Complex Minkowski Reduction and a Relaxation for Near-Optimal MIMO Linear Equalization

First, this letter presents a Minkowski reduction algorithm working directly on complex lattices. Then, a relaxation is proposed to Minkowski criterion by restricting the search of basis vectors within sublattices whose dimensions are determined by an integer parameter
$\beta $
, and a reduction algorithm following the relaxed criterion is also developed. Simulation results show that when employed to assist linear equalization for multiple-input multiple-output systems, the proposed algorithms can achieve tremendous computational savings compared with the most efficient real-domain Minkowski reduction algorithm, without causing noticeable performance degradation.