Orthogonal Block Code Design for Frequency-Selective Multiple Antenna Channels

Orthogonal Space-Time Block Codes (OSTBCs) have several desirable properties for delay limited communication over a coherent narrowband $({}^{\square} {\rm at})$ fading multiple antenna channel. In particular. they provide full diversity, and maximum likelihood detection can be achieved via linear processing and symbol-by-symbol detection. As a result, the maximal symbol rate and minimal latencies of OSTBCs have been well studied. In this paper, we construct orthogonal block codes for frequency-selective multiple antenna channels, and study their symbol rate and latency properties. Our code construction is based on direct application of the orthogonality constraints. This enables us to show that the maximum symbol rate of an orthogonal block code for a channel with memory length $L$ is $1/L$ times the maximum rate of an OSTBC for the same antenna configuration. Orthogonal codes that achieve this maximal rate can be simply constructed via the Kronecker product of a rate maximal OSTBC with an identity matrix of size $L$. This Kronecker design scheme can also be applied to construct orthogonal block codes for frequency-selective channels with other desirable properties. such as minimal latency.