An adaptive array code acquisition for direct-sequence/code-division multiple access (DS/CDMA) systems was recently proposed to enhance the performance of the conventional correlator-based method. The scheme consists of an adaptive spatial and an adaptive temporal filter, and can simultaneously perform beamforming and code-delay estimation. Unfortunately, the scheme uses a least-mean-square (LMS) adaptive algorithm, and its convergence is slow. Although the recursive-least-squares (RLS) algorithm can be applied, the computational complexity will greatly increase. In this paper, we solve the dilemma with a low-complexity conjugate gradient (LCG) algorithm, which can be considered as a special case of a modified conjugate gradient (MCG) algorithm. Unlike the original conjugate gradient (CG) algorithm developed for adaptive applications, the proposed method, exploiting the special structure inherent in the input correlation matrix, requires a low computational-complexity. It can be shown that the computational complexity of the proposed method is on the same order of the LMS algorithm. However, the convergence rate is improved significantly. Simulation results show that the performance of adaptive array code acquisition with the proposed CG algorithm is comparable to that with the original CG algorithm.

A reduced complexity multiple-input multiple-output (MIMO) equalizer with ordered successive interference cancellation (OSIC) is proposed for combating intersymbol interference (ISI) and cochannel interference (CCI) over frequency-selective multipath channels. It is developed as a reduced-rank realization of the conventional MMSE decision feedback equalizer (DFE). In particular, the MMSE weight vectors at each stage of OSIC are computed based on the generalized sidelobe canceller (GSC) technique and reduced-rank processing is incorporated by using the conjugate gradient (CG) algorithm for reduced complexity implementation. The CG algorithm leads to a best low-rank representation of the GSC blocking matrix via an iterative procedure, which in turn gives a reduced-rank equalizer weight vector achieving the best compromise between ISI and CCI suppression. With the dominating interference successfully cancelled at each stage of OSIC, the number of iterations required for the convergence of the CG algorithm decreases accordingly for the desired signal. Computer simulations demonstrate that the proposed reduced-rank MIMO DFE can achieve nearly the same performance as the full-rank MIMO MMSE DFE with an effective rank much lower than the dimension of the signal-plus-interference subspace.

This article addresses two issues. Firstly, the convergence property of conjugate gradient (CG) algorithm is investigated by a Chebyshev polynomial approximation. The analysis result shows that its convergence behaviour is affected by an acceleration term over the steepest descent (SD) algorithm. Secondly, a new CG algorithm is proposed in order to boost the tracking capability for time-varying parameters. The proposed algorithm based on re-initialising forgetting factor shows a fast tracking ability and a noise-immunity property when it encounters an unexpected parameter change. A fast tracking capability is verified through a computer simulation in a system identification problem.