Linear space-time codes optimized for successive cancellation decoding

We optimize linear space-time codes for the case when the receiver uses successive cancellation decoding. Specifically, the proposed codes minimize the perfect cancellation bound on word error probability, which assumes error-free cancellation of previously detected symbols. Assuming perfect cancellation, we prove that to minimize the error probability in each stage of decoding, the encoding matrix must have orthogonal columns, regardless of the channel matrix. Given the encoding matrix, the average of the perfect cancellation bound over the random channel matrix serves as an upper bound on word error probability. The bound is minimized by numerically optimizing the distribution of data rate and energy among the various inputs to the space-time code. Simulation results for a 4-input, 4-output Rayleigh fading channel show that, at 12 b/s/Hz, optimizing the data rate and energy allocations for a linear complex field code leads to a performance improvement of nearly 9 dB.