Array processing involves manipulation of signals induced on various antenna elements. Its capabilities of steering nulls to reduce cochannel interferences and pointing independent beams toward various mobiles, as well as its ability to provide estimates of directions of radiating sources, make it attractive to a mobile communications system designer. Array processing is expected to play an important role in fulfilling the increased demands of various mobile communications services. Part I of this paper showed how an array could be utilized in different configurations to improve the performance of mobile communications systems, with references to various studies where feasibility of apt array system for mobile communications is considered. This paper provides a comprehensive and detailed treatment of different beam-forming schemes, adaptive algorithms to adjust the required weighting on antennas, direction-of-arrival estimation methods-including their performance comparison-and effects of errors on the performance of an array system, as well as schemes to alleviate them. This paper brings together almost all aspects of array signal processing.

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Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations

Adaptive beamforming algorithms can be extremely sensitive to slight errors in array characteristics. Errors which are uncorrelated from sensor to sensor pass through the beamformer like uncorrelated or spatially white noise. Hence, gain against white noise is a measure of robustness. A new algorithm is presented which includes a quadratic inequality constraint on the array gain against uncorrelated noise, while minimizing output power subject to multiple linear equality constraints. It is shown that a simple scaling of the projection of tentative weights, in the subspace orthogonal to the linear constraints, can be used to satisfy the quadratic inequality constraint. Moreover, this scaling is equivalent to a projection onto the quadratic constraint boundary so that the usual favorable properties of projection algorithms apply. This leads to a simple, effective, robust adaptive beamforming algorithm in which all constraints are satisfied exactly at each step and roundoff errors do not accumulate. The algorithm is then extended to the case of a more general quadratic constraint.

Robust adaptive beamforming

Adaptive beamforming methods are known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated. In particular, if the desired signal is present in training snapshots, the adaptive array performance may be quite sensitive even to slight mismatches between the presumed and actual signal steering vectors (spatial signatures). Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration, distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance. It turns out that the natural formulation of this adaptive beamforming problem involves minimization of a quadratic function subject to infinitely many nonconvex quadratic constraints. We show that this (originally intractable) problem can be reformulated in a convex form as the so-called second-order cone (SOC) program and solved efficiently (in polynomial time) using the well-established interior point method. It is also shown that the proposed technique can be interpreted in terms of diagonal loading where the optimal value of the diagonal loading factor is computed based on the known level of uncertainty of the signal steering vector. Computer simulations with several frequently encountered types of signal steering vector mismatches show better performance of our robust beamformer as compared with existing adaptive beamforming algorithms.

http://www.ece.ualberta.ca/~vorobyov/RobBeamformer.pdf

Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem

It is well known that calibration errors can seriously degrade performance in adaptive arrays, particularly when the input signal-to-noise ratio is large. The effect is caused by the perturbation of the presumed steering vector from its optimal value. Although it is not as widely known, similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data. Under these conditions, performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly. In the paper, a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors. The method involves projection of the presumed steering vector onto the observed signal-plus-interference subspace. An analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots. Both analytical and experimental results are presented that illustrate the advantages of the proposed method. >

A projection approach for robust adaptive beamforming

This paper proposes a new robust adaptive beamformer applicable to microphone arrays. The proposed beamformer is a generalized sidelobe canceller (GSC) with a new adaptive blocking matrix using coefficient-constrained adaptive filters (CCAFs) and a multiple-input canceller with norm-constrained adaptive filters (NCAFs). The CCAFs minimize leakage of the target-signal into the interference path of the GSC. Each coefficient of the CCAFs is constrained to avoid mistracking. The input signal to all the CCAFs is the output of a fixed beamformer. In the multiple-input canceller, the NCAFs prevent undesirable target-signal cancellation when the target-signal minimization at the blocking matrix is incomplete. The proposed beamformer is shown to be robust to target-direction errors as large as 200 with almost no degradation in interference-reduction performance, and it can be implemented with several microphones. The maximum allowable target-direction error can be specified by the user. Simulated anechoic experiments demonstrate that the proposed beamformer cancels interference by over 30 dB. Simulation with real acoustic data captured in a room with 0.3-s reverberation time shows that the noise is suppressed by 19 dB. In subjective evaluation, the proposed beamformer obtains 3.8 on a five-point mean opinion score scale, which is 1.0 point higher than the conventional robust beamformer.

A robust adaptive beamformer for microphone arrays with a blocking matrix using constrained adaptive filters

Antenna designers often employ linearly constrained adaptive beamforming as an antijamming measure. With minimal a priori knowledge of the signal environment, this technique nulls out jammers while simultaneously preserving the quality of the main lobe so that a friendly look-direction signal can be received with unity gain. Unfortunately, in the absence of special strategies, linearly constrained adaptive beamforming is hypersensitive to array imperfections when the input signal-to-noise ratio exceeds a certain threshold. This hypersensitivity manifests itself as a nailing of the friendly signal as if it were a jammer. Luckily, the signal nulling problem can be easily remedied by artificial receiver noise injection. A particularly simple and general structure for linearly constrained adaptive beamforming was proposed during the 1970's, and is known as the generalized sidelobe canceller. A detailed analysis of the generalized sidelobe canceller in the presence of array imperfections is discussed, and two new artificial receiver noise injection algorithms are proposed. Computer simulations are included to demonstrate that use of these new algorithms alleviates the signal nailing problem without seriously compromising jammer nulling. For the special case of the Capon maximum-likelihood beamformer, simple approximations are presented for: 1) the Wiener output signal-to-interference-plus-noise ratio ( SINR_{0}\astr ), 2) the antenna element error variance that causes a 3 dB loss of SINR_{0}\astr from its value for an ideal array, and 3) the optimal artificial receiver noise that maximizes SINR_{0}\astr .

N. Jablon

Papers

Adaptive beamforming with the generalized sidelobe canceller in the presence of array imperfections