Trade-offs among signal correlation, SNR, and number of snapshots for direction of arrival estimation using sparse arrays
Date of Award
Master of Science in Electrical Engineering (MSEE)
Electrical, Computer, and Biomedical Engineering
Arrays can be designed as a full array of sensors or a sparse array of sensors with an equivalent aperture. Reductions in cost, size, weight and power consumption are important factors to consider when designing an array of sensors. Sparse arrays can provide a reduction in these factors. It is important to observe the performance of sparse arrays in relation to full arrays to see if they are able to achieve similar performance. The ability for the full and sparse arrays of sensors to accurately estimate the direction of arrival (DOA) of plane waves impinging them is observed in this thesis. The Mean-squared error (MSE) of the DOA estimation is measured against the Creamer-Rao bound (CRB) as a benchmark for optimal performance for an unbiased estimator. We derive an optimal way to remove sensors for one signal impinging on an array by finding the minimum CRB. This method considers all the unique combinations a sparse array could be assembled for a given number of sensors and aperture.
Parameters such as number of sensors, sensor locations, signal-to-noise ratio (SNR), number of snapshots, and signal correlation affect the MSE and CRB. Through observing trends in the MSE as a result of changing these parameters we can come to conclusions to how full and sparse arrays perform as a result of adjusting these parameters. The MSE of the DOA of the full and sparse arrays is obtained through a covariance estimation from subspace-based DOA algorithms. The sample covariance and the diagonal-averaged sample covariance matrix performances are compared.
The sample covariance matrix for a full array provides the best estimations at high SNR while the diagonal-averaging method provides a more accurate estimation at low SNR. The sparse array diagonal-averaged covariance matrix estimation performs similarly to the diagonal-averaged covariance matrix of the full array, but is still slightly worse due to missing information. How sparsity affects performance was also observed. As sparsity increases for an array, the performance change is non-linear for the MSE and CRB. Increases in signal correlation cause an increase in the overall MSE and a decrease in the overall CRB for both sparse and full arrays.
Beshara-Flynn, Kevin, "Trade-offs among signal correlation, SNR, and number of snapshots for direction of arrival estimation using sparse arrays" (2022). Open Access Master's Theses. Paper 2273.