Infinity-Norm Sphere-Decoding

TL;DR

This paper analyzes the performance and complexity of infinity-norm sphere decoding in MIMO systems, showing it achieves full diversity with reduced hardware complexity but exponential scaling in system size.

Contribution

It provides an analytical performance and complexity analysis of infinity-norm sphere decoding, including closed-form complexity expressions and behavior characterization.

Findings

Achieves full diversity order in Rayleigh fading MIMO channels.

Complexity scales exponentially with system size.

Behavior of tree pruning differs from l-2 norm SD.

Abstract

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.