Bit metric generation for Gray coded QAM signals

A simple and general bit metric generation method by using the log likelihood ratio (LLR) for a Gray coded QAM signal over an additive white Gaussian noise channel is proposed. The mathematical max (min) functions of the conventional LLR expression are replaced with basic arithmetic functions. Since the derived LLR expression can be used as a soft bit metric for input to a conventional binary turbo decoder, it is suitable for practical applications with a turbo decoder or other related applications as an alternative to conventional methods.