Reduced-Rank Adaptive Filtering Based on Joint Iterative Optimization of Adaptive Filters

Abstract

This letter proposes a novel adaptive reduced-rank filtering scheme based on joint iterative optimization of adaptive filters. The novel scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that forms the projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters.We describe minimum mean-squared error (MMSE) expressions for the design of the projection matrix and the reduced-rank filter and low-complexity normalized least-mean squares (NLMS) adaptive algorithms for its efficient implementation. Simulations for an interference suppression application show that the proposed scheme outperforms in convergence and tracking the state-of-the-art reduced-rank schemes at significantly lower complexity. Index Termsdaptive filters, iterative methods.daptive filters, iterative methods.A I. INTRODUCTIONIn adaptive filtering [1], one can find a huge number of algorithms with different trade-offs between performance and complexity. They range from the simple and low-complexity least-mean squares (LMS) algorithms to the fast converging though complex recursive least squares (RLS) techniques. Several attempts to provide cost-effective adaptive filters with fast convergence performance have been made with variable step-size algorithms, data-reusing, sub-band and frequency-domain schemes and RLS algorithms with linear complexity. A challenging problem which remains unsolved by conventional techniques is that when the number of elements in the filter is large, the algorithm requires a large number of samples to reach its steady-state behavior. In these situations, even RLS algorithms require an amount of data proportional to 2M [1] in stationary environments to reach steady state, where M is the filter

Bidirectional algorithms for interference suppression in multiuser systems

“…At this point, in order to improve the convergence performance of the NLMS algorithm, the bracketed error terms of (25) are modified by replacing the receive filters with the most recently calculated one, w[i − 1]. The resulting gradient expression is given by…”

“…However, the stability of adaptive step-sizes and forgetting factors can be a concern unless they are constrained to lie within a predefined region [19]. Other alternative schemes include those based on processing the received data in subblocks [20][21][22] and subspace algorithms [23][24][25][26][27][28]. In addition, the fundamental problem of obtaining the unfaded symbols whilst suppressing MUI remains.…”

Reduced-Rank STAP Schemes for Airborne Radar Based on Switched Joint Interpolation, Decimation and Filtering Algorithm

“…The joint domain localized (JDL) approach, which is a beamspace reduced-dimension algorithm, was proposed by Wang and Cai [22] and investigated in both homogeneous and nonhomogeneous environments in [23], [24], respectively. Recently, reduced-rank filtering algorithms based on joint iterative optimization of adaptive filters [25], [26] and based on an adaptive diversity-combined decimation and interpolation scheme [27], [28] were proposed, respectively.…”

“…The joint domain localized (JDL) approach, which is a beamspace reduced-dimension algorithm, was proposed by Wang and Cai [22] and investigated in both homogeneous and nonhomogeneous environments in [23], [24], respectively. Recently, reduced-rank adaptive processing algorithms based on joint iterative optimization of adaptive filters [25], [26] and based on an adaptive diversity-combined decimation and interpolation scheme [27], [28] were proposed, respectively. In our prior work [26], a joint iterative optimization of adaptive filters STAP scheme using the linearly constrained minimum variance (LCMV) was considered and applied to airborne radar applications, resulting in a significant improvement both in convergence speed and SINR performance as compared with the existing reduced-rank STAP algorithms.…”

A Mixing Vector Based an Affine Combination of Two Adaptive Filters for Sensor Array Beamforming

“…Several reduced-rank methods have been proposed in the last decade, such as auxiliary vector filter (AVF), conjugate gradient reduced-rank filter (CGRRF) [21], multistage nested Wiener filter (MNWF) [22] and its modified approaches applied in a wide area of adaptive array beamforming [23][24][25]. Many important results on how to improve the convergence rate and/or how to reduce the computational complexity of reduced-rank adaptive filters have been obtained in the literature (see, e.g., [26,27]). However, there is a tradeoff between convergence rate and steady-state signal to interference plus noise ratio (SINR).…”