Space-time diversity systems based on linear constellation precoding

We present a unified approach to designing space-time (ST) block codes using linear constellation precoding (LCP). Our designs are based either on parameterizations of unitary matrices, or on algebraic number-theoretic constructions. With an arbitrary number of N_t transmit- and N_r receive-antennas, ST-LCP achieves rate 1 symbol/s/Hz and enjoys diversity gain as high as N_tN_r over (possibly correlated) quasi-static and fast fading channels. As figures of merit, we use diversity and coding gains, as well as mutual information of the underlying multiple-input-multiple-output system. We show that over quadrature-amplitude modulation and pulse-amplitude modulation, our LCP achieves the upper bound on the coding gain of all linear precoders for certain values of N_t and comes close to this upper bound for other values of N_t, in both correlated and independent fading channels. Compared with existing ST block codes adhering to an orthogonal design (ST-OD), ST-LCP offers not only better performance, but also higher mutual information for N_t>2. For decoding ST-LCP, we adopt the near-optimum sphere-decoding algorithm, as well as reduced-complexity suboptimum alternatives. Although ST-OD codes afford simpler decoding, the tradeoff between performance and rate versus complexity favors the ST-LCP codes when N_t, N_r, or the spectral efficiency of the system increase. Simulations corroborate our theoretical findings.