A Multimode Adaptive Beamformer for Quadrature-Amplitude-Modulated Signals

IEEE 1988 International Conference on Acoustics, Speech, and Signal Processing
April 11—14, 1988

This paper presents the results of recent work on an adaptive beamformer designed to enhance the reception of N-state quadrature amplitude modulated (N-QAM) signals in the presence of multipath distortion and cochannel interference. Adaptation of the beamformer is based upon a series of performance criteria derived from known properties of the transmitted signal. Neither calibrated look-direction constraints nor prearranged training signals are required. Instead, the beamformer uses “blind” adaptation to initially suppress multipath distortion and cochannel interference and then switches into decision-directed adaptation to achieve optimal combining.

Introduction

Due to the ever-increasing need to transmit wideband digital data over the airwaves, the RF spectrum is rapidly becoming overcrowded. As a result, newly installed communication links (e.g., cellular and microwave radio) are tightly constrained in both channel allocation and geographical placement. Frequency reusage, whereby neighboring or intersecting links use the same channel allocation, has caused cochannel interference to become an increasingly significant problem. In addition, constraints placed on link siting combined with the use of spectrally efficient high-order modulations (e.g., 64-QAM) have increased the severity of the multipath encountered.

While adaptive equalization and selection diversity have long been employed to combat multipath, only recently has adaptive linear combining (beamforming) come into consideration as a potential solution. In selection diversity, the outputs of two independent receiving systems are monitored to determine which system gives the better signal and that signal is then selected for the overall system output. In linear diversity combining, the outputs of two coherent receiving systems are linearly combined to generate the overall system output. A major design issue involving the linear combining approach is the method used to adjust the relative weighting (amplitude and phase) applied to each channel. If appropriately designed, the weight-adjustment algorithm should be capable of handling both multipath distortion and cochannel interference.

This paper introduces a multi-mode adaptive beamformer (combiner) that uses a succession of minimum output power, dispersion direction, and decision direction to adjust the combiner weights. It begins with a brief description of relevant weight-adjustment algorithms and then describes the proposed multimode beamformer. It then presents the results of a lab experiment designed to evaluate the multimode beamformer performance. The experiment demonstrates the operation of the beamformer on a 16-QAM signal corrupted by both multipath distortion and cochannel interference. The results to date indicate the robust acquisition properties and performance improvement awarded by the multimode beamformer.

A relevant weight-adjustment technique proposed in [1,2] uses a least-squared error algorithm (such as LMS) to minimize the error between detected symbols and the combiner output. In so doing, the combiner is capable of minimizing both long and short-delay multipath in addition to cochannel interference. The technique is appropriately called decision-directed combining. The problem with this approach is that inaccurate decisions resulting from signal fading and/or strong cochannel interference will often cause the combiner to diverge from the optimal solution never to reacquire.

A technique that integrates decision-directed adaptation with spread spectrum has been proposed, experimentally demonstrated, and analyzed in [3,4]. This system is more resistant to multipath fading and cochannel interference than straight decision direction due to the processing gain associated with spread spectrum; however, it still suffers from the problem that the symbol error rate after PN gain must be fairly good in order for the beamformer to acquire. This greatly reduces the jam-resistant capabilities of the adaptive beamformer.

To circumvent the problems associated with divergence due to inaccurate symbol decisions, a nondecision-directed algorithm must be designed. In the adaptive equalization field, such algorithms are referred to as “blind” adaptation methods.

One such blind weight-adjustment method as described in [5,6] uses noncoherent spectral measurements of the combiner output to form a measure of signal dispersion. A relaxation type control algorithm is used to minimize the spectral dispersion measure. The technique is appropriately referred to as a minimum-dispersion combiner. The problem with the minimum-dispersion combiner is that the spectral dispersion measure is insensitive to signal phase and therefore can exhibit degraded performance for certain multipath and cochannel interference conditions. An additional disadvantage is that it requires a relatively large number of spectral measurements to handle long-delay multipath or narrow-band cochannel interference.

More recently, a blind weight-adjustment technique has been proposed in [7,8] that minimizes a time-domain measure of the signal dispersion. This dispersion measure is the difference between the modulus of the complex combiner output and unity. The algorithm that minimizes the dispersion measure is called the constant modulus algorithm (CMA). For truly constant modulus (envelop) signals such as FM, MSK, and CPSK, the addition of interference and/or multipath will cause an increase in the constant modulus dispersion measure. Consequently, use of CMA to adjust the array weights should result in nulling of the multipath and/or cochannel interference. A laboratory experiment using a similar time-domain dispersion measure was described in [9] that verified the concept on an FM signal corrupted by cochannel interference. While it is clear that CMA should work for truly constant modulus signals, it is not so clear that it will work for QAM signals. However, recent analytical results [10] and extensive computer simulations have demonstrated that it does converge to near-optimal solutions for high-order modulations such as 64-QAM. The near-optimality of the solution is a problem that can be cured by switching to decision-directed adaptation after the dispersion-directed mode has acquired. Another problem with the constant modulus dispersion measure is that it can capture a strong cochannel interferer instead of the signal of interest when the initial output SIR is near zero or worse. This capture problem has been analyzed [8] but not solved.

The last relevant weight-adjustment technique to be mentioned here is the minimum output power method [11]. This algorithm adjusts the beamformer weights to minimize the overall array output power. For a linear array with one weight constrained to unity, it can be shown that the algorithm will invert the signal-to-interference ratio (SIR) present at the beamformer input. Thus, it is useful for situations where the input SIR is less than one. The minimum output power algorithm is relevant to the interference capture problem because the poor SIR situation is just the situation where weight adjustment using CMA fails. In situations where interference capture occurs, minimum-output power can be used prior to entering the dispersion-directed mode.

Figure 1 shows a simplified block diagram of the proposed multimode adaptive beamformer. Quadrature (complex) signals,

, from N coherent receiving systems are linearly combined using the complex weighting,

, to form the beamformer output y. This output is then compared with a reference signal to generate the adaptation error signal, e. The error signal is correlated with the input to each weight to generate the current weight value. As usual, the single complex weight on each channel could be replaced by a multiple-weight tap-delay-line filter to increase the relative bandwidth of the beamformer.

Figure 1. Simplified block diagram of the multimode adaptive beamformer.

The multimode nature of the beamformer is evident from the switched selection of three possible reference signals. The first switch position supplies a reference signal of zero. This is the minimum output power mode and requires an additional constraint to be placed on the beamformer weights in order to prevent their collapse to zero. The constraint used here is to initialize a weight to one and then restrain updating of that weight. The second switch position supplies a reference signal that is the beamformer output vector normalized to unit length. This is the constant modulus or dispersion-directed mode. The third reference signal is comprised of decisions based upon the beamformer output. This is the decision-directed mode, requiring accurate decisions in order to properly acquire and track time variability.

Selection of the appropriate operating mode for the beamformer requires a certain amount of external intelligence. For instance, the dispersion-directed mode will generally be used first unless outside information has been supplied indicating the likelihood of interference capture. If interference capture is likely to occur then the minimum power mode will be switched on prior to dispersion direction. Finally, decision direction will be turned on once an assessment of the symbol error rate indicates accurate decisions are being made at least 90% of the time. Fallback from decision to dispersion direction under poor symbol error rate conditions can be implemented so that it will occur automatically.

The following laboratory experiment was conducted to evaluate the performance of a multimode beamformer. The experiment was designed specifically to provide a good example of strong cochannel interference. The data collected from the experimental setup was used to compare performance of a single channel equalizer to that of a two channel beamformer, with the weights adjusted using the previously described algorithms.

Two-channel IF data was collected using the laboratory setup shown in Figure 2. A horn antenna was used to transmit a 33.9 Mbaud 16-QAM signal-of-interest (SOI) at 10.9 GHz. Across the room, this signal was received by a dual-polarized slot array. The two sections of this array are both spatially separated and diverse in polarization. The horn antenna was physically tilted at about 45 degrees with respect to the slot array so that the SOI was received on both polarizations. An in-band interference signal, generated with a high frequency sine wave generator and transmitted with a conical antenna, was also received on both polarizations of the slot array.

Figure 2. Illustration of laboratory experiment setup.

The two RF signals from the slot array were then fed into separate receivers where they were downconverted to an IF of 70 MHz. The synthesizers in the two receivers were phase locked in order to insure coherency between the two channels. The two signals were fed into a LeCroy Digitizer, which synchronously sampled them at 200 MHz. This digital data was then stored on an IBM PC and downloaded to a MicroVAX. These real data “snapshots” were then filtered, downconverted to complex basebands, and resampled to twice the modem’s baudrate. Baud-synchronous resampling was necessary in order to use decision-directed updating.

The power spectra of the two channel snapshots, prior to resampling and conversion to baseband, are shown in Figure 3. The narrowband interference signal is clearly apparent on both channels, as well as some distortion of the spectrum due to multipath. The signal to interference ratio (SIR) of channel 1 was 11.2 dB and of channel 2 was -3.0 dB. The signal to noise ratios (SNR) were estimated to be about 30 dB on channel 1 and 22 dB on channel 2.

Figure 3. Power spectra of two-channel snapshots.

The data was then processed using two different simulations in order to compare the performance of a single channel equalizer to the two-channel multimode adaptive beamformer. First, the channel 1 data was processed using a 65 tap single channel equalizer. The data from both channels was also simultaneously processed using a two-channel beamformer with 33 taps per channel. The total number of taps used in each system was therefore about equal.

Since the initial SIR of channel 1 was fairly good (11.2 dB) the single channel equalizer could bypass the minimum-output power mode. It initially used CMA for its blind algorithm and then switched into decision direction to find the optimum solution. In the two channel equalizer, however, with both channel filters initialized to unity-gain allpass filters, initial use of the CMA mode resulted in interference capture. This is not surprising since, under those initial conditions, the SIR of the beamformer output was only 1.4 dB. The beamformer weights were therefore reinitialized and the simulation was restarted with the weights initially adjusted using the minimum output power algorithm, followed by CMA, and then decision direction. With this acquisition procedure, the multimode beamformer captured the signal-of-interest.

The frequency response of the final single-channel equalizer is shown in Figure 4. Notice that the equalizer has attempted to attenuate the interference signal by forming a notch at the frequency of the interferer. However in the process of notching the interference, the equalizer has created additional intersymbol interference. The final constellation of the single channel equalizer output is shown in Figure 6(a). The cluster variance is equivalent to an SNR of 16.1 dB which is far less than the original SNR on channel 1 of 30 dB.

Figure 4. Frequency response of converged single-channel equalizer.

The two-channel beamformer yielded better results. The reasons for this become apparent after examining the frequency responses of the two channel filters shown in Figure 5. As can be seen in the channel 1 response shown in Figure 5(a), the channel 1 filter provides shaping for the SOI without introducing a notch in the middle of the band. This is because the channel 2 filter, shown in Figure 5(b), has essentially passed only the interference signal. This signal has been properly scaled and phase shifted such that when the two channels are added, the interference is canceled. The in-band interference signal was therefore entirely eliminated without introducing additional intersymbol interference on the signal of interest.

Figure 5. Frequency responses of converged filters in two-channel beamformer.

The constellation of the two-channel beamformer output is shown in Figure 6(b). Here the cluster variance is equivalent to an SNR of 25.0 dB. The two channel combiner has therefore made an improvement of 9 dB over the single channel equalizer using virtually the same number of weights.

Figure 6. Output polar plots of (a) single-channel equalizer, (b) two-channel beamformer.

An adaptive beamformer with multiple adaptation control modes has been presented. Relevant weight-adjustment algorithms were briefly discussed and referenced. Preliminary experimental results were given to indicate the promise of the proposed approach. Further work is required to characterize the beamformer’s performance in a variety of interference scenarios and to investigate efficient hardware implementations. In closing, the authors wish to acknowledge the help of Tim Geyer in setting up and conducting the laboratory experiment.