The concatenation of the multiple-input multiple-output (MIMO) linear precoder with an outer forward error correction (FEC) code at the transmitter is investigated in this paper. At the receiver side, the turbo detection is taken into account. It iteratively exchanges the extrinsic information between a soft-demapper and a FEC soft-decoder. We firstly propose a new precoder named FI1designed from an extrinsic information transfer (EXIT) chart analysis. The proposed precoder aims to optimize the iterative receiver convergence by maximizing the ending point I1of the soft-demapper EXIT function. For the sake of low-complexity, FI1is designed for two data streams MIMO transmission with 4-QAM only. Secondly, to cope with the higher data streams transmission, a global b = 2K data streams system is split into K two data streams subsystems. FI1is then applied at each subsystem. Finally, we propose a new algorithm to optimize the inter-subsystems power allocation by maximizing the I1of the global system.

Precoder optimization with full channel state information for finite alphabet signals over multiple-input multiple-output random channels is investigated in this paper. The precoder is represented by a product of power allocation matrix and constellation-forming matrix. There was an optimal algorithm introduced in the literature to globally maximize the channel mutual information by iteratively optimizing these two matrices. However, the computational complexity of the optimal algorithm is painfully high, especially when it is used with the high-order modulation and the high-data stream number. In this paper, we propose a novel sub-optimal low-complexity precoding algorithm and compare it with the optimal one. The new algorithm proceeds in two steps. First, the constellation-forming matrix is fixed in order to maximize the minimum Euclidean distance between the received symbols, which ensures high channel mutual information. Then, given the constellation-forming matrix, an iterative algorithm searches for the power allocation matrix that maximizes the channel mutual information. Since optimizing only one matrix instead of two, the new algorithm not only achieves a lower computational complexity but also avoids the use of initial values, which must be carefully selected for each channel and signal-to-noise ratio for fast convergence. Another advantage of the new algorithm is that the resulting precoder has a fixed form of received constellation thanks to the fixed constellation-forming matrix. This allows us to optimize the symbol mapping on the received constellation. Simulation results show that the proposed low-complexity precoder achieves error-rate performance that is close to performance of the optimal one when the conventional mapping is used. In addition, the new precoder used with optimized mapping at received constellation shows significant error-rate performance improvement.

In this paper, we investigate the concatenation of the multiple input multiple output (MIMO) max-dminlinear precoder with an outer forward error correction (FEC) code at the transmitter. At the receiver side, the turbo equalization is taken into account, which iteratively exchanges the extrinsic information between a minimum mean square error interference canceller (MMSE IC) and a FEC decoder. The analysis done by extrinsic information transfer (EXIT) chart shows that a higher mutual information (MI) at the convergence state of the turbo equalization is observed thanks to the linear precoder. In addition, we exploit this property to propose a new precoder named max-dmin-mod. Numerical simulations are in accordance with the theoretical analysis, which exhibits a significant improvement of the error-rate of the turbo equalization as well as a significant gain of max-dmin-mod compared to original max-dminprecoder.