A new Hybrid Automatic Repeat reQuest (HARQ) combining scheme for a 4x4 Multiple Input Multiple Output (MIMO) system in invariant and variant fading channel conditions is proposed and analized. Based on the Extended Alamouti Quasi-orthogonal Space-Time Block Coding (Q-STBC), the use of the so-called Alternative Matrices for transmission, depending on the Channel State Information (CSI) received as feedback, is compared to other existing solutions.

Sign changes and permutations in the retransmission sequences allow reducing the interference while exploiting the spatial diversity to introduce some gain in the signal power. The best transmission order is selected by the Determinant Criterion, which optimizes the SNR in each receiver antenna to minimize the Bit Error Rate (BER) and maximize the throughput.

Studying the performance of a priori different alternatives, both analytically and empirically, several equivalents are found. Finally, the simulation results show that the proposed scheme achieves an improvement for the case of an invariant channel, but not for the time varying model, where the Auto-Regressive of order 1 (AR-i) is chosen for simplicity.