Maximum entropy array processing

Abstract

Results of a simulation study of the application of the complex one‐dimensional maximum entropy spectral analysis algorithm to the problem of localizing and resolving discrete targets using a linear array are reported. Of particular interest in this study were the errors in bearing esitimation and statistical stability of the estimated array response. The rms error in the source bearing estimates was observed to increase with decreasing signal‐to‐noise ratio (SNR), when the model order (p) approached the number of array elements (N=31), and when the source of interest was not well separated from adjacent sources. Typical rms errors observed for isolated sources (for p?N/3) ranged from 0.02λ/D at an SNR of 17 dB to 0.5λ/D at −9 dB. The statistical variability and number of spurious peaks in the array response were observed to increase rapidly as p approached N. At SNR less than 0 dB the array response, even when averaged over 50 independent data sets, indicated numerous spurious sources when the model order was large. The equivalent number of degrees of freedom (df) of the array response, estimated as twice the square of the average divided by the variance of the response, were calculated and compared with df=N/p as conjectured by Parzen and demonstrated (asymptotically) by Kromer. Parzen’s conjecture was consistent with the observed results for p≪N, but was found to be very optimistic at high model orders. It was also found that for the given array parameters the spatial response to an individual point source increases in width in the presence of nearby targets as well as with decreasing signal‐to‐noise ratio; and while the spatial response to a single point source is typically much narrower for maximum entropy processing, the minimum angular separation required for the resolution of adjacent sources is only slightly less (roughly a factor of one‐half) than that of a conventional beamformer even at relatively high (17 dB) signal‐to‐noise ratios.