Dinesh Ramasamy

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.

Compressive tracking with 1000-element arrays: A framework for multi-Gbps mm wave cellular downlinks

We propose and demonstrate the feasibility of multi-Gbps cellular downlinks using the mm-wave band. The small wavelengths allows deployment of compact base station antenna arrays with a very large number (32×32) of elements, while a compressive approach to channel acquisition and tracking reduces overhead while simplifying hardware design (RF beamforming with four phases per antenna element). The base station array transmits multiple compressive (≪ 32 × 32) training beacons by choosing different sets of phases from 0°, 90°, 180°, 270° at random at each of the elements. Each mobile, equipped with a single antenna, reports the observations corresponding to the different beacons (e.g., on an existing LTE link at a lower frequency), allowing the array to estimate the angles of departure. We observe that tracking overhead can be reduced by exploiting the sparsity of the spatial channel to a given mobile (which allows parametric estimation of departure angles for the different paths), and the continuity in the users mobility at microsecond timescales (for tracking the evolution of departure angles). We first illustrate the basic feasibility of such a system for realistic values of system parameters, including range of operation, user mobility and hardware constraints. We then propose a compressive channel tracking algorithm that exploits prior channel estimates to drastically reduce the number of beacons and demonstrate the efficacy of the system using simulations.

Compressive Channel Estimation and Tracking for Large Arrays in mm-Wave Picocells

We propose and investigate a compressive architecture for estimation and tracking of sparse spatial channels in millimeter (mm) wave picocellular networks. The base stations are equipped with antenna arrays with a large number of elements (which can fit within compact form factors because of the small carrier wavelength) and employ radio frequency (RF) beamforming, so that standard least squares adaptation techniques (which require access to individual antenna elements) are not applicable. We focus on the downlink, and show that “compressive beacons,” transmitted using pseudorandom phase settings at the base station array, and compressively processed using pseudorandom phase settings at the mobile array, provide information sufficient for accurate estimation of the two-dimensional (2D) spatial frequencies associated with the directions of departure of the dominant rays from the base station, and the associated complex gains. This compressive approach is compatible with coarse phase-only control, and is based on a near-optimal sequential algorithm for frequency estimation which approaches the Cramér Rao Lower Bound. The algorithm exploits the geometric continuity of the channel across successive beaconing intervals to reduce the overhead to less than 1% even for very large (32 × 32) arrays. Compressive beaconing is essentially omnidirectional, and hence does not enjoy the SNR and spatial reuse benefits of beamforming obtained during data transmission. We therefore discuss system level design considerations for ensuring that the beacon SNR is sufficient for accurate channel estimation, and that inter-cell beacon interference is controlled by an appropriate reuse scheme.

Compressive Parameter Estimation in AWGN

Compressed sensing is by now well-established as an effective tool for extracting sparsely distributed information, where sparsity is a discrete concept, referring to the number of dominant nonzero signal components in some basis for the signal space. In this paper, we establish a framework for estimation of continuous-valued parameters based on compressive measurements on a signal corrupted by additive white Gaussian noise (AWGN). While standard compressed sensing based on naive discretization has been shown to suffer from performance loss due to basis mismatch, we demonstrate that this is not an inherent property of compressive measurements. Our contributions are summarized as follows: (a) We identify the isometries required to preserve fundamental estimation-theoretic quantities such as the Ziv-Zakai bound (ZZB) and the Cramér-Rao bound (CRB). Under such isometries, compressive projections can be interpreted simply as a reduction in “effective SNR.” (b) We show that the threshold behavior of the ZZB provides a criterion for determining the minimum number of measurements for “accurate” parameter estimation. (c) We provide detailed computations of the number of measurements needed for the isometries in (a) to hold for the problem of frequency estimation in a mixture of sinusoids. We show via simulations that the design criterion in (b) is accurate for estimating the frequency of a single sinusoid.

Compressive estimation in AWGN: General observations and a case study

Compressive random projections followed by l1 reconstruction is by now a well-known approach to capturing sparsely distributed information, but applying this approach via discretization to estimation of continuous-valued parameters can perform poorly due to basis mismatch. However, we show in this paper it is still possible to capture the information required for effective estimation using a small number of random projections. We characterize the isometries required for preserving the geometric structure of estimation in additive white Gaussian noise (AWGN) under such compressive measurements. Under these conditions, estimation-theoretic quantities such as the Cramer- Rao Lower Bound (CRLB) are preserved, except for attenuation of the Signal-to-Noise Ratio (SNR) by the dimensionality reduction factor. For the canonical problem of frequency estimation of a single sinusoid based on N uniformly spaced samples, we show that the required isometries hold for M = O(log N) random projections, and that the CRLB scales as predicted. While we prove isometry results for a single sinusoid, we present an algorithm to estimate multiple sinusoids from compressive measurements. Our algorithm combines coarse estimation on a grid with iterative Newton updates and avoids the error floors incurred by prior algorithms which apply standard compressed sensing with an oversampled grid. Numerical results are provided for spatial frequency (equivalently, angle of arrival) estimation for large (32 × 32) two-dimensional arrays.

Newtonized Orthogonal Matching Pursuit: Frequency Estimation Over the Continuum

We propose a fast sequential algorithm for the fundamental problem of estimating frequencies and amplitudes of a noisy mixture of sinusoids. The algorithm is a natural generalization of Orthogonal Matching Pursuit (OMP) to the continuum using Newton refinements, and hence is termed Newtonized OMP (NOMP). Each iteration consists of two phases: detection of a new sinusoid, and sequential Newton refinements of the parameters of already detected sinusoids. The refinements play a critical role in two ways: 1) sidestepping the potential basis mismatch from discretizing a continuous parameter space and 2) providing feedback for locally refining parameters estimated in previous iterations. We characterize convergence and provide a constant false alarm rate (CFAR) based termination criterion. By benchmarking against the Cramér-Rao Bound, we show that NOMP achieves near-optimal performance under a variety of conditions. We compare the performance of NOMP with classical algorithms such as MUSIC and more recent Atomic norm Soft Thresholding (AST) and Lasso algorithms, both in terms of frequency estimation accuracy and run time.

Frequency estimation for a mixture of sinusoids: A near-optimal sequential approach

We propose a fast sequential algorithm for the fundamental problem of estimating continuous-valued frequencies and amplitudes using samples of a noisy mixture of sinusoids. Each step consists of two phases: detection of a new sinusoid, and refining the parameters of already detected sinusoids. The detection phase is performed on an oversampled DFT grid, while the refinement phase enables continuous-valued estimation, thus avoiding basis mismatch. By benchmarking against the Cramér Rao Bound, we show that the proposed algorithm achieves near-optimal performance under a variety of settings. We also compare our algorithm with the classical MUSIC, and more recent Lasso algorithms in terms of estimation accuracy and computational complexity.

On the capacity of picocellular networks

The orders of magnitude increase in projected demand for wireless cellular data require drastic increases in spatial reuse, with picocells with diameters of the order of 100-200 m supplementing existing macrocells whose diameters are of the order of kilometers. In this paper, we observe that the nature of interference changes fundamentally as we shrink cell size, with near line of sight interference from neighboring picocells seeing significantly smaller path loss exponents than interference in macrocellular environments. Using a propagation model proposed by Franceschetti, which compactly models increased interference in small cells, we show that the network capacity does not scale linearly with the reduction in cell size with standard frequency reuse strategies. Rather, more sophisticated resource sharing strategies based on beamforming and base station cooperation are required to realize the potential of small cells in providing high spectral efficiencies and quasi-deterministic guarantees on availability. Numerical results justifying these conclusions include Chernoff bounds on outage probability for random base station deployment (according to a spatial Poisson process), and simulations for deployment in a regular grid.

Can geographic routing scale when nodes are mobile

We begin by asking whether geographic routing can scale when nodes are mobile; that is, can the overhead involved in tracking node locations be accommodated within the transport capacity of large-scale mobile ad hoc networks (MANETs)? We answer this question in the affirmative by proposing an efficient position publish protocol which fits within the transport capacity and a routing protocol that operates with imperfect information of the destinations location. The routing protocol guarantees, with high probability, routes whose lengths are within a constant “stretch” factor of the shortest path from source to destination. The key idea underlying the scalability of the publish protocol is for each potential destination node to send location updates (with frequency decaying with distance) only to a subset of network nodes, structured as annular regions around it (the natural approach of updating circular regions in distance-dependent fashion does not scale). The routing protocol must then account for the fact that the source and/or relay nodes may not have estimates of the destinations location (or may have stale estimates). Spatial and temporal scaling of protocol parameters are chosen so as to guarantee scalability, route reliability and route stretch.