Space-time block codes based on precoding

We propose a space-time block coding framework based on precoding. The code design is aimed to the tradeoff between rate, diversity and complexity. Specifically, for P transmit antennas, our block codes are based on L distinct precoding matrices, where L less than or equal to P. We further propose a simple structure for the precoding matrices that are product of distinct permutation matrices and a diagonal unitary matrix, whose diagonal elements are design parameters. In particular, when L = P, the codewords are constructed as circulant matrices. And we explicitly give the expression of the eigenvalues of the error codeword matrix, derive the bounds for the coding gain. If the design parameters are chosen according to algebraic number theory, diversity advantage L can be guaranteed for the resulting codes. Our framework is also appealing on that simple decoding strategies can be applied.