Maximum Likelihood Detection With a Closed-Form Solution for the Square QAM Constellation

A low complexity maximum likelihood (ML) detection method is proposed for the square quadrature amplitude modulation (QAM) constellation. In order to reduce the implementation complexity of ML detection, set-partition, subset-selection, and subset-shift are recursively applied to the square QAM constellation. The estimated square QAM symbol is finally given in a closed form as a function of the received signal and the estimated channel. Complexity analysis and numerical simulation confirm that the proposed detection method reduces the implementation complexity substantially and achieves exactly the same performance as the conventional ML detection irrespective of the channel estimation error.

I. Introduction

Maximum likelihood (ML) is a non-linear symbol detection method that has been used for optimal symbol detection in various engineering fields. Especially, its importance has been emphasized in wireless communication systems [1]–[3]. The complexity of the conventional ML detection is proportional to the number of the detection candidate symbols. Therefore, given a large symbol constellation, the application of ML detection appears to be impractical even with a single-input single-output data transmission system. In [4], a low complexity ML detection based on the concept of set-partition and subset-selection was suggested for estimating the square quadrature amplitude modulation (QAM) symbols. Although the detection method in [4] reduced the implementation complexity of ML detection considerably, it still required a series of metric computation and comparison, so it left room for further complexity reduction.