Gwen Barriac

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 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.

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

Spread-spectrum techniques for distributed space-time communication in sensor networks

Communication is widely acknowledged as a fundamental bottleneck in sensor networks with large numbers of low-cost, low-power nodes. We consider cooperative transmission of a common message signal from a cluster of sensor nodes to a remote receiver, under realistic transmission models accounting for timing and frequency synchronization offsets across the nodes. The purpose is to obtain range extension by combining the powers of the nodes in a cluster and to obtain robustness against channel impairments by exploiting the diversity naturally arising from the spatial distribution of the sensor nodes. For a simple scheme in which all nodes asynchronously transmit the same signal, we analyze the available diversity gains using an information theoretic analysis of outage capacity for wideband systems. We show that standard modulation formats can be adapted to realize diversity gains in the presence of synchronization errors. We propose simple receiver architectures that realize diversity gains and have desirable scaling properties as the number of sensors increases.

Characterizing outage rates for space-time communication over wideband channels

We provide a compact characterization of outage rates for a wideband wireless communication system whose parameters are chosen to model an outdoor cellular downlink. The base station transmitter is equipped with an antenna array, while the mobile receiver has a single antenna. Our analysis quantifies the effects of frequency and spatial diversity for measurement-based channel models available in the literature. Design prescriptions based on our framework would apply, for example, to fourth-generation cellular systems using orthogonal frequency-division multiplexing. Our information-theoretic computations yield the following findings. Complex models typically employed in simulations can be replaced by simple, bandwidth-dependent, tap-delay-line models without loss of accuracy. The spectral efficiency (i.e., the achievable rate, divided by the bandwidth) is well approximated as a Gaussian random variable, so that it is only necessary to specify its mean and variance in order to compute the outage rates. We provide analytical formulas for the mean and variance as a function of the space-time channel model, and verify that the resulting outage rates match closely with simulation. For a wide class of outdoor channels, the mean spectral efficiency depends only on the spatial diversity, while the variance depends on the spatial and frequency diversity via a product. Our definitions of frequency and spatial diversity have physically motivated interpretations, and do not rely on high signal-to-noise ratio asymptotics, as in prior work.

Characterizing outage capacity for space-time communication over wideband wireless channels

We provide a compact characterization of the outage rates for wideband wireless communication, quantifying the effects of frequency and spatial diversity. Our information-theoretic computations yield the following findings. (a) Complex models typically employed in simulations can be replaced by simple, bandwidth-dependent, tap delay line models without loss of generality. (b) The spectral efficiency (i.e., the achievable rate, divided by the bandwidth) is well approximated as a Gaussian random variable, so that it is only necessary to specify its mean and variance to obtain outage rates. (c) The mean spectral efficiency depends only on the spatial diversity, while the variance depends on the spatial and frequency diversity via a product. Our definitions of frequency and spatial diversity have physically motivated interpretations, and are not based on high signal-to-noise ratio (SNR) asymptotics as in prior work.

Antenna selection for space-time communication with covariance feedback

We consider space-time communication for a cellular downlink in which the base station (BS) transmitter has multiple antennas, while the mobile receiver has one or two. Only a subset of the available antennas at the BS are used for transmission, thus reducing the number of RF chains and the complexity of the baseband signal processing. It is assumed that the BS does not know the instantaneous downlink channel realization, but has estimates of the covariance of the space-time channel: covariance information can be easily obtained in wideband systems by averaging uplink channel measurements over frequency. Based on the optimization of a lower bound for capacity, we are able to provide rules of thumb for antenna selection as a function of the physical channel characteristics and the number of receive antennas. This procedure is shown to be optimal or near-optimal (relative to exhaustive computation of the best antenna subset) at moderate SNR.

Noncoherent eigenbeamforming for a wideband cellular uplink

In this paper, we investigate wideband space-time communication on the uplink of an outdoor cellular system, in which the base station is equipped with N antennas and the mobile has a single antenna. We assume noncoherent reception at the base station, which incurs significantly less overhead than pilot-based estimation of the space-time channel from each mobile to the base station. Noncoherent communication techniques are particularly well suited to outdoor cellular systems for which channel time variations are significant due to mobility at vehicular speeds

Optimizing medium access control for rapid handoffs in pseudocellular networks

The steadily decreasing cost of wireless local area network (WLAN) technology motivates the concept of pseudocellular networks that support real-time traffic and seamless mobility with WLAN-type infrastructure, in addition to the standard low-mobility data applications of WLAN. A key challenge in such networks is the support of highly mobile users with real-time traffic, because of the high handoff rate resulting from small cell sizes. In this paper, we show that timely mobile-centric handoffs can be achieved using optimized ALOHA-like reservation schemes which, for a given call drop probability, require significantly fewer reservation resources than conventional methods. For Poisson handoff traffic, we employ dynamic programming to derive an optimal stationary policy. We then use these results as a building block for obtaining adaptive reservation schemes (dynamically varying the number of minislots per frame) for bursty handoff traffic.