Low-complexity iterative detection in coded linear systems

Abstract

Since the advent of Turbo codes, the concept of “Turbo” (or “iterative”) has been extensively applied in modern communication systems. An iterative detection and decoding receiver (or simply, an iterative receiver) typically consists of two local operators, namely an elementary signal estimator (ESE) for handling the channel effect and a decoder (DEC) for soft-input soft-output (SISO) decoding. Such a receiver can achieve impressive performance gain by refining the estimates during the iterative execution of the ESE and the DEC. In this thesis, we examine iterative principles on a generic coded linear system that may involve inter-symbol interference (ISI), multiple-access interference (MAI), crossantenna interference (CAI) or their combinations. We focus on the realization of the ESE since the DEC operation is well studied. The optimum realization of the ESE is possible in theory but may usually incur prohibitively high complexity in implementation. A low-complexity alternative is to follow the linear-minimum-meansquare- error (LMMSE) approach to the ESE that can provide an attractive tradeoff between performance and complexity. The LMMSE approach to the ESE may still be too computationally intensive especially when the ISI effect is involved. The well-known cyclic-prefix (CP) technique can be used to transform a linear system involving ISI into a circulant or block-wise circulant system. Based on the so-called equal-variance approximation, we propose a joint LMMSE frequency-domain-equalization (FDE) multiuser-detection algorithm that can be efficiently implemented even in the highly complicated multiuser multiple-input multiple-output (MIMO) ISI channels. The involved complexity (normalized per user and per symbol) is independent of the number of users, the number of transmit antennas and, more importantly, the channel memory length. A semi-analytical signal-to-noise-ratio (SNR) -variance evolution technique is developed for performance evaluation of an iterative LMMSE-FDE receiver. One attractive feature of the SNR-variance evolution is that the transfer function of the ESE has a simple analytic expression that can be evaluated for each channel realization online (i.e., during the evolution process) at a very low cost. Intensive numerical results demonstrate the accuracy of the proposed technique in various ISI, MIMO and multiuser environments. The SNR-variance evolution technique can be used not only for performance evaluation, but for performance optimization. Our first attempt is to investigate precoding for ISI channels, as inspired by the well-known fact that shaping the input spectrum can potentially improve the transmission efficiency in such channels. We realize spectrum shaping using cyclic precoder that can be incorporated into iterative LMMSE-FDE schemes without increasing the detection complexity. The precoder can be optimized for any predetermined forward-error-correcting (FEC) code based on the SNR-variance evolution. Analysis and numerical results demonstrate that considerable performance gain can be achieved by the optimized precoder. We further analyze iterative schemes from an information-theoretic point of view. We establish an area theorem for iterative schemes involving optimal or suboptimal local operators, based on which the achievable information rate of the LMMSE approaches can be quantified. We show that the information rate loss due to the suboptimality of the LMMSE estimation is not significant, especially in the relatively lowrate region. We also show that the extra performance loss incurred by the equalvariance approximation is marginal. This result is promising since the low-complexity LMMSE-FDE technique can be developed with near-capacity performance. We also consider optimizing the performance of iterative schemes using the aforementioned spectrum-shaping precoder. We show that the precoder can be optimized to maximize the achievable rate of the iterative scheme. Particularly, we show that, if circulant systems with iterative LMMSE-FDE are involved, the optimum precoder can be found using standard convex optimization tools. We also show that the water-filling precoder is near-optimum, yielding an attractive low-cost option for implementation. We finally consider the design of FEC code for approaching the performance limit of iterative LMMSE-FDE promised by our analysis. We use quadrature-phase-shiftkeying (QPSK) modulation for low-rate systems, and superposition coded modulation (SCM) for high-rate systems. Curve-matching irregular low-density parity-check (LDPC) codes are designed as the forward-error-control (FEC) codes. Numerical results show that the performance of the designed codes agrees well with the analysis.

Date of Award	16 Feb 2009
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Ping LI (Supervisor)