Effect of Power Difference of Two Signal Sources on Resolving Performance of MUSIC Algorithm

Effects of finite samples on the resolution performance of the rank reduction estimator

“…Figure 14 depicts the curves of ξ T versus the phase factor ϕ when the power ratio r and the amplitude factor |ρ| are set at 1 and 0.1, respectively. http://engine.scichina.com/doi/10.1007/s11432-011-4525-z From Figures 9-14 we can summarize the results for both the RARE and the MUSIC algorithm as follows: 1) The resolving threshold decreases as the number of snapshots improves; 2) The resolving threshold improves as the power ratio increases, which conforms to the results in [17]; 3) The resolving threshold improves very fast along with an increasing amplitude factor, but it takes a slow and periodical fluctuation when the phase factor increases, because how the two sources are correlated relies heavily on the amplitude factor; 4) The resolving threshold exhibits the characteristic of a convex function as the power ratio, but takes the property of a concave function as the amplitude factor, i.e., the increasing rate of the resolving threshold decreases as the power ratio increases, but increases as the amplitude factor increases.…”

“…Consequently, the RARE can be viewed as an extension of the MUSIC algorithm, or equivalently, the MUSIC algorithm is a special case of the RARE in the absence of array errors. The angle resolution performance of the MUSIC algorithm has been studied in [14][15][16][17][18]. Therefore, in this paper, we focus on the angle resolution performance of the RARE.…”

“…In light of the results in [14][15][16][17][18], the resolution capability of the spatial spectrum relies mainly on the expectation. Hence, the expression for the expectation of the spatial spectrum of the RARE is derived in this subsection.…”

“…In [17,18], the SNR resolving threshold suitable for the two unequal-power sources is defined, called mean SNR resolving threshold. The definition is stated as follows.…”

“…Ref. [17,18] studied the effects of the power difference and the correlation coefficient of the sources on the resolution capability of the MUSIC algorithm. Although the RARE can be viewed as an extension of the MUSIC algorithm, the resolution performance of the RARE in the finite sample case has not yet been addressed in the literature.…”