Beam Forming from Linear Arrays with Randomly Spaced Elements
The design of linear arrays with constant weights and randomly positioned elements is investigated. The objective is to determine probability distributions from which element positions can be selected to transmit and/or receive in preferred directions. The performance of such arrays is compared to that of uniformly spaced arrays with respect to number of elements and desired side lobe levels in the directivity function. A theoretical model for the distribution of element positions is derived in the continuum limit constrained on matching the response to that produced by a target response of a Dolph-Chebyshev array. The expected value of the random beam responses as a function of the observation angle is shown to approach the target function. The variance of the side lobe amplitudes is inversely proportional to the number of array elements.
The analytical probability distribution for element positions is found to be comparable with the distribution estimated from an optimization algorithm based on the swarming behavior of fireflies. In this model, each firefly represents an array of fixed number of elements with randomly initialized positions. The objective beam function with a specified beam width and maximum side lobe level serves as the fitness function that governs the directed movement and clustering of fireflies at successive iterations. The algorithm generates ensembles of element positions that satisfy the beam constraints with a reduced variance in the side lobe amplitudes compared to the analytical model. This data is analyzed to identify and model the correlation structure in the inter-element positions. The performance of a hypothesized joint probability distribution for element positions that captures this dependence is discussed.
University of Massachusetts, Lowell
Dr. Kavitha Chandra is a professor of Electrical and Computer Engineering at the University of Massachusetts Lowell. Her research interests include design of computational models for acoustic and radio wave propagation and performance analysis of networks. She directs the Vibes and Waves in Action program in the Center for Advanced Computation and Telecommunications at UMASS Lowell. This program was created during the NSF funded GK-12 project to address the technical
communication skills of graduate students and forge partnerships with public high school districts in the Commonwealth of Massachusetts. She is currently investigating the design of blended learning and flipped classroom models of education using the edX open source platform for designing course modules in collaboration with graduate students and high school teachers.
Prof. Chandra received her doctoral degree in Electrical Engineering from UMASS Lowell and was a recipient of the NSF Career award. Prior to joining the University she was a member of technical staff in the Teletraffic and Performance Analysis Department at AT&T Bell Labs.
She is here with her student Nick Misiunas, a PhD candidate in ECE who is investigating the design of parallel algorithms for optimization problems in wireless communications.
Host: Professor Jie Fu