The Demod-Remod Technique for Demodulating Cochannel FSK Signals

Richard P. Gooch, Christine Jorgensen, and Michael Ready
Applied Signal Technology, Inc.

Twenty-fifth Asilomar Conference on Signals, Systems, and Computers, November 4—6, 1991

This paper describes the demod-remod method of demodulating two cochannel MEFSK signals. The technique uses a conventional demodulator to obtain an estimate of the primary data sequence. The primary data is then remodulated and subtracted from the received signal to obtain an estimate of the secondary signal. Finally, the secondary signal is demodulated using conventional demodulation techniques. The paper includes a description of phase noise, its effect on demod-remod performance, and methods used to mitigate it. Experimental results showing the range of signal power separations and carrier-to-noise ratios over which the demod-remod technique works are presented.

Introduction

Increased frequency reusage and spectral crowding are causing cochannel interference to become a major limitation on the performance of modern digital communication systems. Figure 1 illustrates a typical cochannel scenario. Two frequency-shift-keyed (FSK) signals, separated in power by 6 dB and possessing the same carrier frequency, illuminate the receiving antenna. The stronger signal is termed the primary signal, and the weaker the secondary. The polar plots and eye diagrams show that the primary signal suffers severe distortion due to the presence of the secondary signal. In cochannel environments such as this, conventional FSK demod techniques generally lock onto the stronger FSK signal and do not recover data from the cochannel signal. It is the goal of the demod-remod technique described in this paper to recover both the primary and secondary FSK data streams. A similar technique was used to demodulate cochannel QAM signals in [1].

Figure 1. Cochannel FSK signal scenario.

The block diagram of the demod-remod technique is shown in Figure 2. The basic premise associated with the technique is that the primary FSK signal is strong enough to permit demodulation using conventional methods. The demodulated bit stream is then adaptively remodulated and subtracted from the aggregate received signal. Provided the remodulated signal accurately mimics the primary signal component of the received signal, the difference should consist of the weaker secondary FSK signal plus noise. This difference signal is then demodulated using a second conventional FSK demodulator. The heart (and soul) of the demod-remod technique lies with the adaptive remodulation process and is the main focus of this paper.

Figure 2. Block diagram of the demod-remod technique.

The paper begins by reviewing Manchester-encoded FSK (MEFSK) signal generation and goes on to describe the MEFSK demodulation and remodulation processes in detail. Next, experimental results are presented that demonstrate the performance of the demod-remod algorithm for two different signal power separations. Phase noise is shown to be a major limitation on the performance of the technique. The characteristics of phase noise, as well as methods used to combat it, are also described. Finally, quantitative guidelines defining the scenarios for which the demod-remod technique can effectively demodulate both the primary and secondary signals are given.

This paper is concerned with a specific type of FSK signaling known as Manchester-encoded FSK (MEFSK). To provide a basis for discussion, a MEFSK modulator and demodulator are first described. Manchester encoding exclusive-or’s the input bit stream with a 50% duty-cycle bit clock. The resulting signal is lowpass filtered to suppress frequency components greater than twice the bit rate. At this point, the waveform can be interpreted as a BPSK signal with carrier frequency equal to the symbol rate. The signal is then frequency modulated to create the Manchester-encoded FSK signal.

The block diagram of a Manchester-encoded FSK demodulator is shown in the upper half of Figure 2. The received signal is assumed to have been previously digitized and converted to complex I/Q form. The signal is first resampled to eight samples/bit synchronous with the primary signal symbol rate. The resampler phase control signal is generated by extracting the symbol clock and comparing it to a reference. The phase difference is then used to speed-up or slow-down the resampling rate. Care must be taken in choosing the resampler rate change small enough that resampling jitter is not a limiting factor in the remodulated signal accuracy.

The signal is then FM discriminated with a delay-line discriminator in which the complex input signal is delayed, conjugated, and multiplied by itself. The phase of the resulting product comprises the discriminator output. It can be shown that this process is mathematically equivalent to differentiating the (unwrapped) phase of the input signal. The output of the FM discriminator is the BPSK signal.

The output of the FM discriminator is fed to an adaptive fractionally-spaced passband equalizer [2] to generate a complex equalized output signal decimated to one sample per bit. The equalizer is initialized with a complex bandpass filter with a center frequency equal to the symbol rate and bandwidth equal to twice the symbol rate. The converged equalizer performs quadrature splitting, matched filtering, and intersymbol interference (ISI) equalization.

The equalizer output is fed into a complex mixer where BPSK carrier recovery (or equivalently Manchester decoding) is performed. The mixer output is hardlimited to generate a bit decision which corresponds to the transmitted bit. The error signals for both the phase lock loop and the adaptive equalizer are formed by comparing the hard bit decision with the mixer output. This process is known as decision-directed adaptation and carrier recovery [3].

The estimated primary data sequence is fed into the adaptive remodulator where it is reshaped into a replica of the primary component of the received waveform. This reshaping process is comprised of a filter followed by an FM modulator followed by a second filter and a phase locked loop (PLL). The first filter generates the Manchester encoding and spectral shaping. The FM modulator converts the shaped data signal into an FSK signal. The second filter models linear distortion imparted on the signal by transmitter or receiver filters as well as propagation-induced distortion. The PLL tracks phase noise imparted on the primary FSK signal by both the transmitter and the receiver.

The objective of the remodulator is to mimic the primary signal component of the received signal. Ideally, the coefficients of both the pre and post FM modulation (pre-m and post-m) filters should be jointly chosen to minimize the variance of the “final error.” Unfortunately, optimization of the pre-modulation filter based upon the final error variance is a difficult nonlinear optimization problem. In order to simplify the optimization, an interim error signal is used. As shown in Figure 2, this interim error is the difference between the FM discriminator output and the premodulation filter output. The variance of the interim error is a quadratic function of the filter coefficients and can therefore be readily minimized using least mean square (LMS) techniques, e.g., the LMS algorithm [4].

Optimization of the pre-m filter using the interim error is biased in the presence of uncorrelated additive interference since the output of the FM discriminator will consist of the demodulated primary signal plus a distortion component correlated with both the primary and secondary signals. Consequently, minimization of the interim error variance will result in a biased filter solution that attempts to model both the undistorted primary signal component and the distortion components. The bias will become worse as the primary-to-secondary signal power ratio (PSR) decreases. Fortunately, in situations where the PSR is low, the required remodulation accuracy (and subsequent primary signal cancellation) will be less stringent. The experimental results presented in the next section show that interim filter bias is non-problematic.

The pre-m adaptive filter also must account for carrier frequency offset in the receiver tuning as well as frequency drift in both the transmitter and receiver. Carrier offset manifests itself in terms of a dc offset in the FM discriminator output. Frequency drift shows up as a slow variation of that dc offset. The frequency offset can be modeled by injecting a constant value into the adaptive filter output. This value can be adaptively determined by incorporating an additional weight in the adaptive filter with the weight input tied to a constant value. The LMS adaptation will then choose the weight value that results in a best match to the dc offset in the desired response. Frequency drift (or slow dc offset variation) is tracked by a time-varying weight value. The time constant of the dc tracker is determined by the step size and the constant value tied to the weight input.

Once the pre-m adaptive filter converges to its optimal value, the filter output signal should closely mimic the FM discriminator output component corresponding to the primary signal. The FM modulator integrates the input signal and then exponentiates the complex result. This process perfectly inverts the FM discriminator operation modulo a constant phase offset corresponding to the initial state of the integrator. The appropriate phase offset is determined by the complex channel filter following the FM modulator.

For the moment ignore the PLL in the post-m modeling process used to track phase noise. The post-m filter coefficients are determined using the LMS algorithm applied to the final error. This filter time-aligns the steady-state amplitude and phase offset of the FM modulated signal with the primary signal component of the received signal. Small misalignment of either the time, amplitude, or phase can severely degrade cancellation.

When the remodulation process was applied to simulated signals, the final fit was almost perfect. However when applied to snapshots of real FSK signals taken in the laboratory, it was discovered that phase noise in both the transmitter and receiver caused a significant error. The PLL phase noise tracker was added to the remodulator to mitigate this degradation.

To mitigate phase noise, the number-control oscillator (NCO) output is mixed with the post-m filter output to generate the final remodulator output. The NCO is controlled by the phase error between the remodulated signal and the aggregate received signal. The loop filter realizes a critically-damped second-order response with a user-specified time constant, t.

The final error signal is fed to a second demodulator identical to the first. As the secondary FSK signal may have a symbol rate different from the primary signal, a second synchronous resampler is employed.

To provide a realistic test of the demod-remod technique, a cochannel signal scenario was created by adding a MEFSK signal received off-the-air to a second MEFSK signal generated using a test generator as shown in Figure 3. The off-the-air signal was always the secondary signal while the test generator provided the primary signal. The test generator output power was adjusted to control the PSR. The composite signal was fed into a receiver, downconverted to baseband, and snapshot digitized. The noise floor was set by adding artificially-generated white Gaussian noise to the snapshot.

Figure 3. Experimental test setup.

Typical processing results from two snapshots are presented in this section for a low PSR case and a high PSR case. These cases were chosen to illustrate the performance limitations of the demod-remod technique at both ends of the possible range of PSRs. Case #1 consists of a composite signal which has a PSR of 3 dB and a primary signal carrier-to-noise ratio (CNR) of 18 dB. Case #2 consists of a composite signal which has a PSR of 18 dB and a primary signal CNR of 30 dB. Performance of the primary and secondary demodulators for case #1 can be observed in the eye patterns shown in Figures 4(a) and 4(b), respectively. The wide-open eye shown in Figure 4(b) indicates that BER of the secondary signal will be relatively low. The fuzzy, narrow eye shown in Figure 4(a) indicates the presence of considerable interference and an increased likelihood of bit errors in the primary signal demodulation.

Figure 4. (a) Primary and (b) secondary demodulator eye diagrams for the 3 dB power separation case.

Associated with each eye diagram is an “equalized SNR” that provides a quantitative measure of the eye opening. The equalized SNRs of the primary and secondary signals are 8 dB and 11 dB, respectively. For low PSRs, the equalized SNR of the primary demodulator is limited by cochannel interference, while the secondary signal SNR is limited by the additive noise and remodulation errors (caused by bit errors in the estimated primary data sequence). In this case, the primary demodulator makes few bit errors, and the AWGN is well below the secondary signal power. As the PSR drops below 3 dB, primary signal bit errors will degrade the secondary equalized SNR considerably.

The remodulator performance is quantified through the interim fit and the final fit. The interim fit measures the accuracy with which the first adaptive filter models the Manchester encoding and spectral shaping. It is defined as the ratio of the primary signal power at the FM discriminator output to the interim error signal power (see Figure 2).

For case #1, the interim fit is 3 dB. While this sounds like a poor fit, the interim error power is dominated by the presence of the secondary signal, and, consequently, a 3 dB interim fit does not necessarily imply a poor final fit.

The final fit measures how well the remodulator matches the primary signal. The final fit is defined as the ratio of the received primary signal power to the final error power (see Figure 2). For case #1, the final fit was 5 dB, indicating that the final error was mainly dominated by the secondary signal.

The primary and secondary eye patterns for case #2 are shown in Figures 5(a) and 5(b), respectively. The primary equalized SNR is 21 dB, and the secondary equalized SNR is 8 dB. In this case, the cochannel interference is low, and the primary demodulator is capable of achieving a high equalized SNR and a wide-open eye. The interim fit is 18 dB indicating that the primary data sequence has been remodulated to provide a near-perfect match. The final fit was also 18 dB indicating that the final error was dominated mainly by the secondary signal. However, as the eye diagram of Figure 5(b) shows, the secondary demodulator is making many bit errors. The source of the demodulation error is not AWGN, but rather untracked phase noise from the primary signal. The performance limitations induced by this phase noise are addressed in the next section.

Figure 5. (a) Primary and (b) secondary demodulator eye diagrams for the 18 dB power separation case.

The performance of the demod-remod technique is limited by additive white Gaussian noise, secondary signal interference, and phase noise on the primary signal. Phase noise is caused by a random, time-varying carrier frequency and phase drift. This drift originates in the transmitter, the receiver, or both, and exists on all real signals.

Phase noise fundamentally limits the ability to remodulate and cancel a real FSK signal. The PLL in the post-m filter can, however, partially track this phase noise. Phase noise consists of both high and low frequency components. The PLL time constant (the reciprocal of the loop filter bandwidth) controls how much phase noise is tracked. The smaller the PLL time constant (the wider the loop bandwidth), the more closely the PLL is able to track the phase noise. Although decreasing the PLL time constant causes the PLL to track more phase noise, it also makes the PLL more sensitive to additive noise, creating jitter on the NCO. Since the secondary signal is uncorrelated with the primary signal, it appears as noise to the PLL and contributes to the jitter. Increasing the loop time constant reduces the jitter but also reduces the ability to track phase noise on the primary signal. Untracked phase noise and jitter both degrade the secondary demodulation performance. Figure 6 shows the secondary equalized SNR as a function of the PLL time constant and PSR. The optimal time constant provides the best compromise between the amount of phase noise tracking and jitter reduction. As expected, the optimal time constant decreases as the PSR increases since the jitter caused by the secondary signal decreases.

Figure 6. Secondary equalized SNR as a function of PLL time constant.

Figure 7 illustrates the PSR/CNR region of operability for the experimental test setup of Figure 3. The shaded region shows the range of scenarios over which both the primary and secondary signals can be demodulated with an equalized SNR of 7 dB or better.

Figure 7. Typical region of operation of the demod-remod technique.

The upper boundary of the shaded region is set by phase noise limitations. When the secondary signal power is low (high PSR), the distortion caused by untracked phase noise significantly degrades secondary demodulation. In the 18 dB case described earlier, phase noise causes most of the distortion seen in Figure 5(b). As the PSR increases above 20 dB, the secondary signal suffers too much phase noise distortion to be demodulated. Thus, phase noise limits the maximum PSR to 20 dB, regardless of the CNR. Note that the phase noise limitation depends directly on the phase noise characteristics of the transmitter and receiver.

The lower boundary of the shaded region determines the minimum power separation required to demodulate the primary signal. In the previous section, it was shown that the primary demodulator was capable of functioning at a PSR of 3 dB. Below 2 dB, the cochannel interference on the primary signal becomes so severe that incorrect bit decisions are frequently made, and neither the primary nor the secondary signals can be demodulated. Thus, secondary interference limits the minimum power separation to 2 dB. As the CNR decreases below 20 dB, the primary demodulator performance is degraded by Gaussian noise as well as cochannel interference, and the PSR must increase in order to maintain the same 7 dB performance. This explains the rise in the lower boundary as the CNR decreases.

Finally, the boundary on the left defines the maximum power separation that allows demodulation of the secondary signal in the presence of additive white Gaussian noise. As the CNR decreases, the additive noise power degrades the secondary demodulation. To maintain the same 7 dB performance, the maximum PSR must decrease as the CNR decreases to boost the secondary signal power relative to the noise. This explains the rise in the left boundary as the CNR increases.

The region enclosed by these boundaries represents the region over which the demod-remod technique can accurately demodulate both cochannel signals for the experimental scenario discussed above. Although this region is specific to this example, the general shape and principles used to establish these boundaries are general to all cochannel situations.

This paper has presented a method for demodulating two cochannel FSK signals based upon a demod-remod approach. Experimental results indicate that this technique is effective over a wide range of PSRs and CNRs. The technique was evaluated on live signals under realistic scenarios. Phase noise in the received signal causes a fundamental limitation in the technique. This limitation is partially mitigated by a tracking PLL. Further performance evaluation on live signals as a function of the demod-remod parameters is necessary before implementation should be considered.