Soft Input Soft Output MMSE-SQRD Based Turbo Equalization for MIMO-OFDM Systems under Imperfect Channel Estimation

Abstract

In this paper, a turbo equalization scheme for MIMO-OFDM systems under imperfect channel estimation based on soft-input soft-output (SISO) minimum mean-square error (MMSE) sorted QR decomposition (SQRD) is proposed. A turbo structure consists of a SISO detector and a SISO decoder where extrinsic information is exchanged between the two SISO modules. Turbo equalization schemes are preferable in practical communication systems due to their good performance and acceptable computational complexity. MMSE-SQRD based SISO detection derives from SISO MMSE detection, and successive interference cancellation (SIC) is performed using a posteriori information obtained from previous detected symbols. Compared to SISO MMSE detection, MMSE-SQRD based SISO detection is of low complexity but has significant bit error rate (BER) performance enhancement. However, the derivation of the MMSE-SQRD based SISO detection scheme is under perfect knowledge of channel information at receivers. When channel estimation errors are presented, it has been pointed out that the system performance will degrade. In this paper, we studied this practical issue, and proposed the SISO MMSE-SQRD based turbo equalization under imperfect channel estimation. We first model the channel estimation error as added random Gaussian noise over the channel estimation matrix; based on that, we rederive the SISO MMSE detection for the data, and then redefine the extended channel matrix and receive vector by taking into account of channel estimation errors; after that, the SQRD algorithm is adjusted in accordance; MMSE-SQRD based data detection algorithm is finally performed. Numerical simulation results show that the proposed SISO MMSE-SQRD based turbo equalization for MIMO-OFDM systems under imperfect channel estimation outperforms the traditional MMSE based SISO detection with imperfect channel estimation in terms of BER performance and computational complexity.

MMSE‐based iterative processing with imperfect channel and parity check in MIMO systems

“…Multiple‐input multiple‐output (MIMO) systems have the advantages of high spectrum and energy efficiency due to the spacial diversity and multiplexing gain over single antenna systems [1–13]. MIMO techniques have been successfully applied to current mobile cellular networks [6–8], underwater acoustic communication systems [9, 10], and vehicular communications [11]. By extending the MIMO system from a small scale to a large scale, the potential spectrum and energy efficiency can be boosted in orders of magnitude [14–18].…”

“…The employment of turbo processing techniques in MIMO systems has been well investigated. It has also been demonstrated that with iterative processing, a simple equaliser can eventually approach the system bit error rate (BER) performance of the optimal equalisers [1, 2, 6–10, 19–28]. Therefore, most studies have focused on the design of low complexity and fast convergence turbo equaliszers.…”

“…Turbo equalisation schemes for single‐carrier frequency domain equalisation systems are studied in [10, 28], where the low‐complexity turbo equalisation schemes in frequency domain achieve high robustness compared to the time domain equalisation schemes. A class of QR decomposition‐based turbo equalisation schemes has been studied in [2, 6, 13, 21]. By using the QR decomposition algorithms, an upper triangular matrix is obtained; hence, the original estimation solutions can be obtained using the successive detection method [29].…”

“…Second, channel estimation error is inevitable since the channel is contaminated by noise. Therefore, taking into account channel estimation error in the design of turbo equalisation schemes is significant [1, 6, 7, 32–36]. Nevertheless, many studies assume perfect channel knowledge in the development and this assumption is usually adopted in massive MIMO scenarios [20, 22–24, 37].…”

“…Another strategy is to treat the channel estimation error as an independent component from the channel estimate. The results in [6, 7] demonstrate the performance improvement over the conventional one. Recently, we propose a new turbo equalisation scheme conditioned on channel estimate for MIMO MMSE receivers [1].…”