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.

We investigate a new approach to uplink communications in wideband outdoor cellular systems that can take advantage of multiple antennas at the base station in a scalable manner, while eliminating or minimizing overhead for channel estimation. The proposed techniques, which focus on exploiting correlated channels with the use of closely spaced antenna arrays, are applicable to emerging Orthogonal Frequency Division Multiplexing (OFDM) based Wireless Metropolitan Area Network (WMAN) systems, such as those based on the IEEE 802.16/20 standards. Outdoor channels frequently have a small number of dominant spatial modes, which can be learned from overhead-free estimation of the spatial covariance matrix by averaging across subcarriers. We describe an eigenbeamforming receiver which projects the received signal along the dominant spatial modes, yielding a beamforming gain that scales up with the number of receive elements and a diversity level depending on the number of dominant spatial modes. Shannon limits are first computed for block fading approximations to time- and frequency-selective channels. The suboptimal noncoherent diversity-combining receiver is shown to approach these limits, with linear complexity in the number dominant modes. Further, for dealing with spatially non-white interfering signals, adaptive suppression techniques are shown to mitigate strong interference with minimal training overhead.

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

We consider optimization of the capacity of a multi-input single-output wideband cellular "downlink," in which the base station has estimates of the statistics of the spatial channel. Our main focus is on orthogonal frequency-division multiplexed (OFDM) systems, although some of our results apply to single-carrier systems, as well. Prior work has shown that estimates of the channel spatial covariance can be obtained without overhead for both frequency-division duplex (FDD) and time-division duplex (TDD) systems by suitably averaging uplink measurements. In this paper, we investigate the benefits of supplementing this "free" covariance feedback with mean feedback, where the latter refers to estimates of the spatial channel realization in each subcarrier. Mean feedback can be obtained using reciprocity for TDD systems, and requires explicit feedback for FDD systems. We first devise strategies for using both covariance and mean feedback, mainly restricting attention to beamforming, which is optimal or near-optimal for many outdoor channels with narrow spatial spread. Second, since mean feedback degrades rapidly with feedback delay for mobile channels, we develop quantitative rules of thumb regarding the accuracy required for the mean feedback to be a useful supplement to the already available, and robust, covariance feedback. Our results validate the following intuition: the accuracy requirements for mean feedback to be useful are more relaxed for channels with larger spatial spread, or for a larger number of transmit elements.

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

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.

Energy efficient transfer of data from sensors is a fundamental problem in sensor networks. In this paper, 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.

This paper focuses on optimizing the capacity of a cellular "downlink" in which the base station (BS) is equipped with multiple antennas, while the mobile has a single antenna. The BS has access to both the first and second order statistics of the channel, obtained from mean feedback and covariance feedback, respectively. Our results apply to wideband orthogonal frequency division multiplexing (OFDM) systems, where accurate covariance feedback is obtained without overhead by averaging uplink measurements. Mean feedback is obtained from uplink measurements using reciprocity for time division duplex (TDD) systems, and would require explicit feedback for frequency division duplex (FDD) systems. Since mean feedback degrades rapidly with feedback delay for mobile channels, and requires feedback overhead for FDD systems, our purpose is to quantify the tradeoffs in using covariance feedback alone versus using both covariance and mean feedback.

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

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.

We consider wideband communication (e.g., using orthogonal frequency-division multiplexed (OFDM) systems) over a typical cellular "downlink," in which both the base station and the mobile may have multiple antennas, but the number of antennas at the mobile is assumed to be small. Implicit channel feedback can play a powerful role in such systems, especially for outdoor channels, which typically exhibit narrow spatial spreads. A summary of our findings is as follows: a) Implicit channel feedback regarding the covariance matrix for the downlink space-time channel can be obtained, without any power or bandwidth overhead, by suitably averaging uplink channel measurements across frequency. Since this approach relies on statistical reciprocity, it applies to both time-division duplex (TDD) and frequency-division duplex (FDD) systems. Using such covariance feedback yields significantly better performance at lower complexity than conventional space-time or space-frequency codes, which do not employ feedback; b) We provide guidelines for optimizing antenna spacing in systems with covariance feedback. Theoretical investigation of a hypothetical system with completely controllable channel eigenvalues shows that the optimal number of channel eigenmodes is roughly matched to the (small) number of receive antenna elements. Thus, while antenna elements in conventional systems without feedback should be spaced far apart in order to ensure uncorrelated responses, the optimal antenna spacing with covariance feedback is much smaller, thereby concentrating the channel energy into a small number of eigenmodes.

We consider space-time communication over a typical cellular "downlink" based on orthogonal frequency division multiplexing (OFDM), in which the base station may have several antenna elements, while the mobile has 1 or 2 antenna elements. A summary of our findings is as follows: (a) Implicit channel feedback regarding the covariance matrix for the downlink space-time channel can be obtained, without any power or bandwidth overhead, by suitably averaging uplink channel measurements across frequency. Since this approach relies on statistical reciprocity, it applies to both time division duplex (TDD) and frequency division duplex (FDD) systems. The covariance feedback can be used to obtain better performance on the downlink, at lower encoding and decoding complexity, compared to standard space-time coding (which does not employ channel feedback). (b) The conventional design without channel feedback is to space the transmit antennas far enough apart so as to ensure uncorrelated responses. However, when implicit feedback is available, much better performance is obtained with significantly smaller antenna spacing, optimized such that the number of dominant eigenmodes of the channel matches the number of receive antenna elements.