PERFORMANCE COMPARISON OF SOQPSK DETECTORS: COHERENT VS. NONCOHERENT Tom Bruns L-3 Communications Nova Engineering, Cincinnati, OH ABSTRACT Shaped Offset Quadrature Shift Keying (SOQPSK) is a spectrally efficient modulation that has been promoted in the airborne telemetry community as a more spectrally efficient alternative for legacy PCM/FM. First generation demodulators for SOQPSK use coherent detectors which achieve good bit error rates at the expense of long synchronization times. This paper examines the performance of a noncoherent SOQPSK detector which significantly improves the signal acquisition times without impacting BER performance in the AWGN environment. The two detection methods are also compared in their ability to combat other channel impairments, such as adjacent and on-channel interference. KEY WORDS SOQPSK, Trellis Detection, Detection, Spectral Efficiency, Power Efficiency. INTRODUCTION SOQPSK is a non-proprietary modulation technique that has been established as one of the Advanced Range Telemetry (ARTM) Tier I waveforms. detectors have historically been used to demodulate this waveform taking advantage of its OQPSK nature. A new noncoherent sequence detector is now available for SOQPSK which promises to reduce synchronization time without sacrificing BER performance. This paper starts by revisiting the SOQSPK waveform definition followed by a brief overview of the coherent and noncoherent detectors. The remainder of the paper presents hardware test results for these two detectors for a variety of channel impairments. DESCRIPTION OF SOQPSK The SOQPSK waveforms described by Hill [1] are constant envelope, continuous phase modulations that allow a designer to easily trade-off spectral and power efficiency by varying a few simple parameters. The waveforms are completely described by either their instantaneous phase or frequency. Figure 1 illustrates a conceptual SOQPSK modulator that maps a binary 1
input stream a(i) into ternary valued (+1, 0, -1) frequency impulses α(t), passes them through a shaping filter with response g(t), and applies the instantaneous frequency f(t) or phase φ(t) to an appropriate modulator which produces the desired SOQPSK waveform. 100110... +1 0 t t -1 a(it/2) Data to Impulse Mapping α(t) Frequency Filter g(t) f(t,α ) Integrator Frequency Modulator s(t,α ) SOQPSK φ(t,α ) t Phase Modulator s(t,α ) Figure 1. SOQPSK Modulator The frequency pulse shapes for several variants of SOQPSK are given by g(t) = n(t) * w(t), where n(t) = Acos(πρ Bt T) sin(π Bt T) 2 * 1 4(ρ Bt T) (π Bt T) 1, for t T <T 1, w(t)= 2 + 1 2 cosπ(t T T ) 1, for T 1 < t T <T 1 +T 2 T 2 0, for t T >T 1 +T 2 Four parameters ρ, B, T 1, and T 2 serve to completely define the frequency pulse shapes for SOQPSK. The telemetry community has chosen specific values for a variant termed SOQPSK- TG to obtain a good tradeoff between bandwidth and power efficiency: A = 0.5, T 1 = 1.5, T 2 = 0.5, ρ = 0.7, B = 1.25 The remainder of this paper discusses detectors for the SOQPSK-TG waveform. SOQPSK DETECTORS Two SOQPSK detector types for demodulating SOQPSK are examined. First, a standard symbol by symbol detector is used as described in [2]. This coherent detector passes the baseband I and Q channels thru a Butterworth filter with a 3 db bandwidth equal to the bitrate. The I and Q filter outputs are then compared to a threshold to make data decisions. The second detector is a noncoherent sequence detector which utilizes a variant of the trellis mapping outlined in [3]. This noncoherent detector correlates the received signal against several candidate phase trajectories which correspond to valid data streams. The output bit stream is chosen from the phase trajectory whose magnitude is greatest. The remainder of this paper compares the performance of these detectors as they are implemented in L-3 Nova s MMD44 multimode demodulator platform. In all experiments run, the desired signal is modulated with the IRIG 106-00 differential encoder. With both detectors, the differential decoding is built in to the demodulator. 2
PERFORMANCE ANALYSIS A. Performance in AWGN The initial performance metric for the two detectors is the performance in the presence of additive white Gaussian noise (AWGN). Figure 2 plots the BER performance of the two detectors. As seen in Figure 1, both detectors have comparable BER performance at E b /N o greater than 7 db. The most significant difference between the two detectors is at lower signal levels. The coherent detector looses phase lock at an E b /N o of 5 db while the noncoherent detector is able to maintain signal lock down to 0 db. This lower signal lock threshold makes the noncoherent detector more suited for applications where Turbo coding is applied. 10 0 0 2 4 6 8 10 12 14 Eb/No (db) Figure 2. Measured BER results for the two SOQPSK detectors B. Performance with frequency offset The noncoherent detector s frequency response is measured by repeating the BER test from above at E b /N o level of 11.5 db. In addition, the desired signal s frequency offset relative to the receiver is offset while all frequency tracking loops are disabled. This test only applies to the noncoherent detector since the coherent detector cannot tolerate any frequency offset when frequency and phase tracking are disabled. The results shown in Figure 3 demonstrate that the noncoherent detector maintains its BER performance over a modest range on the order of 1/1000 th of the bit rate of the modulation. For most telemetry application, this range is sufficient for data rates over 10 Mbps. For lower data rates, a frequency tracking loop is needed to center the desired signal relative to the receiver. 3
at 11.5 db Eb/No -2-1.5-1 -0.5 0 0.5 1 1.5 2 Frequency offset as fraction of bit rate x Figure 3. vs Frequency Offset for both detectors with frequency tracking disabled at E b /N o = 11.5 db C. Signal Acquisition Another area where the noncoherent detector has an advantage over the coherent detector is in recovering from a signal fade. Because phase lock is not required, the noncoherent detector is able to output correct bit decisions sooner once the signal returns. Table 1 shows the average number of symbols required to achieve bit sync when the system is transitioned from a state with only noise present to a state where the signal is 15 db above the noise level. For comparison, the results of this test using a noncoherent PCM/FM detector are also shown. Table 1. Average number of symbols required to achieve bit sync after a fade recovery Mode 1 Mbps 5 Mbps 10 Mbps SOQPSK 22816 6363 2016 SOQPSK 221 289 409 PCM/FM 185 204 219 This test shows that the fade recovery performance of the noncoherent SOQPSK detector approaches that of the PCM/FM detector. The improvement of the noncoherent SOQPSK detector relative to the coherent SOQPSK detector ranges from 100X to 5X depending on the data rate. D. Adjacent Channel Interference A detector s performance in the presence of an adjacent channel interferer is also important for most telemetry applications. A series of BER tests were run with a single interfering signal present that is 20 db stronger than the desired signal. The offset of the center frequency of the interfering signal is varied from 1.0 to 0.8 times the bit rate. Figures 4a and 4b show the test results when both the desired and interfering signals are 7 Mbps SOQPSK. This rate was chosen to match the one of the IF filter selections available in the MMD44 demodulator. 4
10 0 10 0 0.80R 0.85R 0.90R 0.95R 1.0R Baseline 0 2 4 6 8 10 12 Eb/No (db) Figure 4a. ACI rejection performance for the Detector 0.80R 0.85R 0.90R 0.95R 1.0R Baseline 0 2 4 6 8 10 12 Eb/No (db) Figure 4b. ACI rejection performance for the The ACI testing revealed that the noncoherent detector degrades more quickly as the interfering signal is brought closer to the desired signal. Both detectors perform well when the frequency separation is 1.0 times the bit rate. E. On Channel Interference On channel interference was also examined for both detectors. In this test, the SOQPSK modulated interferer is placed in the center of the received signal bandwidth. The relative power level between the desired and interfering signal is varied to produce the test results shown in Figure 5 below. Similar to the trend observed in the ACI tests, the coherent detector performs slightly better in the presence of an on channel interferer. 1 2 3 4 5 6 7 Power delta in db between desired and interfering signals Figure 5. On channel interference performance for noncoherent and coherent SOQPSK detection. 5
F. Multipath performance Multipath reflections are a common issue that impacts RF telemetry systems. An representative multipath channel is established according to the following equation: y(t) = x(t) + d*x(t-t) where y(t) = the received signal at time t x(t) = the transmited signal d = the reflection coefficient T = the time delay of the reflected path Testing with this channel used a 5 Mbps data stream, a time delay of 20 us, and a reflection coefficient that varied from -0.5 to -0.8. The use of a purely negative reflection coefficient produces a null at the center of the signal with larger magnitude reflections resulting in more severe nulls. 10 0 10-8 -0.85-0.8-0.75-0.7-0.65-0.6-0.55-0.5-0.45 Reflection coefficient (d) Figure 6. Performance of both detectors in a representative two-ray multipath channel The coherent detector outperforms the noncoherent detector in this multipath test with low bit error rates maintained at reflection magnitudes up to 0.65. The noncoherent detector is able to maintain a 1e-5 BER at a reflection magnitude of 0.53 with a slow link degradation at more severe multipath profiles. CONCLUSIONS Two detectors for SOQPSK were analyzed and tested against their ability to combat a variety of channel impairments common in an RF telemetry system. The coherent symbol by symbol detector was shown to perform well in interference environments as well as multipath fading. This testing indicates that the sequence detection algorithm in the noncoherent detector is more sensitive to phase distortions due to these types of channel impairments. The noncoherent trellis 6
detector outperforms in the simple AWGN channel holding signal lock down to 0 db E b /N o. The elimination of a phase lock loop allows the noncoherent detector to maintain a low BER performance over a range of frequency offsets while also reducing the time required to acquire the signal after a flat fade. These advantages make the noncoherent trellis detector the preferred approach for most telemetry systems. ACKNOWLEDGEMENTS The author acknowledges the help of Kevin Hutzel and Mark Geoghegan at L-3 Communications Nova Engineering for acquiring and interpreting the hardware test data results. REFERENCES [1] T. Hill, An Enhanced, Constant Envelope, Interoperable Shaped Offset QPSK (SOQPSK) Waveform for Improved Spectral Efficiency, Proceedings of the International Telemetering Conference, San Diego, CA, October 2000. [2] Mark Geoghegan, Optimal Linear Detection of SOQPSK, Proceedings of the International Telemetering Conference, Vol. XXXVII, San Diego, CA, October 2002. [3] M. Geoghegan, Implementation and Performance Results for Trellis Detection of SOQPSK, Proceedings of the International Telemetering Conference, Las Vegas, NV, October 2001. 7