Joint processing of sensor array outputs improves the performance of parameter estimation and hypothesis testing problems beyond the slim of the individual sensor processing results. When the sensors have high data sampling rates, arrays are tethered, creating a disadvantage for their deployment and also limiting their aperture size. In this paper, we develop the signal processing algorithms for randomly deployable wireless sensor arrays that are severely constrained in communication bandwidth. We focus on the acoustic bearing estimation problem and show that when the target bearings are modeled as a sparse vector in the angle space, low dimensional random projections of the microphone signals can be used to determine multiple source bearings by solving an l(1)-norm minimization problem. Field data results are shown where only 10 bits of information is passed from each microphone to estimate multiple target bearings.