Soft-decision equalization techniques for frequency selective MIMO channels

Multi-input multi-output (MIMO) technology is an emerging solution for high data rate wireless communications. We develop soft-decision based equalization techniques for frequency selective MIMO channels in the quest for low-complexity equalizers with BER performance competitive to that of ML sequence detection. We first propose soft decision equalization (SDE), and demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered, and linear in the signal constellation size. Building upon the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Motivated by the need for low-complexity receiver processing, we further present an alternative low-complexity soft-decision equalization approach for frequency selective MIMO communication systems. With the help of iterative processing, two detection and estimation schemes based on second-order statistics are harmoniously put together to yield a two-part receiver structure: local multiuser detection (MUD) using soft-decision Probabilistic Data Association (PDA) detection, and dynamic noise-interference tracking using Kalman filtering. The proposed Kalman-PDA detector performs local MUD within a sub-block of the received data instead of over the entire data set, to reduce the computational load. At the same time, all the inter-ference affecting the local sub-block, including both multiple access and inter-symbol interference, is properly modeled as the state vector of a linear system, and dynamically tracked by Kalman filtering. Two types of Kalman filters are designed, both of which are able to track an finite impulse response (FIR) MIMO channel of any memory length. The overall algorithms enjoy low complexity that is only polynomial in the number of information-bearing bits to be detected, regardless of the data block size. Furthermore, we introduce two optional performance-enhancing techniques: cross- layer automatic repeat request (ARQ) for uncoded systems and code-aided method for coded systems. We take Kalman-PDA as an example, and show via simulations that both techniques can render error performance that is better than Kalman-PDA alone and competitive to sphere decoding. At last, we consider the case that channel state information (CSI) is not perfectly known to the receiver, and present an iterative channel estimation algorithm. Simulations show that the performance of SDE with channel estimation approaches that of SDE with perfect CSI

Combined Semi-definite Relaxation and Sphere Decoding Method for Multiple Antennas Systems

In this paper, a new detection method which combines the semi-definite programming relaxation (SDR) with the sphere decoding (SD) is proposed for 256-QAM multiple-input multiple-output (MIMO) system. In this method, the SDR algorithms are engaged to obtain a primary result. Then, a hyper-sphere is constructed which is centered at the received signal and has its radius equals to the Euclidean distance between the primary result and the received signal. Finally, the SD searching strategy is employed to determine the final result which satisfies the principle of maximum likelihood. Simulation results show that the proposed method can offer optimum BLER performance as well as lower computational complexity than the conventional SD detectors. © 2011 IEEE.published_or_final_versio

Application of semi-definite relaxation to multiuser detection in a CDMA context

- De nombreuses problématiques de traitement du signal se ramènent à la résolution d'un problème d'optimisation combinatoire. Récemment, la Relaxation Semi-Définie (SDR) s'est révélée être une approche prometteuse en la matière, permettant une relaxation réaliste de problèmes NP-complets. Dans cet article, nous présentons un algorithme efficace pour résoudre SDR avec une complexité réduite. L'objet principale est d'étudier des méthodes de programmation non linéaires qui reposent sur un changement de variable consistant à remplacer la variable symétrique définie positive X intervenant dans SDR par une variable rectangulaire V à travers la décomposition X =V TV. Des résultats récents sur les rangs de matrices de corrélations extrémales permettent de conduire à un algorithme de faible complexité avec une perte négligeable en matière de performances. Des résultats très encourageants ont été obtenus pour résoudre des problèmes d'optimisation combinatoire de grande dimension, tel que celui qui intervient dans la détection multi utilisateur en mode CDMA

Polynomial Moment Relaxation for MIMO Detection

We develop a polynomial-time detector for maximum likelihood (ML) detection over multiple-input multiple-output (MIMO) channels. Our proposed polynomial moment relaxation (PMR) detection gives a unified framework for MIMO detection with relaxation including semi-definite relaxation as a special case. We give three approaches to replace a finite alphabet constraint with a polynomial constraint. Since both the objective function and the constraints are polynomials, we use a moment relaxation approach by applying the dual theories of moments and positive polynomials solvable by semi-definite programming. With different relaxation orders, our PMR achieve a flexible trade-off between complexity and performance

A Family of Likelihood Ascent Search Multiuser Detectors: an Upper Bound of Bit Error Rate and a Lower Bound of Asymptotic Multiuser Efficiency

In this paper, the bit error performance of a family of likelihood ascent search (LAS) multiuser detectors is analyzed. An upper bound on the BER of any LAS detector is obtained by bounding the fixed point region with the worst initial detector. The concept of indecomposable errors developed by Verdu is applied to tighten the upper bound. In a special instance, the upper bound is reduced to that for all the local maximum likelihood detectors. The upper bound is comparable with that of the optimum detector obtained by Verdu. A lower bound on the asymptotic multiuser efficiency (AME) is then obtained. It is shown that there are nontrivial CDMA channels such that a LAS detector can achieve unit AME regardless of user number. The AME lower bound provides a means for further seeking a good set of spreading sequences and power distribution for spectral and power efficient CDMA.Comment: To appear in IEEE Trans. on Communication

Beamforming in Wireless Networks

This chapter is about the beamforming approach in wireless 5G networks, which involves communication between multiple source-destination pairs. The relays can be multiple-input multiple-output (MIMO) and/or distributed single-input single-output (SISO), and full channel state information of source-relays and relay-destinations are assumed to be available. Our design consists of a two-step amplify-and-forward (AF) protocol. The first step includes signal transmission from the sources to the relays, and the second step contains transmitting a version of the linear precoded signal to the destinations. Beamforming is investigated only in relay nodes to reduce end user’s hardware complexity. Accordingly, the optimization problem is defined to find the relay beamforming coefficients that minimize the total relay transmit power by keeping the signal-to-interference-plus-noise ratio (SINR) of all destinations above a certain threshold value. It is shown that this optimization problem is a non-convex, and can be solved efficiently