Compressive adaptation of large steerable arrays

Abstract

Abstract-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 continuousvalued 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.

Achieving multiple degrees of freedom in long-range mm-wave MIMO channels using randomly distributed relays

“…Both the transmitter's and receiver's architecture and algorithm from such a system could be reused for our proposed system, since the transmitter and receiver can be oblivious to the presence of relays. Several papers have addressed other design concerns at 60 GHz, such as steering arrays with a very large number of elements (e.g., 1000) and imperfect phase-shifters [7] or digitally controlled analog processing for reducing the stress on the AGCs [8]. The impact of scattering on the capacity and diversity of MIMO systems for RF frequencies was analyzed in [9].…”

Compressive estimation in AWGN: General observations and a case study

“…In contrast, we focus on the problem of estimating the original continuous-valued frequency, and provide algorithms that can bootstrap with a much coarser grid, while avoiding error floors due to gridding by using Newton methods. The estimation algorithm improves on our prior work [9] and also extends it to multi-dimensional frequencies.…”

“…We generalize the setup we have been considering in two ways: (1) we allow the signal to contain multiple sinusoids and (2) we investigate twodimensional frequencies, motivated by the problem of AoA estimation using large arrays explained in [9]. The (m, n)-th sample we obtain (without compressive measurements) takes the form ge j(ωxm+ωyn) , 0 ≤ m, n ≤ N 1D − 1 where ω = (ω x , ω y ) is the two-dimensional frequency we wish to estimate.…”

Compressed sensing based multi-user millimeter wave systems: How many measurements are needed?

“…Compressed sensing measurements: Thanks to the sparse formulation of the mmWave channel estimation problem in (7), compressed sensing tools can be leveraged to design efficient training beamforming/combining matrices [5,15]. Considering the measurement matrix Φ = P T ⊗ Q H , and the dictionary Ψ = A * BS ⊗A MS , one interesting research direction is to study the conditions on Φ, Ψ under which the support of the sparse vector z u can be recovered with high probability and with low training overhead.…”