Power Spectrum of Hard-Limited Gaussian Processes

Abstract

The power spectral density at the output of an ideal hard limiter (one-bit quantizer) is examined when the input is driven by a narrowband gaussian signal plus an additive gaussian noise that consists of a broadband background component plus narrowband interference. Assuming that the input signal-to-noise power ratio is small by virtue of the large bandwidth of the observed broadband noise, calculations are made of the average output signal power, the average output noise power in the signal band, and the average power of the strongest intermodulation product. The results support the intuitive conclusion that spectrum analyzer performance is degraded by the presence of the limiter and that this degradation is more pronounced when a strong narrowband interfering signal is present. They also indicate that the degradation can be minimized by making the bandwidth observed by the limiter sufficiently wide that the broadband noise power dominates both the signal and interference powers. In particular, for a typical example, the signal-to-noise power ratio measured in the signal band is degraded by less than about 1.3 dB by the presence of the limiter and the ratio of output signal power to power of the strongest intermodulation product is greater than about 14.5 dB as long as the broadband noise power exceeds the interfering-signal power.