Infinity-norm sphere-decoding

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 l²-norm. It was, however, recently shown that using the l^infin-norm instead significantly reduces the VLSI implementation complexity of SD at only a marginal performance loss. These savings are due to a reduction in the length of the critical path and the silicon area of the circuit, but also, as observed previously through simulation results, a consequence of a reduction in the computational (algorithmic) complexity. The aim of this paper is an analytical performance and computational complexity analysis of l^infin-norm SD. For i.i.d. Rayleigh fading MIMO channels, we show that l^infin-norm SD achieves full diversity order with an asymptotic SNR gap, compared to l²-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^infin-norm SD.