching of RF paths or by varying the pha~se velocity in
waveguides by using ferromagnetic m~ten~l~ (known as ferrite's). Phased arrays have many
advantages, which include speed and flexibility [8]. The beam can also be given ahmost any
shape, swept in any fashion, or switched almost in~t~nt~neously to any desired position. The
pattem can also be split into several beams. and thus track muhiple targets ~imllh~neously.
However, electronic scanning also has several key disadvantages. The systerns are
generally very complex and expensive, the efficiency of phased arrays are lower than those of
f~ed beam systems, the arravs suffer extreme main-beam broad~ning at extreme scan angles.
and they are also generally larger and require more space and power.
2195925 23
Phased arrays can use clc~,llol~ically controlled phase shifters on the transrnit ~ntonn~
receive ~ntPnn~, or both. Ferrite phase shifters are usually used on transrnitters due to the high
power-h~nllling capabilities [26-28]. PIN diode switched-line-phase shi~ers are generally used
with receive antenna arrays due to the low power levels [29-31]. Many phased arrays
iUurninate the target area with a broad transmit beam and used a switched beam phased-array to
locate the target within this area. A detailed analysis of phased array systerns is presented in the
literature [6,13,16].
A post-amplification beam-forming network is shown in Figure 10 [6]. The network
has three receive ~nt~nn~c, power splitters, LNAs, and three sets of phase shi~ers, as well as
three power combiners. A portion of the receive signal from each of the rh~nnel.c is phase
shifLed (relative to the other channels) and recombined to form a fixed antenna beam pattern.
The network forms three of these separate antenna bearns ~ h~neously. The RF signals
could have been converted to a lower IF frequency and combined, so long as a common LO
signal was used to preserve phase il.fol~ion. (The advantage of pe~rul~ g phase shif~ing at
lower frequencies is reduced cost.) Many other systems have been developed which provide
multiple radar beams ~iml-h~neously [32-37].
In any type of beam-forming systern, the channel-to-channel amphtude and phase
errors must be controlled. Sources of phase error include antenna mic~lignmPnt RF and IF
channel phase mismatches and phase incoherence due to path differences in the LO signaL RF
path lengths, etc. In addition. variations in the IF and RF channels cause amplitude differences
[38]. These errors can seriously degrade the target detection capability [39].
219~25 24
Nô 2 /~)
\\ I
+ ~'~ +
IAmplifi I IAm~lifi I IAmplifi I
1.1 ... ...
ISUMI ISUMI ISUM
+ + +
Beam Beam Beam
No. 3 No. 2 No. I
Figure 10 Post Amplification Beamforming Network
219Sg25
2.4 Adaptive Beam-Formin~ Techniques
In the systems described in Section 2.3, it was ~cqlmPd that the m~ le and phase
errors in each of the receive channels were controlled and held below a determined threshold.
Furthermore, it was assumed that the relative locations of the receive elem~ntc were known? in
other words the ~l.om~ts were fixed in space. In some applications, however, the element
locations are not fixed over time? so the m~gn~lde and phase errors are very large. This section
discusses one method of removing these errors.
Adaptive Bearn-Forming (ABF) techniques have been applied to an X-band radar
system to compensate ffir geometric and electrical distortions, allowing the system to produce
images of an airplane with good angular resolution [40]. In this system, the phase errors due to
channel micm~t~ element location, and LO errors were grouped into a single error term for
each charmeL (The m~gni~lde termc in the different receive channeLs are determined to be
negligible, and are therefore ignored.) These error terms were determined by ana~yzing the
complex returns of the target being imaged. Once the error terms were known, the rnatrix of
complex returns was combmed to form an irnage of the target.
The ABF procedure assumed that there existed a point-like scatterer or source havmg a
large radar cross-section some~hhere m the field of view of the imagmg system. The physical
size ofthis source is govemed by Equation 2.4 [41,42].
AR
Ph.,sicalSi e= ~L (2.4)
2195g25-
26
where ~ is the wavelength, R is the radar to target distance, and L is the size of the imaging
qntPnn- Furthermore, the echo strength from the scatterer must exceed the total backscatter
from all other sources in its range bin by at least 4 dB.
The system under questien is shown in Figure 11 [42]. The receiving array is shown
distorted in t~,vo dimensions: the elPm~ntc are displaced from a datum line, and the element
spacing is not uniform. During operation, an RF pulse is transmitted toward the point scatterer.
The re'dected wavefront is then sampled at each of the receivers. The measured amphtudes and
phases are effected by the displ~cPmPnt of the antenna elpm-pnts from the design positions. The
phase error can be significant, and must be less than a tenth of a wavelength if the gain of the
antenna is to be held within I dB; smaller if the sidelobes must be controlled [41,42]. Similarly,
the variation in the receiver RF and IF hardware must be held under tight controL In practice,
the measured arnpl~tudes at the individu~l receivers vary little due to the geometric errors ofthe
receiving array and the receiver channel variations in the individual receivers. However, the
phase information is more sensitive, and is ec~Pntiqlly destroyed if the displacement error or
receiver channel phase errors exceed a small fraction of a wavelength.
The application of adaptive beam-forming has been used to cornpensate for the
displqcPmPnt errors and channel phase errors. Since the m,qgni1~lde variations in the receivers
are minimql the signal processor searches across all range bins for the smallest variation, and
d~PcignqtPs this range as the reference range. Then the signals in each channel are phase shifted
such that the reference range phases are all equaL This process is called phase conjugation
-- 2195925 27
[43,44], and is shown as the feedback network in the lower right of Figure 11. A~er the phase
errors are normqli7~, the beam-forming algorithms are applied to fficus the signals ~om all
channels and form narrow beams or images.
Table I describes the ABF imaging algorithm [40,42]. In step 1, the echoes received by
each antenna element are sampled, rligiti7e~1, and stored. Step 2 consists of searching through
the ranges for that range bin which exhibits the smallest normqli7~d variance of the echoes
across the array. This range is decignq-ted as the reference range, R". In step 3, the signal
processor conyugates the phases (in each channel) at R~, to form a weight vector, and in step 4
phase shi~s echoes in other range bins by the weight vector. The array is focused at all range
bins in step 5, and is scanned in a_imuth to form the two--lim~n.ci- n~l image in steps 6 and 7.
Thic algorithrn is ~om~timPC called the "~ ~;""ll~ variance algorithrn (MVA) or the dom~nt
scatterer algorithm (DSA) [39].
A bistatic radar system was used to d~m-.nctrate the abihty ofthis technique to produce
an aircraft image. An X-band trqn.cm~er radiated I kW peak power, in 7 ns pulses. This fixed
the range resolution to I m. The radiated and received signal bandwidth was 150 MHz. The
transrnit antenna was a 1.2 m parabolic dish and was mec~llq-ni~qvlly steerable to follow the
target. The receive array consisted of 32 X-band receivers deployed on a laboratory rooftop,
spaced approximately I m apart. The total array size was approximately 1,000 wavelengths.
Assuming the antenna is diffraction limited, the beamwidth is approximately the reciprocal of
its si_e in wavel~ngths [45]. This assurnption is valid once the ABF has been performed.
~ lss~a~
- ~8-
fr~i~S~n9 ~hen r~ ed in ~il~ pre
~ 219592S 29
Table l Adaptive Beam-Forming Algonthm
1. Measure and store complex envelopes of samples. Aineifin
Range bin Ain.
2. Find Ro such that Ao")~A for aU channels n. Aei~n
3. Phase rotate at R{, by phase conjugate in relation to Aei~o
referenceellern~nt ei(ff)~~n)
4. Phase rotate all range elements. Aj ei(fin~~
A J[fin~ll)~+kx2n/2( I/R l+ I/RO)~OB
5. Focus at each range Rj. ~n~ - in
6. Phase shift linearly with angle. Bjnexp(jkxnu)
7. Sum at each range element. . Sj(u)=SBjnexp(jkxnu)
Therefore, the expected beamwidth of the array is approxi~ ely 10-3 rad or 1 mrad. At
3 km,this corresponds to a transverse resolution cell width of 3 m. Each receiver used a 19 X
14 cm hom antenna with a horizontal beamwidth of 12~.
All receivers were phase locked to a common 120 M~ master oscillator. The
oscillator's output was frequency multiphed to provide the proper RF and LO power. Each
antenna in the array received a modulated RF wave from the echoes of the targets and clutter.
The received waveforms were detecte-l~ coherently quadrature-demodulated, and sarnpled at
200 meg~camrles per second. Each quadrature sarnple was converted into an 8 bit digital
word. Each receiver had a number associated with each range bin. Therefore, if there are m
range bins, and n receivers. an ~7~X7l rnatrix was formed with the associated return signals. The
function of the signal processor was to transform this matrrx into an irnage. If the array had no
geometric or electrical phase errors in each of the arrays, an irnage could have been formed
- ~lg5925
immP li~tP~y However, because of the sensitivities discuss,ed earlier, and the large s~e of the
array, the adaptive beam-folming techniques were needed to form an image.
DETATT.~n DESCRIPTION OF ~K~r~KK~v EMBODIMENT
2.5~CVVBeam-Steer~Radar
.
ThLs thesis describes a new and unique FMCW radar with bea_-steering capabilities.
This new technique combines the radar IF signaLs in software to provide angular resolution. A
system block diagram of a four-channel radar is shown in Figure 12. This system consists of a
single, broad beam transmit ~mPnn~ a voltage controlled oscillator (VCO) and m u~iple receive
channels. Each receiver consists of an ~nt~nn~, a mixer, and an IF filter and arnphfier stage. All
mixers are driven by a common LO source (the VCO). The IF signals are synchronously
(ii{~i7PIl, and an FFT is performed to det~rm~e the complex spectral components of each
return signaL These complex spectral components from each channel are co~ined to provide
angular resolution of the target or targets. This section outlines the principles and algorithms
used in the F~ICW beam-steering radar.
In F~ICW radar with digital bear~steering, a linearly modulated CW signal is first
transmitted. The energy reflects off of the target and is then retumed to the receive antennas.
The magni1~ldes of the retums should be approximately equalL, but the relative phases will be
determined by the locations of the receive ~ntPnn~s within the array. These signals are then
modulated to the IF frequency by the receive mixers, introducing m~gni~lde and phase errors.
These errors are due to variations in mixer conversion loss, variations in path lengths in the LO
feed network, RF receive network, etc. These signals are then amplified and filtered in the IF
- 219S925
amphfier and f}ter chain, adding additional phase and m~ de errors. Finally, all channels are
sampled synchronously.
The digital signals from each of the channels are combined to det~.rmme the angular
positions ofthe target or targets. ~-l's are used to decompose the signals from each charmel
into a complex _atrix with a m~gnit~lde and phase term for each ofthe range bins. For a single
target, the resultant magnitllde term is a product of the ~F signal level (which is proportional to
the RF return m~gnit~lde) and the individual error ter_s ~cc~ ted in the signal due to
channel variations. The resultant phase term is a ~Imm~tion of the phase of the return signal
~ and the individual phase errors which accllmlll~ted in the signal due to channel variations. The
errors in these terms are removed by using a cahbration algorithm~ and the resultant complex
signals are cornbined using array theory to determine the angular position of the target or
targets.
A mathem~ti~l representation of the calibration process ffillows. The return signal
received by the antenna is given in Equation 2.5:
Fn = MRF e , (2.5 )
where n is the channel number index, ~RF is the m~ lde of the RF signal and ~RFn is the
relative RF phase angle. In general, if the target is a large distance from the array, the
m~gnitlldec will be appro~imately equal. However, the RF phase angles will vary depending on
the location of the target. The absolute phase angle of the return is not important, however, the
219S925 32
relative phase di~erences between dilrerelll channels must be preserved if accurate bearns are
to be produced.
A~er this signal is converted to the IF frequency, it is appro~mated by Equation 2.6:
G = M e~Fn E eSn (2.6)
where C is the rnixer conversion loss, MIF = CMRF is the IF signal level, q~lFn iS the IF phase
angle (in general it is proportional to the RF phase angle), En1n is the magnitude variation error
associate with rnixer n, and sn is the phase error associated with the rnixer, LO and RF feed
network, etc. A~er the signal is amplified by the lF chain, the signal is given by Equation 2.7:
Hn MlFe E~nn e E1FAn~Pe, (2.7)
where EIFAMP is the magni~1de error introduced by the IF arnplifiers and filters, rn is the phase
error due to the IF chain, and Hn is the resultant IF signaL This is rewritten with the error terms
grouped, and is shown in Equation 2.8:
Hn = MIF e~Fn Etn e~n = M eAn (2.8)
where Etn is the total ma~ de error m channel n, ~n is the total phase error, Mn = M~FE,n is
the total m~gnitllde response, and An = ~Ifn + Tn is the total phase angle. These phase and
m~gni~lde error terrns are due to hardware variations, and can be ~c.qlm~d to be time invariant.
The problem at hand is removing the error terms, leaving only the target mqgnihlfle and
phase information. The phase term can be uniquely determined for by me~ mg a target at a
known angle. The m~gni~lde terrns can be normqli7t d to a common m~grihlde, thus removing
any variat~on errors. This is accomph hed by performing a calibration mea~ of a target
- 219S~25 33
Receive
~_NA I F~3ter 1~ D I
Receive
Filter 2h'l~ 2
Receive - LO
NA 3 Filter 3~D 3
Receive LO
Filter4h D4
LO
VCO
Transrnit
D/A
~y
~Figure 12 Four Channel FMCW Radar with Digital Beam-Forming
- 2195~25
34
at 90~ for each of the range bins. According to array theory, the RF ma~itlldPs and phases in
each channel should be equal for targets at all 90~. Therefore, any differences in signal
mqgnih~ c and phases between the channels can be attributed to the error terms. A calibration
vector, comprised of a mq.~hude term and phase term, is cql~lqted from the return at 90~ and
used to remove these errors. The mqgnit lde terms from each of the channels are normqli7~d by
rnultiplying the mq.~ihl-le in each channel by the calibration term CM(n) = M~ / Mn for each
channel n. The phase terrns are normqli7~d by adding the cahbration term CA(n) = -An from
each ofthe measured phase values in each channeL
It should be noted that the channel errors are due in part to the di~e~ phase and
ma~it~l(le responses of the IF filter and amplifier chain. These filters are constructed of
components with moderately large tolerance values (10% for capacitors and 1% for resistors).
It is reasonable to assume that the phase and m~gnitllde errors of the dilrt;~ lF filters will
vary over the IF frequency range. Therefore, in order to assure an accurate calibration vector, a
~ target calibration should be performed at each range of interest.
219532~ -
The general algolilhlll ofthe FMCW radar with bea~fomnng follows:
Step 1: Measure the return of a target at range R~ at 90~.
Step 2: Perform cornplex ~-1 on retum. Determine range bin k with largest target response.
(Yields Hn = Mn eAn in range bin k.)
Step 3: C~ e calibration vector for each channel for this range bin. (Yields CM(n) = M//~Mn
and CA(n) = -An = -m.)
Step 4: Measure retum of target at range R~ at angle ~. (Yields Hn = Mn e~Fn +rn- )
Step 5: Calibrate the retlun for each charlneL (Yields Hn(cal) = [Mn ~MI/Mn ]e~Fn +rn e-~n
= Ml e~7n~ the desired result with error terms removed.)
Step 6: Perform bea~steermg to det~.mine target location by cornbi~ing results of all
channels.
21gS925 3~
Chapter 3
FMCW RADAR SYSTEM WITH DIGITAL BEAM-FORMING
PROTOTYPE DESCRIPTION
This thesis describes a new and unique FMCW radar with digital beam-forming
capabilities. Part ofthe contribution ofthe thesis is the design, construction, and testing of
a unique radar prototype to demonstrate the concept and verify the pel~o~ ce. This
prototype includes a new implementation of a VCO linearization technique critical to the
radar performance.
This chapter discusses the hardware and software components of the new F~fCW
radar system with digital beam-forming capabilities. Section 3.1 describes the radar
hardware. Section 3.2 describes the software used to control the radar. The post-
processing routines and beam-forming algorithms are described in Section 3.3, the VCO
linearization technique and implementation are described in Section 3.4, and a discussion
ofthe dominant radar non-ideal effects is presented in Section 3.5.
3.1 Radar Hardware Description
This section describes the hardware used in the radar system. The overall system
block diagram is sho~n in Figure 13. The system is composed of a VCO (with an
integrated D/A converter system), various power splitters and isolators, a transmit
D/A FlFO's D/A Transmit
--d~ ¦ Y'~~ -~J -3 dB LO Feed
d7 'r -1~ -3 dB
4 Delayq) ~ DelayLine
FIFO #l A/D #l
Mixer BaDk I
do l I I ~ Rx4
d~ I r.H~
O-~tp + ('H4 ~K ~) I O Fl~n~l ~ ~< C~5
Filter/Gai~ ~tages
FIFO #2 A/D #2 Mixer Bank 2 ~
dn ~ HS ~_~ Rx
PC Controller ~H~
d, ~H
(~H~ ~
FigureZ Eight Cha~nel FMCW Radar with Digital Beam-Forming
21~92S 38
antenna, a bank of 8 identical receivers (each with a receive antenna, mixer, and lF filter
and arnplifier chain), an overall system-control circuit with a master clock and AID
converter system, and a computer controller. The radar system also has a VCO linearizing
circuit, comprised of a delay line. a coupler, a mixer, and an IF filter and gain stage.
3.1.1 VCO with Integrated D/A Converter
This section describes the VCO and the integrated D/A converter system used as
the frequency source for the radar system. The VCO is a Voltage Controlled/Dielectric
Resonator Oscillator (VC/DRO) constructed of a FET, a dielectric resonator, a varactor
diode, arld DC power supply and bypass components. The VCO is built on low-cost soft-
substrate microstrip material. The circuit configuration is shown in Figure 14. The
oscillator is in a series feedback configuration, with the common terminal (the drain)
termin~ted with an open circuit tr~ncmi.c.cion line [46]. The oscillator frequency is
determined by the resonant structure of the two rnicrostrip coupled lines on either side of
the dielectric resonator, the varactor capacitance, and the resonant frequency of the
dielectric resonator. The resonant frequency of this structure can be changed slightly by
varying the capacitance in the varactor diode, achieved by changing the varactor voltage.
(The gate output ofthe VCO, usually terminated in a 50Q load, is instead used to feed the
delay line used for linearization, as discussed in Section 3.4.)
219~925
39
+5.00 Volts
~, Output #l
1~
~ 20Q
Control <
Voltage
Output #2
Figure 14 11.2 GHz DR/VCO with Dual Output
219Sg2S
The important characteristics of a VCO are the DC operating conditions. the
frequency and tuning range, the power output and change in power level over the tuning
range, the phase noise, and the spurious outputs. The DC supply voltage is +6.00 V, at
80 mA. The fun~l~m~nt~l frequency (at zero control voltage) is 1 1.176 GHz, with a power
output of +15.6 dBm. The VCO tuning range is +0.0 to +7.0 V, with a bandwidth of 96
MHz. The power output, taken off of the source port, varies approximately 3.8 dB over
this measured tuning range. The plots of power and frequency versus tuning voltage are
shown in Figure 15. (The actual tumng range used for the radar is limited to +5.0 V,
providing 80 MHz of bandwidth and less than 1.8 dB of amplitude variation. The effects
~ of this amplitude modulation are further reduced because of the use of a balanced mixer. )
The phase noise and spurious response are provided in Table 2.
.30 ~ 20.0
28 ~ - 18.0
26 ~ - - - - - 16.0
24 ~ ~ ------= - - - ~- 140
.22--~ --- .- 120 ~
11.20---- - ~ - - - loo ~.
-11 18 -/ ~ ~ ~ - 8 0
6 - - - - 6.0
.14 - - - ¦Frequ~CY (GHz) ¦ 4 0
- - - - - Power (dBm)
11.12 -- - - - ~ - - - 2.0
I 1. 10 o,o
ooooooooooooooo
~ '~ ~ '~ ~ ~ O ~ o ~ o v) o v~ o
VCO Voltage (volts)
Figure 15 VCO Power and Frequency versus Tuning Voltage
2195925
41
Table 2 Voltage Controlled Oscillator Characteristics
Power Supply Voltage +6.00 V
Power Supply Current 80 mAmps
Output Power +15.6 dBm
Frequency ((~,) zero control voltage) 11.176 GHz
Tuning Range (0 to +7 V tuning voltage) 96 MHz
Output Power Variation over Tuning Range 3.8 dB
Phase Noise -100 dBC ~,) lOkhz offset
Spurious Power <60 dBC
A custom D/A converter system was used to accurately control the VCO voltage,
as shown in Figure 16. The system used a 12 bit Analog Devices D/A chip (P.N. AD7845)
[47], two Dallas Semiconductor 8K x 9 bit FIFOs (P.N. DS2013) [48], various flip-flops,
and a master control clock of 12.8 MHz. The converter system had five major inputs: a
load pulse for the low bits, a load pulse for the high bits, a reset/initi~li7e pulse from the
computer interface board, a start pulse from the overall system control circuit, and the
master clock from the system control circuit.
The operation of the D/A control circuit proceeded as follows. The D/A
coefficients were loaded into the FlFOs using the computer-intelface board. The 12.8 Mhz
master clock was reduced to a lower clock rate of 800 KHz (using a divide-by- 16 circuit).
A start pulse was received from the system control circuit (discussed in Section 3.1.6),
and 4096 D/A samples were clocked from the FIFOs into the D/A converter. This process
took approximately 5.12 msec (the radar modulation time period). The D/A output
voltage was then used to sweep the VCO, providing the modulation for the radar. The
output was filtered using ~ I kQ resistor and the varactor's naturaL internal capacitance.
219~92~
42
D0 VCO
D(~
PC CorltrolleD/, ¦¦¦ F{FO 1 ~ 20Q 7k~ Output
D7 ~,
R D/A
W D8
- Dll
FIFO 2 ~D
'~? D15
~L
12.8 Mhz System Clock .16 800 Khz 4096 Counter
EN
Figure~Digital-to-Analog Converter Circuitry
16
- 219S925 43
3.1.2 Couplers, Isolators, and Power Splitters
Various couplers, isolators, and power splitters were used in the radar to provide
isolation and to couple portions of the VCO power for various uses. Two 10 dB couplers
were used to provide energy to the transmit antenna as well as the linearization mixer
(described in Section 3.1.7). Willcinson splitters were used to provide in-phase power for
the 8 receiver channels. Because load variations can cause frequency pulling and amplitude
modulation, the isolators were used to buffer the VCO output.
3.1.3 Transmit Antenna and Transmit Power
A 4x2 microstrip antenna array was used as the transmit antenna for the radar, as
shown in Figure 4. The antenna characteristics are provided in Table 3. The operating
frequency is 11.125 GHz to 11.300 GHz, with a VSWR less than 1.5:1. The gain is
approximately 16 dBi, and the antenna in vertically polarized. The ~7iml1th 3 dB
beamwidth is approxirnately 30~, and the elevation beamwidth is approximately 16~. The
antenna is fed via an SMA connector. A 10 dB coupler is used to provide approxirnately
+3 dBm from the output of the VCO to the transmit antenna.
-- 2195925 44
Table 3 Transmit Antenna Characteristics
Frequency 11 .125 GHz to 11 .300 GHz
VSWR(50Q) < 1.5 1
Gain >16 dBi
Size 2.0"x4.0"
Connector Type SMA Female
Polarization Vertical E-Field
Elevation Beamwidth (3 dB) 16~
Azimuth Beamwidth (3 dB) 30~
3.1.4 Receive Antenna, Mixer, and IF ~ilters and Amplifiers
This section describes the radar receiver. The receiver is co_prised of 8 identical
channels. Each channel has a receive antenna, a mixer, and an IF filter and amplifier stage.
Each receive antenna is a 4x4 microstrip array made on soft substrate material, and is
shown in Figure 5. The receive antenna characteristics are given in Table 4. The operating
frequency is 11.125 GHz to 11.300 GHz, with a VSWR less than 1.5:1. The gain is
appro~mately 18 dBi and the antenna is vertically polarized. Both the a7imllth and the
elevation 3 dB beamwidths are approximately 16~. The antenna is fed via an SMA
connector, and is designed to attach directly to the mixer units.
Table 4 Receive Antenna Characteristics
Frequency 11 .125 GHz to 11 .300 GHz
VSWR(50Q) < 1.5:1
Gain >18 dBi
Size 3.2"x4.0"
Connector Type SMA Male
Polarization Vertical E-Field
Elevation Beamwidth (3 dB) 16~
Azimuth Beamwidth (3 dB) 16~
-- 2195925 45
The rnixer used in each receive channel is a single-balanced design. An ~'
HMS3202 dual diode package cont~ining two Schottky Barrier diodes is used as the
active device [49]. The mixer circuit is a "Rat Race" coupler design [50], and is made on
soft-substrate material. The recommended drive level for each diode is -5 dBm to +2 dBm
(or -2 dBm to +5 dBm per diode pair). The IF output is taken directly offthe common
terminal between the diodes and fed into the input stage of an audio LNA (a T.I. TL084
JFET input op-amp [51]), with an input impedance of 1000Q. Each mixer has a measured
conversion loss of 6. 0 to 6. 5 dB.
The 8 mixers are subdivided into t~,vo banks of four mixers, each bank cont~ining
one input port for the LO and four inputs for four sets of receive antennas. The banks also
contain integrated Wilkinson power spl'itters to provide equal, in-phase LO power to each
mixer [52]. The total LO drive power for each bank is approximately +9 dB~
3.1.5-lF Filter, Gain, and Offset Ampliflers
This section describes the IF gain and filter stages. The IF channels are constructed
of five sets of arnplifiers and filters: the LNA section, a fixed gain stage, a low-pass filter
stage, a variable gain stage. and a DC offset stage. All of the filters and amplifiers used
precision resistors and standard capacitor values. A second-order Butterworth high-pass
filter was used as the LNA [53]. The filter had a cutofffrequency of 1.0 KHz, and a rollup
of +20 dB per decade from DC to the passband. The fixed gain stage provided +20 dB of
gain. The low-pass filter was a fourth order Butterworth design with a cutoff frequency of
- 219~925 46
10.0 KHz. This filter also acted as a Nyquist filter for the AID converter and the signal
processing software. A variable gain stage provided channel-to-channel leveling, and the
offset stage provided a DC offset of approximately 1.25 V to each channel. A Bode plot
of the measured frequency response of the Channel 1 IF filter and gain stages is shown in
Figure 17.
70.0
60 .0 ~ Gain (C H 1 ) j
40 o ---
o 30.0-- - /
O~ 20.0-~
O 10.0------
00 0 ---- - - ' - - - --- ' - ~ - ~ \
-10.0----- -- - ~ --- ~ \
-20.0
O ~ ~O N O 00 N ~~ o cr~ c~ ~ o
O ~ ~ ~ O ~ ~ N O 0~ N C~ O
O ~ ~ ~ O ~ C~ ~ G
~ ~ C~ U~ O ~ ~ a~i O
Frequency (Hz)
Figure 17 Channel 1 Filter and Gain Stage Frequency Response
3.1.6 System Control Circuit and Analog-to-Digital Converter
The system control circuit and A/D converter block diagrams are shown in Figure
18. The control circuit serves the following major functions: generates the proper A/D
- 2195925
47
sarnpling rate and tirning sequence; provides means for an external reset; provides
ternporary storage for sampled values; and provides the radar with a system clock rate of
12.8 MHz. The inputs to the control circuit are the reset/initi~ tion pulse, the 8 analog
inputs, a system start pulse, and inputs to read the digital data stored in the FIFOs from
the contro~ circuit to the cornputer.
The AID converter system uses two MAX-156 four-channeL cimlllt~neous sample
and hold, 8 bit analog-to-digital converters [54]. The 8 analog inputs are .~imnlt~neously
sampled at 51.2 KHz. A~er conversion, the 8 data bytes are then read from the A~D
converters into two FIFOs (DS-2013), one for each A/D converter. An on-board counter
stops the process after 256 samples. The controlling software then reads the data from the
FIFOs into the computer, and the control circuit awaits a new resetliniti~ tion pulse
from the computer.
The control circuit provides the master clock rate of 12.8 MHz to the rest of the
radar system. The circuit also provides a start pulse to the D/A converter circuit to
synchronize the VCO sweep with the sampling process. All of the resets and read/write
pulses to the D/A, FIFOs, and control circuit are provided through the computer interface
card, and are easily controlled by the software.
2195g2!~ 18
C~ l DO
PC Controller ~ -- MAX156-1 AIN1
lll~FO 1 D7 AIN2
START D7 1 1 1 AIN3
~, r W ~ R W
DO
~ CLR CLR
W AIN4
MAX156-2
-- AIN5
FIFO-- D7 AIN6
AIN7
W,~ R W
51.2 Khz
rL START
12.8 Mhz System Clock Control Circuit 51.2 Kh~ 256 Counter
C~$R EN
FigureA'Analog to Digital Converter Control Circuitry
18
- 2195925 49
3.1.7 VCO Linearizing IIardware
The radar system has a VCO line~n7ing circuit, constructed of a coupler, a delay
line, a mixer, and an LF filter and gain stage, as shown in Figure l9. The two outputs of
the VCO, one from the gate (port 2) and one from the source (port l), are at exactly the
same frequency [55]. A portion of the signal from port l is coupled off as the LO to the
line~n~ng mixer. The energy from port 2 is delayed in a 39.42 m delay line and is treated
as the mixer RF signal. The resultant I:F signal is then filtered, amplified, and .li~ti7Pd for
processing. If the VCO modulation is exactly linear, then a perfectly sinusoidal IF
frequency is generated. However, if the VCO modulation is non-linear, then a frequency
modulated IF output results.
Transmit
D/A FIFO's D/A <
r~, ~ To Mixer
~ -1~
Delay (p ~ Delay Line
(39.42m) IF Output
Figure 19 Voltage-Controlled Oscillator Linearization Circuitry
- 219592~ 50
The electrical specifications for the VCO linearizing circuit are sufficient to supply
a full-scale signal at the lF output. The VCO port-2 power output level is approximately
+11 dBm over the full tuning range. The delay line loss is -54.2 dB and the electrical delay
is 131.5 nsec (39.421 m). The mixer conversion loss is 6.5 dB, and the LO power level for
the mixer is approximately +3.0 to + 5.0 dBm over the VCO tuning range. The rF filter
and amplifier stage uses a second-order Butterwolth high-pass filter with a cutoff
frequency of 1.017 KHz and a fourth-order Butterworth low-pass filter with a cutoff
frequency of 7.234 KHz. The IF chain also has several fLxed and variable gain stages, as
well as a DC offset stage to provide +1.25 V of offset. A Bode plot of the frequency
response ofthe IF chain is shown in Figure 20.
50.0 ~ ~ ~
40 0 ~ Gain (IF CKT)
__ 30 o ~
20.0~
~--10.0- -/ - - ~ ~~ ~ \ ~ ~ ~
O 00.0-~ ' ~ ' ' '\ ~
o-10~0-- ~ - ~ ~ ~ . .\ ~ .
-20.0-
30.0
-40.0
O ~-- tD N O C~ C~l C') O ~ C~) ~t O
O ~ ) O ~ C~ ~ 0 00 ~ C~ O
~) o r~ ~ ~ o r~ o
O r~ ~ ~ o
Frequency (Hz)
Figure 20 Linearizing Circuit IF Filter and Gain Stage Frequency Response
219~925
51
3.1.8 Computer Interface Circuitry
This section describes the computer interface circuitry used to communicate
between the computer, the system control circuit, and the D/A converter circuit. The JDR
Microdevices PR-2 circuit board and interface circuitry was used [56]. The PR-2 is
designed to be cornpatible with the IBM PC-AT computer bus architecture, providing 8
bit data transfers. The card contains an 8 bit data bus, a 10 bit address bus, and 8 decoded
address lines (S0-S7). The decoded select lines can be addressed with one line of
progli1."",;..g in QuickBasic. Data transfers (both input and output) can also be achieved
with one line of QuickBasic Prog~ ,.,.;.-g The radar operation was controlled using 6 of
the 8 decoded outputs and by transferring data on the buffered data bus. The decoded data
lines, their addresses, and use are shown in Table 5.
Table 5 Decoded Address Lines (Select Lines) and Functions
Select Line Computer Address System Function
Select 0 (S0) H300 System Reset & Tniti~ tion
Select 1 (Sl) H304 System Start
Select 2 (S2) H308 Write to D/A FIFO, Low Bits (D0-D7)
Select 3 (S3) H30C Write to D/A FIFO, High Bits (D8-Dl 1)
Select 6 (S6) H3 18 Read A/D FIFO ffl, Channels 1-4
Select 7 (S7) H3 lC Read A/D FIFO #2, Channels 5-8
~195925 52
3.2 Software Description
This section describes the software used to control the radar. A software block-
diagram is shown in Figure 21. The main software tasks are initi~li7~tion/reset,
line~ri7~tinn (tli~c~lc.ced in Section 3 .4), loading of the D/A converter coefficients, starting
the radar system and reading the sampled data, and data plotting and storage. The data
processing routines are discussed in Section 3.3.
3.2.1 l~iti7l1i77ltion and Reset Subroutine
The initi~li7~tion and reset subroutine initi~li7es all internal con~nt.~, resets the
radar to proper initial values, and zero's all data arrays. Input and output addresses are
set, as are the software sample rates, number of channels selected, and nurnber of samples
per channel. The D/A converter is preset and latched to 0.00 V.
3.2.2 Generating and Loading D/A Coef~lcients
Generating the D/A coefficients is one of the major software tasks. A total of
4096 data coefflcients, each 12 bits wide, are stored in two FIFOs and are later clocked
sequentially into the D/A converter. sweeping the VCO. Each of these coefficients is
between a value of 0 and ~ l (4,095). The difference between the nth and the (~I+I)'h
coefficient is stored in the (n+l)'h position of an array dVolt(i). The nth coefficient is
generated by summing the dVolt(i) values from i=l to n. This essenti~lly stores the
instantaneous derivative of a linearized coefficient equation. For example, for a VCO with
perfect frequency versus ~ oltage characteristics, all of the coefficients of the array dVolt(i)
2195g2~ '
53
( Start Program
rnitialize and Reset
'< Linearize'~ >YES , L~nearizeVCO
\/ ' ''~ '
- 1NO ~ \
Load D/A Coeff's ~ , NO <~ave Coe~s~
\/
Start Radar 1YES
Save Coefficients
Read A/D FIFO's
Reset System
r
NO
END
Figure ~ I Sofh~are Block Diagram of Radar Prototype
2195925
would be 1. The D/A coefficients are calculated, stored, and processed in this way to
sirnplify the linearization process discussed in Section 3.4.
Once the data coefficients are generated, they are divided into high and low bits.
Low bits vary between 0 and 2~-1 (255), and the high bits vary between 0 and 24-l (15).
The 4,096 coefficients are then loaded into two FIFOs, and the radar is set for operation.
Loading of the low and high bits is accomplished with two lines of prog~ g
OUTHIGHBITS, 15
OUT LOWBITS, 255
where HIGHBITS is Hex value 30C and LOWBITS is Hex value 308, the addresses of
the two D/A FIFOs (see Table 5). (This exarnple loads all 1 's into the FIFOs.)
The rarnp rate of the radar can be easily changed by scaling each value of dVolt(i).
For exarnple, the ramp rate can be doubled by multiplying each value of dVolt(i) by two.
This provides great progr Imming flexibility.
3.2.3 Sweeping the Radar and Reading the Di~ i;Ged Return Signal
The radar begins a sweep-and-sample cycle by selecting the start address. This is
accompli~hed by the follo~ing line of prog~g: -
OUT START, ~x
where START is Hex value 304, and xx can be any value, since the data bus is not
activated with the Select I line (see Table 5).
219S925 55
A~er the radar completes the sweep-and-sample cycle (approximately 5.12 msec),
the 256 samples from each of the 8 channels are read firom the storage FIFOs into the
computer. This is again accomplished by using a sin~le line of pro~ n;~g~ as shown
below:
DATA(I,J)=INP(ADDRI )
where ADDRI is Hex Value 318 (FIFO 1) and I and J correspond to the channel number
(I to 8) and sample number (I to 256). A~er all 2 Kbytes are read (8 channels x 256
bytes), the radar is reset and initi~li7e(i
3.2.4 Data Plotting and Storage
A~er the data is read into the cornputer, all 8 tirne-domain retur.ns are ternporarily
plotted for comparison. The data sarnples are values between 0 and 28-l (255). These
values are rescaled to represent a voltage value (0 corresponding to 0.00 V a~d 255
corresponding to +2.50 V). The data is then saved in a user-specified file. This data is later
processed using an FFT and beam-forming algorithms to provide angular information
about the targets. The user can then specify if another target is to be measured, and the
process begins over again.
In one preferred embodiment of the invention, the computer is
configured to proces6 the received data samples immediately after
receiving the data so that the angular information of the targets
can be determined and displayed on a real-time or near real-time
basis (as is required in vehicular applications). An output device
is preferably attached to the computer to allow a representation of
the angular information to be displayed to a user.
3.3 Data Processin-~ Routines
This section describes the data processing routines used to generate the different
beam pattems from the return data. The first routine described is a standard FFT routine.
This routine generates a comple:Y vector in the frequency-domain (or range-dornain) from
2195g25
56
the time-domain samples. The second routine is a calibration method used to remove
channel-to-channel phase and m~gni1llde errors resulting from hardware differences. The
third routine uses the synthetic beam-forming algorithms to generate the effective returns
from the different radiation beams.
3.3.1 FFT Routine
The first data processing routine is a complex FFT. The algorithm is a standard
mathematical-library subroutine [57]. The inputs are the complex time-domain samples,
the number of sample points (NS), and the value NU, where NS=2~U. For this routine,
there are 8 separate channels of data, each with NS=256. The real part of the complex
time-domain samples are the sampled data values, and the im~gin~ry part is set to zero for
all samples.
The FFT subroutine returns the complex frequency-domain value in each
frequency bin. There are 128 di~rert;.l~ frequency bins, each with a 200 Hz bandwidth
(~iven by Equation 1.14). For this particular application, only the first 51 frequency bins
contain useful information. The other bins contain target information beyond the range of
the radar (targets > 100 m or frequencies above lOKHz).
The m~gni~lde of the return for each frequency bin is calculated by taking the
square root of the sum of the real part, squared plus the im:lgin~ry part, squared. The
relat*e angle of the return for each frequency bin is found by taking the arctangent value
of the im~ginary portion. divided by the real portion. Performing these operations results
2195925 57
in the generation of a complex vector, with a mq~ de and phase angle in each frequency
bin. Since the frequency of the IF signal is proportional to the range of the target, each of
the frequency bins can be interchangeably labeled a range bin.
3.3.2 Calibration Routine
The FFT routine described above calculates a complex vector for each of the 51
range bins, for all 8 channels. Since the channels are all sampled synchronously, the
relative phase difference from channel-to-channel should be zero for a target at 90~. The
mqgni~lde of the returns should also be equal for this target. Any phase or rllqgT itllde
errors should therefore be the result of channel-to-channel differences in the hardware. RF
hardware differences can result in channel to channel errors. Slight length tolerances can
cause significant phase errors. IF filter vanations, caused by capacitor and resistor
tolerances, can also cause variations in phase and mq~ de responses.
A calibration measurement with a target at 90~ is taken at each range bin of
interest (for a response in each frequency bin). This measurement is then used to calibrate
the return signals for a target at any angular position for this ran~e. A calibration vector is
derived using the following three steps: First, the target return at 90~ is measured. This
results in a complex vector, consisting of a magnitude Mn and an angle An, for each
channel ~1. Next, the phase calibration vector, CA, is formed for each range bin, where
CA(~ An. And third, the magnitude calibration vector, C~I, is formed for each range
bin, where C~l(n)=M,/,~f".
The resultant complex vector, with magnitude MA and angle CA, is used to
calibrate returns from tar_ets at any angular positionfor this particular ra~lge bin. To do
2195925
58
this, let RMn and RAn be the return m~ de and angle, respectively, for a target in
channel n at any angle in the corresponding range bin. A new calibrated return, CRAn and
CRMn~ is generated in the foUowing two steps:
Step 1: CRAn = RAn + CA(n);
Step 2: CRMn = RAn x CMf~l).
Note that if the measured retum is from a target at 90~, the resultant CRAn is 0~ for all
-channels, and the resultant CRMn is equal to the return m~ de of Channel 1, which is
the desired result.
3.3.3 Digital Beam-Forming Algorithms
The final data-processing routine is the digital beam-forming algorithms. The
calibrated complex returns from each of the 8 channels are combined to produce affective
returns for each beam position at each of the range bins. A progressive phase shift is
applied across the array for each beam position, according to the array theory discussed in
Section 2.1. The result is a complex power return for each of the beam positions. The
target.'s angular position can be found by comparing the m~gni~lde of these returns for
each ofthe angular beam positions.
3.4 VCO Linearization Technique
In an FMCW radar. the linearity of the modulation is critical. Any unwanted non-
linearity will result in increased noise in the return signal [4]. If the non-linearity is large.
219592~
59
the target return can be spread across several range bins, making target detection difficult
or impossible.
A new implem~nt~tion of a VCO linearization technique is presented in this
section. First, the problems associated with a non-linearized VCO modulation are shown,
then the basic theory behind the technique is reviewed. The new implem~qnt~tion is
presented along with the results of the VCO linearization.
The frequency-tuning characteristics of the radar VCO were shown in Figure
3~... These characteristics indicate a non-linear frequency change per unit modulation
voltage change. The output of the VCO linearization mixer for a linear voltage ra~ is
shown in Figure 22 (A linear voltage ramp indicates that the modulation voltage for the
VCO varies linearly with time, and a linear VCO sweep indicates the VCO frequency is
ch~ging linearly with time.)
This output shows several important characteristics. First, it should be obvious that
the resultant sinusoidal IF signal is frequency modulated. Second, a short delay is present
before the system hardware settles and the resultant "steady-state" waveform is present.
Third, there is a DC offset of 1.25 V. And finally, a small amount of low frequency
modulation due to system generated clutter and system response is present in the IF signal.
2195925 60
2.50
r ¦ Voltage ¦
o~
0 50 ~ J v~
0.00 , ' ~ '
oooooooooooooooooo
LL1 LT~ LT ~ Ll~ LL~ L~ LL~ LL1 L- L- Ll~ L~ LL~ L~ L~ LL1 L~ LT~
U~ ~ V') ~o ~ X X ~ o
G~ -- O C' -- ~ 1-- 0 ~ -- ~ ~ O
Time (msec)
Figure 22 VCO Linearizing Network Mixer Output for Linear Voltage Ramp
The return spectrum of this signal is shown in Figure 23. The power spectrum is
concentrated in range bins between 12 m and 38 m. (Since the "target" in this case is a
delay line, the spectrum should have a peak corresponding to a target at one-half the delay
line electrical distance, or 19.71 m.) It is clear that the spectral purity of this IF signal is
very poor.
The general theory of using iterative feedback to linearize the VCO comes directly
from Klimkiewicz and Grosch [58]. Figure 24 shows the general configuration of the
Mixer-Delay Line (MDL) system. The VCO modulation input voltage is controlled by the
computer. and is represented by the digital words V(~l). A~er a D/A converter and a low-
pass filter, this digital signal becomes modulation voltage v(t). The output of the VCO is
represented by x(t), and the instantaneous frequency is given by F(t). The frequency is a
2195925
_ 6
~0
30 - Power (dB)
/~\
~- 20 - f ~ \
~ IO-~J ~
O-
-10 -
-20 - : ~
0 10 20 30 40 50 60 70 8090 100
Range (meters)
Figure 23 Spectrurn for VCO Linearizing Network Output for Linear Voltage Ramp
function of the modulahon voltage via the non-linear operator ~(v(t)). For this application,
it is assumed that the goal of the linearization process is to produce a linear FM chirp of
the VCO. Therefore, the product of the VCO output and a delayed portion of this output
should produce a sinusoidal term, y(t) in Figure 24, dependent on the delay h and ~(v(t)).
Computer v(n), D/A , LPF v(t), VCO x(t) Output
F~
LO J
y(n) ~(t) lF ~3 ' (h secs)
Figure 24 FM VCO ~\,ith Digital Feedback Using a Mixer-Delay Line System
219592S 62
The goal of the linearization process is to produce an output F(t) = G~t), where
G(t) is the ideal linearly modulated RF signal. If the output F(t) is sampled directly, then
let En(t) represent the error a~er the n"' modulation cycle, defined as follows:
En (t) = ¦Fn (t)--G(t)¦ (3 . I )
If the first derivativ-e of ~(v(t)) is continuous, then an iterative feedback control system
can be used to reduce the error with each iteration, and
En(t) = ¦Fn(t) - G(t)¦ < C¦Fn l(t) - G(t)¦, (3.2)
where O<C<l, shows convergence of F(t) to G(t) for increasing n. Further_ore, En(t)
approaches O for increasing n, indicating ideal modulation.
For the MDL system, the measured and ideal outputs become f(t) and g(t),
respectively. If the delay line is ideaL then the following relationships hold:
f(t) = h * F '(t), (3.3 )
and g(t) = h * G '(t). (3.4)
Furthermore, def~lling several terms:
S~(vo) = Fo, (3.5-a)
and ~(v~) = F~ . ~ (3. 5-b)
where vO and v, are the minimllm and rnaximum tuning voltages, and Fo and F, are the
resultant output frequencies~ where
F, - Fo (, . 6 )
V~--Vo
represents the tuning band~,idth to tuning voltage ratios, and
2195925 63
O~'<y, (3.7)
where y is the maximum slope coefficient, and
<~ (H /v2) (3.8)
for some ~.
If the second derivative of ~(v(t)) is continuous, then iterative feedback control can
be used to provide convergence of f(t) to g(t). This is accomplished by using the following
relationship:
vn(t) = vn ~(t) - a[Avn ~(t)~, (3 9)
where
~v" ,(t)= S h¦O[fn l(r)-g(r)]dr, (3.10)
and ~z is confined by the following relationship:
o<~x ~SvlY (3.11)
The implementation of Equation 3.9 is somewhat difficult, because this involves
using an approximation of the modulation voltage functions vn(t) and vn l(t), and has finite
accuracy. It also involves the evaluation of the integral in Equation 3.10, which can be
difficult to solve and may introduce additional errors.
An improved implementation scheme has been developed as part of this thesis.
This improved scheme uses the derivatives of vn(t) and vn ,(t) and the derivative of
2195925
~[~vn./(t)~. This leads to a simple implementation scheme that does not require an
approximation for Vn(t) and Vn l(t) or the evaluation of the integral in Equation 3. 10.
DiLre~ ting Equation 3.9 yields the following result:
V n (t) = v n-l (t)--~¦fn_1(t)--g(t)j, (3. 12)
where
~ = ~ I [Sv*h] (3. 13)
The linearization technique used with this system is based on Equation 3.12. The
function v 'n(t) represents the derivative of the new modulation function for the VCO, and
the function V'n l(t) represents the derivative of the previous modulation function. Note
that v'(t) is implemented in software in the array dVok(i), and is already in a form for
direct application of Equation 3.12. The constant ~ is a calculated constant with several
constraints. The function g(t) is the desired IF output function of the mixer, and the
function f(t) is the actual measured output function of the mixer. In general, f(t) and g(t)
can be any measure of frequency linearity in the IF signal. This choice provides a ~reat
deal of flexibility in choosing an appropriate measurement process.
The linearization technique is accomplished in five steps. First, the VCO is
modulated using a linear ~oltage ramp (dVolt(i)=l for all i). Second, the resultant mixer
IF signal is analyzed, and some measure of the lineanty of this signal is recorded (yielding
f(t)). Third, a polynomial p(t) is fit approximating the measured linearity of the IF signal
219592S 65
(p(t)~f(t)). Fourth, an error function is calculated (e(t)=p(t)-g(t)), providing a measure of
the amount of non-linearity of the IF signal over the ramp period. Finally, a new
modulation voltage is calculated using this error fimction as iterative feedback. The five
steps are repeated until the IF signal is linear (and hence the VCO modulation is linear).
The first step in the linearization is to modulate the VCO using a linear voltage
over time signal. This is generated by setting all values of dVolt(i)=l. (The modulation
voltage at the i'h sample is produced by summing dVolt(i) from 1 to i and supplying the
integer value of this number to the D/A converter. )
During this initial modulation cycle, the mixer output is recorded, and some
measure of the linearity of this signal is observed. In the prototype radar system, the time
between "zero crossings" of the IF signal is used to approxirnate the IF linearity. This
"spacing" is termed DEL(t) (for DELta) and has units of "samples". The DEL(t) is related
to the instantaneous frequency by Equation 3.14,
(2* DEL(t)* Ts~ e ) (3 . 14 )
where Tsa~ e= 1/5 1,200.
For a perfectly linearly modulated VCO, the resultant output should be a perfect
sinusoidal voltage (excluding DC offsets and system-generated clutter). This would also
result in a constant DEL(t) for the sampled time period. By contrast, the measured DEL(t)
- 219~92~ 66
values for a linear modulation voltage are shown in Figure 25. It is clear from Figure 25
that the DEL(t) values vary from values of 7 to 15 for a linear voltage ramp.
8 - - ~ ~ ~
6 -
~, 14-
0 1 2 - - - - _ - - - - ~ - -
8 ~
-- 6 --- - - . . . . . .
", 4 -- - - . . ~ stimate ¦-
2 - ~ Meaured I
O , , ~
oooooooooooooooooo
LTj LTj LS LTj L~ L~ ~ LTj L- LT LTj LTj L~ LLI Lb LTj LTj LTI
~ _ O O~ O , ~ ~ r~ g
Time(sec)
Figure 25 Measured DEL(t) and Estimated p(t) Values for Linear Voltage Ramp
~ he third step in the linearization process reql~ires fitting a polynomial
appro~mation to the measured DEL(t) values, in other words, generating p(t). A standard
library subroutine for a fifth-order polynornial regression algorithm is used. The estimated
DEL(t) values are plotted in Figure 25. (Note that the smoothing properties of the
regression function remove any short-term DC offset from the delta values.)
2195g2S
67
The fourth step in the linearization process is to calculate an error function using
the approximate p(t) values and the ideal delta values (represented by DDEL, for Desired
DELta). The value of DDEL is dependant on the desired modulation ra_p rate, the delay
line length, and the sampling frequency. The desired radar modulation rate is 15 GHz per
second. Since the delay line is 39.421 m long, the IF will be the same as a target at 1/2 this
length, that is 19.21 m. Using Equation 1.12, the ideal IF frequency should be 1,971 Hz.
Plugging this into Equation 3.14, the DDEL value emerges as 12.988 sarnples.
The error function can now be calculated directly from Equation 3. 15:
e(t)=p(t)-DDEL. (3. 15)
The final step in the linearization technique is to calculate the new modulation
voltage function using the calculated error function as feedback. This is performed using
Equation 3 . 16:
d Volt(i) =d Volt(i) + ~ e(t). (3 .1 6)
This new modulation function is then used to sweep the VCO, and this iterative
process continues until the desired level of linearity in the IF signal is achieved. The value
of ~ iS constrained by Equation (3.13) and is determined experiment~lly. A srnall ~ value
will reduce the robustness of the process, requiring a large number of iterations to achieve
a given linearity, while a large ~ value can result in instabilities. An experimentally
219592~ 68
determined value of 0.0025 was used to achieve a linearity of approximately 2% in less
than 10 iterations.
This modified VCO linearization technique results in an improved frequency vs.
time modulation characteristic. Figure 26 shows a plot of the estim~ted delta values for the
first four iterations (Sweep-00 indicates a linear modulation voltage). Figure 27 shows a
plot of the delta values for the next 6 iterations. A linearity within 5% is achieved by the
fifth iteration, and this is further improved to approximately 2 % by the tenth iteration.
The time-domain response of the tenth iteration is shown in Figure 28. The measured and
polynomial approximation of the delta values are shown in Figure 29, and the return
spectrum for the tenth iteration is shown in Figure 30. All of these results indicate a
significant improvement over the original modulation. The initial and final modulation
voltage is shown in Figure 31 for co_parison.
1 4
2 _ ~
8 - - ~ - sweep-oo
--6 --- ----- sweep-oI
---- SWeeP-02
---- SWeeP-O3
a 2 -- - ~ ~ - SWeeP-04
O O o o ~ o O o o o o o o o o o o O
Lj LTj Ui Ui U~ Ui Ui Ui U L- Ui LTj LTj U; LTj L'j L'j LTj
3 -- O C~ O ~ ~ ~ ~ ~ OC -- ~ r-- C
- Time(sec)
Figure 26 Estimated Delta Values (p(t)) for Linearization Iterations 1-4
21959~5
69
18 --
~, 16-
1 4
o1 2 - - - ~ - --- - - - ~ . . . . _~
10- : . ~
8 -- - -- we~-0: -
- - - we~-O
--6 ~ wee~-0
-- wee~-g~ -
2 -- - - . : :-- wee -- I
O
o o o o o o o o o o oo o o o o o o
L~ LII L~l L~l LL1 Ll~ Ll~ Lr~ . L-- L-- Ll~ LI1 LI~ LI~ Lll LT~ Lll LLI
x a~ O
_ o c~ o ~ oo -- ~ ~ o
Time(sec)
Figure 27 Estimated Delta Values (p(t)) for LineaTi7~tinn Iterations 5-10
2.50 ~ ~
Voltage ¦
2 00 ~ - A ~
~o~so~ V
0.00
o o o O O o O O OO O O O O O O O O
L~ LI~ LL1 L~ LIJ L~ L~ L~l L~l r L~ ~ LI~ LI~ 1~ LI~ L~l LII
I~ ~ v~ oo 5~ oo X ~ ~ t ~ ~ r ~ -- -- O
G~ -- O C~ 0 ~7 ~ ~ O
Time (msec)
Figure 28 VCO Linearizing Network Mixer Output for Linearized Modulation
2195925
-~ 18
~~_ 1 6
8 ~
6 - - ~ Estimate
~ 4 ---- - - . ----- Meaured
a 2--- - - i . .. .. ~...... .........
O , . . .
o, o, o, o,o o o o o o o, o, o, o, o, o, o o
L l LLl L~ L~L~ Ll~ LLl LU L- L- Lr~ L~l Ll~ LT~ Ll~ Ll~l Lll LL1
X C~ X ~ ~ ~-- ~
T~me(sec)
Figure 29 Measured and Fstim~ted Delta Values for Linearized Modulation
30 ~ POwer(ds
~~ 20- ~/ \ ~ .. ..
~, lo-f - - \--\ - - - : - - - -: ' ''
-10- ~ ~
-20
o lo ~o 30 40 50 60 70 80 90 100
Range (meters)
Figure 30 Spectrum for VCO Linearizing Network Output for Linearized Modulation
21959~S
5.00
4 50 - - /
4.00--
~
", 3.50
o 3 00
2.50-
0 2.00--- /
1 . 50 - --
1.00 - -- -- - /~ -¦ - Initial VolTage Ramp ¦
50 / - - - I - - - - Fillal Voltage Ramp ¦
0. 00 . ~
ooooooooooooooooo
L~ LTI LT~ LT~ U Ul U~ LT~ L- LT L~ LTI L~ L~ LTI LTI LT~
o o o o o o ~ ~ ~ o o ~ ~ ~ oo o ~
o ~ ~ '-0 ~ o ~1 v) 00 -- t 00
Time (sec)
Figure 31 Initial and Final Modulation Voltage Rarnps
3.5 Svstem Noise AnalYsis
This section includes an analysis of the dorninant noise sources in the FMCW radar
systern. The received noise power is the sum of therrnal noise, receiver noise figure, IF
noise, LO phase noise, and modulation noise. The thermal nolse, receiver noise, and IF
noise analysis is well documented [59] and will not be covered. The LO phase noise is the
dorninant source, and it wiU be analyzed in detail. The effect of a non-linear VCO ramp
will also be examined. Ou~nti7~tion errors, due to the finite number of bits in the A/D
converters, and roundoff and truncation errors, will also contribute to the overall noise.
These effects will also be analyzed.
2195S~ 72
3.5.1 AM and FM LO Phase Noise
The LO noise is the dominant noise source in the received signal [4]. This noise
will have both an AM and FM cornponent. The AM noise is suppressed by using a
balanced rnixer. This analysis begins by ex~mining the AM noise co~ il,ulion [7].
The AM noise on a carrier ~0 in a narrow frequency band about _ ~, is "quasi-
sinusoidal," and can be expressed by Equation (3.17):
~ (t) = Eo [(I - a) + a cos(~" t)~ cos(~O t), (3.17)
where cx/(a-l) is the modulation index, and Eo is the peak signal level. This can be
expressed in terms of the canier and the sidebands:
E(t) = Eo (I - a) sinfc~O t) + Eo cc~2 cos(~O - c~")t + Eo a/2 cos(~O + ~",)t. (3.18)
If a balanced rnixer is used to suppress the AM noise on the LO, then the local
oscillator output can be represented by ELo(t) in Equation (3.17):
ELo(t) = E~o sin(~o t - ~). (3.19)
The low frequency cornponent of the AM noise at the output of the mixer will be:
~IF (t) = a~O k/2 [cos(c~, t + 4~) + cos(-c~", t + ~)~, (3.20)
and the ratio of the detected lF AM noise power to single sideband AM noise is:
r/,~, = 4k cos~ ~ = 4L cos~ ~, (3.21)
where L is the conversion loss. This means, esst-nti ~lly, that the IF-noise power varies
between zero and four times the single sideband noise level of the RF signal. This variation
is caused by the variation of the relative phase of the RF and LO signals, and so the
- 2195~25
sidebands either cancel or add. The mean noise power level is 2L, which is double the
sideband power level multiplied by the conversion loss.
An F~I signal can be expressed as:
E(t) = Eo sin (~0 + ~a~ sin ~",t)t. (3.22)
The FM noise due to the local oscillator cannot be suppressed in the mixer. However, if
the modulation is narrowband, that is ~ << ~", then the LO sigllal can be represented
by Equation 3.22 and rewritten as:
ELO (t) = Eo ~sin ~0 t + ~ /2~ [sin (~0 - ~t~ - ~/2CIJ", [sin (~0 + ~t~. (3.23)
The RF signal has a tirne delay, r, relative to the LO, as shown in Equation 3.24:
ERF (t) = Eo ~sin ~0 (t - r) + ~J~/2c~", sin [(c~O - ~J(t - r)~
/2~, sin [(c~0 + ~(t - r)~. (3.24)
The following IF cornponents are generated in the rnixer:
EIF (t) = ~Eo k/2~,~-cos[(c~ + c~")(t - r) - ~0 t~ + cos[(~ - ~(t - r~ O t]
-cos[(c~) + c~J t- c~O (t- r)~ + cos[(c~ ) t- c~O (t- r)~. (3.25)
This can be reduced to:
ErF (t) = 2k(~/~Eo ~sin(c~O r) cos(~", r~2) sin[~", (t - r/2)~. (3.26)
The noise power in the IF is then:
PIF = ~k~ (E2 / ZO) [sin~ (~0 r) sin(c~", r/2)~. (3.27)
The detected noise power in the I:F signal relative to the RF noise level is:
= 16 L [sin~ (c~O r) sin~ (c~" r/2)~. (3.28)
If we let ~ = ~Or, then Equation 3.28 can be rewritten as:
2195~5
71F~ = [4L sin~ (~)~ [45i~1- (~m r/2)~. (3.29)
The first term is the phase sensitive term, equivalent to Equation 3.21, except that
this term is prevalent when the LO is in phase quadrature with the RF leakage signaL and
in the AM noise case, the term is prevalent when the two are in phase. This trigonometric
~imil~rity iS due to the fact that the upper and lower AM sidebands are in phase and the
F~I sidebands are antiphase.
The second term in Equation 3.28 is the FM noise cancellation. If the time delay r
is much less than the modulation rate (~m / 2~T), the LO and RF signals are strongly
correlated and the noise output is very low. However, as the time delay increases (i.e., as
the target range increases), the degree of correlation decreases and the IF noise increases.
3.5.2 Effects of Non-Linear VCO Ramp
Another important source of noise is due to the non-linearity of the modulation
slopefm [4]. Consider Equation 1.12 withfm replaced withfm +fe, wherefe is the slope
error term. Iffe is independent of time (i.e. a constant offset in the ramp slope), then
Equation 1.12 becomes:
flF = 2 (fm + fe)ro /c = 2fm rO /c + 2fe rO /c. (3 30)
This shows an offset in the IF frequency which is proportional to the error in the
modulation slope. This also shows that the absolute error increases with increasing range.
2195925 75
If the slope varies with time, then the error term must be integrated in Equation
1.2. Whenfe is decomposed into its Fourier sine components cl~F, each multiplied by t and
integrated, the transmit signal becomes:
a(t) ~ aO sin[2~zfO t + ~fmt~ + 21ZCF~ /~ (Sin~Ft - ~Ft COS~Ft)~ (3 31 )
This transmit signal is delayed and mLxed with itself to produce an IF signal b(t). If CF- /~
is small compared tOfm and ~0, then the IF signal b(t) can be reduced to:
b(t) ~ bo sin[~O t + 7Tfmt + 2n~F /C~F (~0 - ~)F)t + 2~F /~F (~0 + ~)F)t~ (3.32)
This introduces the following error in the IF signal:
PIF = (I6LCF/ ~F) sin (~oT) sin (~Fr/2c). (3.33)
This error term is similar to the FM component of the LO phase noise shown in Equation
3.28. The error component at each Fourier frequency ~F will add phase noise to the target
IF and frequencies close to it. The IF spectral peak will be spread out by this noise. Since
(~Fr/2c) << I, then the IF noise power due to this source is proportional to range. As the
target range increases, the spreading of the targets spectrai response will also increase.
Eventually, the range resolution of the radar will be proportional to the target range.
3.5.3 Digital Signal Processing Errors
Digital signal processing errors can introduce a significant amount of noise as the
received signal is processed, and seriously degrading signal-to-noise ratios. There are three
main types of DSP errors [60]: the D/A converter qll~nti7~tion error, due to the finite
number of bits used to represent the sampled signal, roundoff errors produced by adding
two b-bit numbers (the resulting number must be represented by a single b-bit number),
- 2195Y25 76
and truncation errors, caused by multiplying two b-bit numbers and truncating the result to
a single b-bit number. The error introduced by the A/D converter will be discussed in
detail, and the roundoffand truncation errors will be presented in su~ y form. It will be
shown that the A/D converter qu~nti7~tion error is the dominant DSP noise source for the
radar prototype.
An A/D converter is used to quanti_e a discrete time signal with finite accuracy.
This qu~nti7~tion process is nonlinear and converts the input signal into a finite set of
prescribed values, each represented by b-bits. This process is represented by
Equation 3.34:
*[nl = Q(x[n~) (3 34)
where Q(x[n~) is the qll~nti7~tion process, and x[n~ is the qu~nti7ed sample. Figure 32
shows a typical qu~nti7~tion transfer function between x[n~ and x[n~. Several features
from Figure 32 should be noted. First, the sampled values are rounded to the nearest
qu~nti7~tion level. Second, the analog input signal varies from O volts and FS volts. Third,
the least significant bit (lsb) is FS/2b, where b is the number of bits. Fourth, there are 2b
levels, or outputs. The difference between output levels is 4 which is the value
ofthe lsb. Therefore, the largest error introduced from the qll~nti7~tion process (~csllming
that the input signal is not saturated) is less than FS/2J. This error e[n~ is given in
Equation 3.35:
e[~l] = x[n] - x[n]- (3.35)
2195925 77
For example, for the qll~nti7~tion represented by Figure 32, if ~1/2 < x[n~ <3~1/2, then
x[n~ = a, and it follows that
-a/2< e[n~ <~1/2. (3.36)
Several assumptions are rnade about the error function e[n] First, e[n~ is a sample
sequence of a stationary random process. Second, e[n~ is uncorrelated with x[n~ Third,
the random variables of the qll~nti7~ti~ln process are uncorrelated, i.e. the error is a white
noise process. Fourth, the probability distribution of e[n~ is u~ o~ over the range of the
q~l~nti7~tion error.
For qll~nti7~tion processes that round to the nearest level, as shown in Figure 32,
the amplitude of the error function is bounded by Equation 3.36. For small ~, it is
reasonable to assume that e[n~ is a random variable u~irol~ly di~ uled from -a/2 to
~1/2. The probability density function for ehis noise is shown in Figure 33. If successive
noise samples are uncorrelated with each other and e[n] is uncorrelated with x[n~ then
the mean value of e[n~ is zero and the variance is given by the E~uation [60]:
~ ~2 / 12 = 2-2b F52 / 12.
_ 2ig~i925 78
Output
111111-- --- ---- --- ...............
111111- --- - ......... ~J
111111-- - - -- . .... ...
- FS=2Vref=2.5 V
~~~~~l-- r 1 LSB--FS.256=~
oooooo-- r~ '
000000-- ~ ;
000000--~
000000 1 1 1 1 1 ~ -'AIN
3~ FS-~
0 2~ 4~ FS-2~ FS
Analog ~put (AIN)
- Figure 32 MAX156 A/D Converter Transfer Function for Unipolar Operation
- 2195925 79
Pen (e)
~ 2bFs
b = # bits
1/~
-~12 +~12
Figure 33 Probability Density Function of Error due to Q~l~nti7~tinn
For an 8 bit A/D converter, with an input signal between 0.0 and 2.5 V, the noise
var;ance or power level is calculated to be 7.9473 x 10~ W.
The other rnajor DSP noise sources are due to roundoff errors, truncation errors,
and errors due to the qll~nti7~tion ofthe sine and cosine multiplication constants [57]. The
noise due to roundoffand truncation in the FFT are grouped together and presented below
in Equation 3.38 [61-64]. The literature has shown that negligible error is introduced by
the sine and cosine constant q~l~nti7~tion if these constants are rounded to the word length
ofthe FFT computations [64-65].
-- 2~ 9S~25 80
The roundoff and truncation noise in each stage of a complex FFT can be grouped
together. If a fixed point representation is used, then the total noise contribution at each
stage is given by
~ 6 = (4 / 3) 2 , (3.38)
where b is the word length of the FFT co_putations. Further_ore, for N stages, the total
noise co~ il)ulion is ,~
~ C~ T ~ N (4 / 3) 2-2b / ~ ~ (3.38)
For a 256 point FFT using 16 bit nurnbers, the noise power in the output spectrurn is
79.473 x 10-9 W. In floating point arithmetic, the noise depends on the mq~ de of the
numbers in the FFT calculations, but in general the noise effects are reduced [65-66].
The ratio of noise due to the A~D converter and noise generated in the FFT is
shown in Equation 3.39:
[ 12~/[N(4/3) 22b2~1 = [22b~-2bl~/[2c-~
where bl = nurnber of A/D bits, b2 = nurnber of FFT bits, and N = 2L. These two noise
powers are equal when b2-bl = L/2-1.
The calculated noise conllil)ulions for the protot,vpe are shown in Table 6. It is
clear that the A~D converter noise is the dominant noise source.
Table 6 Comparison of DSP Noise Co~ ulions of D/A Converter and FFT Algorithm
Noise Source Noise Power
AiD Converter Noise (FS = 2.5 V, b=8) 7.9473 x 10~ Watts
FFT Processing Noise (N=256, b=16) 79.473 x 10-9 Watts
219592~ ~
Chapter 4
FMCW RADAR SYSTEM WITII DIGITAL BEAM-FORMING
PROTOTYPE PERFORMANCE
The results in this chapter show the angular resolution capabilities of the F~ICW
radar prototype. These results demonstrate the concept and efficacy of digital beam
forming. In Sections 4.1 and 4.2, the radar generates narrow main beams at di~erent
angles. The radar's ability to discriminate between two targets at di~eleLl~ ranges and
angles is shown in Section 4.3. In Section 4.4, the ability to discrimin~te two targets at the
same range but dilreLenl angles is demonstrated.
In the first test,- discussed in Section 4.1, the return from a single target located at
a range of 16 m was measured from 0~ to 180~ in 1~ increments. The power measured at
each of these 181 points was used to generated a radiation pattern for each of the 4x4
receive antennas. Section 4.2 describes how this measured data was combined digitally to
synthesize the main beam radiation patterns of the 8x(4x4) array with beam positions at
90~, 92~, and 94~.
In the second test~ discussed in Section 4.3, two targets at di~erel-t ranges and
different angles were measured and identified. This ability to uniquely identify two targets
is critical in many radar applications. In automotive applications, the radar must determine
- 2195925 82
if a target is directly ahead. ahead but to the right, or ahead but to the left. The results
show that the radar can discriminate these targets, providing range and angular position.
The final test, ~iccllssed in Section 4.4, shows that the radar can discrirninate two
targets at the same range but at di~ e~lt angular positions. Again, this ability is critical in
many radar applications. The angular discrimination shown in this chapter would not be
possible with conventional FMCW radars.
4.1 Measured Radiation Pattern of the 4x4 Receive Antennas
This section describes the test setup and procedure used to measure the radiation
patterns of the radar. The measured pattern of a single channel of the radar is presented
and compared with the theoretical pattern of a single 4x4 array. First, a description of
conventional pattern measurement procedures is provided, then the test setup used to
measure the radar receive radiation pattern is described.
Two conventional radiation pattern test setups are shown in Figure 34. In both
setups, the transmit power and the distance between transmit and receive antennas are
fixed. Therefore, the incident power to the receive antenna is also fixed. In Figure 34(a),
the receive antenna is rotated from ~= 0~ to ~= 180~. As this antenna is rotated, the
receive power level is measured and recorded as a function of the angle ~, thus providing
the radiation pattern. (This power level is sometimes measured directly at RF and is
sometimes converted to an lF signal and measured.) In Figure 34(b), the receive antenna is
- 219~925 83
fL~ced, and the transmit antenna is rotated along a constant arc at a fixed distance. Again,
the receive power versus the angle ~ is recorded.
There are three major sources of measurement error in these setups. First, the
power density incident on the receive antenna can fluctuate. Second, the receiver gain
and/or IF gain can vary during the measurement. Third, there are inaccuracies in
mPasllring the angle ~. All three of these errors co~ ilJule to the measurement error in the
radiation pattern.
The same principles used in the conventional pattern measurements were applied
to the FMCW radar to measure the receive antenna patterns. In this setup, the radar
receive ~ntenn~ were fL~ced at the origin. A target was moved along an arc at a fixed
range of 16 m. The target angular position was moved between 0~ and 180~ in 1~
increments. A transmit antenna tracked the target, so that the reflected power from the
target was held constant. The radar was swept, and the received power was converted to
an IF signal, amplified, and digitized in the radar for each angl.lar position. An FFT was
performed on this data, resulting in a matrix of retum power levels at each of the 51 range
bins. The radiation pattern is produced by plotting the power in the 16 m range bin (the
only one of interest) as a fùnction of the target angle ~.
- 219S925 84
Transmit (fixed)
... ..
Direction of / ~=45~
~ Receive (rotaledl
.
Figure 34(a)
Transrnit (rotated along
Direction o~
/'r \
.
~-45~ \/ Receive (fixed)
Fi~re 34(b)
Figure 34 Conventional Pattern Measurement Setup
'- 2195925 85
The measurements were performed in an open parking lot on The Pennsylvania
State University property. The area was more than 120 m long, and clear of objects visible
to the radar beam in all directions. The radar test platform, contqining the radar, power
supplies, and the computer interface, was set in a fixed position at zero range. An arc
(centered at the test platform) with a radius of 16 m was drawn on the parking lot surface.
This arc was then sequentially subdivided into 1~ increments so as to minimi7e the error at
any particular angular position.
The test proceeded by moving a target (a small corner reflector on a tripod) to
each angular position, sweeping the radar, and saving the time-domain return data for each
of the eight channels. During data collection, a broad beam antenna, with a 30~, 3 dB
beamwidth was used as the transmit antenna. This antenna was rotated to track the target
as the target was moved to di~erenl angular position, thus mqintqining a constant reflected
power level to the receive antennas.
Several errors can effect the accuracy of the measured radiation pattern: The
power incident on the receive antenna can vary, the lF and RF receiver gain can fiuctuate
between measurements, and there are errors associated with the measurement of angle ~.
All ofthese errors can seriously degrade the resultant radiation pattem.
The return power incident on the receive array is assumed to be the dominant
cause of error in these measurements. There are several factors that can contribute to this
219~92~ 86
error. First, the comer reflector ~lignmPnt is critical. Small vertical or horizontal errors can
result in significant changes (~ + 1.0 dB) in the receive power level. Also, small errors in
the pavement flatness over the area of the arc can result in power fluctuation due to the
vertical change in the comer reflector position. A second factor is the alignment of the
transmit antenna and the target. A small error in this ~lignmPnt can result in the incident
power at the target varying from 0.5 to 1.0 dB. This in tum results in a decrease in the
reflected power, and therefore a decrease in the received power at the radar. The
~lignmP.nt ofthe transmit antenna was estimated to be within + 3~.
Figure 35 shows the IF voltage from Channel I for the target at 16 m and three
di~elel~l angular positions. Note that the signal frequencies are the same, but the
amplitude varies. This amplitude variation is due to the variation in the receive antenna
gain at the particular angular position. Clearly, the return of the target at 90~ exhibits the
greatest voltage level, with the return for 120~ (the first major sidelobe in the receive
pattern) as the next greatest in m~gnilllde. The return from 0~ is nearly 0, indicating a deep
null in the pattern of the receive antenna (as expected). Similar returns were measured for
each ofthe 181 angular positions ofthe target.
An FFT was performed on the IF signal recorded for each angular position of the
target. Each FFT resulted in a relative power value for each of the 51 frequency bins.
Since the frequency is proportional to range, this corresponds to a reflected power level in
each range bin. The target range can be determined by comparing the power level for all
range bins and identifying the peak level. Figure 36 shows the reflected power level in all
- 2~ 95925 87
2. 50 1--O degrees
~ - 90 degrees
,~ ------ 120 de8rees
2 . 00 ~
o 1 50-- -
O ~ t --,
0.50 - - - ' - ~ . . ' ~ .
0.00
ooooooooooooooo,oo,
X '~ ~O ~ ~ ~ -- ~ ~ ~ ~ ~ ~O O
Ttme (sec)
Figure 35 Time-Domain Return for Corner Reflector at 16 m and 0~, 90~, and 120~
range bins for a target at 16 m and 90~. Clearly, the peak in return power is centered in the
16 m range bin, indicating target location. All other peaks are at least 20 dB below this
level.
Figure 37 shows the return power versus target range for the target at three
di~e.ellL angular positions: 0~, 90~, and 120~. In this particular measurement, the only
range of interest is the 16 m range bin. Again, it is clear that the target at 16 m and 90~ has
the greatest measured power level.
2195g2S 88
30 - A ~ 90 degrees
'~20~
, O~
-10--
-20
0 1020 30 40 50 60 70 80 90 100
Range (meters)
Figure 36 Spectral Return for Corner Reflector at 16 m and 90~
O degrees
30 - -- - - - ---- t '' ' ' ' ' " - - - - ' 90 deglees
1 20 degrees
_~ 20 - ~ t\
~ I \ . ~ ~
~'J ~,i~,n;\ /~l~;\ ,
0 10 20 30 40 50 60 70 80 90 100
Range (meters)
Figure 37 Spectral Return for Corner Refiector at 16 m, 0~, 90~, and 120~
219S925 89
The radiation patterns for all eight channels were derived by calculating the power
level in the 16 m range bin for all 181 angular measurements. This measured power leYel is
plotted as a function ofthe target position 0. E;igure 38 shows the measured and calculated
radiation pattern for Channel 1. This measured pattern shows a sidelobe level of
approximately 15 dB and a first null beamwidth of approximately 40~. There is some
measurement error in the main beam, due to the ~lignment errors of the transmit antenna
and the target under test, and the :~lionmP.nt errors of the corner reflector. It should be
noted that this measurement error is less than +1.5 dB in the worst case. Overall, there is
good agreement bet~,veen the measured and calculated patterns. The sidelobes and nulls
are located at the same angles in both patterns, and the pattern shapes are similar.
.' /~ Mea~red Pattem
~ Theore~cal Pattem ¦
J
40 1
--5 0
-60
~ ~ ~ OD ~-- x~ G~ O ~ ~ ~ ~ V, ~O r~ oC
_
Angle (degrees)
Figure 38 Channel I Measured and Calculated Radiation Patterns
-2195925 90
4.2 Synthesized Radiation Pattern of the 8x(4x4) Receive Antennas
~ n this section, the returns from all eight channels are combined in software to
synthesize radiation paKerns of the 8x(4x4) array. The resultant patterns have 2~
beamwidths and main beam angles of 90~, 92~, and 94~. First, a calibration measurement
of a target at 16 m and 90~ was taken. A calibration vector was calculated using this data,
as described in Section 2.5. This calibration vector was then applied to all 181 returns
from each ofthe eight channels, as described in Section 3.2. The resultant (8x181) matrix
was combined, using array theory, to form digitally synthesized patterns with main beams
~ at 90~, 92~, and 94~. These synthesized patterns were then compared to the theoretical
patterns that were calculated in Section 2.2.
Figure 39 shows a comparison of the synthesized radiation pattern and the
calculated pattern with a main beam position of 90~. For this pattern, the m~ le at
each angular position of the synthesized beam is calculated by directly sl.mming~ in vector
form, the calibrated data from each of the eight channels. (rne progressive phase shift
across the array is 0~.) Both patterns have a 3 dB beamwidth of approximately 2~. The
measured pattern has sidelobe levels (close to the rnain beam) of approximately 19 dB.
Most other sidelobes are less than 25 dB. The measured pattern shows excellent
agreement on sidelobe and null locations.
2195925 91
.
Figure 40 shows a comparison of the measured and calculated pattems with a main
beam position of 92~. The synthesized pattern is calculated in two steps. First, a
progressive phase shift is applied to the calibrated data from each of the eight channels.
(Channel 1 data has a -35.7~ phase shift applied, Channel 2- data has a -71.4~ phase shi~
applied, Channel 3 has a -107.1~ phase shift applied, etc.) Then the data at each angle is
summed, in vector form, to yield the m~ de of the return signal for the synthesized
pattern at angle ~. The resultant pattern beamwidth is 2~, and the sidelobe level of the
synthesized beam is approximately 15 dB.
SynthesizedPattem ¦
-10 ~ - - Theoreacal Pattem ¦--
,, ~
~ 40 ~J~
-60 ~ '.
ooooooooooooooooooo
-- ~ ~ -t ~ ~ 1-- 00 ~ O ~ 0! ~
Angle (degrees)
Figure 39 Synthesized and Theoretical Radiation Patterns
for 8x(4x4) Array with a Main Beam at 90~
- 2195925 92
Synthes~zed Pattem ¦
-10 ~ - Theore~cal Patterrl ¦
- 2 0 ~
ooooooooooooooooooo
-- ~ ~ ~ '~ 'D ~ 00 G' O -- ~ ~ ~ ~ ~ ~' ~~
_
Angle (degrees)
Figure 40 Synthesized and Theoretical Radiation Patterns
for 8X(4X4) Array with a Main Beam at 92~
Figure 41 shows a comparison ofthe measured and calculated patterns with a main
beam position of 94~. Again, the synthesized pattern is calculated in two steps. First, a
progressive phase shift is applied to the calibrated data from each of the eight channels.
(Channel I data has a -71.4~ phase shiflc applied. Channel 2 data has a -142.8~ phase shift
applied, Channel 3 has a -214.2~ phase shift applied, etc.) Then the data at each angle is
summed, in vector form, to ,vield the m l~nitl~de of the return signal for the synthesized
pattern. Again, the resultant beamwidth is 2~. However, the sidelobe level of this
synthesized beam is approximately 8 dB. This increasing sidelobe level is expected and is
due to the increase in the progressive phase shift required to steer the rnain beam. Figure
41 shows excellent agreement between the measured and calculated grating lobe location.
- 219$9~5 93
--Measured Pattem
-10 ~ - - - - Theorebcal Pattem
A ~ g~l~
, .. .. .
-60 ' .
ooooooooooooooooooo
~ O ~ CC O~ O = ~ ~ ~ co
Angle (degrees)
Figure 41 Synthesized and Theoretical Radiation Patterns
for 8x(4x4) Array with a Main Beam at 94~
A comparison of the measured radiation pattern from Channel 1 and the
synthesized pattern at 90~ is shown in Figure 42. This comparison shows the beam
focusing capability ofthe radar system. The beamwidth is reduced from approximately 16~
to 2~ using the digital beam forrning technique. In addition, the effective sidelobe power
levels were greatly reduced.
4.3 Multiple Tar~ets at Different Ran~es and An~les
The test described in this section demonstrates that the radar can distinguish two
targets at different ranges and different angles. This ability is critical for many applications.
-- 219~925 94
including automotive radar. Two corner reflectors were placed at 20 m and 90~, and 26 m
and 88~. The return data from the radar was calibrated, and the signals from all
- ~\ Channel 1 4x4
-10 ~ - - - - Synthesized 8x(4x4) ¦
-50~
-60 ~;,
ooooooooOoooooo.oooo
~ ~ ~ ~ ~ ~ 00 o~ o ~ 00
Angle (degrees)
Figure 42 Comparison of Measured Patterns of Channel 1 4x4 Array
and Synthesized 8x(4x4) Beam at 90~
eight channels were combined to form returns in three main beams at 88~, 90~, and 92~.
The target locations were determined by ex~mining the return spectrum in all three main
beams.
In the ideal analysis~ for a target at an angle of ~72, main beams at angles ~, and ~
will have zero measured power. However, in actual operation, measured power levels will
be non-zero, and will depend on sidelobe level, main beam shape, etc. Therefore? the
power level in all three main beams is examined, and the beam with the highest power
- 2195925 95
level is assumed to be the beam with the target. For the radar prototype, there are three
main beams for this test, each with 51 range bins. All 153 power levels are examined, and
the 2 peak levels are assumed to be those corresponding to targets.
The Channel l time-domain return signal for the targets is sho-,vn in Figure 43.
This signal is the combination of two IF frequencies (one from each target), each given by
Equation 1.12. The frequency-domain spectrum for these signals is shown in Figure 44. It
is clear that the return spectrum contains two peaks, indicating two separate targets at 20
and 26 m. However, there is no information available to indicate angular position.
2.50
Chamlel I Voltage
2.00~
~ 100 ~
0.50 ~
0.00 , ~ ~
O t 't 't o o o o o o o o o o o o o
O r~ oo ~ ~O o C~ O ~ O oo G~ O
o -- ~ ) o -- U~ oo ~ o r~ ~o o
Time (msec)
Figure 43 Channel l Time-Domain Return for Targets at [26 m, 90~] and [20 m, 88~]
'' 219~925 96
~o
Channel I Power(dB)¦
20~
0 lO 20 30 10 50 60 70 80 90 100
Range (meters)
Figure 44 Channel I Spectral Return for Targets at [26 m, 90~] and [20 m, 88~]
The signals from each of the eight channels were combined to form returns in the
synthesized beam positions at 88~, 90~, and 92~. (For the main beam at 88~, a progressive
phase shi~ of+35.7~ was applied across the eight channels, and for the main beam at 92~,
a progressive phase shi~ of-35.7~ was applied. No phase shift was applied for the main
beam at 90~.) This resulted in an effective power level fo.r each main beam at each range
bitl. The target location can be determined by comparing the relative power levels in each
range bin at each angular position and selecting the peak power levels.
Plots of the return spectrum for the two targets for each of the three synthesized
beam positions are sho~n in Figure 45. It is clear from Figure 45 that there are t~o peaks
in the power spectrums. one at a range of 20 m in the 88~ main beam, and the other at a
- 21959~5 97
range of 26 m in the 90~ main beam (For each of these range bins, there is some non-zero
power in the other two angular bins. These power levels are due to the antenna array
sidelobes. However, these power levels are approximately 10 dB lower than the measured
target retums.)
~ ~ 88 Degrees
~ 90 De~ees
r ¦ . ~ ~ 92 Degrees
~~ 3 0 - - ~
c
- 0 10 20 30 40 50 60 70 80 90 100
Ran~r,e (meters)
- Figure 45 Spectral Retums of Synthesized Main Beams at 88~, 90~, and 92~
for Targets at [26 m, 90~] and [20 m, 88~]
4.4 Multiple Tar~ets at the Same Ran~e and Different An~les
The test described in this section demonstrates that the radar can distinguish two
targets at the same range but different angles. Again, this ability is critical for rnany
applications, including automotive radar. Two comer reflectors were placed at 30 m, one
at 90~, and the other at 94~. The return from the radar was calibrated, and the signals from
all eight channels were combilled to fomm retums in five main beams at 86~, 88~, 90~, 92~.
21~13925 98
and 94~. The target locations were deterrnined by examining the return spectrum in all five
of these main beams.
Figure 46 shows the Channels I and 2 time-domain return signals. The returns for
Channels 3 and 4, 5 and 6, and 7 and 8 are shown in Figures 47 - 49, respectively. It is
noted that the return signals have the same frequency, but the amplitude and phase varies
from channel-to-channel. This amplitude variation is caused by the diaele~lt interference
patterns from the reflected signals at the different receiver positions. This difference in
m~gni~ldes (and slight phase difference) in each of the channels is critical for the anguiar
resolution ofthe targets.
Figure 50 shows the return spectrum for each of these eight channels. All eight
channels have peaks in their spectrums in the 30 m range bin, and the channel-to-channel
power level varies by about 12 dB for this range bin. Once again, the target range can be
~ identified by this spectrum, but target angular position cannot. (Note the high response in
the 64 m range bin for Channels 5-8. This is due to sampling noise, 51.2 KHz/8, on the
second AID converter power supply. Although this noise level is high, it is still
significantly lower than the target power level. In addition. this noise source-can be
eliminated in future measurements.)
~1959~5
.50
--Channel I
-- - Channel '
2.00 --
~$ ,00 ~ '~ r~
0.50 -- -
0.00
~ t ~ 't r~ ~
O O O O o o o o o o o o O O O O O
O ~ I ~ 00 C~ ~ oo ~ d '~ o 00 G' O
Time (msec)
Figure 46 Channel I and 2 Time-Dornain Returns for Targets
at [30 m,90~] and [30 m, 94~]
2.50
Channel 3
- - - - - - Channel 4
2. 00 ~
o~ 100 ~1
0.50 - -
0.00
o O O O O O O O O O O O O o o o o
o ~ ~ 0~ ~ ~ O G~ O -- ~ ~ Vl ~ 0~ C~ O
O _ ~ r~ o _ v~ o~ -- ~ r~ O ~ ~O O
Time (msec)
Figure 47 Channel 3 and 4 Time-Domain Returns for Targets
at [30 m,90~] and [30 m~ 94~]
- 2195925 loo
2.50
--Channel 5
- - Channel 6
2.00 - - '
-
0 1.50~
1.00 ~
0.50-- - - . . .
o.oo ~ '
O ~ ~ _ ", , ,, ~ ~
O O O ~, o O O o O o o o o o o, o O
O ~ ~ LT LT~ L- LT~ L ~LT~ LT~ L ~ LT L I L~ LT~ L~ LT~
O ~ oo ~ ~oo ~ o ~ ~o o
T~me (msec)
Figure 48 Channel 5 and 6 Time-Dornain Returns for Targets
at [30 m,90~] and [30 m, 94~]
2.50
Channel 7
- - --- Cham~el 8
2.00----
~ 1,00 ~ ~ ~ V:
0.50-- ~ :
0.00
o O O c ~ O O O OO O O O O o o o
LT~ L~ LT~ ~LTI LT~ LTI LTI LTI LT~ LTJ L~ LTI LT~
O -- ~ r~ ~ 00 -- ~ 00 _ t V) O 00 C~ ~0
o ~ \D ~ ~ t ~ t '~
Time (msec)
Figure 49 Channel 7 and 8 Time-Dornain Returns for Targets
at [30 UL90~] and [30 m~ 94~]
-- 219592S
101
C lanne
30 ~ ~C~anne
--x--Clanne
_O ,~ Clanne~ '
3 ~ ~}CIanne ~
/110~
0 10 20 30 40 50 60 70 80 90 100
Range (meters)
Figure 50 Spectral Return for all Eight Channels for Targets
at [30 rn,90~] and [30 m, 94~]
The complex power vectors from each of the eight channels were combined to
form synthesized beam positions at 86~, 88~, 90~, 92~, and 94~. This results in a two-
dimensional power spectrum in the range and angle. Plots of the return spectrum for the
two targets versus range for each of the five synthesized beam positions are shown in
Figure 51. It is clear from this figure that there are two peaks in the power spectrum, both
at a range of 30 m, but at angles of 90~ and 94~. For these range bins, there is some non-
zero power in the other three angular bins. This is due to the sidelobe response in the
synthesized beam at these angles. However, this power level is approximately 10-12 dB
lower than the actual target return.
- 2195925 102
h ~e ~rees
e~rees
~ ~ rl ~e rees
I ~ ~eVrees
X--q ~e qees
_~~
0 10 20 30 ~0 50 60 7080 90 100
Range (meters)
Fig~e51SpectralRetu~sofS~es~ed Ma~Beam~at86~,88~,90~,92~,~d94~
forTargetsat~30 ~90~] ~d[30 ~ 94~~
Although plots of power versus range and angular position are
displa~ed above, in the preferred embodiment of the invention the
computer is configured to compar~ the magnitudes of the returns for
each of the angular beam positions in each of the range bins and
automatically select (based on the-points with the highest values~
the angular resolution of the targets and the range of the targets,
and supply this information to an output device-so that it may be
displayed to a user, preferably on a real-time basis.
2195925 ~o3
Chapter 5
CONCLUSION
5.1 Research Summarv
The research in this thesis describes a new method for implem~onting beam-steering
in FMCW radar systems. A unique radar prototype was designed, built, and tested as a
proof of the concept. Testing procedures in Chapter 4 showed the beam-forrning
capabilities of the radar prototype. The VCO linearity, a critical pelro~ ce parameter of
the radar, was greatly improved in the prototype by implem~nting a novel linearizing
algorithm, as discussed in Section 3.4.
The FMCW radar with digital beam-forming represents an advancement in the art
of radar technology. This radar has several advantages over traditional RF-based beam-
forrning techniques. First, the hardware costs are lower and the reliability is higher.
Second, the target detection time is reduced. Third, sophicticated signal processing
techniques can be applied to further improve the accuracy of the radar.
A unique contribution of this thesis is the angular resolution capabilities of the
FMCW radar prototype. The prototype hardware was described in Chapter 3. The results
presented in Chapter 4 sllow that the IF signals from di~rert;lll receive channels can be
digitized, phase shifted. and combined in software to provide angular resolution. Radiation
patterns from a single receive channel were measured and compared to the theoretical
~195925 104
pattem. The returns from all receive channels were then combined in software to yield
several synthesized pattems with a narrow rnain beam at different positions.
AfklitiQn~l tests indicated that the radar determined the range and angular position
of multiple targets. In the first test, the radar identified two targets at di~,e,ll ranges and
dilT~ n~ angular positions. ln the second test, the radar uniquely id~ntifie~l two targets at
the same range but different angles. This ability to identify range and angular position
using digital beam-steering is a unique and significant contribution to the reported radar
capabilities in the literature.
5.2.1 Improve Signal Processing Capability
Array tapers and FFT windowing functions can be used to improve the range and
angular resolution of the radar. In the prototype discussed in Chapters 3 and 4, basic
signal processing techniques were used to determine the spectral purity of the signals. A
standard FFT subroutine was used to determine the power spectrum in the range bins. To
irnprove DSP capabilities, FFT windowing functions can be used to decrease the
'leakage" between range bins. In the beam-forming algorithms, uniform array tapers were
219S925 105
used, resulting in sidelobe levels on the order of 13 dB. Array tapers can be applied during
beam-forming to reduce sidelobes and grating lobes.
5.2.2 Develop Real-Time Prototype with Range, Rate, and Angular Capabilities
Throughout the thesis, it was assumed that all targets were stationary. This is
rarely the case in practice. The principles of digital beam-forming can be applied to detect
moving targets, and the system should be able to perform target detection in rnilliseconds,
which is essentially real-time for many applications. This would extend the radar operation
to provide range, rate, and angular position, not just range and angular position.
It will be appreciated that the radar system disclosed above
could easily be adapted for use with moving targets by using
several modulation schemes. For example, the multiple receive
channels and digital beam forming techniques of the present
invention could be combined with the multiple modulation scheme
disclosed in U.S. Patent No. 5,268,692 (referenced above), to
provide a radar capable of tracking moving' targets. Data from
subsequent modulation ~lopes can be matched in order to provide the
velocity, range and angular resolution of moving targets.
5.2.3 Reduce l~eceive Antenna Size
The receive antenn~s used in this system had an ~7imnth~1 beamwidth of 16~. This
is sufficient for narrow synt_esized bearns, but it also produced grating lobes at the
extreme mam beam positions. Smaller receive antennas, with broader patterns, could be
used to provide wider beam-steering capabilities (though witk less angular resolution).
Errors in experimental data would be reduced due to the decreased sensit~vity of the
receive antenna in the main beam.
5.2.4 lmplementing an lmaging Display
The rëturn from the radar indicates power versus range and angular position. This
information could then be used tO display target return in two dimensions, with color
2195g2~
~- 106
indicating intensity (and therefore target size). This would provide the user with a
snapshot of the targets in view.
'-- 21 95~2S 107
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