Threshold performance of MUSIC when using the forward-backward data matrix

Abstract

The multiple signal classification (MUSIC) frequency estimator is a suboptimal method for estimating the frequencies of multiple sinusoids buried in white noise and has a threshold of around 14 dB for the well-known two-sinusoid example (equal amplitudes f/sub 1/=0.52, f/sub 2/=0.5, /spl phi//sub 1/=/spl pi//4, and /spl phi//sub 2/=0). We point out that this threshold value is the result of estimating the autocorrelation estimates using the forward data matrix alone. Instead, if the autocorrelation estimates are obtained from the data matrix, the threshold is lowered to 4 dB (lower than Kumaresan-Tufts method's 7 dB and within 1 dB of maximum-likelihood estimator). We offer an explanation of why the threshold is lowered by examining the noiseless autocorrelation matrix based on the forward and data matrices. Also, it is well known that the Crame/spl acute/r-Rao lower bound (CRLB) is also a function of the relative phases. We point out that when /spl phi//sub 1/=/spl pi//2, the estimates obtained using MUSIC become increasingly biased and cause the variance to fall below CRLB at 23 dB for the forward-backward root MUSIC and at 25 dB for forward-only root MUSIC. The use of the data matrix in spectral estimation is not novel, but to our knowledge, the improvement in threshold for /spl phi//sub 1/=/spl pi//4 has not been reported, nor the comparative performance as /spl phi//sub 1/ varies.