Optimum Linear Transmitter Design for MIMO Systems with Two QPSK Data Streams

We present the optimum design of a linear transmitter for a multi-input multi-output communication system when the input data consists of two QPSK streams and the receiver performs maximum likelihood detection. The transmitter design is optimal in the sense that it minimizes the worst-case pairwise error probability. We prove that the resulting linear transmitter constructs, as a function of the two input QPSK streams, a new signal constellation. Moreover, we show that this new signal constellation is such that the minimum distance among the points of the received constellation is maximized and, indirectly, the number of neighbors at minimum distance is also maximized.