L. N. MA
Communication Laboratory
TRW Systems Group
Summary For high data rate telemetry (above 100 Mbits/sec) multiphase modulation
effectively trades transmitter power to alleviate the RF bandwidth requirements. This
paper presents a unified method of synthesizing and analyzing multiphase systems. In
particular, the design of multiphase modulators and three types of coherent demodulators
are discussed in detail.
Included is a description of 400 Mbits/sec quadriphase system fabricated by TRW which
employs direct modulation and demodulation of an 8.5 GHz carrier and a transversal
filter to effect matched data filtering. This system operates within 2.5 db of theoretical
performance of coherent quadriphase.
Introduction At high data rates, bandwidth is more of a constraint than transmitter
power. Therefore, telemetry system performance can no longer be improved by the well
known coding techniques that trade bandwidth for signal power. In this situation one
must attempt to improve system accuracy by trading signal power for bandwidth.
Multiphase modulation systems provide a means of attaining such a tradeoff. As is well
known, coherent biphase (PCM/PM) yields almost the lowest probability of error among
all multiphase systems. It can be shown that quadriphase yields the same probability of
error per bit as biphase but requires one-half the bandwidth of biphase. Higher order
phase systems, while requiring less bandwidth for a given data rate, yield increasingly
higher error probability for the same transmitter power.
In this paper, methods are given that allow one to synthesize multiphase systems. A
description of the methods of modulation is presented. Three ways of demodulation are
discussed. They are the multiplier loop, analog I-Q loop, and data estimation I-Q loop.
Of these methods the data estimation I-Q loop is preferred.
TRW has fabricated a 400 Mbits/sec quadriphase system which consists of a quadriphase
modulator, data estimation I-Q loop, and matched filter data detectors. The performance
of this system was measured and found to operate within 2.5 db of the theoretical
Synthesis of Multiphase Systems A digital N-phase modulated signal without regard
to filtering may be represented as
Tc /2B
amplitude scale factor
arbitrary carrier phase
carrier frequency
phase modulation; ns(t) takes on one of N discrete values in each baud
For a quadriphase signal, (1) becomes
where F4(t) is a four-level pulse train which takes on the values ±3, ±1. Equation (2) may
be alternatively expressed as
where A(t) and B(t) are independent rectangular pulse trains which take on the values
±1. From the above it can be seen that a quadriphase modulator can be constructed as
shown in Figure 1.
For octaphase the representation is
where F8(t) takes on the values ±7, ±5, ±3, and ±1. A realization of an octaphase
modulation can be obtained by noting that (4) can be rewritten as
where A(t), B(t), and C(t) are independent rectangular pulse trains which take on the
values ±1. Another form of (5) is
The equation above shows that octaphase can be viewed as the sum of two dependent
quadriphase signals of unequal level. Further manipulation yields
This last equation shows that an octaphase modulator may be constructed by summing
the outputs of two dependent equal level quadriphase modulators as shown in Figure 1.
The procedure outlined above may be easily generalized to design of multiphase
Coherent detection of an N-phase signal entails obtaining a carrier reference and
demodulating the data. Assuming for the moment that such a reference exists, one may
describe the detection process vectorially.
The received signal can be represented as a vector of the form
The demodulator is thus a device that operates on this vector so as to determine which
signal was sent with the smallest probability of error. It can be shown that if each signal
has equal probability of being transmitted and is perturbed by white gaussian noise, then
the receiver should select the signal point closest to the received point.1 Geometrically,
this means that the plane should be divided into disjoint areas or decision regions. An Nphase demodulator will have N regions, each encompassing 2B/N radians.
An N-phase demodulator requires N/2 phase detectors and associated equipment as
illustrated in Figure 2. By placing the phase detector references orthogonal to the
boundaries of the decision regions, the output of each phase detector and integrate and
dump circuit combination, which is obtained by comparing the output to a threshold,
represents a specific region of the plane. Then by performing logic operations on these
outputs, the decision regions are realized.
In order to accomplish coherent detection, it is necessary to provide a carrier reference at
the receiver. The alternative to transmitting a residual reference is to construct a suitable
reference from the received data modulated signal. For an N-phase PCM/PM signal
(disregarding the effect of link filtering on the data signal), this can be accomplished by
multiplying by N, filtering, and then dividing by N. This removes the data and provides a
reference which has a log2N bit ambiguity. A tracking loop is desired for the filtering
operation to provide a narrow filter after the multiplication and to track the time
variations of the carrier phase. One wants to limit the bandwidth of the noise before the
nonlinear device but would still like to preserve the phase transitions in the signal. Thus,
the predetection and/or post-modulation filtering operation becomes a tradeoff between
preserving the signal waveshape and limiting the noise power. A basic multiplier loop to
provide a reference for N-phase is shown in Figure 3. In this mechanization, the VCO
output is multiplied by N to provide the phase detector reference for carrier
demodulation of the signal. This is equivalent to the use of a divider in performance. The
multiplier is simpler to construct and operate and only affects the frequency at which the
VCO operates.
The error signal developed by the N-fold multiplier loop is essentially sin [N,(t)], where
,(t) is the difference between the input carrier phase (excluding data transitions) and the
VCO phase. An alternative mechanization of this loop, referred to as the in-phase/
quadrature (I-Q) loop, can be generated by simply expanding sin [N,(t) ] as follows:
The generalized I-Q loop of (9) and Figure 4 simply consists of N-phase detectors
separated in carrier phase by B/N, the outputs of which are multiplied together to provide
an error signal to drive the VCO. The only essential difference between the multiplier
loop and the I-Q loop is that the I-Q loop allows filtering of the data at the outputs of the
various phase detectors before the final multiplication derives the error signal. The
equivalent filtering for the multiplier loop must be done in the IF filters before the
multiplier. This limits the flexibility somewhat. Given the outputs of any two of the
N-phase detectors of Figure 4, the output of any other can be generated by a linear
combination of these two. Therefore, the I-Q loop can be implemented by two phase
detectors, summers, and the product device which multiplies all of its inputs.
Inherent in the operation of the phase tracking loops discussed to this point is that noisy
signals are multiplied together. This problem is largely overcome by the use of the socalled data estimation I-Q loop. This type of loop may be realized by passing the output
of the phase detectors through lowpass filters and operating on the resultants in a linear
manner. In the absence of noise, these outputs, Li(t), when the phase error is equal to ,
For quadriphase, using (3), equation (10) becomes
L1(t) = V [A(t) cos , - B(t) sin ,]
L2(t) = V [A(t) cos , + B(t) sin ,]
This loop is shown in Figure 6. Note that by breaking the lead as shown in the figure, the
loop may be used for biphase.
Performance of Multiphase Systems This section is devoted to a review of some of
the analytical information on multiphase systems that is available in the literature. To
begin with, the probability of error is given by
= S/NoR (2 log2 N)
= signal power-to-noise spectral density ratio
= data rate
For N = 2, equation (14) becomes
For N = 4, equation (14) becomes
Note that on a per symbol basis the performance of biphase exceeds that of quadriphase,
but when the two systems are operated at the same data rate their performance is
equivalent on a per bit basis.
For larger values of N, (14) must be evaluated by computer. Arthurs and Dym1 have
obtained upper and lower bounds for error probability by geometrical arguments which
lead to
Figure 7 presents the theoretical and measured quadriphase bit error rate versus S/NoR.
Curves can also be found in Cahn2 that illustrate the tradeoff between signal power and
bandwidth for given error rates.
400 Mbits/sec Quadriphase System In order to verify that a high data multiphase
modulation system could be synthesized, TRW undertook a task of building a 400
Mbits/sec quadriphase system. This system consists of a quadriphase modulator,
quadriphase demodulator, and matched filter data detectors. Additionally, a set of test
equipments which consists of a 31 bit pseudo-random (PRN) code generator, code
correlation detector, and bit error comparator, were built to measure system performance.
The design and performance of these equipments are discussed in the following sections.
Quadriphase Modulator The quadriphase modulation is performed directly onto a
8.5 GHz carrier. Using the same configuration as shown in Figure 1, the quadriphase
modulator consists of two biphase modulators whose carriers are 90E out of phase.
Figure 8 presents the completed 8.5 GHz quadriphase modulator. The performance of the
modulator is tabulated in Table 1.
Table 1. X-Band Quadriphase Modulator Performance
Center frequency
Insertion loss
Maximum RF input
Residual carrier
8.5 GHz
9.6 db
23 dbm
-54 db
Quadriphase Demodulator The quadriphase demodulator, as shown in Figure 6, is of
the data estimation I-Q loop variety and is operated at 8.5 GHz. The complete unit is
shown in Figure 9 and its performance characteristics are tabulated in Table 2.
Table 2. X-Band Quadriphase Demodulator Performance
Center frequency
RF input frequency stability
RF input power
VCO stability
Loop characteristics
Noise bandwidth, two-sided
Loop gain
Data output response
8.5 GHz
# 500 kHz peak-to-peak
10 dbm
# ±6 x 10-5
second order
600 kHz
lower 3 db # 500 kHz
upper 3 db # 6 00 MHz
Detection System The detection portion of the system consists of a bit synchronizer
and a matched filter. The bit synchronizer generates a local clock by differentiating the
received PCM waveform, then frequency doubling the output and filtering with a phaselocked loop.
As shown in Figure 10, the matched data-filter employs a transversal filter4. The filter
operates as a stair-step approximation to an integrate and dump circuit.
The output of the transversal filter is sampled at the end of each bit period through a
bilateral switch. The sampling pulse used to drive the switch is derived from the bit
synchronizer output. To reconstruct the data, the sampled output is used to drive a
decision-and-hold circuit. Figure 11 depicts the noise corrupted input to the data filter
and the resultant reconstructed output.
Bit Error Rate Measurement The configuration for measuring the bit error rate is
shown in Figure 12. The setup utilized a 31 bit PRN code as a data source and a delay
line correlator for comparing only one selected bit per code cycle. As shown in
Figure 13, this goal is achieved by selecting one of 31 bits by setting the variable delay
corresponding to the time delay of the selected bit. The delayed output (inverted if
necessary for proper polarity) is applied along with the correlation output to the twoinput “AND” gate. Since code phasing is known precisely at the time of correlation, the
signal at the delayed output, i.e., binary “ 1” or binary “0” is also known. If the proper
polarity is used at the “AND” gate and no error occurs at the selected bit position, no
output will be seen. However, if a bit error occurs at this position in the code, the
amplifier output will go positive and trigger the AND gate since the correlation pulse is
simultaneously present. Figure 14 shows the bit error output voltage waveform in
relation to the correlation waveform when the error amplifier input connection is set to
generate zero error and 10076 error condition. The results of a typical test are shown in
Figure 7.
Conclusion This paper has presented an analysis of communication systems utilizing
multiphase modulation and demodulation. Methods have been derived to generate and
coherently detect multiphase signals. The carrier references for the appropriate phase
detectors were deduced from considerations of the decision regions for optimal
A unified method was presented for synthesizing cohe-rent demodulators of the
multiplier/divider, multiplier loop, analog I-Q loop, and data estimation I-Q loop
varieties. This allows a straightforward extension of biphase systems to higher order
phase systems.
An X-band 400 Mbits/sec quadriphase system which was built by TRW Systems verifies
the analysis and synthesis procedure.
Arthurs and Dym, “On the Optimum Detection of Digital Signals in the Presence
of White Gaussian Noise -- A Geometrical Interpretation and a Study of Three
Basic Data Transmission Systems,” IRE Trans. on Comm. Systems, vol. CS-10,
no. 4, December 1962.
C. R. Cahn, “Performance of Digital Phase-Modulation Communication Systems,”
IRE Trans. on Comm. Systems, vol. CS-7, May 1959.
R. V. Garver, “Broadband Binary 180E Diode Phase Modulators,” IEEE Trans. on
Microwave Theory and Techniques, vol. MTT-13, no. 1, pp. 32-38, January 1965.
H. E. Kallmann, “Transversal Filters,” Proc. IRE, vol. 28, pp. 302-310, July 1940.
Figure 1. Generation of Quadriphase and Octaphase
Figure 2. N-Phase Demodulator
Figure 3. Multiplier Loop for the Generation of the
Phase References for N-Phase
Figure 4. Generalized I-Q Loop for N-Phase
Figure 5. Multiphase Data Estimation I-Q Loop
Figure 6. Quadriphase Data Estimation I-Q Loop
Figure 7. Quadriphase Error Rate
Figure 8. 8.5 Ghz Quadriphase Modulator
Figure 9. X-Band Quadriphase Demodulator
Figure 10. Matched Data Filter
Figure 11. Matched Data Filter Waveforms
Figure 12. Bit Error Rate Measurement Configuration
Figure 13. Frame Sync and Bit Error Detector
Frame Sync Output
0.5 v/cm vertically
20 nsec/cm horizontally
No. 31 Bit Error Output (100% errors)
0.2 v/cm vertically
20 nsec/cm horizontally
Frame Sync Output
0.5 v/cm vertically
20 nsec/cm horizontally
No. 31 Bit Error Output (no errors)
0.2 v/cm vertically
20 nsec/cm horizontally
Figure 14. Error Detection Waveform
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