Optimized max-dmin precoder assuming maximum squared Euclidean weight-mapping and turbo detection

The concatenation of multiple-input multiple-output (MIMO) linear precoder with an outer forward error correction (FEC) encoder is investigated at the transmitter. Turbo detection is applied at the receiver for the decoding. The bit-interleaved codeword is considered to be grouped and mapped directly onto the received constellation thanks to a MIMO symbol mapper. We exploit the optimal maximum squared Euclidean weight (MSEW) mappings for two forms of max-d_min precoder to propose a novel precoder referred to as max-ℓ_min. The switching threshold between both forms is optimized by considering all received sequences whose binary mappings differ by exactly one bit and by first maximizing the minimum Euclidean distance within this set and then minimizing the number of pairs achieving it. Extrinsic information transfer (EXIT) chart is also used to validate the analysis. Simulation results show significant improvement, in terms of system error-rate performance, of the max-ℓ_min compared to the conventional max-d_min.