Sriram Venkateswaran

Channel Modeling and MIMO Capacity for Outdoor Millimeter Wave Links

Recent work has shown that mesh networks based on short-range outdoor millimeter (mm) wave links in the unlicensed 60 GHz band are a promising approach to providing an easily deployable broadband infrastructure. In this paper, we investigate the robustness of such links, focusing in particular on the effect of multipath fading resulting from reflections from the ground and building walls for a lamppost deployment of mm wave nodes. Our ray tracing based model shows that, while only a small number of paths are significant for the highly directional links considered, they can cause significant fluctuations in the received signal strength. Our simulations show that 10-20 dB fades below the benchmark of free space propagation can occur quite easily (e.g., 5-15% of the time, averaging across typical deployment scenarios), and that the received power is extremely sensitive to small variations in geometry (e.g., altering the position of the antenna by 1 cm can reduce the received power as much as 46.7 dB). We also demonstrate, however, that extremely robust performance can be obtained by employing multiple antennas at appropriately chosen separations, using standard space-time communications strategies such as transmit precoding (when the transmitter knows the channel) and space-time coding (when the transmitter does not know the channel).

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 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.

RF source-seeking by a micro aerial vehicle using rotation-based angle of arrival estimates

We investigate a computationally and memory efficient algorithm for radio frequency (RF) source-seeking with a single-wing rotating micro aerial vehicle (MAV) equipped with a directional antenna. The MAV is assumed to have no knowledge of its position and to have only an estimate of orientation through a magnetometer. A key novelty of our approach is in exploiting the rotation of the MAV and the directionality of its RF antenna to derive estimates of the angle of arrival (AOA) at each rotation. The MAV then follows the estimated direction until the next rotation is complete. We prove convergence of this greedy algorithm under rather weak assumptions on the noise associated with the AOA estimates, using recent results on the property of recurrence for systems governed by stochastic difference inclusions. These convergence results are supplemented by simulations quantifying the amount of excess travel, relative to the straight line distance to the source. Indoor experiments using Lockheed Martins Samarai MAV demonstrate the efficacy of the greedy algorithm both for static source-seeking, and for the more challenging problem of tracking a moving source.

Analog multitone with interference suppression: Relieving the ADC bottleneck for wideband 60 GHz systems

Commercial exploitation of the large amounts of unlicensed spectrum available at 60 GHz requires that we take advantage of the low-cost digital signal processing (DSP) made available by Moores law. A key bottleneck, however, is the cost and power consumption of high-precision analog-to-digital converters (ADCs) at the multiGigabit rates of interest in this band. This makes it difficult, for example, to apply traditional DSP-based approaches to channel dispersion compensation such as time domain equalization or Orthogonal Frequency Division Multiplexing (OFDM), since these are predicated on the availability of full-rate, high-precision samples. In this paper, we investigate the use of analog multitone for sidestepping the ADC bottleneck: transmissions are split into a number of subbands, each of which can be separately sampled at the receiver using a lower rate ADC. For efficient use of spectrum, we do not allow guard bands between adjacent subbands, hence the receiver signal processing must account for intercarrier interference (ICI) across subbands as well as intersymbol interference (ISI) within a subband due to channel dispersion. We illustrate our ideas for short-range (100–200 meters), highly directional, outdoor 60 GHz links, as might be employed for wireless backhaul. Given the large coherence bandwidth of the sparse multipath channels typical of such links that we consider, reliable performance requires spatial diversity, in addition to the beamforming required to close the link. We therefore consider one transmit and two receive antenna arrays, each with 4 × 4 elements. We investigate linear equalization strategies corresponding to different combinations of: (a) combining samples from both arrays/choosing the stronger array and (b) equalizing the subbands independently/jointly. We find that exploiting the spatial diversity completely by combining samples from both arrays is critical for combating fading and inter carrier interference.

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.

Localizing Multiple Events Using Times of Arrival: a Parallelized, Hierarchical Approach to the Association Problem

A fundamental problem in localizing multiple events based on Times of Arrival (ToAs) at a number of sensors is that of associating ToAs with events. We consider this problem in the context of acoustic sensors monitoring events that are closely spaced in time. Due to the relatively low speed of propagation of sound, the order in which the events arrive at a sensor need not be the same as the order in which they occur, potentially creating fundamental ambiguities. We first explore such ambiguities in an idealized setting with two events and noiseless observations, showing that it is possible to localize both events with nine or more sensors (as long as degenerate sensor placement is avoided), but that we can construct examples with six sensors for which unambiguous space-time localization is not possible. We then show that these potential ambiguities are not a bottleneck in typical practical settings, proposing and evaluating an algorithm that successfully localizes multiple events using noisy observations. The algorithm employs parallelism and hierarchical processing to avoid the excessive complexity of naïvely trying all possible associations of events with ToAs. We use discretization of hypothesized event times to enable us to efficiently generate a set of candidate event locations, which contain noisy versions of true events as well as phantom events. We refine these estimates iteratively, discarding “obvious” phantoms, and then solve a linear programming formulation for matching true events to ToAs, while identifying outliers and misses. Simulation results indicate excellent performance that is comparable to a genie-based algorithm which is given the correct association between ToAs and events.

Localization with sparse acoustic sensor network using UAVs as information-seeking data mules

We propose and demonstrate a novel architecture for on-the-fly inference while collecting data from sparse sensor networks. In particular, we consider source localization using acoustic sensors dispersed over a large area, with the individual sensors located too far apart for direct connectivity. An Unmanned Aerial Vehicle (UAV) is employed for collecting sensor data, with the UAV route adaptively adjusted based on data from sensors already visited, in order to minimize the time to localize events of interest. The UAV therefore acts as a information-seeking data mule, not only providing connectivity, but also making Bayesian inferences from the data gathered in order to guide its future actions. The system we demonstrate has a modular architecture, comprising efficient algorithms for acoustic signal processing, routing the UAV to the sensors, and source localization. We report on extensive field tests which not only demonstrate the effectiveness of our general approach, but also yield specific practical insights into GPS time synchronization and localization accuracy, acoustic signal and channel characteristics, and the effects of environmental phenomena.

Multiple event localization in a sparse acoustic sensor network using UAVs as data mules

We report on a field demonstration of autonomous detection, localization, and verification of multiple acoustic events using sparsely deployed unattended ground sensors, unmanned aerial vehicles (UAV) as data mules, and a ground control interface. A novel algorithm is demonstrated to address the problem of multiple event acoustic source localization in the presence of false and missed detections. We also demonstrate an algorithm to route a UAV equipped with a radio to collect data from sparsely deployed ground sensors that takes advantage of the communication range of the aircraft while adhering to kinematic constraints of the UAV. A second UAV was utilized to provide video verification of localized events to a human operator at a ground control station.