Raghuraman Mudumbai

On the Feasibility of Distributed Beamforming in Wireless Networks

Energy efficient communication is a fundamental problem in wireless ad-hoc and sensor networks. In this paper, we explore the feasibility of a distributed beamforming approach to this problem, with a cluster of distributed transmitters emulating a centralized antenna array so as to transmit a common message signal coherently to a distant base station. The potential SNR gains from beamforming are well-known. However, realizing these gains requires synchronization of the individual carrier signals in phase and frequency. In this paper we show that a large fraction of the beamforming gains can be realised even with imperfect synchronization corresponding to phase errors with moderately large variance. We present a master-slave architecture where a designated master transmitter coordinates the synchronization of other (slave) transmitters for beamforming. We observe that the transmitters can achieve distributed beamforming with minimal coordination with the base station using channel reciprocity. Thus, inexpensive local coordination with a master transmitter makes the expensive communication with a distant base station receiver more efficient. However, the duplexing constraints of the wireless channel place a fundamental limitation on the achievable accuracy of synchronization. We present a stochastic analysis that demonstrates the robustness of beamforming gains with imperfect synchronization, and demonstrate a tradeoff between synchronization overhead and beamforming gains. We also present simulation results for the phase errors that validate the analysis

Distributed transmit beamforming: challenges and recent progress

Distributed transmit beamforming is a form of cooperative communication in which two or more information sources simultaneously transmit a common message and control the phase of their transmissions so that the signals constructively combine at an intended destination. Depending on the design objectives and constraints, the power gains of distributed beamforming can be translated into dramatic increases in range, rate, or energy efficiency. Distributed beamforming may also provide benefits in terms of security and interference reduction since less transmit power is scattered in unintended directions. Key challenges in realizing these benefits, however, include coordinating the sources for information sharing and timing synchronization and, most crucially, distributed carrier synchronization so that the transmissions combine constructively at the destination. This article reviews promising recent results in architectures, algorithms, and working prototypes which indicate that these challenges can be surmounted. Directions for future research needed to translate the potential of distributed beamforming into practice are also discussed.

Distributed beamforming for information transfer in sensor networks

Energy efficient transfer of data from sensors is a fundamental problem in sensor networks. We propose a distributed beamforming approach to this problem, with a cluster of sensors emulating a centralized antenna array. While it is well-known that beamforming can provide large performance gains, such gains presuppose not only accurate knowledge of the channel, but also time and phase synchronization at the transmitter. We propose explicit methods for achieving such synchronization in a distributed fashion, and analyze the effects of various sources of coordination error on the attained performance. We find that, as long as the error in range measurements or placement of the sensor nodes is within a fraction of a carrier wavelength, the proposed distributed beamforming strategies achieve most of the gains available from a centralized beamformer.

Distributed Transmit Beamforming Using Feedback Control

The concept of distributed transmit beamforming is implicit in many key results of network information theory. However, its implementation in a wireless network involves the fundamental challenge of ensuring phase coherence of the radio frequency signals from the different transmitters in the presence of unknown phase offsets between the transmitters and unknown channel gains from the transmitters to the receiver. In this paper, it is shown that such phase alignment can be achieved using distributed adaptation by the transmitters with minimal feedback from the receiver. Specifically, each transmitter independently makes a small random adjustment to its phase at each iteration, while the receiver broadcasts a single bit of feedback, indicating whether the signal-to-noise ratio (SNR) improved or worsened after the current iteration. The transmitters keep the ¿good¿ phase adjustments and discard the ¿bad¿ ones, thus implementing a distributed ascent algorithm. It is shown that, for a broad class of distributions for the random phase adjustments, this procedure leads to asymptotic phase coherence with probability one. A simple analytical model, borrowing ideas from statistical mechanics, is used to characterize the progress of the algorithm, and to provide guidance on parameter choices. This analytical model is based on a conjecture on the distribution of the received phases when the number of transmitters becomes large. Finally, the proposed system is shown to be scalable: the random phase perturbations can be chosen such that the convergence time is linear in the number of collaborating nodes.

Interference analysis for highly directional 60-GHz mesh networks: the case for rethinking medium access control

We investigate spatial interference statistics for multigigabit outdoor mesh networks operating in the unlicensed 60-GHz “millimeter (mm) wave” band. The links in such networks are highly directional: Because of the small carrier wavelength (an order of magnitude smaller than those for existing cellular and wireless local area networks), narrow beams are essential for overcoming higher path loss and can be implemented using compact electronically steerable antenna arrays. Directionality drastically reduces interference, but it also leads to “deafness,” making implicit coordination using carrier sense infeasible. In this paper, we make a quantitative case for rethinking medium access control (MAC) design in such settings. Unlike existing MAC protocols for omnidirectional networks, where the focus is on interference management, we contend that MAC design for 60-GHz mesh networks can essentially ignore interference and must focus instead on the challenge of scheduling half-duplex transmissions with deaf neighbors. Our main contribution is an analytical framework for estimating the collision probability in such networks as a function of the antenna patterns and the density of simultaneously transmitting nodes. The numerical results from our interference analysis show that highly directional links can indeed be modeled as pseudowired, in that the collision probability is small even with a significant density of transmitters. Furthermore, simulation of a rudimentary directional slotted Aloha protocol shows that packet losses due to failed coordination are an order of magnitude higher than those due to collisions, confirming our analytical results and highlighting the need for more sophisticated coordination mechanisms.

Scalable feedback control for distributed beamforming in sensor networks

Recent work has shown that large gains in communication capacity are achievable by distributed beamforming in sensor networks. The principal challenge in realizing these gains in practice, is in synchronizing the carrier signal of individual sensors in such a way that they combine coherently at the intended receiver. In this paper, we provide a scalable mechanism for achieving phase synchronization in completely distributed fashion, based only on feedback regarding the power of the net received signal. Insight into the workings of the protocol is obtained from a simple theoretical model that provides accurate performance estimates

Target tracking with binary proximity sensors

We explore fundamental performance limits of tracking a target in a two-dimensional field of binary proximity sensors, and design algorithms that attain those limits while providing minimal descriptions of the estimated target trajectory. Using geometric and probabilistic analysis of an idealized model, we prove that the achievable spatial resolution in localizing a targets trajectory is of the order of 1/ρR, where R is the sensing radius and ρ is the sensor density per unit area. We provide a geometric algorithm for computing an economical (in descriptive complexity) piecewise linear path that approximates the trajectory within this fundamental limit of accuracy. We employ analogies between binary sensing and sampling theory to contend that only a “lowpass” approximation of the trajectory is attainable, and explore the implications of this observation for estimating the targets velocity. We also consider nonideal sensing, employing particle filters to average over noisy sensor observations, and geometric geometric postprocessing of the particle filter output to provide an economical piecewise linear description of the trajectory. In addition to simulation results validating our approaches for both idealized and nonideal sensing, we report on lab-scale experiments using motes with acoustic sensors.

Distributed Control for Optimal Economic Dispatch of a Network of Heterogeneous Power Generators

In this paper, we present a simple, distributed algorithm for frequency control and optimal economic dispatch of power generators. In this algorithm, each generator independently adjusts its power-frequency set-points of generators to correct for generation and load fluctuations using only the aggregate power imbalance in the network, which can be observed by each generator through local measurements of the frequency deviation on the grid. In the absence of power losses, we prove that the distributed algorithm eventually achieves optimality, i.e., minimum cost power allocations, under mild assumptions (strict convexity and positivity of cost functions); we also present numerical results from simulations to compare its performance with traditional (centralized) dispatch algorithms. Furthermore, we show that the performance of the algorithm is robust in the sense that, even with power losses, it corrects for frequency deviations, and, for low levels of losses, it still achieves near-optimal allocations; we present an approximate analysis to quantify the resulting suboptimality.

A Scalable Architecture for Distributed Transmit Beamforming with Commodity Radios: Design and Proof of Concept

We describe a fully-wireless prototype of distributed transmit beamforming on a software-defined radio platform. Distributed beamforming is a cooperative transmission technique that can achieve orders of magnitude increases in range or energy efficiency of wireless communication systems. However, this technique requires precise synchronization of the radio frequency signal from each transmitter. The significance of our prototype is in demonstrating that this requirement can be satisfied using digital signal processing methods on commodity hardware with low-quality oscillators. Our synchronization approach scales to large numbers of transmitters: each transmitter runs independent algorithms based on periodically transmitted feedback packets from the receiver. A key simplification is the decoupling of the algorithms for frequency locking and beamsteering at each transmitter, even though both processes use the same feedback packets. Frequency locking employs an Extended Kalman filter to track the local oscillator offset between a transmitter and the receiver, using frequency offset measurements based on the feedback packet waveform, while the phase adjustments for beamsteering are determined using a one-bit feedback algorithm based on the feedback packet it payload. Our prototype demonstrates that distributed transmit beamforming can be incorporated into wireless networks without requiring hardware innovations, and provides open-source building blocks for future research and development.

Fully wireless implementation of distributed beamforming on a software-defined radio platform

We describe the key ideas behind our implementation of distributed beamforming on a GNU-radio based software-defined radio platform. Distributed beamforming is a cooperative transmission scheme whereby a number of nodes in a wireless network organize themselves into a virtual antenna array and focus their transmission in the direction of the intended receiver, potentially achieving orders of magnitude improvements in energy efficiency. This technique has been extensively studied over the past decade and its practical feasibility has been demonstrated in multiple experimental prototypes. Our contributions in the work reported in this paper are three-fold: (a) the first ever all-wireless implementation of distributed beamforming without any secondary wired channels for clock distribution or channel feedback, (b) a novel digital baseband approach to synchronization of high frequency RF signals that requires no hardware mod-ifications, and (c) an implementation of distributed beam-forming on a standard, open platform that allows easy reuse and extension. We describe the design of our system in de-tail present some initial results and discuss future directions for this work.