# Asymptotic Performance Analysis of the MUSIC Algorithm for Direction-of-Arrival Estimation
## 1 Introduction
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Ref.** & **How to Validate the Schemes Presented in [17; 18; 19; 20; 21; 22; 23; 24; 25; 26]** & **How to Apply the Derivations of This Paper to the Problems in [17; 18; 19; 20; 21; 22; 23; 24; 25; 26]** \\ \hline
[17] & Agreement between analytic MSE and simulation-based MSE & [17]: Performance analysis of amplitude comparison monopulse algorithm. This paper: Performance analysis of the MUSIC algorithm \\ \hline
[18] & Reduction in estimation error of the motion compensated conventional beamforming algorithm in comparison with the estimation error of original conventional beamforming algorithm without motion compensation in the DOA spectrum \\ \hline
[19] & Superiority of performance of SCC-MVDR algorithm over MVDR algorithm in the view point of RMSE & The analytic expression of the MSE of SOC-MVDR algorithm can be obtained by modifying the derivation in this paper \\ \hline
[20] & Superiority of the proposed scheme over the previously existing algorithms in terms of gross error rate (GER) and mean square error (MSE) & Performance of the proposed algorithm in terms of the MSE can be analytically obtained by modifying the derivation in this paper \\ \hline
[21] & Performance comparison in terms of signal-to-noise ratio, signal-to-interference ratio, signal-to-interference ratio, signal-to-interference plus noise ratio, log spectral density, and perceptual evaluation of speech quality & Performance of preprocessing DOA estimation with AVS algorithm, given by estimation error, can be obtained by modifying the derivation leading to (38) and (39), since the derivation of the MUSIC estimate should be modified to the derivation of the AVS-based DOA estimate \\ \hline
[22] & Not applicable [Review paper] & Performance of AOA-based localization algorithm depends on performance of DOA estimation: The MSE of the MUSIC algorithm can be obtained from (40) of this paper. The MSE of other DOA estimation algorithm can be obtained by modifying the derivation leading to (40). \\ \hline
[23] & Comparison of images in terms of quality and localized estimations on image noise & Rician beamforming-based array design is formulated as a convex optimization problem, and the MSEs of the array design parameters can be analytically obtained by modifying the derivation leading to (40) since array design can be formulated as parameter estimation problem \\ \hline
[24] & Superiority of the proposed scheme in terms of throughput, [PERSON]’s fairness model, and SINR. & The MSEs of the estimated array parameters in array design problem can be analytically derived by modifying the approach leading to (40). \\ \hline
[25] & Superiority of the proposed algorithm in terms of average sum-rate and energy efficiency & The MSEs of the estimates in hybrid beamforming based array design can be evaluated by modification of the derivation leading to (40). \\ \hline
[26] & Improvement in MSE, SegSNR and PESQ & The MSE of the estimated array design parameters can be evaluated by modification of the derivation leading to (40). \\ \hline \end{tabular}
\end{table} 
Table 2: How to validate the schemes presented in [17; 18; 19; 20; 21; 22; 23; 24; 25; 26], and how to apply the derivations of this paper to the problems in [17; 18; 19; 20; 21; 22; 23; 24; 25; 26].