On the Log-Likelihood Ratio Evaluation of CWCU Linear and Widely Linear MMSE Data Estimators
Sprache des Vortragstitels:
Asilomar Conference on Signals, Systems, and Computers
Sprache des Tagungstitel:
In soft decoding of data bits, the log-likelihood ratios are evaluated from the estimated data symbols. For proper constellation diagrams such as for quadrature phase-shift keying (QPSK) or 16 quadrature amplitude modulation (16-QAM), the data symbols are often estimated using the linear minimum
mean square error (LMMSE) estimator. The LMMSE estimator only fulfills the weak Bayesian unbiased constraint. Recently, estimators fulfilling the more stringent component-wise conditionally unbiased (CWCU) constraints have been investigated, such as the CWCU LMMSE estimator. In this paper, we prove
that the CWCU LMMSE data estimates result in the same log-likelihood ratios as the LMMSE estimates. For improper constellation diagrams such as 8-QAM, widely linear estimators are more appropriate.We also show that the widely linear MMSE (WLMMSE) estimator and the CWCU WLMMSE estimator yield identical log-likelihood ratios. Finally, we give a simulation example which illustrates a number of interesting properties of the discussed widely linear estimators.