On performance analysis and design criteria for trellis coded unitary space-time modulation

In this paper, the formulae for the pairwise error-event probability (PEP) and the bit error probability (BEP) of the trellis coded unitary space-time modulation (TC-USTM) in a piecewise constant Rayleigh fading channel are derived. These analyses demonstrate that a multi-input multi-output (MIMO) system with M transmit and N receive antennas, apart from a diversity gain of MN for the space-time signal design, a coding gain of l_min can also be obtained for the TC-USTM, where l_min is the length of the shortest error event. Additional coding gain comes from the product of the dissimilarities along the path of the shortest error event. These analyses suggest the design criteria of the TC-USTM encoder to obtain an optimal BEP performance. Propositions are also presented to satisfy these criteria. We demonstrate through simulations that these analyses are accurate, especially at sufficiently high signal to noise ratio (SNR).