Maximum-Likelihood Decoding for Nonorthogonal and Orthogonal Linear Space–Time Block Codes

It is a general consensus that an orthogonal space-time block code can achieve full diversity, and due to its orthogonal nature, the multiple-input-multiple-output (MIMO) maximum-likelihood (ML) decoding metrics can be decoupled into single-input-single-output (SISO) ML metrics based on linear processing at the receiver, thus greatly reducing the decoding complexity. In fact, nonorthogonal codes also currently exist that can achieve better symbol-error-rate performance without rate reduction and complexity increase for correlated fading channels. In this paper, we show by detailed derivations that nonorthogonal linear space-time block codes can also be decoded by ML decoupling through receiver linear processing. Our derived expressions for the decoupled ML metrics automatically contain the design information for the receiver linear processors.