Space-time D-block codes via the virtual MIMO channel representation

We apply the recently introduced virtual channel representation to the problem of space-time coding for correlated multiple-input multiple-output (MIMO) channels. The virtual channel representation clearly reveals the essential degrees of freedom in correlated MIMO channels and the corresponding statistical channel structure. Coding design criteria for general correlated channels are derived from pairwise error probability analysis, which reveal the effect of channel statistics and codeword properties on code performance. We focus on the K-diagonal model for correlated channels whose nonvanishing elements correspond to K diagonals of the virtual channel matrix. The K-diagonal model can be motivated by physical scattering considerations or as a low-dimensional approximation to the channel matrix that serves as a building block for general correlated channels. Space-time D-block codes that attain D-level diversity (related to K) per receive dimension are constructed using the theory of space-time block codes. Compared with space-time block codes, identical performance but with significantly smaller delay and complexity can be achieved by matching space-time D-block codes to the K-diagonal channel structure. Our construction also facilitates a natural tradeoff between rate and diversity by decomposing the original channel into several parallel virtual K-diagonal subchannels. Simulation results demonstrate the excellent performance of the proposed techniques.