Performance and Complexity Analysis of Infinity-Norm Sphere-Decoding

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

^¿
-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

^¿
-norm SD. For independent and identically distributed (i.i.d.) Rayleigh fading MIMO channels, we show that
l

^¿
-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

^¿
-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

^¿
-norm SD and show that it behaves fundamentally different from that of
l

²
-norm SD.