Abstract
This paper proposes a new method to get explicit expressions of some quantities associated with performance analysis of the maximum likelihood DOA algorithm in the presence of an additive Gaussian noise on the antenna elements. The motivation of the paper is to make a quantitative analysis of the ML DOA algorithm in the case of multiple incident signals. We present a simple method to derive a closed-form expression of the MSE of the DOA estimate based on the Taylor series expansion. Based on the Taylor series expansion and approximation, we get explicit expressions of the MSEs of estimates of azimuth angles of all incident signals. The validity of the derived expressions is shown by comparing the analytic results with the simulation results.
Highlights
There has been a lot of research on the direction-of-arrival (DOA) estimation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
The constraints used for derivation of estimation errors are equations (A) and (B): equation (A) is valid since, in a noiseless environment, no estimation error occurs in the azimuth estimates
The estimation error due to an additive noise in noisy environment is formulated as equation (B)
Summary
There has been a lot of research on the direction-of-arrival (DOA) estimation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. Empirical performance from Monte Carlo simulation is present to illustrate the superiority of the proposed scheme over the other DOA algorithms. Closed-form expressions for the signal parameters and noise parameters are derived, implying that the proposed scheme results in significant reduction in computational complexity in comparison with exhaustive multidimensional search-based ML DOA algorithms. In comparison with the previous studies on the performance analysis of the maximum likelihood algorithm [7,8,9,19], a more explicit representation of the MSE of the azimuth estimate is proposed in this paper. Our contribution lies in a reduction in computational cost in getting the MSE of an existing ML DOA algorithm by adopting an analytic approach, rather than the Monte Carlo simulation-based MSE under measurement uncertainty which is assumed to be Gaussian distributed. The scheme presented in this paper can be adopted to predict the accuracy of the ML DOA algorithm for different values of various parameters
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