Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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METHOD OF QUADRATURE-PHASE AMPLI~E MODULATION
This invention relates to a method of quadrature-phase amplitude modulation,
more conveniently referred to as QAM.
Back~round of the Invention
In QAM, two carrier signals in phase quadrature are arnplitude modulated by
modulating signals, and are subsequently combined for example for transmission in a
microwave radio transmission system. Each transmitted symkol can thus have any one
of a relatively large number of phase and amplitude states, which are generally
illustrated as signal points in a signal point constellation in a phase plane diagram.
1 0 Various signal point constellations, of triangular, rectangular, circular, and hexagonal
forrns and for various numbers of signal points, are described for exarnple in "Digital
Amplitude-Phase Keying with M-ary Alphabets" by C. Melvil Thomas et al., presented
at the 1972 International Telemetry Conference, Los Angeles, California.
For digital transmission of binary data signals? it is convenient for the number1 5 of signal points in the signal point constellation to be an integral power of 2. Thus for
example 64-QAM transmission systems, in which there are 64 signal points in the
constellation so that each transmitted symbol can repres~nt 6 bits (26=64), are well
known. With increasing demands for data ~ransmission, and increasingly more
sophisticated techniques, it is desimble to provide higher numbers of signal points in the
constellation. Accordingly,256-QAM transmission systems, in which each transmi!ted
symbol represents 8 bits (28=256), have been proposed.
It is well known that the signal points should be spaced in the phase plane as
far apart as possible to provide the greatest possible sigr~l-to-noise (S/N) ratio, and that
the signal points should have the smallest possible amplitudes to minimize the peak
2 5 power of the transmitted signal. It is also desirable to simplify as far as possible 2he
coding and decoding CircuitrJ required for converting between the signal points in the
phase plane and the digital signals which ~ey represent. Particularly in view of this last
matter, rectangular signal point constellations, in which the signal points are arranged on
a rectangular matrix or grid~ have been pre~erred. Where the number of signal points is
an even power of 2, the signal point constellation becomes a square array, for example
of 16 by 16 signal points for 256-QAM.
A problem with a square array of 256 signal points is that the points at the
corners of the square have relatively large amplitudes, and hence result in a high peak
power and a high peak-to-average power ratio for the transmitted signal. In order to
reduce this problem, it is known ~or example from Uchibori et al. U.S. Patent No.
4,675,619datedJune23,1987andentitled"MultipleQuadrature-PhaseArnplitude
Modulating System Capable of Reducing a Peak Amplitude" to provide a modified, or
stepped, square 256-QAM signal point constellation in which the peak amplitude is
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reduced, relative to a square constellation, by relocating 6 signal points from each corner
of a 16 by 16 point square so that the signal points are arranged in an extrapolated
square matrix within a generally circular pattern. While this relocation of signal points
results in reduced peak amplitudes, it introduces a further disaclvantage, discussed
below.
More specifically, Gray coding of digital input signals is generally used so
that the digital signal represented by each signal point in the constellation differs from
the digital signal represented by any immediately adjacent signal point in only one bit
position. Thus a transmitted symbol or signal point which is corrupted and consequently
1 0 interpreted mistakenly as an adjacent signal point contains only a single bit error. Such
a single bit error can be relatively easily detected and corrected using known FEC
~forward error correction) coding schemes; for example, a (511,493) BCH code can be
used which can correct up to two bits in error in a block of 511 bits, with a resulting
increase in the transmitted bit rate of about 3.~%.
1 5 However, relocating signal points in the manner discussed above results in 32
of the 256 signal points representing digital signals having 3 bits different from the
signal represented by an immediately adjacent signal point; in other words they have a
Hamming distance of 3 rather than the preferred Hamming distance of 1. Corruption
and consequent rnisinterpretation of such a signal point results in 3 bits being in error,
2 0 and this is not correctable using the (511,493) BCH code discussed above.
In order to reduce this and o~her disadvantages, in Kennard et al. Canadian
patent application No. 569,280 filed June 10, 1988 and entitled "Method of Quadrature
Phase Modulation" there is described and clairned a modified square ~AM transmission
system in which the relocation of signal points is effected in a manner to rninimize the
2 5 adverse effects of transmission errors.
It is becoming increasingly desirable for microwave radio transmission
channels, which have bandwidths of nominally 20, 30, or 40MHz for the various
microwave radio bands at frequencies of the ord~r of 4, 6, and 1 lGHz, to accommodate
standardized forms of signals for transmission. One of the currently most significant
3 0 standardized signal forms is SONET, in which signals, referred to as STS-N signals
where N is an integer having preferred values of 1, 3, 9, 12, etc., have bit rates of N
times 51.84Mb/s. In particular, a so-called STS-3 SONET signal has a bit rate of155.52Mb/s.
Unfortunately, using 256-QAM with FEC, and allowing for necessary
3 5 charmel filter roll-offs, these microwave channel bandwidths provide a poor and
ineffi1cient match for the bit rates of SONET signals. For example, a 256-QAM 40MHz
channel provides a transmission rate which is a little less than that required for two STS-
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3 signals. Accommodating only one STS-3 signal on such a channel would be very
inefficient, and accommodating one STS-3 signal together with other, e.g. two STS-l,
signals would result in undesired complexity.
In order to avoid this problem, it is desirable to use a modulation scheme
which provides a more convenient and efficient matching of microwave radio
transmission channels to SONET transmission rates. In particular, a 512-QAM
modulation scheme enables this to be done. Por example, the use of 512-QAM enables
one STS-3 signal to be ca~ied by a 20MHz channel, and two STS-3 signals to be
carried by a 40MHz channel, in a convenient and relatively efficient manner.
1 0 However, the u se of 512-QAM means that the techniques discussed above,
relating to modifying a square signal point constellation to make it nearly circular, can
no longer be used because 512 is an odd, not an even, power of 2.
For QAM signal point constellations with an odd power of 2 points, e.g. with
32 or 128 signal points, it is known to use a ~ or cross arrangement of the signal points
1 5 to reduce peak amplitudes. For example, such arrangements are described in the paper
by Thomas et al. referred to above, and in a companion paper by J. G. Smith entitled
"Odd-Bit Quadrature Amplitude-Shift Keying", presented at the 1974 InternationalTelemetry Conference, Los Angeles, California. The latter paper also describes arectangular block signal point constellation. In either case, however, the peak amplitude
2 0 for a constellation of 512 signal points is undesirably high.
An object of this invention, therefore, is to provide an improved QAM method
in which the above disadvantages are reduced or avoided.
~urnmQrv of the Invention
According to one aspect of this invention there is provided a method of
2 5 quadrature-phase arnplitude modulation comprising the step of amplitude modulating
two carrier signal components I and Q in phase quadrature in accordance with signal
points in a signal point constellation, the signal point constellation comprising 22n+
signal points, where n is an integer equal to or greater than 4, arranged in a modi~led
rectangular array with substantially 22n-1 points in each of four quadrants defined by I
3 0 and Q axes intersecting at an o~igin of a phase-plane diagram, the signal pOilltS in each
quadrant of the array having I and Q component amplitudes of 1, 3, 5,... units, the
rectangular array being modified by relocating a plurality of points in each quadrant
from positions adjacent to a corner of the rectangle to positions extrapolated from the
rectangular array and having reduced distances from the origin, wherein in each
3 5 quadrant each of a majority of the points so relocated is located in a position, relative to
the position which it would have in the rectangular ~ray, rotated through an angle of
180 about a point having I and Q arnplitude co-ordinates of substantially (2n,2n).
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Preferably, in each quadrant each of a plurality of the signal points which are
relocated is located in a position, relative to the position which it would have in the
rectangular array, in which one of its I and Q amplitude co-ordinates is increased by 2n
and the other is reduced by 2n.
The relocation of points in each quadrant by rotation and translation in this
manner enables the rectangular array to be made approximately circular whiie
maintaining a small Hamming distance between the signal points.
In preferred embodiments of the invention for 51 2-QAM for which n=4,
preferably about 32 signal points ario relocated in each quadtant, and said majority of the
l 0 relocated points whose positions are rotated ~Irough 180~ comprises about 22 points in
each quadrant. In this case said plurality of si,gnal points which are relocated each with
one of its I and Q amplitude co-ordinates increased by 2n and the other reduced by 2n,
i.e. whose positions are tmnslated, comprises at least about 8 signal points in each
quadrant.
l 5 Advantageously, the relocation of the signal points is effected in such a
manner that the signal point constellation is symmetrical about the I and Q axes and
about lines passing through the origin at angles of 45 with respect to the I and Q axes.
For a 512-QAM arrangement ~orwhich n=4, the greatest distance of any
signal point from ehe origin is desirably not more than about ~r666 units, and may be as
little as ~r650 units.
According to another aspect this invention provides a method of quadrature-
phase amplitude modulation comprising the step of amplitude modulating two carrier
signal componenls I and Q in phase quadsature in accordance with signal points in a
signal point constellation, the signal ps)int constellation comprising 512 signal points
2 5 arranged in a modified rectangular artay with 12B poin~s in each of four quadrants
defined by I and Q axes intersecting at an origin of a phase-plane diagram, the signal
points in each quadrant of the array having I and Q component amplitudes of 1, 3, 5,
units, the rectangular array being modified by relocating 32 poin~s in each quadmnt from
positions adjacent to a corner of the rectangle to positions eactrapolated from the
3 0 rectangular array and having reduced distances from the origin, wherein in each
quadrant: each of about 22 points so relocated is located in a position, relative to the
position which it would have In ~e rectangular array, rota~ed through an angle of 180"
about a point having I and Q amplitllde co-ordinates of substantially ( 16,16); and each
of at least about 8 other points so relocated is located in a position, relatiYe to the
3 5 position which it would have in the rectangular array, in which one of its I and Q
amplitude co-ordinates is increased by 16 units and the other is reduced by 16 units.
In this case pre~erably two fur~her ones of the points which are so relocated
are relocated from posîtions with co-ordinates (27,1) and (31,5) to positions with co-
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ordinates (11,23) and (9,21) respectively. The signal point constellation can
consequently be symmetrical about the I and Q axes and about lines passing through the
origin at angles of 45 with respect to the I and Q axes, with the greatest distance of any
signal point from the origin being substantially ~r650 units.
Brief Description of the Drawin~s
The invention will be further wldestood from the following description with
reference to the accompanying drawings, in which:
Fig. 1 illustrates a first ~uadrant of a cross-shaped 51 2-QAM signal point
constellation in accordance with the prior art;
1 0 Figs. 2 and 3 illustrate respectively a first quadrant and all four quadrants of a
512-QAM signal point constellation arranged in accordance with an embodiment of the
method ofthis invention; and
Fig. 4 illustrates a first quadrant of an alternative 51 2-QAM signal point
constellation arranged in accordance with an embodiment of the method of this
l 5 invention.
Description of Prior Art
Referring to Fig. I, the first quadrant of a ~ or cross-shaped 512-QAM signal
point constellation as would be provided in accordance with the prior arl is illustrated.
The signal points are represented in a phase plane diagram showing the relative
2 0 amplitudes of phase-quadrature carrier signal components I and Q for each point. The
128 points in this first quadrant are arranged in a rectangular array, with I and Q
component amplitudes of 1, 3, 5, ...23 units. In ~e other three quadmnts there are
another 128 points in each quadrant correspondingly arranged but with negative values
of the I and~or Q eomponents.
2 5 A point such as the point 10 having the I,Q co-ordinates ( 15,23) has a greatest
distance from the origin 12 (intersection of the I and Q axes) of, and correspondingly
represents a peak amplitude proportional to, ~754 units. As has already been explained,
it is desirable to reduce this peak power, without adversely affecting the complexity of
the coding equipment which must be used or increasing the effects of errors which may
3 0 occur during signal transmission.
Description of Preferred Embodiment
Referring now to Fig. 2, there is illustrated a first quadrant of a 51 2-QAM
signal point constellation arranged in accordance with an embodiment of the method of
this invention.
In Fig. 2, solid dots represent signal points which are used ~or transmission,
and open dots represent original positions from which some of the transmitted signal
point positions are relocated, as described further below. The relocation of signal points
is achieved in a similar manner to that described in U.S. Patent No. 4,675,619, using a
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code converting unit which may, for ~xample, comprise logic circuitry. As the form of
such a code converting unit is known to those of ordinary skill in the art, it need not be
described here.
As is kno vn, each transmitted 512-QAM symbol represents 9 bits of a digital
signal which is being transmitted (29=sl~-). In the arrangement of Figs. 2 and 3, 5 of
the 9 bits determine an I-component amplitude and the remaining 4 bits determine a Q-
component amplitude of the transmitted signal. As shown for only the first quadrant in
Fig. 2, this results in a rectangular ar~ay of signal points with I-component amplitudes
from I to31 andQ-componentamplitudesfrom 1 to lS,assumingasignalpoint
l 0 spacing of 2 units in each direction. The 128 signal points in the first quadrant thus
comprise 22 points shown within an area 14, 8 points shown within another area 16,
and two points referenced A and B, all of which signal points are relocated for
transmission as described further below and which are shown as open dots, and 96points with Q-component amplitudes of 15 or less and I-component amplitudes of 25 or
l 5 less, which are not relocated and which are shown as solid dots.
The digital signals which are represented by the 512 signal points are Gray
coded, so that adjacent signal points differ from one another in only one bit position. In
other words, there is a Hamming distance of one between any two adjacent signal
points. The relocation of signal points for transmission is effected in a manner to
preserve as far as possible this Hamming distance, while at the same time reducing as
far as possible the distance of each transmitted signal point from the origin 12, thereby
to reduce the peak transmitted power and peak-to-average power ratio.
Accordingly, the 22 points within the area 14 are all relocated by rotation
through an angle of 180 about a point 18 having the I,Q co-ordinates ( 16,15) to
2 5 corresponding positions within a n area 14', as shown by a semi-circular line 20. This
relocation reduces the distance of each point from the origin 12 and preserves the
Hamming distance of one for these relocated points.
Furthermore, the 8 points within the area 16 are all relocated by translation, in
a direction as shown by a line 22, to corresponding positions within an area 16';
ef~ectively the area 16 is t~anslated through the point 18 to the area 16'. Moreparticularly, each point within the area 16 is translated to a new positiorl within the area
16' by increasing its Q-component amplitude by 16 (24) units and decreasing its I-
component amplitude by 16 units. Viewed alternatively, the points within the arPa 16
can be regarded as being relocated by two consecutive rotations each through 180 about
3 5 a respective point. The first such rotation is about a point 24 having the l,Q co-
ordinates (24,8), and the second such rotation is about the point 18 ~or the first rotation
can be considered to be about the point 18, and the second rotation being about a point
with the I,Q co-ordinates (8,24)).
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The above-described relocation of the 8 points within the area l 6 again
reduces the distances of these signal points from the origin 12, whilst to a large extent
maintaining the Hamming distance of one for these points. More particularly, theHamming distance of one is maintained among the translated points, and is only
increased in respect of points at boundaries of the translated set of points.
For example, consider a point 26 h~Ying the (I,Q) co-ordinates (29,1). This
is relocated for transmission, by the code converting unit, to a point 26' having the co-
ordinates ( 13,17). Due to an error, this may be wrongly interpreted at a receiver as
being an adjacent point 28 having the co-ordinates ( 13,15~. The points 26' and 28 are
l 0 on different sides of a boundary bet veen poin!ts which are relocated and other points
which are not relocated. The original point 26 has the 9-bit Gray code value
10001,1000 forthe I,Q components respectively. The incorrectlyinterpretedpoint 28
has the 9-bit Gray code value 11101, I 100, which has 2 bits in error for the I component
and I bit in error for the Q component. These incorrect bits are corrected using FEC
l 5 coding applied individually to each of the 9 bit lines supplying the code converting unit
in the transmission system modulator, with corresponding FEC decoding in the 9 bit
lines leading from the code converting unit in the receiver's demodulator.
The two further points referenced A and B are relocated to the respective
positions A' and B', which are selec~ed to provide an optimum relocation of these points
especially in respect oftheir distances from the origin 12. More particularly, the point A
attheco-ordinates(27,1)isrelocatedtothepointA'attheco-ordirlates(11,23),andthe
point B at the co-ordinates (31,5) is relocated to the point B' at the co-ordinates (9,21).
Alternatives for these points are discussed further below.
With the relocated signal points as shown by solid dots in Fig. 2, the greatest
2 5 distance of any point from the origin 12 is ~r650 units, which is considerably less than
the ~754 figure for the cross constellation of Fig. I, with a corresponding decrease in
peak power required of the transmissioD system. At the same time, the relocation of
points is effected in a manner which m~intains a smail Hamming distance between
adjacent signal points, whereby errors can be largely eliminated by using appropAate
3 0 error correcting codes.
It is important to note the plactical and commercial significance of the peak
power reduction which is achieved in this embodiment of the invention. Relative to the
650 peak figure provided as described above, the prior art fgure of ~754 corresponds
to an increased peak power requirement for the transmitter of lOlog(754/650)dB, or
3 5 about 0.65dB. At a typical incremental cos~ of the order of $1,000 per dB of transmitter
peak power, the decreased peak power provided by this invention enables a substantial
saving in costs.
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Fig. 3 illustrates the overall signal point constellation which results from therelocation of points as described with reference to Fig. 2 being applied to all four
quadrants of an initially rectangular block of 512 points. The relocation is applied
syrnmetrically in the four quadrants, whereby the resulting constellation has both
quadrant symmetry and symmetry with respect to 45 phase angles. A 45 phase angle
would be represented in the drawings by lines at 45 with respect to the I and Q axes,
for example a l;ne passing through the points 12 and 18 in Fig 2. This 45 phase angle
symmetry is a significant advantage in practice, in that the modulation scheme is
consequently "well-behaved" at times before carAer recovery is established, whenl 0 frequency errors produce resulting phase changes having the effect of the signal point
constellation rotating about the I and Q axes.
As mentioned above, alternatives exist for relocating the points A and B.
While these alternatives still provide a reduction in peak power in relation to the cross
constellation of the prior art, they require greater peak powers than the embodiment of
l 5 the invenffon described ab~ve with reference to Figs. 2 and 3 and are less preferred for
this reason.
One of these alten~atives is not to relucate the point A but to leave it in its
original position, and to relocate the point B as one of the points in the area 14, so that it
is moved to the I,Q co-ordinates ( 1,27). The point A and the relocated puint B would
then have the greatest distance from the origin of ~r730 units. In this case, it would be
less necessary to relocate other points which ar~ at positions closer than this to the
origin, such as the points with the I,Q co-ordina~es (21,15), (23,13), and ~25,7).
A further alternative is to modify the relocation of points to be as shown in
Fig. 4. In ~ig. 4, the areas 14 and 16 are modified so ~at the points A and B can both
be included within the area 16; the point at the I,Q co-ordinates (21,15) is consequently
omitted from the area 14 and is not relocated. This point now defines the greatest
distance from the origin, whish in this case is lf666 units. The point at the I,Q co-
ordinates (23,11) is in this case ~ncluded within the area 14 and is moved accordingly,
so that the resulting signal point constellation is syrnmetrical about the I and Q axes and
3 0 about 45 lines or phase angles with respect thereto.
Other alternative relocations of points may be effected along similar lines to
those described above, as deemed appropriate in particular circumstances.
The signal point constellations described above provide 512 points, for 512-
QAM. The ;nvention may be similarly applied to higher numbers of points which are
odd powers of 2, for example for 2048-QAM.
Although in the above description reference is made to re]ocating points by
translating them or rotating them through 1 80D, it should be appreciated that this is to
provide a full undeîstanding and appreciation of the invention and that in carrying out
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the invention there need be no actual movement of any signal point. In other words, the
rectangular arrays of points would not themselves be produced, but rather the points of
the signal point constellations s)f Figs. 2 to 4 would be produced directly from digital
input signals, for example using a PROM (programmable read-only memory). Thus for
example for the 51 2-QAM signal point constellations a PROM having 512 storage
Iocations each for the I and Q component values (S bits each) of a respective signal point
of the constellation could be addressed with a 9-bit digital input signal to read out
directly the respective I and Q component values.
Although particular embodiments of the invention have been described in
detail, it should be appreciated that numerous modifications, variations, and adaptations
may be made thereto without departing from the scope of the invention as defined in the
claims.
