Reduced-rank Signal Processing Research Articles

Robust Rank Reduction Algorithm with Iterative Parameter Optimization and Vector Perturbation

In dynamic propagation environments, beamforming algorithms may suffer from strong interference, steering vector mismatches, a low convergence speed and a high computational complexity. Reduced-rank signal processing techniques provide a way to address the problems mentioned above. This paper presents a low-complexity robust data-dependent dimensionality reduction based on an iterative optimization with steering vector perturbation (IOVP) algorithm for reduced-rank beamforming and steering vector estimation. The proposed robust optimization procedure jointly adjusts the parameters of a rank reduction matrix and an adaptive beamformer. The optimized rank reduction matrix projects the received signal vector onto a subspace with lower dimension. The beamformer/steering vector optimization is then performed in a reduced dimension subspace. We devise efficient stochastic gradient and recursive least-squares algorithms for implementing the proposed robust IOVP design. The proposed robust IOVP beamforming algorithms result in a faster convergence speed and an improved performance. Simulation results show that the proposed IOVP algorithms outperform some existing full-rank and reduced-rank algorithms with a comparable complexity.

Adaptive Reduced-Rank Processing Based on Joint and Iterative Interpolation, Decimation, and Filtering

We present an adaptive reduced-rank signal processing technique for performing dimensionality reduction in general adaptive filtering problems. The proposed method is based on the concept of joint and iterative interpolation, decimation and filtering. We describe an iterative least squares (LS) procedure to jointly optimize the interpolation, decimation and filtering tasks for reduced-rank adaptive filtering. In order to design the decimation unit, we present the optimal decimation scheme and also propose low-complexity decimation structures. We then develop low-complexity least-mean squares (LMS) and recursive least squares (RLS) algorithms for the proposed scheme along with automatic rank and branch adaptation techniques. An analysis of the convergence properties and issues of the proposed algorithms is carried out and the key features of the optimization problem such as the existence of multiple solutions are discussed. We consider the application of the proposed algorithms to interference suppression in code-division multiple-access (CDMA) systems. Simulations results show that the proposed algorithms outperform the best known reduced-rank schemes with lower complexity.

Optimal and adaptive reduced-rank STAP

This paper is concerned with issues and techniques associated with the development of both optimal and adaptive (data dependent) reduced-rank signal processing architectures. Adaptive algorithms for 1D beamforming, 2D space-time adaptive processing (STAP), and 3D STAP for joint hot and cold clutter mitigation are surveyed. The following concepts are then introduced for the first time (other than workshop and conference records) and evaluated in a signal-dependent versus signal independent context: (1) the adaptive processing region-of-convergence as a function of sample support and rank, (2) a new variant of the cross-spectral metric (CSM) that retains dominant mode estimation in the direct-form processor (DFP) structure, and (3) the robustness of the proposed methods to the subspace leakage problem arising in many real-world applications. A comprehensive performance comparison is conducted both analytically and via Monte Carlo simulation which clearly demonstrates the superior theoretical compression performance of signal-dependent rank-reduction, its broader region-of-convergence, and its inherent robustness to subspace leakage.

Matched-field localization in high noise environments: A reduced-rank signal processing approach

A new matched-field source localization technique using generalized likelihood array processing is proposed. The problem is posed as a joint detection and parameter estimation problem in the face of structured noise of unknown power. Recent developments in reduced rank signal processing are exploited to solve it; they yield an algorithm that provides effective interference cancellation, high resolution, a constant false alarm rate detection statistic, and accurate source location estimates. Its performance is tested and evaluated in a simulated shallow water environment. It was found that it yields excellent results at the price of moderate computational overhead as compared to the Bartlett and Capon estimators.

The SVD and reduced rank signal processing

The basic ideas of reduced-rank signal processing are evident in the original work of Shannon, Bienvenu, Schmidt, and Tufts and Kumaresan. In this paper we extend these ideas to a number of fundamental problems in signal processing by showing that rank reduction may be applied whenever a little distortion may be exchanged for a lot of variance. We derive a number of quantitative rules for reducing the rank of signal models that are used in signal processing algorithms.