Design of closed-loop space-time codes with MMSE receivers

In recent years, research on closed-loop STCs show that with the help of feedback, the achievable rate and/or the diversity order can further be improved in space-time coded systems. In this paper, we study on the optimal closed-loop STCs with low-complexity receivers and any amount of feedback. A unified framework for designing closed-loop STCs is firstly proposed by extending the conventional linear dispersion codes to the cases with feedback. Then a new design method is proposed, where the stochastic gradient descent algorithm is employed to obtain optimal set of LDC candidates particularly for spacetime coded systems with linear minimum mean square error (MMSE) receiver. The proposed method allows for flexible system parameters such as the number of transmit/receive antennas, modulated symbols and the length of codewords thus include most of the existing closed-loop STCs. Simulation results confirm the advantages of the newly-proposed design method of closed-loop STCs.