Linear Toeplitz Space Time Block Codes

In this paper we consider coherent flat fading wireless communication systems with multiple transmitter antennas and single receiver antenna (MISO). We propose a Toeplitz linear space time block code (STBC) that converts an original MISO flat fading channel into a Toeplitz virtual multiple inputs multiple outputs (MIMO) channel. We show that our proposed code has the following main features: (a) The symbol transmission rate is ${T-M+1\over T}$, where $M$ is the number of transmitter antenna and $T$ - is the number of channel uses $(T>M)$. (b) Linear receivers (zero-forcing and minimum mean square error) can extract full diversity. Moreover, when the channel coefficients are independent and the maximum likelihood (ML) detector is employed, our Toeplitz STBC minimizes the exact worst case average pair-wise error probability. (c) When channels are correlated, we design our Toeplitz STBC that minimizes the exact average worst case pair-wise error probability. By transforming this non-convex optimization problem into a convex one, the problem can be solved efficiently by employing an interior point method. In particular, when the design criterion in question is approximated by the Chernoff bound, we obtain a closed form solution. (d) Finally, for the independent MISO flat fading system, we prove that our proposed codes can approach the optimal diversity-vs-multiplexing tradeoff developed by Zheng and Tse with a linear zero-forcing receiver when the number of channel uses is large.