We propose a concept system termed distributed base station (DBS), which enables distributed transmit beamforming at large carrier wavelengths to achieve significant range extension and or increased downlink data rate, providing a low-cost infrastructure for applications such as rural broadband. We consider a frequency division duplexed (FDD) system, using feedback from the receiver to achieve the required phase coherence. At a given range, @math cooperating transmitters can achieve @math -fold increase in received power compared to that for a single transmitters, and feedback-based algorithms with near-ideal performance have been prototyped. In this paper, however, we identify and address key technical issues in translating such power gains into range extension via a DBS. First, to combat the drop in per-node SNR with extended range, we design a feedback-based adaptation strategy that is suitably robust to noise. Second, to utilize available system bandwidth, we extend narrowband adaptation algorithms to wideband channels through interpolation over OFDM subcarriers. Third, we observe that the feedback channel may become a bottleneck unless sophisticated distributed reception strategies are employed, but show that acceptable performance can still be obtained with standard uplink reception if channel time variations are slow enough. We quantify system performance compactly via outage capacity analyses.
A simple example of distributed beamforming with aggregated feedback is the one bit feedback algorithm @cite_4 @cite_3 , in which transmitters use small random phase perturbations to perform stochastic ascent on the received signal strength, based on the receiver feedback, broadcast to all transmitters, of one bit per iteration. This approach is simple and has formed the basis for several prototypes @cite_24 @cite_12 . The relatively slow convergence of the original algorithm (e.g., @math iterations to reach 75 knowledge of previous perturbations @cite_17 , or using knowledge of channel statistics at the receiver @cite_34 . However, the method is fundamentally mismatched to low per-node SNRs @cite_2 , roughly speaking, because noise masks the effect of small phase perturbations. This motivates our approach, in which the transmitters employ large phase perturbations during a training phase, rather than attempting to make small adjustments while beamforming.
@cite_4 @cite_3 @cite_24 @cite_2 @cite_34 @cite_12 @cite_17
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We consider distributed transmit beamforming from a cluster of cooperating nodes towards a distant destination, over a wideband dispersive channel. We consider explicit aggregate feedback, with the destination broadcasting its feedback to all nodes in the transmit cluster. Explicit feedback allows for frequency division duplex (FDD) operation, since there is no reliance on channel reciprocity. Aggregate feedback enables scalability, since the destination is agnostic to the number and identity of the transmitters. There are two key contributions. First, it is shown in a narrowband setting that, unlike a well-known one bit aggregate feedback scheme, a training-based approach in which each transmitter learns its channel to the destination based on aggregate feedback, is resilient to noise, even when the feedback is heavily quantized. Second, extending the scheme to wideband settings by using OFDM, training on a subset of subcarriers, we show that interpolation across subcarriers using sparse time domain modeling provides accurate channel estimates. In particular, at low SNR per node, our approach, which exploits the correlation across subcarriers, outperforms independent per- subcarrier channel estimates in a hypothetical benchmark system in which training and feedback is applied to all subcarriers. Our simulation results show that the beamforming performance obtained by our approach is a substantial fraction of the ideal beamforming gain, even for typical received SNRs per node as low as −20 dB, and coarse 4-phase feedback quantization. In general, the method requires training time linearly proportional to the number of cooperating nodes and inversely proportional to the per-node SNR. We investigate distributed beamforming from a cluster of N cooperating transmitters to a distant destination over a wideband dispersive channel. Feedback from the destination is critical for enabling this. In order to develop protocols that scale to arbitrarily large numbers of cooperating nodes, we restrict attention to aggregate feedback broadcast from the destination to the entire transmit cluster, rather than per-transmitter channel feedback as in conventional feedback-based MIMO systems. We first show that naive application of a one-bit feedback algorithm developed for narrowband channels to each subcarrier in an OFDM system does achieve beamforming gain on each subcarrier, but results in an effective channel at the destination with severe phase discontinuities across frequency, which is not amenable to standard receive channel estimation algorithms. We then show that it is possible to enforce smoothness of phase across frequency by augmenting the feedback to 2 bits per subcarrier, which enables modeling and estimation of the effective channel as sparse in the time domain. Our preliminary results show that, even when the SNR per node is well below the threshold for reliable demodulation, it is possible to bootstrap using the N-fold power pooling gain obtained from incoherent combining of the signals from multiple transmitters, and to attain a significant fraction of the N2-fold beamforming gain using the proposed algorithm. We also discuss a number of open issues, recognizing that this is only a first step in developing scalable, wideband, distributed MIMO systems. Distributed transmit beamforming with N cooperating nodes, each with fixed transmit power, provides a received power scaling with N2, corresponding to a “power pooling” gain of N and a beamforming gain of N. Prior work has shown that the optimal beamforming solution can be attained using a decentralized, iterative algorithm based on one bit (per iteration) feedback broadcast from the receiver to the transmitters. The algorithm is provably convergent in a noiseless setting, and is the basis for several successful prototypes. In this paper, we develop a framework for providing analytical insight into the effect of receiver noise, with the following key question in mind: can we bootstrap the algorithm from the incoherent power-pooled solution to operate in a regime in which the received SNR per node can be made arbitrarily small as we scale up the number of nodes N? Our analytical computations, validated by simulations, yield a somewhat negative answer: while the power-pooling gain guarantees a linear increase in received power with N, the per-node SNR cannot be scaled down with N if we wish to attain a quadratic increase in received power. Specifically, the fraction of the ideal beamforming gain attained using the one-bit algorithm is asymptotically independent of N, and depends only on the per-node SNR. However, the one-bit algorithm provides significant performance gains in practical regimes with a moderate number of cooperating nodes: the per-node SNR required for attaining a substantial fraction of the beamforming gain is low enough (e.g., − 5dB for 65 of the beamforming gain) to provide significant extension in operation regimes, while providing aggregate SNRs which permit reliable communication at high spectral efficiency: for example, starting from −5 dB per-node SNR, we obtain about 11 dB aggregate SNR with 10 cooperating nodes, and 17 dB SNR with 20 cooperating nodes. In this paper an improved iterative algorithm is proposed for distributed transmit beamforming to achieve carrier phase alignment at the receiver. The transmitters adjust their phase offsets based on one-bit feedback from the receiver in each time slot. The proposed algorithm has an improvement in the convergence speed of phase alignment compared to a previously proposed algorithm in the literature by exploiting one-bit feedback information more efficiently. Simulation results show that the improved algorithm on average has a 20 faster convergence speed. The minimum number of time slots required to achieve specified beamforming gains and the corresponding perturbation steps are obtained by Monte Carlo simulations. We propose and demonstrate a scalable architecture for distributed receive beamforming. In a receive cluster of N + 1 nodes receiving a message from a distant transmitter, N nodes are designated as amplify-and-forward relays and one node is designated as the receiver. The relay nodes apply a phase shift to their received signal and forward it such that their forwarded signals add up constructively at the receiver, with received SNR scaling linearly with N. This approach transforms a distributed receive beamforming problem on the "long link" from transmitter to receive cluster into a distributed transmit beamforming problem on the "short link" from relays to receiver, so that the number of degrees of freedom on the short link need not scale with N. A key simplification relative to distributed transmit beamforming is that, for stable oscillators, relay frequency synchronization is not required. For oscillators with drift, we provide a simple rule of thumb for when explicit frequency synchronization can be avoided. Explicit timing alignment can also be avoided by exploiting the timing of the message received on the long link. That leaves the problem of phase adjustment at the relays, and we employ an algorithm originally invented for distributed transmit beamforming for this purpose, using one bit (per iteration) feedback from the receiver. Experimental results with software-defined radios (whose oscillators have significant drift) demonstrate that the expected gains in received signal strength are obtained with the proposed architecture. 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. This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signal-to-interference-plus-noise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear Perron-Frobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear Perron-Frobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution. Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple-input multiple-output (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector; both are hard to realize. In this article, a quantized maximum signal-to-noise ratio (SNR) beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter. By using the distribution of the optimal beamforming vector in independent and identically distributed Rayleigh fading matrix channels, the codebook design problem is solved and related to the problem of Grassmannian line packing. The proposed design criterion is flexible enough to allow for side constraints on the codebook vectors. Bounds on the codebook size are derived to guarantee full diversity order. Results on the density of Grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or SNR loss. Monte Carlo simulations are presented that compare the probability of error for different quantization strategies. In this letter, we study the robust beamforming problem for the multi-antenna wireless broadcasting system with simultaneous information and power transmission, under the assumption of imperfect channel state information (CSI) at the transmitter. Following the worst-case deterministic model, our objective is to maximize the worst-case harvested energy for the energy receiver while guaranteeing that the rate for the information receiver is above a threshold for all possible channel realizations. Such problem is nonconvex with infinite number of constraints. Using certain transformation techniques, we convert this problem into a relaxed semidefinite programming problem (SDP) which can be solved efficiently. We further show that the solution of the relaxed SDP problem is always rank-one. This indicates that the relaxation is tight and we can get the optimal solution for the original problem. Simulation results are presented to validate the effectiveness of the proposed algorithm. We propose an efficient open-loop channel estimator for a millimeter-wave (mm-wave) hybrid multiple-input multiple-output (MIMO) system consisting of radio-frequency (RF) beamformers with large antenna arrays followed by a baseband MIMO processor. A sparse signal recovery problem exploiting the sparse nature of mm-wave channels is formulated for channel estimation based on the parametric channel model with quantized angles of departures arrivals (AoDs AoAs), called the angle grids. The problem is solved by the orthogonal matching pursuit (OMP) algorithm employing a redundant dictionary consisting of array response vectors with finely quantized angle grids. We suggest the use of non-uniformly quantized angle grids and show that such grids reduce the coherence of the redundant dictionary. The lower and upper bounds of the sum-of-squared errors of the proposed OMP-based estimator are derived analytically: the lower bound is derived by considering the oracle estimator that assumes the knowledge of AoDs AoAs, and the upper bound is derived based on the results of the OMP performance guarantees. The design of training vectors (or sensing matrix) is particularly important in hybrid MIMO systems, because the RF beamformer prevents the use of independent and identically distributed random training vectors, which are popular in compressed sensing. We design training vectors so that the total coherence of the equivalent sensing matrix is minimized for a given RF beamforming matrix, which is assumed to be unitary. It is observed that the estimation accuracy can be improved significantly by randomly permuting the columns of the RF beamforming matrix. The simulation results demonstrate the advantage of the proposed OMP with a redundant dictionary over the existing methods such as the least squares method and the OMP based on the virtual channel model. In this paper, we consider two different models of partial channel state information at the base station transmitter (CSIT) for multiple antenna broadcast channels: 1) the shape feedback model where the normalized channel vector of each user is available at the base station and 2) the limited feedback model where each user quantizes its channel vector according to a rotated codebook that is optimal in the sense of mean squared error and feeds back the codeword index. This paper is focused on characterizing the sum rate performance of both zero-forcing dirty paper coding (ZFDPC) systems and channel inversion (CI) systems under the given two partial CSIT models. Intuitively speaking, a system with shape feedback loses the sum rate gain of adaptive power allocation. However, shape feedback still provides enough channel knowledge for ZFDPC and CI to approach their own optimal throughput in the high signal-to-noise ratio (SNR) regime. As for limited feedback, we derive sum rate bounds for both signaling schemes and link their throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for both schemes for asymptotically high SNR. Distributed beamforming is a form of cooperation among nodes in a wireless network to efficiently deliver a common message to a distant receiver. The critical requirement to achieve electromagnetic coherence is to synchronize the initial phases of all local oscillators, introducing minimal overhead and complexity. In the paper we introduce random, deterministic and hybrid algorithms, all based on feedback from the common receiver as the driving force, but with different phase update strategies. Our numerical results show that these algorithms achieve faster convergence time than previously proposed approaches. Feedback of quantized channel state information (CSI), called limited feedback, enables transmit beamforming in multiple-input-multiple-output (MIMO) wireless systems with a small amount of overhead. Due to its efficiency, beamforming with limited feedback has been adopted in several wireless communication standards. Prior work on limited feedback commonly adopts the block fading channel model where temporal correlation in wireless channels is neglected. In this paper, we consider temporally correlated channels and design single-user transmit beamforming with limited feedback. Analytical results concerning CSI feedback are derived by modeling quantized CSI as a first-order finite-state Markov chain. These results include the information rate of the CSI quantizer output, the bit rate a CSI feedback channel is required to support, and the effect of feedback delay on throughput. In particular, based on the theory of Markov chain convergence rate, feedback delay is proved to reduce the throughput gain due to CSI feedback at least exponentially. Furthermore, an algorithm is proposed for CSI feedback compression in time. Combining the results in this work leads to a new method for designing limited feedback beamforming as demonstrated by a design example. Maximizing the output signal-to-noise ratio (SNR) of a sensor array in the presence of spatially colored noise leads to a generalized eigenvalue problem. While this approach has extensively been employed in narrowband (antenna) array beamforming, it is typically not used for broadband (microphone) array beamforming due to the uncontrolled amount of speech distortion introduced by a narrowband SNR criterion. In this paper, we show how the distortion of the desired signal can be controlled by a single-channel post-filter, resulting in a performance comparable to the generalized minimum variance distortionless response beamformer, where arbitrary transfer functions relate the source and the microphones. Results are given both for directional and diffuse noise. A novel gradient ascent adaptation algorithm is presented, and its good convergence properties are experimentally revealed by comparison with alternatives from the literature. A key feature of the proposed beamformer is that it operates blindly, i.e., it neither requires knowledge about the array geometry nor an explicit estimation of the transfer functions from source to sensors or the direction-of-arrival. We consider the joint optimization of beamformers and linear receivers in a MIMO interference network. Each transmitter transmits a single beam corresponding to a rank-one precoder. When the number of users K is greater than the number of antennas at each terminal N, the maximum degrees of freedom is achieved via spatial interference alignment. Interference alignment is feasible for up to K = 2N−1 users, in which case there is a finite number of solutions to the alignment conditions. This number of solutions increases rapidly with N, and the solutions depend only on the cross-channel coefficients (i. e., they are independent of the direct channels). To maximize the achievable sum rate at high SNRs we therefore wish to select an aligned solution which is best matched to the direct channels. We evaluate the performance of this scheme for large K and N, assuming that the solution is the best out of a random subset of aligned solutions. We then compare numerically this performance with the performance of previously proposed numerical (e. g., forward-backward) techniques for optimizing beams, and a new technique which tracks the local optimum as the SNR is incrementally increased, similar to a homotopy method for improving convergence properties. We observe that the incremental technique typically achieves better performance than the previously proposed methods. In multiple antenna wireless systems, beamforming is a simple technique for guarding against the negative effects of fading. Unfortunately, beamforming requires the transmitter to have knowledge of the forward-link channel which is often not available a priori. One way of overcoming this problem is to design the beamforming vector using a limited number of feedback bits sent from the receiver to the transmitter. In limited feedback beamforming, the beamforming vector is restricted to lie in a codebook that is known to both the transmitter and receiver. Random vector quantization (RVQ) is a simple approach to codebook design that generates the vectors independently from a uniform distribution on the complex unit sphere. This correspondence presents performance analysis results for RVQ limited feedback beamforming Multicell coordinated beamforming (MCBF), where multiple base stations (BSs) collaborate with each other in the beamforming design for mitigating the intercell interference (ICI), has been a subject drawing great attention recently. Most MCBF designs assume perfect channel state information (CSI) of mobile stations (MSs); however CSI errors are inevitable at the BSs in practice. Assuming elliptically bounded CSI errors, this paper studies the robust MCBF design problem that minimizes the weighted sum power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the MSs. Our goal is to devise a distributed optimization method to obtain the worst-case robust beamforming solutions in a decentralized fashion with only local CSI used at each BS and limited backhaul information exchange between BSs. However, the considered problem is difficult to handle even in the centralized form. We first propose an efficient approximation method for solving the nonconvex centralized problem, using semidefinite relaxation (SDR), an approximation technique based on convex optimization. Then a distributed robust MCBF algorithm is further proposed, using a distributed convex optimization technique known as alternating direction method of multipliers (ADMM). We analytically show the convergence of the proposed distributed robust MCBF algorithm to the optimal centralized solution. We also extend the worst-case robust beamforming design as well as its decentralized implementation method to a fully coordinated scenario. Simulation results are presented to examine the effectiveness of the proposed SDR method and the distributed robust MCBF algorithm. This paper extends Khatri (1964, 1969) distribution of the largest eigenvalue of central complex Wishart matrices to the noncentral case. It then applies the resulting new statistical results to obtain closed-form expressions for the outage probability of multiple-input-multiple-output (MIMO) systems employing maximal ratio combining (known also as "beamforming" systems) and operating over Rician-fading channels. When applicable these expressions are compared with special cases previously reported in the literature dealing with the performance of (1) MIMO systems over Rayleigh-fading channels and (2) single-input-multiple-output (SIMO) systems over Rician-fading channels. As a double check these analytical results are validated by Monte Carlo simulations and as an illustration of the mathematical formalism some numerical examples for particular cases of interest are plotted and discussed. These results show that, given a fixed number of total antenna elements and under the same scattering condition (1) SIMO systems are equivalent to multiple-input-single-output systems and (2) it is preferable to distribute the number of antenna elements evenly between the transmitter and the receiver for a minimum outage probability performance. 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 Cramer 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 ( @math ) 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. We study downlink beamforming in a single-cell network with a multi-antenna base station (BS) serving cache-enabled users. For a given common rate of the files in the system, we first formulate the minimum transmit power with beamforming at the BS as a non-convex optimization problem. This corresponds to a multiple multicast problem, to which a stationary solution can be efficiently obtained through successive convex approximation (SCA). It is observed that the complexity of the problem grows exponentially with the number of subfiles delivered to each user in each time slot, which itself grows exponentially with the number of users in the system. Therefore, we introduce a low-complexity alternative through time-sharing that limits the number of subfiles that can be received by a user in each time slot. It is shown through numerical simulations that, the reduced-complexity beamforming scheme has minimal performance gap compared to transmitting all the subfiles jointly, and outperforms the state-of-the-art low-complexity scheme at all SNR and rate values with sufficient spatial degrees of freedom, and in the high SNR high rate regime when the number of spatial degrees of freedom is limited.