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
2288934705 1518904094 1644869847 2033503324
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.