Reduced-rank Minimum Mean Squared Error Research Articles

Reduced-rank estimation for ill-conditioned stochastic linear model with high signal-to-noise ratio

Reduced-rank approach has been used for decades in robust linear estimation of both deterministic and random vector of parameters in linear model y=Hx+ϵn. In practical settings, estimation is frequently performed under incomplete or inexact model knowledge, which in the stochastic case significantly increases mean-square-error (MSE) of an estimate obtained by the linear minimum mean-square-error (MMSE) estimator, which is MSE-optimal among linear estimators in the theoretical case of perfect model knowledge. However, the improved performance of reduced-rank estimators over MMSE estimator in estimation under incomplete or inexact model knowledge has been established to date only by means of numerical simulations and arguments indicating that the reduced-rank approach may provide improved performance over MMSE estimator in certain settings. In this paper we focus on the high signal-to-noise ratio (SNR) case, which has not been previously considered as a natural area of application of reduced-rank estimators. We first show explicit sufficient conditions under which familiar reduced-rank MMSE and truncated SVD estimators achieve lower MSE than MMSE estimator if singular values of array response matrix H are perturbed. We then extend these results to the case of a generic perturbation of array response matrix H, and demonstrate why MMSE estimator frequently attains higher MSE than reduced-rank MMSE and truncated SVD estimators if H is ill-conditioned. The main results of this paper are verified in numerical simulations.

Performance of coded DS‐CDMA system using reduced rank MMSE receiver in Rayleigh fading channels

AbstractThis paper examines the performance of a reduced rank minimum mean square error (MMSE) receiver‐based direct sequence code division multiple access (DS‐CDMA) system. For such system, when a large processing gain is employed, substantial time is consumed in computing the filter tap weights. Many schemes for reducing the complexity of the MMSE have been proposed in recent years. In this paper, computational complexity reduction of the MMSE receiver is achieved by using the K‐mean classification algorithm. The performance of the uncoded and coded systems are investigated for the full rank MMSE receiver and reduced rank MMSE receiver and results are compared in terms of bit error rate at different loading levels in both AWGN and fading channels. A system with the matched filter (MF) receiver is also presented for the purpose of comparison and an analytical pair‐wise error bound for the coded system is derived. In the adaptive implementation of the receivers, results show that good performance is achieved for the reduced rank receiver when compared to the full rank receiver in both coded and uncoded systems, while in the optimum implementation of the tap weights, the reduced dimension receiver performance experiences degradation when compared to the full rank scheme. Over the band‐limited channels considered, results for the reduced rank receiver also reiterate the fact that higher code rates tend to yield lower BER than that of low rate codes. Copyright © 2006 John Wiley & Sons, Ltd.

Adaptive reduced-rank MMSE filtering with interpolated FIR filters and adaptive interpolators

In this letter, we propose a broadly applicable reduced-rank filtering approach with adaptive interpolated finite impulse response (FIR) filters in which the interpolator is rendered adaptive. We describe the interpolated minimum mean squared error (MMSE) solution and propose normalized least mean squares (NLMS) and affine-projection (AP) algorithms for both the filter and the interpolator. The resulting filtering structures are considered for equalization and echo cancellation applications. Simulation results showing significant improvements are presented for different scenarios.

Design of Reduced-Rank MMSE Multiuser Detectors Using Random Matrix Methods

Reduced-rank minimum mean-squared error (MMSE) multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in long-sequence code-division multiple-access (CDMA) systems. In this paper, we consider the design of reduced-rank MMSE receivers in a general framework which includes fading, single and multiantenna receivers, as well as direct-sequence CDMA (DS-CDMA) and multicarrier CDMA (both uplink and downlink). In all these cases, random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reduced-rank receiver.

Blind Reduced-Rank MMSE Detector for DS-CDMA Systems

We first develop a reduced-rank minimum mean square error (MMSE) detector for direct-sequence (DS) code division multiple access (CDMA) by forcing the linear MMSE detector to lie in a signal subspace of a reduced dimension. While a reduced-rank MMSE detector has lower complexity, it cannot outperform the full-rank MMSE detector. We then concentrate on the blind reduced-rank MMSE detector which is obtained from an estimated covariance matrix. Our analysis and simulation results show that when the desired user's signal is in a low-dimensional subspace, there exists an optimal subspace so that the blind reduced-rank MMSE detector lying in this subspace has the best performance. By properly choosing a subspace, we guarantee that the optimal blind reduced-rank MMSE detector is obtained. An adaptive blind reduced-rank MMSE detector, based on a subspace tracking algorithm, is developed. The adaptive blind reduced-rank MMSE detector exhibits superior steady-state performance and fast convergence speed.

A low complexity reduced-rank MMSE receiver for DS/CDMA communications

The minimum mean squared error (MMSE) receiver is a linear filter which can achieve optimal near-far resistance in direct-sequence code-division multiple-access communications. However, one of the main problems of this receiver is the required number of filter taps, which is typically large. This is especially true in systems with a large processing gain in which case the receiver's computation burden becomes very high. As a result, methods for reducing the complexity of the MMSE receiver have been of great interest in recent years. We propose an efficient partitioned MMSE receiver based on a classification algorithm. It is shown that the computational complexity (in terms of the filter taps) of the proposed receiver can be reduced significantly while good performance is maintained. Based on the special structure of our proposed receiver, we also propose a release-merge adaptive partition algorithm which can update the partition and the receiver's coefficients simultaneously. In particular, it is demonstrated that the proposed receiver can perform much better than previously proposed reduced-rank MMSE receivers, such as the partial despreading MMSE receiver and the cyclically shifted filter bank receiver, with even a smaller number of taps.

Reduced-Rank Chip-Level MMSE Equalization for the 3G CDMA Forward Link with Code-Multiplexed Pilot

This paper deals with synchronous direct-sequence code-division multiple access (CDMA) transmission using orthogonal channel codes in frequency selective multipath, motivated by the forward link in 3G CDMA systems. The chip-level minimum mean square error (MMSE) estimate of the (multiuser) synchronous sum signal transmitted by the base, followed by a correlate and sum, has been shown to perform very well in saturated systems compared to a Rake receiver. In this paper, we present the reduced-rank, chip-level MMSE estimation based on the multistage nested Wiener filter (MSNWF). We show that, for the case of a known channel, only a small number of stages of the MSNWF is needed to achieve near full-rank MSE performance over a practical single-to-noise ratio (SNR) range. This holds true even for an edge-of-cell scenario, where two base stations are contributing near equal-power signals, as well as for the single base station case. We then utilize the code-multiplexed pilot channel to train the MSNWF coefficients and show that adaptive MSNWF operating in a very low rank subspace performs slightly better than full-rank recursive least square (RLS) and significantly better than least mean square (LMS). An important advantage of the MSNWF is that it can be implemented in a lattice structure, which involves significantly less computation than RLS. We also present structured MMSE equalizers that exploit the estimate of the multipath arrival times and the underlying channel structure to project the data vector onto a much lower dimensional subspace. Specifically, due to the sparseness of high-speed CDMA multipath channels, the channel vector lies in the subspace spanned by a small number of columns of the pulse shaping filter convolution matrix. We demonstrate that the performance of these structured low-rank equalizers is much superior to unstructured equalizers in terms of convergence speed and error rates.