Infinity-Norm Sphere-Decoding
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The most promising approaches for efficient detection in multiple-input multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The conventional (and optimum) norm that is used to conduct the tree traversal step in SD is the l-2 norm. It was, however, recently observed that using the l-infinity norm instead reduces the hardware complexity of SD considerably at only a marginal performance loss. These savings result from a reduction in the length of the critical path in the circuit and the silicon area required for metric computation, but are also, as observed previously through simulation results, a consequence of a reduction in the computational (i.e., algorithmic) complexity. The aim of this paper is an analytical performance and computational complexity analysis of l-infinity norm SD. For i.i.d. Rayleigh fading MIMO channels, we show that l-infinity norm SD achieves full diversity order with an asymptotic SNR gap, compared to l-2 norm SD, that increases at most linearly in the number of receive antennas. Moreover, we provide a closed-form expression for the computational complexity of l-infinity norm SD based on which we establish that its complexity scales exponentially in the system size. Finally, we characterize the tree pruning behavior of l-infinity norm SD and show that it behaves fundamentally different from that of l-2 norm SD.
Submitted to IEEE Transactions on Information Theory, Nov. 2008 (paper was presented in part at IEEE ISIT 2008, Toronto, ON, Canada, July 2008)
Submitted to IEEE Transactions on Information Theory, Nov. 2008 (paper was presented in part at IEEE ISIT 2008, Toronto, ON, Canada, July 2008)