A systematic bit-wise decomposition of M-ary symbol metric

In this paper, we present a systematic recursive formula for bit-wise decomposition of M-ary symbol metric. The decomposed bit metrics can be applied to improve the performance of a system where the information sequence is binary-coded and interleaved before M-ary modulated. A traditional receiver designed for certain system is to de-map the received M-ary symbol into its binary isomorphism so as to facilitate the subsequent bit-based manipulation, such as hard-decision decoding. With a bit-wise decomposition of M-ary symbol metric, a soft-decision decoder can be used to achieve a better system performance. The idea behind the systematic formula is to decompose the symbol-based maximum-likelihood (ML) metric by equating a number of specific equations that are drawn from squared-error criterion. It interestingly yields a systematic recursive formula that can be applied to some previous work derived from different standpoint. Simulation results based on IEEE 802.11a/g standard show that at bit-error-rate of 10^-5 , the proposed bit-wise decomposed metric can provide 3.0 dB, 3.9 dB and 5.1 dB improvement over the concatenation of binary-demapper, deinterleaver and hard-decision decoder respectively for 16QAM, 64QAM and 256QAM symbols, in which the in-phase and quadrature components in a complex M²-QAM symbol are independently treated as two real M-PAM symbols. Further empirical study on system imperfection implies that the proposed bit-wise decomposed metric also improves the system robustness against gain mismatch and phase imperfection. In the end, a realization structure that avails the recursive nature of the proposed bit-decomposed metric formula is addressed