Optimal beam pattern design for very large sensor arrays with sparse sampling

Abstract

The main goal of this work is to adaptively employ a large set of microphone sensors distributed in multiple dimensions to scan an acoustic field. Processing data from a large set of sensors will necessarily involve intelligent definition of suitable subsets of sensors active at various times. This paper presents a novel method for optimal beam pattern design for large scale sensor arrays using convex and non-convex optimization techniques to define optimal subsets of sensors capable to select a target location while suppressing a large number of interferences. The first of two optimization techniques we present, uses a LASSO-type approach to convexify the corresponding combinatorial optimization problem. The second approach employs simulated annealing to search for optimal solutions with a fixed size subset of active sensors. Our numerical simulations show that for scenarios of practical interest, the convex optimization solution is almost optimal.Index Terms-array processing, beam pattern design, sparse sampling, very large scale arrays, convex optimization INTRODUCTIONConsider a large scale sensor array having N sensors (think of N in the order 1000's) that monitors a surveillance area. Data could be collected from all sensors, processed locally, and further communicated to a central processing unit. For example, for N = 10000 sensors and a data sampling rate of 100000 samples per second, the bandwidth requirements for a system performing exhaustive sampling is 1Gsamples/sec. Alternatively, the central processing unit could implement a policy of sparse spatial sampling where only a subset of sensors is polled for data at any time. This may be desirable for practical reasons: cost (in power consumption, communication or processing bandwidth) is simply too high for an exhaustive strategy. This paper advocates the need for advanced, dynamic control and signal processing of what data should be manipulated in place of the full extent of the data, and it introduces novel strategies and formal analysis of what can be achieved when only a sparse subset of sensors is sampled simultaneously.Assume a surveillance area that consists of a set of point-like sources that we are ultimately interested to separate. Our task is to sample the spatial field using a maximum of D sensors of the very large array (D N ) and then to process the raw data in order to estimate each source (see also Figure 1 for a setup scenario). We will thus design and analyze sparse spatial sampling strategies with near-optimal performance. Specifically, we target designs that simultaneously maximize target location gain and minimize the largest