Optimal Space-Time-Frequency Design of Microphone Networks

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Consider a sensing system using a large number of N microphones placed in multiple dimensions to monitor a acoustic field. Using all the microphones at once is impractical because of the amount data generated. Instead, we choose a subset of D microphones to be active. Specifically, we wish to find the D set of microphones that minimizes the largest interference gain at multiple frequencies while monitoring a target of interest. A direct, combinatorial approach - testing all N choose D subsets of microphones - is impractical because of problem size. Instead, we use a convex optimization technique that induces sparsity through a l1-penalty to determine which subset of microphones to use. Our work investigates not only the optimal placement (space) of microphones but also how to process the output of each microphone (time/frequency). We explore this problem for both single and multi-frequency sources, optimizing both microphone weights and positions simultaneously. In addition, we explore this problem for random sources where the output of each of the N microphones is processed by an individual multirate filterbank. The N processed filterbank outputs are then combined to form one final signal. In this case, we fix all the analysis filters and optimize over all the synthesis filters. We show how to convert the continuous frequency problem to a discrete frequency approximation that is computationally tractable. In this random source/multirate filterbank case, we once again optimize over space-time-frequency simultaneously.