Compressive adaptation of large steerable arrays

We consider the problem of adapting very large antenna arrays (e.g., with 1000 elements or more) for tasks such as beamforming and nulling, motivated by emerging applications at very high carrier frequencies in the millimeter (mm) wave band and beyond, where the small wavelengths make it possible to pack a very large number of antenna elements (e.g., realized as a printed circuit array) into nodes with compact form factors. Conventional least squares techniques, which rely on access to baseband signals for individual array elements, do not apply. Hence the preferred approach is to perform radio frequency (RF) beamsteering, with a single complex baseband signal emerging from a receive array, or going into a transmit array. Further, we are interested in what can be achieved with coarse-grained control of individual elements (e.g., four-phase, or even binary phase, control). In this paper, we propose an adaptation architecture matched to these hardware constraints. Our approach comprises the following two steps. The first step is compressive estimation of a sparse spatial channel using a small number of measurements, each using a different set of randomized weights. However, unlike the standard compressive sensing formulation, we are interested in estimating continuous- valued parameters such as the angles of arrivals of various paths. The second step is quantized beamsteering, where weights for beamforming and nulling, subject to the constraint of severe quantization, are computed using the channel estimates from the first step. We provide promising preliminary results illustrating the efficacy of this approach.