Geometrical Detection Algorithm for MIMO Systems

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The channel capacity and error-rate performance of MIMO systems could be improved by increasing the number of transmit antennas and receive antennas and the size of constellation used for modulation (Foschini and Gans, 1998). A main bottleneck that restricts the practical application of MIMO system is the unsatisfactory performance of the decoding algorithms, due to either high computational complexity required or poor symbol error-rate (SER) performance. Maximum-likelihood (ML) decoding which employs an exhaustive search strategy under the minimum Euclidean-distance principle can exploit all the available diversity and provide the optimum SER performance. However, its complexity increases exponentially with the number of antennas and the size of constellation used. Thus, for many cases, it is impractical to implement. Several sub-optimum decoding algorithms such as equalization-based zero-forcing (ZF) and minimum-mean-square-error (MMSE) detectors and nulling-and-cancelling detectors (NC) have been proposed for MIMO systems (Paulraj, Nabar and Gore, 2003). Although their computation complexities are dramatically less, these decoding algorithms have severe degradations in SER performances. Sphere decoding (SD) (Viterbo and Boutros, 1999) is another search-based algorithm. Unlike the exhaustive search engaged in ML decoding, SD confines the searching zone to be inside some hyper sphere constructed in the space spanned by the received lattice points. It can offer optimum SER performance with reasonable complexity. Several searching strategies such as Fincke-Pohst (Fincke and Pohst, 1985) and Schnorr-Euchner (Schnorr and Euchner, 1994) have been developed to further improve the searching efficiency in SD. Since the minimum Euclidean-distance principle could result in an optimum SER performance, the purpose of this chapter is to introduce another perspective of reconsidering this principle from the transmit lattice space. In the space spanned by the transmit lattice points, the Euclidean distance in ML decoding is found to be related to a series of concentric hyper ellipsoids. Searching the lattice point with the minimum Euclidean distance from the received signal vector is equivalent to searching the lattice point that is passed through by the smallest hyper ellipsoid. Decoding algorithms following this perspective are often called geometrical detection (Artes, Seethaler and Hlawatsch, 2003). In this Chapter, the geometrical analysis of signal decoding for MIMO channels is presented. Then, the ellipsoid searching decoding algorithm (Shao, Cheung and Yuk, 2009) is described. It is an add-on detection algorithm to standard suboptimal detection schemes