Method of Moment Rice Parameter Estimators with Improved Performance at Low SNR

摘要

Parameter estimators for Rice distributed data perform poorly in the low signal to noise ratio (SNR) region. For method of moments $(mathrm{M}mathrm{o}mathrm{M})$ estimators we identified the reason is that the inverse functions converting data to estimates have limited domains, and for those data falling outside the domains, inappropriate “default” estimates are assigned, resulting in increased errors. We compared two $mathrm{M}mathrm{o}mathrm{M}$ estimators, based on the $mathrm{l}mathrm{s}mathrm{t}/2mathrm{n}mathrm{d}$ moments and $2mathrm{n}mathrm{d}/4mathrm{t}mathrm{h}$ moments, and found that the former is easier to improve and may return better results. We proposed a partial polynomial fitting on the double $-log mathrm{l}mathrm{s}mathrm{t}/2mathrm{n}mathrm{d}$ moments function so that the domain is extended smoothly. For signal strength s and noise standard deviation $sigma$ estimators, significant improvements have been observed for SNR in the region from $-4mathrm{d}mathrm{B}$ to 4 dB for the number of samples $N=20$ and 100 cases, outperforming maximum likelihood estimators (MLE) and maximum a posteriori (MAP) estimators. Their run times are over two orders faster than MLE in Matlab.