Exact ML Criterion Based on Semidefinite Relaxation for MIMO Systems

In this letter, we propose an exact maximum likelihood (ML) criterion based on semidefinite relaxation (SDR) in multiple-input multiple-output systems. Although a conventional SDR criterion for determining whether a symbol is the ML solution exists, its results cannot be guaranteed when noise is present. In place of the conventional criterion's positive semidefinite (PSD) discriminant, we propose a new, exact ML criterion based on the condition that all diagonal values are positive (PDV), a simple characteristic and necessary condition of PSD. The proposed criterion has a lower calculation complexity for testing than does a PSD and can ensure that the ML solution is always satisfactory.

I. Introduction

Maximum likelihood (ML) detection in multiple-input multiple-output (MIMO) systems is a well-known NP-hard problem for which much effort has gone into developing an efficient implementation algorithm. Sphere decoding (SD) [1] is the well-known efficient method for optimal ML detection; however, because it has exponentially increasing complexity, SD is only efficient for small antenna systems [2]. Even though an improved fixed-complexity algorithm has been proposed [3], it still requires high calculational complexity owing to complex pre-processing and the need to perform Euclidean distance evaluation at every node.