  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
(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: a) The symbol transmission
rate can be made to approach unity. b) Applying the Toeplitz code to any
signalling scheme having nonzero distance between the nearest constellation
points results in a non-vanishing determinant. In addition, if QAM is used as
the signalling scheme, then for independent MISO flat fading channels, the
Toeplitz codes is proved to approach the optimal diversity-vs-multiplexing
tradeoff with a ZF receiver when the number of channel uses is large. This is,
so far, the first non-orthogonal STBC shown to achieve the optimal tradeoff for
such a receiver. On the other hand, when 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 pair-wise error probability.
