Trace-Orthonormal Full Rate Full Diversity Linear Triangular Cyclotomic Space-Time Codes Minimizing Worst Case Pair- Wise Error Probability

We consider the flat fading wireless link where the number of transmitter antennas is greater than the number of receiver antennas and the channel is known to the receiver, For such systems, the currently available linear space-time block codes provide full rate and full diversity, but cannot guarantee that the optimal coding gain is achieved. In this paper, by taking advantage of delay we propose the trace-orthonormal full rate full diversity linear triangular cyclotomic space-time block codes, which actually is a generalization of the linear diagonal space-time block code. A universal lower bound on the worst case average pair-wise error probability is derived for any linear space-time block code. Particularly when the number of the transmitter antennas is equal to $2^{{m}}$, we prove that our proposed code minimizes the worst case average pair-wise error probability of the maximum likelihood detector for $M$-ary Quadrature Amplitude Modulation (QAM). Therefore. in this case, it achieves the optimal coding gain.