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In recent years, soft iterative decoding techniques have been shown to greatly improve the bit error rate performance of various communication systems. For multiple antenna systems, however, it is not clear what is the best way to obtain the soft-information required of the iterative scheme with low complexity. In this paper, we propose a modification of the Fincke-Pohst (sphere decoder) algorithm to estimate the MAP probability of the received symbol sequence. The new algorithm solves a nonlinear integer leastsquares problem and, over a wide range of rates and SNRs, has polynomial-time (often cubic) complexity. The performance of the algorithm, combined with convolutional, turbo, and LDPC codes is demonstrated on several multiple antenna channels.

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A recently proposed method for communicating with multiple antennas over block fading channels is unitary spacetime modulation (USTM), so-called because the transmitted signals form a matrix with orthonormal columns. Since channel knowledge is not required at the receiver, USTM schemes are suitable for use on wireless links where channel tracking is undesirable or infeasible. Recent results have shown that, if suitably designed, USTM schemes can achieve full channel capacity at high SNR. While all this is well recognized, what is not clear is how to generate good performing constellations of (non-square) unitary matrices, that lend themselves to efficient encoding/decoding. The schemes proposed so far either exhibit poor performace, especially at high rates, or have no efficient decoding algorithms. In this paper, we propose to use the Cayley transform to design USTM constellations. This work is a generalization, to the non-square case, of the Cayley codes that have been proposed for differential USTM. The codes are designed based on an information-theoretic criterion, and lend themselves to polynomial-time (often cubic) near-maximum-likelihood decoding using a sphere decoding algorithm.

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