How to use a priori information of data symbols for SNR estimation

We address the problem of how to use a priori information of data symbols to improve signal-to-noise ratio (SNR) estimation. Digital transmission with binary phase-shift keying (BPSK) over additive white Gaussian noise (AWGN) channels serves as a background. At the receive side, both pilot and data symbols are used to estimate the SNR. In addition, we assume that a priori information of the data symbols is available. Our proposed estimator is then derived as an approximate solution of the maximum-likelihood (ML) approach. A significant improvement in the low-SNR regime over the corresponding estimator without a priori information is shown. Hence, an estimator that uses a priori information of data symbols is suitable to be embedded in iterative decoding schemes like, e.g., turbo decoding or turbo equalization. In addition, the Cramer-Rao lower bound (CRLB) for SNR estimators using a priori information of data symbols is derived.