APPROXIMATE LINEAR FM SYNCHRONIZATION SYMBOLS FOR A BANDWIDTH CONFIGURABLE OFDM MODEM

SYMBOLES APPROXIMATIFS DE SYNCHRONISATION FM LINEAIRE, POUR MODEM MROF A LARGEUR DE BANDE CONFIGURABLE

English Abstract

A communications system permits bandwidth configurability using a linear frequency modulated (LFM) waveform for transmitter/receiver synchronization. The system permits enhancement of MIL-STD-1553 data buses, and is likewise applicable to any bandwidth-configurable modem.

French Abstract

Un système de communication permet de configurer la bande passante à l'aide d'une forme d'impulsion à modulation linéaire de fréquence (LFM) la synchronisation de l'émetteur/ récepteur. Le système permet la mise en évidence des bus de données MIL-STD-1553, et est également applicable pour tous les modems dont la bande passante peut être configurée.

Claims

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Claims
1. Within a bandwidth configurable modem, a method of generating
synchronization symbols for a transmitted waveform, comprising:
selecting a frequency sub-band for which synchronization symbols are desired,
said sub-band comprising v frequency bins with associated frequency sub-
carriers;
and
generating synchronization symbols as a discrete time domain LFM signal x'(n)
with signal values obtained using the equation:
<IMG>
where: N is the length of the signal in samples; n=0 to N-1; and k0 is the sub-
carrier
index corresponding to the first frequency bin within the selected sub-band.
2. The method as claimed in claim 1 further comprising generating the
synchronization symbols directly in the time domain using a microprocessor to
perform one of series expansions and CORDIC functions.
3. The method as claimed in claim 1 further comprising generating a time
domain look-up table (LUT) with 2N point complex samples, comprising:
using the equation
<IMG> m = 0,1,.multidot.,2N - 1
to compute the 2N point complex samples to populate the LUT.
4. The method as claimed in claim 3 further comprising generating a time
domain signal by indexing the LUT using the equation:
<IMG>
5. Within a bandwidth configurable modem, a method of generating
synchronization symbols for a transmitted waveform, comprising:

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selecting a frequency sub-band for which synchronization symbols are desired,
said sub-band comprising v frequency bins with associated frequency sub-
carriers;
generating synchronization symbols in a frequency domain using the
approximation equation:
<IMG>
where: N is the number of sub-carrier frequencies for the entire
bandwidth; and k0 is the index of the sub-carrier corresponding
to the first frequency bin within the selected sub-band; and
using an inverse fast Fourier transform (IFFT) to convert synchronization
symbols to a time domain before the waveform is transmitted.
6. The method as claimed in claim 5 further comprising generating the
synchronization symbols directly in the frequency domain using a
microprocessor to perform one of series expansions and CORDIC functions.
7. The method as claimed in claim 5 further comprising generating a frequency
domain look-up table (LUT) wherein LUT synchronization coefficients are
represented by 2N evenly spaced complex coefficients of a unit circle.
8. The method as claimed in claim 7 further comprising generating a frequency
domain signal by mapping LUT synchronization coefficients to consecutive
frequency sub-carriers, using the equation:
<IMG>
wherein k0 represents a first sub-carrier and v is the number of
frequency bins over which the signal is swept.
9. A bandwidth-configurable modem adapted to generate synchronization symbols
comprising:

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logic circuits that select a frequency sub-band for which synchronization
symbols
are desired, said sub-band comprising v frequency bins with associated
frequency
sub-carriers; and logic circuits that generate synchronization symbols as a
time
domain LFM signal x'(n) with signal values obtained by using the equation:
<IMG>
where: N is the length of the signal in samples; n=0 to N-1; and k0 is the sub-
carrier
index corresponding to the first frequency bin within the selected sub-band.
10. The bandwidth-configurable modem as claimed in claim 9 wherein the logic
circuits comprise a microprocessor to perform one of series expansions and
CORDIC functions for generating the synchronization symbols directly in the
time domain.
11. The bandwidth-configurable modem as claimed in claim 9 wherein the logic
circuits comprise a time domain look-up table (LUT) with 2N point complex
samples populated by using the equation:
<IMG>
12. The bandwidth-configurable modem as claimed in claim 11 wherein the logic
circuits generate a time domain signal by indexing the LUT using the equation:
<IMG>
13. The bandwidth-configurable modem as claimed in claim 9 further comprising
a
bus coupler for interfacing with a MIL-STD-1553 data bus.
14. A bandwidth-configurable modem adapted to generate synchronization symbols
comprising:
logic circuits that select a frequency sub-band for which synchronization
symbols are desired, said sub-band comprising v frequency bins with
associated frequency sub-carriers;

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logic circuits that generate synchronization symbols in a frequency domain
using the approximation equation:
<IMG>
where: N is the number of sub-carrier frequencies for the
entire bandwidth; and k0 is the index of the sub-carrier corresponding to the
first frequency bin within the selected sub-band; and
logic circuits for performing an inverse fast Fourier transform (IFFT) to
convert synchronization symbols to a time domain before the waveform is
transmitted.
15. The bandwidth-configurable modem as claimed in claim 14 wherein the logic
circuits comprise a microprocessor to perform one of series expansions and
CORDIC functions for generating the synchronization symbols directly in the
frequency domain.
16. The method as claimed in claim 14 wherein the logic circuits comprise a
frequency domain look-up table (LUT) adapted to store LUT synchronization
coefficients that are represented by 2N evenly spaced complex coefficients of
a
unit circle.
17. The bandwidth-configurable modem as claimed in claim 16 wherein the logic
circuits generate a frequency domain signal by mapping LUT synchronization
coefficients to consecutive frequency sub-carriers, using the equation:
<IMG>
wherein k0 represents a first sub-carrier and v is the number of frequency
bins over
which the signal is swept.
18. The bandwidth-configurable modem as claimed in claim 14 further comprising
a bus coupler for interfacing with a MIL-STD-1553 data bus.

Description

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APPROXIMATE LINEAR FM SYNCHRONIZATION SYMBOLS FOR A
BANDWIDTH CONFIGURABLE OFDM MODEM
TECHNICAL FIELD
The invention relates to orthogonal frequency
division multiplexing (OFDM) based data communications and,
in particular, to symbol and frame synchronization signals
for a bandwidth configurable OFDM modem.
BACKGROUND OF THE INVENTION
MIL-STD-1553b is a 30-year-old standard that
defines electrical and signaling characteristics for
communications over avionics buses used in military and
civilian aircraft, as well as in other applications (ships,
trains, shuttles, space stations, etc.). A Manchester II
bi-phase signaling scheme is used over shielded twisted
pair cabling. That signaling scheme does not efficiently
utilize potential bandwidth available on the bus.
OFDM is a communications protocol that may be used
to more optimally utilize the available bandwidth unused by
the 1553b signaling. Of course, bus coupler type, network
topology and filtering of the Manchester II signaling
affect how much bandwidth is available for an "overlay"
OFDM communications system.
An OFDM based communications system can be
described by transmitter 10 and receiver 30 components
shown in FIGs. 1 and 3. The transmitter 10 includes forward
error correction (FEC) 12 applied to an input data bit
stream, followed by a mapping 14 of encoded bits to
frequency domain sub-carriers, which are transformed to a
time domain digital signal by an inverse fast Fourier
transform (IFFT) 16, which is an efficient implementation
of an inverse discrete Fourier transform (IDFT). FEC 12 may
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be a Reed-Solomon, convolutional, or any other type of
forward error correction encoding scheme.
Before the digital signal is converted to an analog
signal for transmission to the receiver 30, a preamble,
inserted by preamble insertion 18, includes a number of
synchronization symbols 24 (shown in FIG. 2) which are pre-
pended to the transmission sequence to permit
synchronization of the transmitted waveform at the receiver
30, and to facilitate automatic gain control (AGC) and
channel response estimation. A cyclic prefix is usually
added to the OFDM symbols, which are appropriately shaped
(windowed and/or filtered) by symbol shaping 20 before
conversion to an analog signal by an analog front end (AFE)
22. The AFE 22 includes a digital-to-analog converter
(DAC), appropriate analog filtering and may also include an
IF/RF mixing stage to convert the signal to higher
frequencies.
An exemplary OFDM transmission sequence is shown in
FIG. 2. As can be seen, a predetermined number of
synchronization symbols 24 are prepended to data symbols
26.
At the receiver 30, the analog signal is filtered
and converted to a digital signal by an analog-to-digital
converter (ADC), not shown, in a receiver analog front end
32. The appropriate RF/IF stages are used to convert the
received signal to a baseband signal in a manner well known
in the art. An automatic gain control 34 controls input
signal level based on power metrics estimated from the
synchronization symbols 24. A fast Fourier transform (FFT)
which is an efficient implementation of the discrete
Fourier transform (DFT) 36 is applied to the sampled
signal, with the timing of the FFT based on detection and
timing estimations derived from the synchronization symbols
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24. A channel estimation 46 is calculated using the
synchronization symbols detected by the synchronization
detection unit 44 and is used by the demodulator 38 to
remove effects of the channel. This process, called channel
equalization, is perfornted in the frequency domain. An
inverse mapping function 40 is used to convert demodulated
frequency domain sub-carriers to coded data bits followed
by forward error correction (FEC) decoding 42, which
corrects bit errors when possible and passes the decoded
data bits to higher communications layers.
In addition to using OFDM to utilize unused
bandwidth on a 1553b bus, it has been recognized as
desirable to be able to configure multiple independent
networks on the same bus, so that groups of communications
devices can be respectively allocated a certain proportion
of the available spectrum. It would also be useful for some
devices (a host bus controller, for example) to be able to
communicate to devices associated with any of these
independent networks. In order to accomplish these
objectives, the synchronization signaling component of an
OFDM-based communications system must have an efficient
implementation and be configurable "on the fly", as well as
having other required properties. These properties include:
a small transmit peak to average power for all
configurations; and cross-correlation properties such that
a receiver configured to operate in one frequency band will
not detect as a valid synchronization signal leakage energy
of a transmitter configured to operate in another frequency
band.
Linear FM (LFM) signals are used in communications
systems for the transmission of data as well as for
synchronization preambles, automatic gain control (ACC) and
channel response estimation. Advantages of LFM signals
include low peak to average power for transmission using
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limited resolution digital to analog converters and limited
linearity amplifiers, and having a narrow correlation peak
for matched filter reception.
OFDM multi-carrier communications schemes, such as
HomePlug Version I and AV, often synthesize a LFM signal
by storing frequency domain coefficients in a look up table
(LUT) and then transforming to the time domain using an
IDFT. Each LUT coefficient corresponds to an OFDM sub-
carrier and each coefficient has a non-zero value for sub-
carriers ranging over the sweep of the LFM signal. This
system can be configured to sweep over any desired sub-band
by zeroing LUT coefficients corresponding to sub-carriers
outside the sub-band. However this system suffers from the
drawback that when configured for a sub-band, the time
domain LFM sweep will have most of its power concentrated
in the time segment corresponding to the sub-band,
significantly increasing the peak to average power ratio of
the signal. For example, if the system is configured to
sweep the first half of the LFM band by zeroing the upper
half of the coefficients, the first half of the LFM
waveform will sweep over this sub-band and the second half
will be close to zero in amplitude. A bandwidth-
configurable OFDM modem that overcomes at least one of
these shortcomings would be highly desirable.
SUMMARY OF THE INVENTION
The instant inverltion is designed to enhance MIL-
STD-1553 data buses but is likewise applicable to any
bandwidth configurable communications system requiring an
LFM waveform to be generated and therefore not restricted
to an OFDM modem. The invention provides a communications
system that permits bandwidth configurability using a
linear frequency modulated (LFM) waveform for
transmitter/receiver synchronization.
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In accordance with one aspect of the present
invention, a method of generating LFM synchronization
symbols for a bandwidth-configurable modem includes using
jnvn~+j2,rkon
the equation x'(n)=e N~ N where: x' (n) is the discrete
time LFM waveform; N is the length of the waveform in
samples; n=O to N-1; v is the number of frequency bins over
which the signal is swept; and ko is the index of the sub-
carrier corresponding to the start of the sweep.
In accordance with another aspect of the present
invention, a method of generating synchronization symbols
for a bandwidth-configurable modem includes using the
approximation equation
k>+
X'(k+k0 mo ~dN ~ ~X"(k+ko)N~ e' ~4
modN 1/v
0 otherwise
where: X'(k) is the DFT of the LFM waveform x'(n); N is the
number of sub-carrier frequencies; k=O to N-1; v is the
number of sub-carriers over which the signal is swept, and
ko is the index of the sub-carrier corresponding to the
start of the sweep; and using an inverse fast Fourier
transform (IFFT) to convert to the time domain before the
waveform is transmitted.
In accordance with yet another aspect of the
present invention, a bandwidth-configurable modem includes
logic circuits that generate the synchronization symbols in
j7r vn' +j2)r kon
----a time domain using the equation x'(n)=e N ,- N where: x' (n)
is the discrete time LFM waveform; N is the length of the
waveform in samples; n=:O to N-1; v is the number of
frequency bins over which the signal is swept; and ko is
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the index of the sub-carrier corresponding to the start of
the sweep.
In accordance with a further aspect of the present
invention, a bandwidth-configurable modem includes logic
circuits that generate the synchronization symbols in the
frequency domain by using the approximation equation:
'k'+ '
N
k = 0,1, = = = , v -1
X' (k + ka )~nod N ~ X"(k + ko )mod N - ~ e J v ~ 4
0V V V otherwise
where: X'(k) is the DFT of the LFM waveform x'(n); N is the
number of sub-carrier frequencies; k=O to N-l; v is the
number of frequency bins over which the signal is swept;
and ko is the index of the sub-carrier corresponding to the
start of the sweep; and logic circuits for performing an
inverse fast Fourier transform (IFFT) for converting sub-
carrier signals to the time domain before the waveform is
transmitted.
In the above equations, v is understood to be a
positive integer and consequently the equations describe an
LFM sweep going from low to high frequency. However, with
minor modifications obvious to one skilled in the art, the
equations can be modified to describe an LFM sweeping from
high to low frequency.
BRIEF DESCRIPTION OF THE DRAWINGS
Further features and advantages of the present
invention will become apparent from the following detailed
description, taken in combination with the appended
drawings, in which:
Fig. 1 is a schematic diagram of an exemplary prior
art OFDM transmitter;
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FIG. 2 is a schematic diagram of an exemplary prior
art OFDM transmission sequence;
FIG. 3 is a schematic diagram of an exemplary
prior-art OFDM receiver;'
FIG. 4 is a graph plotting the normalized magnitude
response of X(k) and of the Discrete Fourier Transform
(DFT) of x(n) ;
FIG. 5 is a graph plotting the phase response of
X(k) and of the Discrete Fourier Transform (DFT) of x(n);
FIG. 6 is a graph plotting the normalized magnitude
response of X"(k) and of the Discrete Fourier Transform
(DFT) of x'(n), where the bandwidth that is swept (v = 32)
is less than the entire available bandwidth (N = 256) and
where ko = 0;
FIG. 7 is a graph plotting the phase response of
X"(k) and of the Discrete Fourier Transform (DFT) of x' (n) ,
where the bandwidth that is swept (v = 32) is less than the
entire available bandwidth (N = 256) and where ko = 0;
FIG. 8 is a graph plotting the normalized magnitude
response of X"(k) and of the Discrete Fourier Transform
(DFT) of x'(n), where the bandwidth that is swept (v = 32)
is less than the entire available bandwidth (N = 256) and
where ko = 32;
FIG. 9 is a graph plotting the phase response of
X"(k) and of the Discrete Fourier Transform (DFT) of x'(n),
where the bandwidth that is swept (v = 32) is less than the
entire available bandwidth (N = 256) and where ko = 32;
FIG. 10 depicts the use of a single LUT to generate
the LFM synchronization symbols;
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FIG. 11 depicts, in a complex plane, a unit circle
from which 2N evenly spaced complex coefficients are
derived to represent synch coefficients in a LUT;
FIG. 12 is a time-domain representation of a
approximated and exact synchronization symbol for N = 256,
v = 64 and kO = 0;
FIG. 13 is a time-domain representation of the
approximated and exact LFM signals for N = 256, v = 64 and
kO=O; and
FIG. 14 is a schematic diagram of a bandwidth-
configurable modem in accordance with the invention.
It will be noted that throughout the appended
drawings, like features are identified by like reference
numerals.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Linear FM Synchronization Symbols
It can be demonstrated that for the following
complex sampled LFM signal (quadratic phase modulation),
'n,
j'
x(n) =e N Equation 1
the discrete Fourier transform (DFT) defined by
N-( jz~kn
X~k~=~x~n~e N k=0,1, ,N-1 Equation 2
n=0
is given by
~ --
-
X(k) ='\fN-e-J k ,+j"
N 4 k=0,1,= =,N-1 Equation 3
where: n = 0 to N-1 and k = 0 to N-1.
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This implies that the DFT of this particular LFM
signal results in an equivalent LFM signal except for a
scaling of -JN and a n/4 phase shift. The functional form
of the signal is the same in the time and frequency
domains.
This can be seen in the magnitude and phase
responses of the DFT of x(n) and X( k) as shown in FIGs. 4
and 5, for N = 64 (the magnitudes were normalized to 1 for
the purpose of illustration).
It should be noted that the phase of the signals
extends beyond -rn and rn allowing one to see the quadratic
nature of the curve.
x(n) is a specific case (v = N, ko = 0) of the more
general LFM function,
j"vn2+j 2Rkpn
x'(n) =e N N Equation 4
where v can be considered the number of frequency bins over
which the signal is swept, and ko the index of the sub-
carrier corresponding to the start of the LFM sweep. For v
= N, the DFT of x' (n) is
X'W =X(k-ko),noaN Equation 5
where the spectrum of X(k) is circularly shifted by ko
frequency bins.
Unfortunately, for v equal to anything other than
N, the quadratic phase modulation represented by Equation 3
in the frequency domain no longer applies. It can, however,
be shown to be a reasonable approximation, especially for
an efficient generation of synchronization signals for OFDM
based communications systems applications.
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With the appropriate scaling, the DFT of x' (n) is
approximated by
N -Jk'+j
X'(k+k0)modN"X"(k+k0)modN_ rV e k=0,1,===,v-lEquation 6
l
0 otherwise
for v#n .
FIGs. 6 and 7 illustrate the effect of limiting the
bandwidth that is swept (v) to less than the entire
bandwidth (N) for Equation 6. In this case, N = 256, v =
32 and ko = 0. FIGs 8 and 9 show the effect of limiting
the width of the LFM sweep to v=32 and offseting the start
of the sweep by ko=32.
Note that the coefficients are just rotated which
hints at an efficient implementation.
The phase response of Equation 6 is a much better
approximation to the phase response of the DFT of x' (n)
than the corresponding magnitude responses.
The synchronization symbols for an OFDM preamble
can be generated in the time domain or the frequency
domain. In either case, it is desirable to use quadratic
phase modulation (in time or across frequency) to generate
the symbols using the formula of either Equation 4 or
Equation 6, respectively. If the quadratic phase modulated
symbol is generated in the frequency domain, an IFFT is
used to convert the signal to the time domain before it is
transmitted. If the LFM synchronization symbols are
generated directly in the time domain using Equation 4,
this results in a power spectral density that is not
constant. If the synchronization symbols are generated in
the frequency domain using Equation 6, the power spectral
density is constant across the swept band. For an OFDM
based communications system, it is desirable to have a
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constant power spectral density across the swept frequency
band.
Look-Up-Table (LUT) Implementation
In accordance with one embodiment of the invention,
a very efficient method of using a look-up table is
provided for configuring any frequency band with
appropriate coefficients based on the LFM approximation of
Equation 6 for an appropriate selection of configurable
bandwidths. Note that in equation 6 the angle argument is
always an integer multiple of z/N providing that v divides
evenly into N. Consequently a 2N value look up table (LUT)
can be constructed to precisely generate the frequency
domain LFM values of equation 6, as shown in FIG. 10. In
this example, a synchronization coefficient LUT 50 has a
table index of 0 to 15 (i.e. 2N = 16, N = 8), which
provides circular modulo(2N) indexing for the LUT. An IFFT
buffer 52 temporarily stores the LUT coefficients for
inverse FFT processing by an IFFT filter 54, which
generates a LFM time ser_Les x(n) 56. In this example, it
is assumed that N = 8, ko = 2 and v = 4. Once computed,
the step size through the table is translated to a LUT
table index of [0 2 8 2] (as per Equation 7, below) where
the last index value (2) is the result of 18 modulo 16.
The synchronization coefficient look-up table (LUT)
represents 2N evenly spaced complex coefficients of the
unit circle 60 as shown in FIG. 11. Note that any constant
phase rotation of the coefficients is un-important. Also,
because of the symmetry of the coefficients in the complex
plane 62, the number of LUT elements could be reduced at
the expense of some additional logic. Quadratic phase
modulation is obtained by stepping through the LUT
coefficients in a quadratic way (modulus 2N for a circular
table) and mapping them to consecutive frequency sub-
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carriers with the first sub-carrier being ko as defined in
Equation 7.
X'(k+k(,),nodN =LUT I v NkZJ k=0,1,===,v-1 Equation 7
l
mod N
The time series, such as the one shown in FIG. 12,
can be generated by an I:FFT. The time series can be made
complex (in phase and quadrature) with the appropriate FFT
architecture or real, depending on the type of signaling
required. Figure 12 illustrates the time domain
representation of a synchronization symbol for N=256, v=64
taking a real part of the IFFT output. The exact LFM signal
is included for comparison. It should be noted that in this
case every N/v sample is equivalent.
Using a configurable bandwidth specified by a value
of v that divides evenly into N results in precise
quadratic phase modulation across frequency sub-carriers in
all cases.
In practice, if N is large enough, the configurable
bandwidth can be specified by a value of v that does not
divide evenly into N. In this case the LUT index value
calculated by equation 7 may be non integer and the LUT
value can be determined by some interpolation technique
(including nearest neighbor interpolation which amounts to
rounding LUT index). Reductions in LUT size can be obtained
using methods like CORDIC approximations for sine and
cosine functions. As is known in the art, CORDIC
(COordinate Rotation DIgital Computer) functions constitute
a simple and efficient algorithm to calculate hyperbolic
and trigonometric functions.
Other Implementations
Time Domain
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j7r vn'j2nk-on
Equation 4, x'(n) =e N N can be employed to
generate the synchronization symbols directly in the time
domain using a microprocessor (CPU, ALU, floating point co-
processor...) and known methods (series expansions, look-up
table, CORDIC functioris, etc.). For a bandwidth-
configurable system, the parameters are modified for the
different bandwidths (v) and starting frequencies (ko).
This results in a power spectral density that is not
constant (but can be flattened with appropriate windowing
and filtering) . For a system where latency when switching
configurations is an issue, i.e. bandwidth configurable "on
the fly", having better control over the power spectral
density and having an ability to turn off sub-carriers that
may be interfering with sensitive equipment or violating
emissions limits as set by MIL-STD-461e and FCC part 15,
there are more suitable ways to generate synchronization
symbols.
Efficient Look-Up Table Implementation
In accordance with one embodiment of the invention,
an efficient LUT implementation for generating
synchronization symbols in the time domain is possible when
the limitations described above are not an issue. A time
domain LUT with 2N point complex samples is generated using
the formula:
,
-~ -m
LUT(m) =ej N m=0,1,===,2N-1 Equation 8
The time domain signal can be generated by indexing
the LUT according to the following equation:
x(n)=LUT round~NnZ I+2kon) n=0,1,===,N-1 Equation 9
J
mod2n
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which combines linear indexing through the table to
generate the carrier fr.equency with quadratic indexing
through the table to generate the linear frequency
modulation.
The rounding function is required because there are
not enough coefficients to precisely describe the LFM
modulation in the time domain. Instead of the rounding to
obtain an integer LUT index, the LUT can be interpolated.
In any case, the approximation is suitable for most
applications and the LUT can be further reduced if accuracy
requirements permit it. FIG. 13 illustrates the approximate
LFM signal generated in the time domain using this method
for N=256, v=64, taking the real part. The exact LFM signal
is included for comparison.
Frequency Domain
Directly
Equation 6, X(k)=e ~ k(for k=O to v-1, X(k) = 0
N v
otherwise, ignoring n/4 phase rotation) can be employed to
generate the synchronization symbols using a microprocessor
(CPU, ALU, floating point co-processor, etc.) directly in
the frequency domain using known methods (series
expansions, LUT, CORDIC functions, etc.) . For a bandwidth
configurable system, the parameters are modified for the
different bandwidths (v) and starting frequencies (ko)
The time domain signal is generated using an IFFT.
FIG. 14 is a block diagram of a bandwidth-
configurable OFDM modem 100 having logic circuits for
generating synchronization symbols in accordance with
embodiments of the invention. All of the components of the
modem 100 are identical to those described above with
reference to FIGs. 1 and 3 and their descriptions will not
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be repeated for that reason. In addition, the modem 100, or
a microprocessor 106 associated with the modem 100, is
provisioned with algorithms for performing series
expansions and/or Coordinate Rotational Digital Computer
(CORDIC) functions 102, and/or a look-up table 104 for
generating synchronization symbols using the method in
accordance with the invention, as described above in
detail. The microprocessor 106 may be an integral part of
the modem 100 or part of an auxiliary unit. The bandwidth
used by the modem 100 may be statically configured using
hardware or software control parameters in a manner known
in the art. The bandwidth used by the modem may also be
configured "on the fly" by downloading values for N and v
via a modem control channel (not shown). The analog front
end 22 of the transmitter and the analog front end 32 of
the receiver are, in accordance with one embodiment of the
invention, interfaced with a MIL-STD-1553 data bus via bus
couplers 110, 112, respectively.
The main benefit is that the LFM synchronization
signal will be swept only over the configured bandwidth for
the duration of the symbol. This results in a peak to
average power that is constant and independent of the
configured bandwidth. This also permits the inclusion of a
sub-carrier mask to turn off selected tones in the
configured bandwidth as required.
In the foregoing description of the invention, the
variable "v" in the equations is understood to be a
positive integer. Consequently, the equations describe an
LFM that sweeps from a low frequency to a high frequency.
However, with minor modifications obvious to one skilled in
the art, those equations can be modified to describe an LFM
that sweeps from a high frequency to a low frequency.
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CA 02533070 2006-01-17
Our Ref. 17774-1CA
- 16 -
The embodiment(s) of the invention described above
is(are) intended to be exemplary only. The scope of the
invention is therefore intended to be limited solely by.the
scope of the appended claims.
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Representative Drawing