Lossless Size Reduction for Integer Least Squares with Application to Sphere Decoding

TL;DR

This paper introduces a lossless size reduction technique for integer least squares problems that enhances sphere decoding efficiency, especially at low SNRs, while maintaining maximum likelihood detection performance.

Contribution

It derives the minimum achievable complexity for ML detection, proves the existence of lossless size reduction at all SNRs, and proposes a new detection method leveraging this reduction.

Findings

Lossless size reduction enables ML detection without node visits.

The proposed method significantly reduces computational complexity.

Theoretical results are validated through numerical simulations.

Abstract

Minimum achievable complexity (MAC) for a maximum likelihood (ML) performance-achieving detection algorithm is derived. Using the derived MAC, we prove that the conventional sphere decoding (SD) algorithms suffer from an inherent weakness at low SNRs. To find a solution for the low SNR deficiency, we analyze the effect of zero-forcing (ZF) and minimum mean square error (MMSE) detected symbols on the MAC and demonstrate that although they both improve the SD algorithm in terms of the computational complexity, the MMSE point has a vital difference at low SNRs. By exploiting the information provided by the MMSE method, we prove the existence of a lossless size reduction which can be interpreted as the feasibility of a detection method which is capable of detecting the ML symbol without visiting any nodes at low and high SNRs. We also propose a lossless size reduction-aided detection method which achieves the promised complexity bounds marginally and reduces the overall computational complexity significantly, while obtaining the ML performance. The theoretical analysis is corroborated with numerical simulations.