On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.