Achieving the Full MIMO Diversity-Multiplexing Frontier with Rotation-Based Space-Time Codes∗

The recently established diversity-multiplexing frontier characterizes the highSNR tradeoff between the best possible robustness and throughput gains obtainable by employing multiple antennas for digital communication in fading environments. We focus on the case of two transmit and at least two receive antennas, and show that a sufficient condition for a family of codebooks indexed by rate to achieve the full diversity-multiplexing frontier is that the worst-case codeword difference determinant either does not decay to zero with rate or decays subexponentially. We further provide a constructive proof that the full frontier is achievable by codes of length two by developing families of rotation-based space-time block codes with rate-independent nonzero worst-case determinants. These determinants are optimized over reasonably rich code subspaces. By contrast, Gaussian codes of this length were known not to achieve the frontier, and earlier rotation-based codes were known only to achieve the extremal points of the frontier. Simulation results also verify that the new codes have sufficient coding gain to achieve error rates close enough to the infinite length code outage bound, and thus they provide superior performance to Alamouti’s orthogonal space-time block code at spectral efficiencies beyond about 4 b/s/Hz.