Abstract
The performance of the conventional beamforming for angle-of-arrival (AOA) estimation algorithm under measurement uncertainty is analyzed. Gaussian random variables are used for modeling measurement noises. Analytic expression of the mean square error (MSE) is obtained via Taylor series expansion. In traditional performance analysis, estimation accuracy in terms of the MSEs is usually obtained from the Monte Carlo simulation, which is computationally intensive especially for large number of repetitions in the Monte Carlo simulation. For reliable MSE in the Monte Carlo simulation, the number of repetitions should be very large. To circumvent this problem, analytic performance analysis which is less computationally intensive than the Monte Carlo simulation-based performance analysis is proposed in this paper. After some approximations, we derive the closed form expression of the mean square error (MSE) for each incident signal. The validity of the derived expressions is shown by comparing an analytic MSE with an empirical MSEs. The Cramer–Rao bound is also used to further validate the derived analytic expression.
Highlights
Our contribution is on computational cost reduction in getting the mean square error (MSE) of an existing conventional beamforming algorithm by adopting an analytic approach, rather than the Monte Carlo simulation-based MSE under measurement uncertainty which can be modeled as Gaussian distributed. at is, the proposed scheme describes how analytic MSE can be obtained with much less computational complexity than the Monte Carlo simulationbased MSE
E proposed scheme can be used in predicting how accurate the estimate of the conventional beamforming algorithm is without computationally intensive Monte Carlo simulation. e performance of the conventional beamforming algorithm depends on various parameters including the number of snapshots, the number antenna elements in the array, interelement spacing between adjacent antenna elements, and the SNR. erefore, Monte Carlo simulations for different values of the various parameters can be computationally intensive. erefore, the scheme presented in this paper can be adopted to predict the accuracy of the conventional beamforming-based DOA estimation algorithm for different values of various parameters
For the conventional beamforming algorithm, we derive closed-form expressions of the estimates of the AOAs for small estimation error. e formulation accounts for various effects such as the finite number of snapshots, SNR, and the number of repetitions
Summary
Performance analysis of conventional beamforming algorithm for direction-of-arrival (DOA) estimation is considered. In comparison with the previous studies on the performance analysis of the conventional beamforming algorithm, a more explicit representation of the MSE of the estimate is proposed in this paper. Our contribution is on computational cost reduction in getting the MSE of an existing conventional beamforming algorithm by adopting an analytic approach, rather than the Monte Carlo simulation-based MSE under measurement uncertainty which can be modeled as Gaussian distributed. E proposed scheme can be used in predicting how accurate the estimate of the conventional beamforming algorithm is without computationally intensive Monte Carlo simulation. Erefore, the scheme presented in this paper can be adopted to predict the accuracy of the conventional beamforming-based DOA estimation algorithm for different values of various parameters. It is quite straightforward to extend to the case where the noises are modeled as different random variables as long as the moments of the random variables are available
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