# Performance Analysis of Interferometer Algorithm under Phase Measurement Error
## 2 Novelty and Contribution  
Many previous studies [7; 8; 9; 10; 11; 12] focused on how the performance of the interferometer algorithm can be improved by proposing new algorithms or by modifying conventional interferometer algorithm. Note that many studied on ambiguity resolving have been conducted, especially for long-baseline interferometer.  
Our contribution in this manuscript does not lie in how the performance of the interferometer algorithm can be improved by proposing a new algorithm. Our contribution in this paper lies in a reduction in computational cost in getting the MSE of an existing interferometer algorithm by adopting analytic approach, rather than the Monte Carlo simulation-based MSE under measurement uncertainty due to an additive Gaussian-distributed noise or uniformly-distributed noise. That is, the scheme described how analytic MSE can be obtained much less computational complexity than the Monte Carlo simulation-based MSE.  
Contribution of the scheme presented in this paper mainly lies in the computational reduction in getting the MSE analytically in comparison with the Monte Carlo simulation-based MSE. Estimation accuracy, in terms of the MSEs of the direction-of-arrival (DOA) estimation algorithm, is usually obtained from the Monte Carlo simulation, which can be 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, implying a trade-off between reliability of the MSE and computational cost in the Monte Carlo simulation. The performance of interferometer is quantitatively obtained via the MSEs, and the derived expression is validated by comparing the analytic MSEs with the simulation based MSEs.  
In this paper, Gaussian noise and uniform noise are employed to model measurement uncertainty in the implementation of interferometer algorithm. The effect of these noises on the accuracy of the azimuth estimate and the elevation estimate is rigorously derived. Subsequently, explicit expressions of the azimuth MSE and the elevation MSEs are also derived.  
The proposed scheme can be employed for the performance analysis in predicting how accurate the estimate of the interferometer algorithm is without resorting computationallyintensive Monte-Carlo simulation. The performance of the interferometer algorithm is dependent on many parameters, such as the number snapshots, the number antenna elements in the array, inter-element spacing between adjacent antenna elements and the SNR. Therefore, performing Monte Carlo simulations for different values of the various parameters is computationally intensive, which is why the analytic performance analysis proposed can be employed to predict how well the interferometer algorithm works, given the specific values of the various parameters. In this paper, rigorous derivation of how the MSE of the interferometer algorithm for direction-of-arrival can be expressed in terms of various parameters, which include the number of sensor elements and the variance of additive noises on the antenna elements. Two cases of Gaussian-distributed additive noise uniform-distributed additive noise are considered.