Perturbation and Sparsification of a Uniform Linear Array

In modern remote sensing, arrays of sensors, such as antennas in radio frequency (RF) systems and microphones in acoustic systems, provide a basis for estimating the direction of arrival of a narrow-band signal at the sensor array. A Uniform linear array (ULA) is the most well-studied array geometry in that its performance characteristics and limitations are well known, especially for signals originating in the far field. In some instances, the geometry of an array may be perturbed by an environmental disturbance that actually changes its nominal geometry; such as, towing an array behind a moving vehicle. Additionally, sparse arrays have become of interest again due to recent work in co-prime arrays. These sparse arrays contain fewer elements than a ULA but maintain the array length. The effects of these alterations to a ULA are of interest. Given this motivation, theoretical and experimental (i.e. via computer simulation) processes are used to determine quantitative and qualitative effects of perturbation and sparsification on standard metrics of array performance. These metrics include: main lobe gain, main lobe width and main lobe to side lobe ratio. Furthermore, in order to ascertain results/conclusions, these effects are juxtaposed with the performance of a ULA. Through the perturbation of each element following the first element drawn from a uniform distribution centered around the nominal position, it was found that both the theoretical mean and sample mean are relatively similar to the beam pattern of the full array. Meanwhile, by using a sparsification method of maintaining all the lags, it was found that this particular method was unnecessary. Simply taking out any three elements while maintaining the length of the array will produce similar results. Some configurations of elements give a better performance based on the metrics of interest in comparison to the ULA. These results demonstrate that a sparsified, perturbed or sparsified and perturbed array can be used in place of a Uniform Linear Array depending on the application.