Based on the Bartlett's decomposition of a Wishart random matrix, we study the normalized output signal-to-interference-plus-noise ratio (SINR) of a sample matrix inversion (SMI) beamformer with exploiting a priori information on persymmetric structures in the received signal. The persymmetric structure exists when a system is equipped with a symmetrically spaced linear array or symmetrically spaced pulse trains. In the matched case, we obtain an exact expression for the expectation of the normalized output SINR (i.e., average SINR loss) of the persymmetric SMI beamformer. Considering the mismatch in the signal steering vector, we derive an approximate expression for the average SINR loss of the persymmetric SMI beamformer in a non-homogeneous environment where the test and training data have different covariance matrices. These theoretical results are all verified by using Monte Carlo techniques. Simulation results reveal that the exploitation of the persymmetric structure is equivalent to doubling the amount of training data, and thus the SINR loss of the persymmetric SMI beamformer can be significantly reduced. In particular, the persymmetric SMI beamformer can work in the case of limited training data where the traditional beamformers cannot work.

Average SINR Calculation of a Persymmetric Sample Matrix Inversion Beamformer

Part One. Multivariate distributions. Preliminary data analysis. Part Two: Finding new underlying variables. Principal component analysis. Factor analysis. Part Three: Procedures based on the multivariate normal distribution. The multivariate normal distribution. Procedures based on normal distribution theory. The multivariate analysis of variance. The multivariate analysis of covariance and related topics. Part Four: Multi-dimensional scaling and cluster analysis. Multi-dimensional scaling. Cluster analysis.

Introduction to multivariate analysis, by C. Chatfield and A. J. Collins. Pp 246. £13 hardcover, £7·50 paperback. 1980. ISBN 0-412-16030-7/4 (Chapman and Hall)

The direction estimation problem of coherent targets in multiple-input multiple-output (MIMO) radar systems is studied and a scheme with joint transmission and reception diversity smoothing is proposed. When both the transmitting and receiving antenna arrays are located closely in space, the new approach leads to much more available covariance matrices for spatial smoothing to decorrelate the coherent signals. As a result, a better estimation performance is achieved compared to the existing transmission diversity smoothing (TDS) method. It can also identify more coherent targets when sparse antenna arrays are employed. On the other hand, the proposed approach can be applied to joint direction of arrival (DOA) and direction of departure (DOD) estimation using existing direction estimation algorithms when the transmit and receive arrays are separated far away from each other (i.e. the bistatic case). Two specific methods are proposed under the scheme, one is based on forward-only (FO) spatial smoothing and one is based on forward-backward (FB) processing. Due to the increased number of covariance matrices for spatial smoothing, a further improved performance is achieved by the FB-based one.

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Joint Transmission and Reception Diversity Smoothing for Direction Finding of Coherent Targets in MIMO Radar

Adaptive wideband beamforming with sensor delay-lines

We examine the adaptive detection problem in the presence of colored noise with an unknown covariance matrix, by exploiting a persymmetric structure in the received signal. The persymmetric adaptive matched filter (PS-AMF) is used to address this problem, which can significantly alleviate the requirement of secondary data. In G. Pailloux et al. “Persymmetric adaptive radar detectors,” (2011) the probability of false alarm of the PS-AMF has been obtained in terms of the Gaussian hypergeometric function. In this paper, finite-sum expressions for the probability of false alarm of the PS-AMF are derived, which are more convenient to use in calculating the detection threshold. Moreover, the detection probabilities of the PS-AMF for both nonfluctuating and fluctuating target models are derived. In the fluctuating model, the amplitude of the target echoes is described by a generalized Chi distribution that involves the Rayleigh distribution as a special case. These theoretical results are all confirmed using Monte Carlo (MC) simulations.

On the performance of a persymmetric adaptive matched filter

The sample matrix inversion (SMI) beamformer suffers from performance degradation due to the finite sample size effect and the arrival angle mismatch problem. A simple technique to provide robustness to the conventional SMI beamformer is to block the desired signal from the received data before calculating the beamformer's weight vector, which leads to the subtraction-based SMI (S-SMI) beamformer. In this correspondence, closed-form approximations of the expected value of the signal-to-interference-plus-noise ratio (SINR) for the S-SMI beamformer and the SMI beamformer are derived, where the effect of both finite sample size and arrival angle mismatch are considered. Simulations show that the derived approximations are close enough to represent the true values of the SINR, when the sample size is small and the arrival direction mismatch exists.

SINR Analysis of the Subtraction-Based SMI Beamformer

The employment of forward-backward (FB) processing to both batch and adaptive beamformers provides a superior performance than the forward only (FO) algorithm. Based on the finite-sample minimum variance distortionless response (MVDR) beamformer, a set of closed-form expressions for the variance of the weight vector, the output signal-to-interference-plus-noise ratio (SINR) and the mean-square error (MSE) is derived, for both FB and FO algorithms. As shown in our analysis, all errors of the FB algorithm are only approximately half of the FO case.

Performance Analysis for Finite Sample MVDR Beamformer With Forward Backward Processing

Robust beamforming methods for multipath signal reception

The bandwidth performance of a linearly constrained minimum variance (LCMV) beamformer with and without tapped delay-lines (TDLs) processing is examined. A narrowband beamformer (without TDLs) is able to suppress wideband signals, but with the cost of a large number of sensors. As a solution to this problem, TDLs are introduced, which leads to the well-known wideband beamforming structure. It is shown how the SINR (signal to interference plus noise ratio) improves for different signal bandwidths with an increasing number of sensors for the narrowband structure, and by changing the length of the TDLs for the wideband structure

Bandwidth Performance of Linearly Constrained Minimum Variance Beamformers

Severe signal cancellation often occurs in conventional adaptive beam- forming if coherent signals, caused by multipath propagation, are present. To overcome this problem, a recently proposed robust adaptive beamforming technique is extended to this case, where a channel with an increased signal to interference plus noise ratio is first generated and then enhanced, and thereafter a principle component analysis operation is performed on the new set of data with the sig nal of interest being its largest component. Our simulations verify its effectiveness in its application to the multipath environment.

Lei Yu

Papers

SINR Analysis of the Subtraction-Based SMI Beamformer

Performance Analysis for Finite Sample MVDR Beamformer With Forward Backward Processing

Robust beamforming methods for multipath signal reception

Bandwidth Performance of Linearly Constrained Minimum Variance Beamformers

Robust Adaptive Beamforming for Multi-Path Environment Based on Domain Weighted PCA