# Optimum Low-Complexity Decoder for Spatial Modulation

## TL;DR

This paper introduces a low-complexity detection algorithm for spatial modulation called m-M, which significantly reduces decoding complexity while maintaining maximum-likelihood performance across various channel knowledge scenarios.

## Contribution

The paper proposes the m-M algorithm, a novel search method for SM decoding that reduces complexity up to 94% compared to existing methods, with analysis under different CSIR conditions.

## Key findings

- Reduces decoding complexity up to 94% in perfect CSIR.
- Maintains ML performance with lower complexity.
- Effective under various channel estimation error scenarios.

## Abstract

In this paper, a novel low-complexity detection algorithm for spatial modulation (SM), referred to as the minimum-distance of maximum-length (m-M) algorithm, is proposed and analyzed. The proposed m-M algorithm is a smart searching method that is applied for the SM tree-search decoders. The behavior of the m-M algorithm is studied for three different scenarios: i) perfect channel state information at the receiver side (CSIR), ii) imperfect CSIR of a fixed channel estimation error variance, and iii) imperfect CSIR of a variable channel estimation error variance. Moreover, the complexity of the m-M algorithm is considered as a random variable, which is carefully analyzed for all scenarios, using probabilistic tools. Based on a combination of the sphere decoder (SD) and ordering concepts, the m-M algorithm guarantees to find the maximum-likelihood (ML) solution with a significant reduction in the decoding complexity compared to SM-ML and existing SM-SD algorithms; it can reduce the complexity up to 94% and 85% in the perfect CSIR and the worst scenario of imperfect CSIR, respectively, compared to the SM-ML decoder. Monte Carlo simulation results are provided to support our findings as well as the derived analytical complexity reduction expressions.