An Adaptive Nulling System for Digital Microwave Radio

Richard Gooch, Brian Sublett, and Tim Geyer
Applied Signal Technology, Inc. March, 2000

This paper describes the development and operation of an adaptive nulling system designed to enhance the reception of quadrature-amplitude-modulated (QAM) signals which have been corrupted by cochannel and/or multipath interference. More specifically, an adaptive antenna preprocessor to an existing digital demodulator [4] is described. The adaptive antenna preprocessor is used to spatially null undesired directional interference by linearly combining the signals received by two antennas. A 64-tap adaptive equalizer contained within the digital demodulator is used to remove adjacent channel and intersymbol interference (ISI). Incorporated within the demodulator are gradient-search adaptive algorithms that automatically adjust both the equalizer and combiner weights to maximize the SINR of the received signal. These adaptive algorithms do not require knowledge of antenna calibration nor prearranged training signals. Instead “blind” adaptation is used during initial acquisition and decision-directed adaptation is used during tracking.

Introduction

Due to the ever-increasing need to transmit digital data over the airwaves, the RF spectrum is rapidly becoming overcrowded. As a result, newly installed communication links 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 (for example, 64-QAM) have increased the severity of the multipath encountered. While adaptive equalization and space diversity combining have long been employed to combat multipath, only recently has adaptive beamforming (nulling) come into consideration as a potential solution to both the multipath and cochannel interference problems [1-3]. Reference [1] introduced the use of the constant modulus algorithm for adaptive beamforming in the presence of multipath interference. Reference [2] described an adaptive beamforming system that used multiple performance criteria (including the constant modulus criterion) to enhance the reception of QAM signals. Reference [3] described methods for jointly optimizing the weights of an adaptive beamformer preceding an adaptive equalizer using the constant modulus and decision-directed LMS algorithms. This paper details the implementation and operation of a hybrid adaptive nulling and equalization system utilizing the concepts drawn from the above references.

Refer to Figure 1 for a block diagram illustrating the hybrid adaptive combiner-demodulator system. The outputs of separate antennas (or a dual-feed antenna) are fed into two phase-locked receivers where the desired signal is coherently downconverted to a 70 MHz IF. The IF output of each receiver is then fed into the IF combiner which linearly weights (magnitude and phase) one of the signals and combines it with the second. The combiner output is then fed into the equalizer-demodulator where the signal is adaptively equalized and demodulated(1). A parallel digital output from a microcomputer residing within the demodulator is fed back to control the IF combiner weight.

Figure 1. Block diagram of the hybrid adaptive combiner-demodulator system

The microcomputer causes a null to be steered in a given direction by sending the appropriate complex weight value to the IF combiner. Figure 2 provides a simplified pictorial illustrating this effect. The beampatterns of two identical receiving antennas are shown. One antenna output is multiplied by a complex weight and then summed with the second. The overall beampattern of the combined output is also shown. Due to the multiple wavelength separation between the two antennas, the overall beampattern contains a series of nulls throughout the main beam. The number and width of the nulls is determined by the antenna spacing. The depth and location of a given null is determined by the magnitude and phase of the complex weight.

Figure 2. Illustration of main-beam nulling through coherent combination of two antenna outputs.

The basic objective of the combiner weight-control algorithm is to find the complex weight value that steers a null in the direction of the undesired interference while maximizing the gain in the direction of the desired signal-of-interest (SOI). More precisely, the ultimate objective is to find the set of equalizer and combiner weights that maximize the signal-to-interference plus noise ratio (SINR) of the desired signal. In actuality, the system uses a series of performance criteria to approximate the true SINR due to the inability to measure the latter. These performance criteria are inversely related to the SINR so that minimizing the performance function is tantamount to maximizing the SINR.

Two types of steepest-descent algorithms are employed to minimize the selected performance criterion. As described in [4], the equalizer weights are adapted using the LMS algorithm. The complex combiner weight is adapted using a weight-perturbation algorithm [2]. The weight-perturbation technique functions in a manner similar to the method one uses to focus a camera; the algorithm continually “rocks the weights” back-and-forth to determine the correct adjustment direction. Convergence is attained when the performance function takes on equal values at both ends of the perturbation. A detailed description of the weight-perturbation algorithm is given in the next section.

Due to the inability to directly measure the true SINR, the system employs multiple performance criteria during adaptation. It starts with a criterion that is mildly related to the SINR but has a wide acquisition range. It then switches to successively more accurate criteria that have narrower acquisition ranges.

During initial acquisition, the system minimizes the output variance subject to a constraint on the equalizer weights. This minimum output power (MOP) mode, as it is called, is used to suppress strong interference sources. In the MOP mode, the center equalizer tap is constrained to unity and both the equalizer and combiner weights are adapted to minimize the overall system output power. Neither baud nor carrier synchronization is required during this mode of adaptation.

During a second acquisition phase, the system minimizes the constant modulus (CM) error variance. The CM mode is used to better remove both multipath and cochannel interference and to attain symbol phase synchronization. The constant modulus error signal is formed by taking the difference between the complex equalizer output vector and a normalized version of the same vector. Symbol rate synchronization is required during this mode, but not carrier synchronization.

Once carrier synchronization is attained, the system switches into a tracking mode where the decision-directed (DD) error variance is minimized. The DD error variance, or cluster variance as it is often called, is formed by taking the difference between the complex equalizer output vector and the nearest valid constellation point. The cluster variance represents a measure of the residual interference plus noise on the signal. As such, its relationship to the SINR should be apparent.

In all three modes of operation, the system uses steepest-descent algorithms to find the combiner and equalizer weights that minimize the selected performance criterion. The gradient employed in the equalizer weight update is approximated using the LMS algorithm. The gradient employed in the combiner weight update is approximated using a weight-perturbation algorithm.

Let the performance criteria be expressed as one of the three error variances described above.

For a given input signal,

will be a function of both the combiner and equalizer weights. The objective of the adaptive algorithm is to find the set of weights that minimize

. This set of weights is referred to as the optimum weight vector.

Steepest descent is a commonly used method of minimizing a function of several variables. For N complex weights, the performance function can be thought of as a 2N dimensional surface. The gradient of the function is a vector which points “uphill” on the surface and whose magnitude is a measure of the steepness of that uphill climb. To move the weight vector towards the optimum value, the weights can be updated by taking steps in the direction of the negative of the gradient vector which points “downhill” on the performance surface towards a minimum.

The gradient vector is the derivative of the performance function with respect to each of the weights. It can be expressed mathematically as:

The steepest descent update of the weight vector is expressed as:

The LMS algorithm is a steepest-descent algorithm that uses an estimate the true gradient formed by taking the derivative of the quantity

. It can be shown that

where

is a vector of weight input signals. Substituting this gradient estimate into equation (3), the weight update equation for the LMS algorithm becomes:

The LMS algorithm specified as above is used to update the equalizer weights in all modes of adaptation. In decision-directed mode, the time constant of the equalizer adaptation is approximately 10,000 symbol periods. Thus for symbol rates greater than 1 Mbaud, the time constant is less than 10 msec.

Notice that the LMS update requires the vector

. To simplify the IF combiner design, the combiner weight input signal was assumed unaccessible. This assumption permits the IF combiner to be easily replaced by an RF combiner (currently under development) eliminating the need for two receivers. As a consequence, the LMS algorithm was not used to update the combiner weight. Instead, the combiner weight is updated using a steepest-descent algorithm that approximates the gradient with a difference quotient formed by measuring the value of the performance function at small perturbations about the current value of the weight vector.

The operation of the weight-perturbation algorithm is illustrated in Figure 3. Figure 3(a) shows contours of the performance function

with respect to the in-phase and quadrature-phase components of the complex combiner weight. Figure 3(b) shows a cross section of that performance function in a plane defined by holding the quadrature component of the weight constant. It should be pointed out that for every combiner weight value, the adaptive equalizer is assumed to have converged so that the equalizer weight vector is optimum for that value of combiner weight. This is a valid assumption as long as the equalizer time constant is much greater than the combiner time constant.

Figure 3. (a) Performance surface contours. (b) Cross section of performance surface.

The weight perturbation algorithm operates as follows: First, the in-phase component of the weight is perturbed in the positive direction by a small value

, and the performance function is estimated by averaging the error power over

samples. This yields the performance function estimate

. Next, the in-phase component is perturbed by

, from the current weight value, and the error power is again averaged over

samples to yield

. The in-phase component is then returned to its current value and the quadrature component is perturbed in the same manner. The performance function is measured at a perturbation of

to yield

, and also at a perturbation of

to yield

. From these four estimates of the performance function in the neighborhood of the current weight value, the gradient estimate is then calculated according to:

Finally, the complex weight is updated by

The performance function

is a quadratic function of the equalizer weights once the combiner weight is fixed. And vice versa, it is a quadratic function of the combiner weight once the equalizer weights are fixed. However,

is not a quadratic function of all the weights. Thus the contour plots shown in Figure 3(a) may not be elliptical. In fact, the performance function may have multiple local minima. This fact can be demonstrated quite easily by considering a multipath signal environment consisting of a direct path plus a single reflected path. One local minimum arises from the combiner spatially nulling the multipath, while another local minimum results from the equalizer canceling the multipath. The relative time constants of the equalizer and combiner algorithms along with the initial weight vector will determine which of these local minima the system converges to.

Figure 4 provides a simplified diagram of the IF combiner circuitry. The 20-bit parallel bus consists of 12 data bits and 8 control bits. The data bits are fed into a 12-bit quad D/A converter to generate three analog control voltages. The control bits determine the D/A converter being addressed along with read, write, reset, or DAC update operations. Two of the control voltages,

and

, represent the real and imaginary parts of the complex combiner weight (the CPM block) applied to channel one. The third control voltage,

, determines the attenuation applied to channel two. This attenuation is used to remove gross gain imbalances between the two channels so that the CPM can operate in its linear region. While not shown in the figure, the IF combiner also contains circuitry to provide built-in test (BITE) and diagnostics.

Figure 4. Simplified IF combiner circuit diagram.

The heart of the IF combiner is the complex phasor modulator (CPM) used to implement the combiner weight. As shown in Figure 5, the CPM splits the input signal into in-phase (I) and quadrature-phase (Q) components, multiplies each component by the I and Q control voltages, and then recombines the resultant signals to generate a single output. In so doing, the CPM provides a full 360 degrees of phase control and a wide range of attenuation. The CPM used in the combiner provided less than 0.2 dB of amplitude ripple and 2 degrees of differential phase over an octave bandwidth. This translates into the capability to provide better than 35 dB of nulling over 40 MHz of signal bandwidth centered at a 70 MHz IF.

Figure 5. Block diagram of a complex phasor modulator.

Signed gains on the I and Q signal components are realized using a biphase modulator. A biphase modulator consists of an input transformer, two pairs of diodes, and an output transformer. The center tap of the input transformer is control port 1 and the center tap of the output transformer is control port 2. These two control ports are differential driven and used to bias the diodes. If port 1 is sufficiently more positive than port 2, one pair of diodes is biased on and the signal on the input transformer secondary is coupled directly through to the output transformer primary. If the voltages on ports 1 and 2 are reversed, the other pair of diodes is biased on and the input signal is coupled to the output transformer with a 180 degree phase shift, hence biphase modulation. Modulators employing PIN diode were used due to their high intercept points and wide linear control voltage range. Control voltage bandwidths of 100 kHz associated with PIN-diode modulators were adequate for the required combiner update rates.

The following scenario was used to test the combiner-demodulator system. A 33.9 Mbaud 16-QAM modem signal and an in-band sinusoidal interference signal were transmitted from separate locations. These signals were received using two spatially separated antennas and phase-locked receivers. For purposes of comparison, results are shown for the equalizer operating both with and without the combiner.

Figure 6 shows the results from the equalizer-only system. Figure 6(a) shows the power spectrum of the equalizer input signal. The scale of these photos is 10 MHz per division with the center at the 70 MHz IF frequency. The narrowband interference signal is clearly visible at approximately 75 MHz. Figure 6(b) shows the equalizer frequency response and equalizer impulse response after convergence. Notice that the equalizer has attempted to eliminate the interferer by placing a notch at the frequency of the sinusoidal interference. The effect of this can be seen in the equalizer output polar plot, shown in Figure 6(c), where the large clouds around each constellation point indicate considerable residual cochannel interference and notched-induced ISI. The cluster variance of this plot is –14.5 dB.

Figure 6. Results from equalizer-only system.

Figure 7 shows the results from the combiner-equalizer system. Figure 7(a) shows the output spectrum of the combiner, which is also the input signal to the equalizer, after both the combiner and equalizer weights have fully converged. The narrowband signal has been nulled so that its peak is no longer visible in the power spectrum. Superimposed on this photo is the power spectrum of the combiner output with its weight frozen at its final value and the wide band signal turned off. Comparison of these two power spectra to that in Figure 6(a) shows that the interference signal has been nulled by approximately 24 dB by the combiner. Now, as can be seen from the equalizer response shown in Figure 7(b), the equalizer no longer has to notch the interference signal. This eliminates not only the residual interference, but also notch induced ISI from the equalizer output and results in a much cleaner output polar plot, which is shown in Figure 7(c). The cluster variance in this plot is –21.7 dB, which indicates that the combiner has made an improvement of 7.2 dB to the SINR of the SOI.

Figure 7. Results from hybrid combiner-equalizer system.

This paper has described an adaptive antenna preprocessor to an equalized demodulator. The hybrid system is capable of nulling directional cochannel or multipath interference while equalizing residual intersymbol interference not removed by the combiner. Experimental results have been presented which demonstrate the overall system placing a null of approximately 24 dB on a narrow band interference signal. Experimental results not presented here indicate that the system is capable of forming a 30 dB null over a 40 MHz wide interference bandwidth under certain conditions. Time constants of the overall system in tracking mode are estimated to be on the order of 100 msec.