Full-Diversity Codes for MISO Systems Equipped With Linear or ML Detectors

In this paper, a general criterion for space-time block codes (STBC) to achieve full diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas [multiple-input-single-output (MISO)]. Particularly, the STBC with Toeplitz structure satisfies this criterion, and therefore, enables full diversity. Further examination of this Toeplitz STBC reveals the following important properties: (1) the symbol transmission rate can be made to approach unity; (2) applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a nonvanishing determinant. In addition, if quadratic-amplitude modulation (QAM) is used as the signalling scheme, then for independent MISO flat-fading channels, the Toeplitz codes is proved to approach the optimal diversity-versus-multiplexing tradeoff with a zero-forcing (ZF) receiver when the number of channel uses is large. This is, so far, the first nonorthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when maximum-likelihood (ML) detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pairwise error probability.