Design of minimum error-rate Cayley differential unitary space-time codes

The Cayley differential (CD) codes constitute a systematic way to construct differential unitary space-time modulations for noncoherent communication in multiple-antenna systems. The original CD codes are designed based on the criterion of maximizing the expected distance between codeword pairs. However, in practical systems, it is more sensible to design the codes according to the minimum error rate criterion. The main difficulty in such a design is that the error probability does not admit a closed-form expression and, thus, conventional optimization methods cannot be applied. In this paper, we formulate the minimum error-rate CD code design as an unconstrained stochastic optimization problem, and employ the stochastic approximation technique with gradient estimation to solve it. Simulation results show that codes generated by the proposed design procedure generally outperform the CD codes designed by maximizing the expected distance between codeword pairs and the Cayley threaded algebraic space-time codes that satisfy the full rank criterion. The new CD codes also enjoy better or comparable performance over other group based or nongroup designs.