An augmented orthogonal code design for the noncoherent MIMO channel

This paper deals with the design and detection of structured orthogonal codes for the noncoherent multiple-input multiple-output (MIMO) channel. A code is proposed which increases the rate of so-called noncoherent orthogonal designs by taking a union of permuted noncoherent orthogonal codebooks. For symbols taken from a QPSK constellation, the permuted noncoherent orthogonal codebooks have a strong group structure. This structure can be exploited, using coding, to construct codebooks such that the minimum pairwise codeword distance is no less than that of a noncoherent orthogonal codebook. Furthermore, the codewords of the permuted noncoherent orthogonal codebook maintain the orthogonal structure of the original codebooks so that simple detection is still possible at the receiver. This approach results in an increased data rate without sacrificing the minimum distance. Simulation results are provided for a rate 1.25 bit per channel use (bpcu) permuted noncoherent orthogonal design. This code performs 2 dB worse than a rate 1 bpcu noncoherent orthogonal design with symbols from a QPSK constellation and 4 dB better than a rate 1.5 bpcu noncoherent orthogonal design with symbols from an 8-PSK constellation at a frame error rate of 10^-2.