Noise Variance and Signal-to-Noise Ratio Estimation from Spectral Data

In most real-world signal processing and measurement applications, unavoidable measurement noise is one of the key factors that limits overall system performance. To be able to assess the performance of a signal processing system in-situ, noise variance and signal-to-noise ratio, respectively can only be estimated from available measurement data. Furthermore, the statistical performance of these estimates is of importance. While noise variance estimation can be done in theory by simply applying some well-known estimators, this standard approach can fail in many practical applications due to unavoidable modeling inaccuracies. To overcome this, we extend an approach for noise variance estimation from spectral data using data windows. The only necessary prerequisite for the applicability of the algorithm is the existence of a spectral region containing noise only. By applying robust estimation techniques, even this assumption can be relaxed to some extent. We also analyze the corresponding Cramér-Rao bounds and validate the approach by means of Monte-Carlo simulations. The case of signal-to-noise ratio estimation in sinusoidal models is treated as a special case of particular interest, together with a discussion of the colored noise case and practical application examples. Furthermore, the Cramér-Rao bounds and simulation results are compared with real world measurement results from a radioacoustic-sounding-system application.