An improved method of estimating the signal-to-noise ratio (SNR) of a phase-shift keying (PSK) communication link is founded on a rigorous statistical analysis of the input to, and the output from, the PSK demodulator in the receiver. Many methods to estimate SNR ratios of PSK communication links have been developed previously, and all of them are defective (that is, not rigorous) in that all of them are based on tacit and unwarranted assumptions made for the sake of analytical simplification. In addition, some of the prior methods involve (1) the use of a separate receiver, denoted the propagation receiver, to measure a beacon signal distinct from the PSK communication signal and (2) extrapolation of the result of the measurement to an estimate the SNR of the PSK communication channel. In contrast, the improved method is free of unwarranted simplifying assumptions and does not require the use of a propagation receiver.

ImageOne basic concept shared by both the improved method and the prior methods is that the effect of noise in the communication link is not only present in the input to the demodulator but is also convolved within the output of the demodulator. The mathematical analysis in this method is based on (1) established theories of statistical analysis of flows of the signal and noise through a generic M-ary PSK demodulator, and (2) techniques of maximum-likelihood estimation theory. In this analysis, one employs, rather than neglects, all the subtleties of the statistics that characterize the stochastic nature of the phase-modulated signal to derive an estimation procedure that utilizes the inherent phase characteristics of the input to and the output from the demodulator.

The complexity of the analysis precludes a detailed description in this article. It must suffice to summarize as follows: The analysis begins with a description of the signal and noise in the case of binary PSK. This description serves as a foundation for a statistical connection between Gaussian noise and the SNR. This connection leads to a probabilistic description that establishes a rigorous connection between the SNR and the measured phase error of the BPSK signal entering the receiver demodulator. Then techniques of maximum-likelihood estimation theory are used to obtain analytical expressions for biased and unbiased estimates of the SNR from easily measured phase errors.

The method requires the use of a modified BPSK demodulator to obtain the time-dependent phase error, £cE(t) in a composite output signal. The SNR-estimation procedure begins with the acquisition of a sequence of samples £cE(ti) at k successive sampling times ti (i = 1 to k). Next, one calculates a biased estimate, £^*, of the SNR (£^) by use of the equation:


Finally, an unbiased estimate, £^., is obtained from a lookup table that contains solution values for a nonlinear equation that describes the relationship between £^* and £^.. Although the method was derived for BPSK, it can be applied (with modifications) to quaternary and higher-order PSK.

This work was done by Robert M. Manning of Glenn Research Center. For further information, access the Technical Support Package (TSP) free on-line at www. under the Electronics/ Computers category.

Inquiries concerning rights for the commercial use of this invention should be addressed to:

NASA Glenn Research Center
Commercial Technology Office
Attn: Steve Fedor
Mail Stop 4-8
21000 Brookpark Road
Cleveland, Ohio 44135.

Refer to LEW-17597-1.

NASA Tech Briefs Magazine

This article first appeared in the May, 2006 issue of NASA Tech Briefs Magazine.

Read more articles from the archives here.