When Should We Use Geometrical-Based MIMO Detection Instead of Tree-Based Techniques? A Pareto Analysis

The soft-output multiple-input multiple-output (MIMO) detection problem has been extensively studied, and a large number of heuristics and metaheuristics have been proposed to solve it. Unlike classical tree-search based detectors, geometrical heuristic algorithms involved two consecutive steps: (i) an exploration step based on the geometry of the channel matrix singular vectors; (ii) a local exploitation step is performed in order to obtain better final solution. In this paper, new enhancements for geometrical heuristics are introduced to significantly reduce the complexity in quadrature phase-shift keying (QPSK) and allow 16 quadrature amplitude modulation (QAM) capability through new exploration techniques. The performance-complexity trade-off between the new detector and two tree-based algorithms is investigated through Pareto efficiency. The Pareto framework also allows us to select the most efficient tuning parameters based on an exhaustive search. The proposed detector can be customized on the fly using only one or two parameters to balance the trade-off between computational complexity and bit error rate performances. Moreover, the Pareto fronts demonstrate that the new geometrical heuristic is especially efficient with QPSK since it provides a significant reduction in regards to the computational complexity while preserving good bit error rate (BER) performance and ensuring high flexibility.