Nonparametric Spectral Estimation of Phase Noise in Modulated Signals Based on Complementary Autocorrelation

A novel nonparametric spectral estimation technique for phase noise based on the complementary autocorrelation (CAC) is presented. Utilizing the fact that the CAC of phase noise is not zero, this technique offers a distinct advantage that the power spectrum of phase noise is estimated whereas that of other kinds of noise are suppressed as long as they are proper (second-order circularity). This property is most useful when estimating the phase noise spectrum directly from digitally-modulated signals because those signals are typically accompanied by various kinds of undesired noise that easily mask the phase noise of interest. A frequency-domain estimation method based on complementary spectrum is presented for practical computation of phase noise spectrum. For the method, a formula for the noise suppression factor is derived assuming the properness in noise. Furthermore, suppressibility analyses are conducted, which reveal that many of the noises associated with modulated signals are indeed proper, and can thus be suppressed. Numerical simulations demonstrate the method, and verify the noise suppression factor. It is believed that this technique is the first of its kind being able to extract phase noise spectrum while suppressing many other kinds of noise.