Low complexity affine MMSE detector for iterative detection-decoding MIMO OFDM systems

Iterative turbo processing between detection and decoding shows near-capacity performance on a multiple-antenna system. Combining iterative processing with optimum front-end detection is particularly challenging because the front-end maximum a posteriori (MAP) algorithm has a computational complexity that is exponential. Sub-optimum detector such as the soft interference cancellation linear minimum mean square error (SIC-LMMSE) detector with near front-end MAP performance has been proposed in the literature. The asymptotic computational complexity of SIC-LMMSE is O(n_t ²n_r + n_tn_r ³ + n_tM_c2^Mc) per detection-decoding cycle where n_t is number of transmit antenna, nr is number of receive antenna, and Mc is modulation size. A lower complexity detector is the hard interference cancellation LMMSE (HIC-LMMSE) detector. HIC-LMMSE has asymptotic complexity of O(n_t ²n_r + n_tM_c2^Mc) but suffers extra performance degradation. In this paper, two front-end detection algorithms are introduced that not only achieve asymptotic computational complexity of O(n_t ²n_r + n_tn_r ² [Gamma (beta) + 1] + n_tM_c2^Mc) where Gamma(beta) is a function with discrete output {-1, 2, 3, ...,n_t} and O(n_tM_c2^Mc) respectively. Simulation results demonstrate that the proposed low complexity detection algorithms offer exactly same performance as their full complexity counterpart in an iterative receiver while being computational more efficient.

I. Introduction

Ever since Berrou and Glavieux published their landmark paper on iterative decoding between two parallel concatenated convolutional codes (turbo-codes) [1], [2], it has been generally accepted that iterative (turbo) processing techniques have great value. As pointed out in [3] the “Turbo Principle” not only can be used with traditional concatenated channel coding schemes, but also generally applies to many detection-decoding algorithms. Of late, multiple-input multiple-output (MIMO) systems have received tremendous amounts of attention due to the information theoretic studies done by Telatar, Foschini and Gans [4], [5]. To approach channel capacity in a computationally efficient manner, it seems quite natural to apply the “Iterative (Turbo) Paradigm” to MIMO systems. Therefore, many of the aforementioned iterative detection-decoding algorithms have successfully been generalized to MIMO enviroment [6]–[9], especially multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems [10].