Performance analysis of RLS linearly constrained constant modulus algorithm for multiuser detection

Abstract

The linearly constrained constant modulus algorithm (LCCMA) is a blind multiuser detector (MUD) solution to multiple access interference (MAI) suppression that is widely investigated in direct-sequence code division (DS-CDMA) systems. However, the conventional CMA based on the stochastic gradient descent (SGD) has slow convergence speed. Our research introduces an approximation of recursive least square (RLS) into LCCMA for better convergence speed in DS-CDMA system and quantifies the performance of blind adaptive filter based on RLS-LCCMA in both a static and a time-varying channel. In this investigation, we derive the expressions for the excess mean-square error (EMSE) of the MUD with a framework called feedback approach, and further obtain a relationship between the step size of SGD-LCCMA and the forgetting factor of RLS-LCCMA. Eventually, simulation results show the advantage of RLS-LCCMA and verify the performance analysis of the algorithm.

Introduction

The linear minimum mean-square error (MMSE) detector is an effective technique for multiple access interference (MAI) suppression in CDMA system. It can operate completely without the knowledge of signature waveforms and received amplitudes when training sequences are available. However, the bandwidth consumption increased by training sequences should not be neglected especially in the badly deteriorated channel environment.

Consequently, the blind algorithms for the adaptive multiuser detector (MUD) have attracted much attention to improve the bandwidth efficiency. In [1], a linearly constrained constant modulus algorithm (LCCMA) detector based on the stochastic gradient descent (SGD) algorithm, which could achieve output performance the same as that of the MMSE receiver, was proposed. Yet there had never been investigations involving the convergence of LCCMA until Xu and Feng first presented [2], and a further exploration on this subject appeared in the later researches [3], [4]. In [5], a framework, which was called feedback approach, was first proposed to get the steady-state performance by bypassing the complexity caused by the time evolution analysis of the equalizer coefficients. Using the feedback approach, Whitehead derived the excess mean-square error (EMSE) performance of SGD-LCCMA blind adaptive MUD in direct-sequence code division (DS-CDMA) system for both static and time-varying channels in [6]. However, SGD-LCCMA fails in low convergence speed. To overcome that fault and capture the desired user in MUD immediately, the recursive least square (RLS) is available. An RLS approach to the CMA was applied in an adaptive beamforming structure in [7]. Nevertheless, there still exists opportunity to apply the RLS algorithm to the CMA for a blind adaptive MUD and quantify its corresponding performance.

Therefore, our research mainly focuses on the proposition of RLS-LCCMA for MUD and performance analysis. We introduce RLS algorithm into LCCMA in DS-CDMA system for better convergence speed, and further obtain the steady-state performance and tracking ability of RLS-LCCMA that have never been found. According to the EMSE analysis, a relationship is established between step size of SGD-LCCMA and forgetting factor of RLS-LCCMA in the static channel.

The rest of the paper is organized as follows. Section 2 outlines the system model and establishes the RLS-LCCMA. Section 3 is devoted to the derivation of the EMSE expressions in static and time-varying channel environments. Section 4 shows the simulation results. Finally, the conclusion is generalized in Section 5.