An efficient, low-complexity, soft-output detector for general lattices is presented, based on their Tanner graph (TG) representations. Closest-point searches in lattices can be performed as nonbinary belief propagation on associated TGs; soft-information output is naturally generated in the process; the algorithm requires no backtrack (cf. classic sphere decoding), and extracts extrinsic information. A lattice's coding gain enables equivalence relations between lattice points, which can be thereby partitioned in cosets. Total and extrinsic a posteriori probabilities at the detector's output further enable the use of soft detection information in iterative schemes. The algorithm is illustrated via two scenarios that transmit a 32-point, uncoded super-orthogonal (SO) constellation for multiple-input multiple-output (MIMO) channels, carved from an 8-dimensional nonorthogonal latticeD4⊕D4: it achieves maximum likelihood performance in quasistatic fading; and, performs close to interference-free transmission, and identically to list sphere decoding, in independent fading with coordinate interleaving and iterative equalization and detection. Latter scenario outperforms former despite absence of forward error correction coding-because the inherent lattice coding gain allows for the refining of extrinsic information. The lattice constellation is the same as the one employed in the SO space-time trellis codes first introduced for 2 × 2 MIMO by Ionescu et al., then independently by Jafarkhani and Seshadri. Algorithmic complexity is log-linear in lattice dimensionality versus cubic in classic sphere decoders.

In this correspondence, first-tier indirect (direct) discernible constellation expansions are defined for generalized orthogonal designs. The expanded signal constellation, leading to so-called super-orthogonal codes, allows the achievement of coding gains in addition to diversity gains enabled by orthogonal designs. Conditions that allow the shape of an expanded multidimensional constellation to be preserved at the channel output, on an instantaneous basis, are derived; this property, referred to as fading resilience, is first discussed in the context of quasi-static fading, then generalized to coordinate interleaved transmissions for rapid fading. In both cases - and despite of piecing together (in the latter case) a constellation point as a result of coordinate deinterleaving - the channel alters neither the relative distances nor the angles between signal points in a fading-resilient signal constellation. It is shown that nonorthogonal MIMO constellations having a geometric structure that is resilient to fading do exist, and their further study is warranted.

The continued relevance of the Euclidean distance in (flat) fading scenarios renders meaning to distance preserving properties for codes designed for fading channels. Geometrical uniformity can shed more light on the structure of various techniques for jointly encoding across multiple transmit antennas, and can assist in the design of, or systematic search for, better coding schemes. In this correspondence, a family of space-time codes introduced by Ionescu et al. is treated as signal space codes, then proved to be generalized coset codes, and thereby geometrically uniform. It is then shown that geometrical uniformity does remain meaningful in fading channels, for an optimally designed space-time code.

A novel method for performing predictive closed-loop power control is used to illustrate the predictability of uplink channels from downlink channels in a frequency division duplex (FDD) wireless link. In an uplink power control scenario, the proposed scheme performs uplink prediction using downlink-derived (linear) predictor coefficients. Essentially, the lack of correlation between the fading processes on uplink and downlink (due to FDD and frequency selective fading) is circumvented by using the uplink fading history, together with a set of link-independent, autoregressive (AR) coefficients. An AR model is used to formally describe the frequency selective fading process on either link, regardless of the number of Rayleigh paths. It is also proven that the relevant AR coefficients are common to both links, up to a proper normalization, irrespective of whether the number of paths on the uplink differs from that on the downlink. Both an uncoded and a coded system are simulated, and their performance results are compared, on equal grounds, with those of the corresponding nonpredictive systems.

Complex, rate one, orthogonal block space-time codes (STCs) exist only for two transmit antennas and were proposed by Alamouti (1998). Designing rate-one block STCs for more than two transmit antennas implies giving up orthogonality. For more than two transmit antennas a class of rate one block STCs with a controlled number of interference terms per detected symbol is presented. Conditions that link the matrix formulation of the receive equation to the matrix formulation of a multiuser detection scheme are discussed. The block STCs design problem is closely related to the class of linear real Hadamard codes.

It is shown that the separation between space-time code matrices can be described in terms of a metric of Euclidean type, which is defined via the singular values of difference code matrices, and arises naturally from a minimization of the pairwise error probability. Essentially, the distance between complex space-time code matrices is the Euclidean distance between the respective - demultiplexed and concatenated - transmit antenna streams, expressed in terms of the structure inherent to the multiple antenna arrangement. It is further shown that the determinant criterion can be strengthened, in a manner that not only suggests an optimum space-time code matrix structure, but also outlines the central role played by the Euclidean distance in quasi-static fading. Theorem 5 - which claims that in order to optimize the product distance one must optimize the Euclidean distance -establishes a close interdependence between product and Euclidean distances; it thereby links the performance determining factors in quasi-static and independent fading, and rigorously establishes the relevance of combining space-time coding and modulation in fading environments. A multidimensional space-time constellation for two transmit antennas, and its coset partitioning-based on traces of differences between constellation matrices-are described. Example codes constitute the first reporting of a space-time coded modulation scheme for fading channels, whereby a space-time constellation is partitioned in cosets.

A sub-class of space-time codes, defined via compliance with a new criterion of optimality, is introduced. A new distance between two codewords is defined and leads to new criteria for code design. It is shown that, unlike the non-Euclidian metrics currently in use, the new distance measure is a true metric, its square has a useful additive property and, in itself, preserves the traditional form of the upper bound to the probability of mistaking two codewords, as encountered in the union bound. The resulting new criteria for space-time code design are presented.