Orthogonal frequency division multiplexing (OFDM) has been widely used in communication systems operating in the millimeter wave (mmWave) band to combat frequency-selective fading and achieve multi-Gbps transmissions, such as IEEE 802.15.3c and IEEE 802.11ad. For mmWave systems with ultra high sampling rate requirements, the use of low-resolution analog-to-digital converters (ADCs) (i.e., 1-3 bits) ensures an acceptable level of power consumption and system costs. However, orthogonality among subchannels in the OFDM system cannot be maintained because of the severe nonlinearity caused by low-resolution ADC, which renders the design of data detector challenging. In this study, we develop an efficient algorithm for optimal data detection in the mmWave OFDM system with low-resolution ADCs. The analytical performance of the proposed detector is derived and verified to achieve the fundamental limit of the Bayesian optimal design. On the basis of the derived analytical expression, we further propose a power allocation (PA) scheme that seeks to minimize the average symbol error rate. In addition to the optimal data detector, we also develop a feasible channel estimation method, which can provide high-quality channel state information without significant pilot overhead. Simulation results confirm the accuracy of our analysis and illustrate that the performance of the proposed detector in conjunction with the proposed PA scheme is close to the optimal performance of the OFDM system with infinite-resolution ADC.
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我们考虑基于深度学习的检测,并且表明可以在不知道底层信道模型的情况下提供表现良好的检测器。此外,当已知信道模型时,我们证明可以训练不需要信道状态信息(CSI)的检测器。具体地,我们提出了一种称为滑动双向重复神经网络(SBRNN)的技术用于检测,其中在训练之后,当信号流到达接收器时,检测器实时估计数据。我们使用Poisson信道模型评估该算法以及其他神经网络(NN)架构,该模型适用于光学和分子通信系统。此外,我们还评估了这种检测方法的性能,该方法应用于通过分子通信平台发送的数据,其中信道模型难以模拟分析。我们证明了SBRNN在计算上是有效的,并且可以在不知道底层信道模型的情况下在各种信道条件下执行检测。我们还证明了所提出的SBRNN检测器的误码率(BER)性能优于具有不完美CSI的维特比检测器以及先前已经提出的其他NN检测器的性能。最后,我们证明了SBRNN在快速变化的信道中表现良好,其中相干时间在单个符号持续时间的量级上。
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We investigate the uplink throughput achievable by a multiple-user (MU) massive multiple-input multiple-output (MIMO) system in which the base station is equipped with a large number of low-resolution analog-to-digital converters (ADCs). Our focus is on the case where neither the transmitter nor the receiver have any a priori channel state information. This implies that the fading realizations have to be learned through pilot transmission followed by channel estimation at the receiver, based on coarsely quantized observations. We propose a novel channel estimator, based on Bussgang's decomposition, and a novel approximation to the rate achievable with finite-resolution ADCs, both for the case of finite-cardinality constellations and of Gaussian inputs, that is accurate for a broad range of system parameters. Through numerical results, we illustrate that, for the 1-bit quantized case, pilot-based channel estimation together with maximal-ratio combing or zero-forcing detection enables reliable multiuser communication with high-order constellations in spite of the severe nonlinearity introduced by the ADCs. Furthermore, we show that the rate achievable in the infinite-resolution (no quantization) case can be approached using ADCs with only a few bits of resolution. We finally investigate the robustness of low-ADC-resolution MU-MIMO uplink against receive power imbalances between the different users, caused for example by imperfect power control. Index Terms-Analog-to-digital converter (ADC), channel capacity , linear minimum mean square error (LMMSE) channel estimation, low-resolution quantization, multiuser massive multiple-input multiple-output (MIMO).
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This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear MMSE detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a "hidden" Gaussian statistic independent of the interferers. Thus the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio suffers a degradation due to the multiple-access interference. The uncoded error performance (e.g., symbol-error-rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to MIMO channels such as in multiantenna systems. Index Terms-Channel capacity, code-division multiple access (CDMA), free energy, multiple-input multiple-output (MIMO) channel, multiuser detection, multiuser efficiency, replica method, statistical mechanics.
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Coarse quantization at the base station (BS) of a massive multiuser (MU) multiple-input multiple-output (MIMO) wireless system promises significant power and cost savings. Coarse quantization also enables significant reductions of the raw analog-to-digital converter (ADC) data that must be transferred from a spatially-separated antenna array to the baseband processing unit. The theoretical limits as well as practical transceiver algorithms for such quantized MU-MIMO systems operating over frequency-flat, narrowband channels have been studied extensively. However, the practically relevant scenario where such communication systems operate over frequency-selective, wideband channels is less well understood. This paper investigates the uplink performance of a quantized massive MU-MIMO system that deploys orthogonal frequency-division multiplexing (OFDM) for wideband communication. We propose new algorithms for quantized maximum a-posteriori (MAP) channel estimation and data detection, and we study the associated performance/quantization trade-offs. Our results demonstrate that coarse quantization (e.g., four to six bits, depending on the ratio between the number of BS antennas and the number of users) in massive MU-MIMO-OFDM systems entails virtually no performance loss compared to the infinite-precision case at no additional cost in terms of baseband processing complexity. Index Terms-Analog-to-digital conversion, convex optimization , forward-backward splitting (FBS), frequency-selective channels , massive multiuser multiple-input multiple-output (MU-MIMO), maximum a-posteriori (MAP) channel estimation, minimum mean-square error (MMSE) data detection, orthogonal frequency-division multiplexing (OFDM), quantization.
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A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing, and rate of innovation. The redundancy introduced by channel coding in finite and real Galois fields is then related to over-sampling with similar reconstruction algorithms. The error locator polynomial (ELP) and iterative methods are shown to work quite effectively for both sampling and coding applications. The methods of Prony, Pisarenko, and MUltiple SIgnal Classification (MUSIC) are next shown to be targeted at analyzing signals with sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter in rate of innovation and ELP in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method under noisy environments. The iterative methods developed for sampling and coding applications are shown to be powerful tools in spectral estimation. Such narrowband spectral estimation is then related to multi-source location and direction of arrival estimation in array processing. Sparsity in unobservable source signals is also shown to facilitate source separation in sparse component analysis; the algorithms developed in this area such as linear programming and matching pursuit are also widely used in compressed sensing. Finally, the multipath channel estimation problem is shown to have a sparse formulation; algorithms similar to sampling and coding are used to estimate typical multicarrier communication channels.
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Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (gener-alized) additive models, smoothing spline models, state space models, semiparametric regression , spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of struc-tured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality , which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.
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Shannon's determination of the capacity of the linear Gaussian channel has posed a magnificent challenge to succeeding generations of researchers. This paper surveys how this challenge has been met during the past half century. Orthogonal minimum-bandwidth modulation techniques and channel capacity are discussed. Binary coding techniques for low-signal-to-noise ratio (SNR) channels and nonbinary coding techniques for high-SNR channels are reviewed. Recent developments, which now allow capacity to be approached on any linear Gaussian channel, are surveyed. These new capacity-approaching techniques include turbo coding and decoding, multilevel coding, and combined coding/precoding for intersymbol-interference channels.
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In this paper, we propose a new detection algorithm for large-scale wireless systems, referred to as post sparse error detection (PSED) algorithm, that employs a sparse error recovery algorithm to refine the estimate of a symbol vector obtained by the conventional linear detector. The PSED algorithm operates in two steps: First, sparse transformation converting the original nonsparse system into the sparse system whose input is an error vector caused by the symbol slicing; and second, the estimation of the error vector using the sparse recovery algorithm. From the asymptotic mean square error analysis and empirical simulations performed on large-scale wireless systems, we show that the PSED algorithm brings significant performance gain over classical linear detectors while imposing relatively small computational overhead. Index Terms-Sparse signal recovery, compressive sensing, large-scale systems, orthogonal matching pursuit, sparse transformation , linear minimum mean square error, error correction.
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Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Lévy-driven stochastic volatility model.
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Communications receivers that rely on 1-bit analog-to-digital conversion are advantageous in terms of hardware complexity and power dissipation. Performance limitations due to the 1-bit quantization can be tackled with oversampling. This paper considers the oversampling gain from an information-theoretic perspective by analyzing the channel capacity with 1-bit quanti-zation and oversampling at the receiver for the particular case of AWGN channels. This includes a numerical computation of the capacity and optimal transmit symbol constellations, as well as the derivation of closed-form expressions for large oversampling ratios and for high signal-to-noise ratios of the channel.
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新的通信标准需要处理机器到机器的通信,其中用户可以以异步方式随时开始或停止发送。因此,用户的数量是未知的和时变的参数,需要准确地估计,以便适当地恢复系统中所有用户发送的符号。在本文中,我们在多用户通信信道中增加了联合信道参数和数据估计的问题,其中发射机的数量是未知的。为此,我们开发了无限阶乘有限状态机模型,基于马尔可夫印度自助餐的贝叶斯非参数模型,允许无限数量的具有任意信道长度的发射机。我们提出了一种利用切片采样和粒子Gibbs增强采样的推理算法。我们的方法是完全盲目的,因为它不需要先前的信道估计步骤,先前的发射机数量的知识或信令信息。我们的实验结果松散地基于LTE随机接入信道,表明所提出的方法可以有效地恢复各种情况下的数据生成过程,具有不同数量的发射机,接收机数量,星座顺序,信道长度和信号到 - 噪音比。
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Several approximate non-linear fiber propagation models have been proposed over the years. Recent reconsideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-Noise (GN) model. The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy vs. complexity trade-off. This paper tries to pull together the recent results regarding the GN-model definition, understanding, relations vs. other models , validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment.
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We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets, sparsely populated in the radar's unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or perform poorly in noisy conditions. Here we describe a sub-Nyquist sampling and recovery approach called Doppler focusing which addresses all of these problems: it performs low rate sampling and digital processing, imposes no restrictions on the transmitter, and uses a CS dictionary with size which does not increase with increasing number of pulses P. Furthermore, in the presence of noise, Doppler focusing enjoys a signal-to-noise ratio (SNR) improvement which scales linearly with P , obtaining good detection performance even at SNR as low as-25dB. The recovery is based on the Xampling framework, which allows reducing the number of samples needed to accurately represent the signal, directly in the analog-to-digital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. Finally, our approach can be implemented in hardware using a previously suggested Xampling radar prototype.
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移动设备的普及导致网络边缘处的大量数据和计算资源的可用性。为了利用数据和资源,出现了一种新的机器学习范例,称为边缘学习,其中学习算法部署在边缘,为移动用户提供快速和智能的服务。虽然计算速度正在快速增长,但通信延迟正在成为快速边缘学习的瓶颈。为了解决这个问题,这项工作的重点是设计一种用于边缘学习的低延迟多址方案。我们考虑一种流行的框架,联邦边缘学习(FEEL),其中边缘服务器和设备上学习被同步以训练模型而不违反用户数据隐私。建议由设备宽带信道同时发送的模型更新应该通过利用多接入信道的叠加属性来“空中”模拟聚合。因此,“干扰”被用于提供模型聚合的快速实现。与传统的正交接入(即OFDMA)相比,这导致了显着的等待时间减少。在这项工作中,FEEL的性能表征为单细胞随机网络。首先,由于需要聚合的设备之间的功率对准,显示在更新可靠性和预期更新截断比之间存在基本权衡。这促使设计用于FEEL的机会调度方案,其选择具有距离阈值的设备。使用真实数据集显示该方案以在高移动性的情况下产生令人满意的学习性能。其次,分析了所提出的模拟聚合和OFDMA方案的多访问延迟。它们的比率(量化了变压器的延迟减少量)被证明与器件数量几乎呈线性关系。
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We study the approximate message-passing decoder for sparse superposition coding on the additive white Gaussian noise channel and extend our preliminary work [1]. We use heuristic statistical-physics-based tools such as the cavity and the replica methods for the statistical analysis of the scheme. While superposition codes asymptotically reach the Shannon capacity, we show that our iterative decoder is limited by a phase transition similar to the one that happens in Low Density Parity check codes. We consider two solutions to this problem, that both allow to reach the Shannon capacity: i) a power allocation strategy and ii) the use of spatial coupling, a novelty for these codes that appears to be promising. We present in particular simulations suggesting that spatial coupling is more robust and allows for better reconstruction at finite code lengths. Finally, we show empirically that the use of a fast Hadamard-based operator allows for an efficient reconstruction, both in terms of computational time and memory, and the ability to deal with very large messages.
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通过基于神经网络的自动编码器对通信系统进行端到端学习的想法存在缺点,即它需要可区分的信道模型。我们在本文中提出了一种新颖的学习算法来缓解这个问题。该算法使得能够使用未知信道模型或使用不可微分的组件来训练通信系统。它在使用真实梯度的接收器训练和使用渐变的近似训练发射器之间进行迭代。我们表明,这种方法与各种渠道和任务的基于模型的培训一样有效。此外,我们通过软件定义无线电上的硬件实现证明了算法的实用可行性,它通过同轴电缆和无线信道实现了最先进的性能。
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The CDMA channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods. Furthermore, its analysis provides a comparison baseline for CDMA channels with deterministic signature waveforms spanning one symbol period. We analyze the spectral efficiency (total capacity per chip) as a function of the number of users, spreading gain, and signal-to-noise ratio, and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading. White Gaussian background noise and equal-power synchronous users are assumed. The following receivers are analyzed: a) optimal joint processing, b) single-user matched filtering, c) decorrelation, and d) MMSE linear processing.
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We present a general problem formulation for optimal parameter estimation based on quantized observations, with application to antenna array communication and processing (channel estimation, time-of-arrival (TOA) and direction-of-arrival (DOA) estimation). The work is of interest in the case when low resolution A/D-converters (ADCs) have to be used to enable higher sampling rate and to simplify the hardware. An Expectation-Maximization (EM) based algorithm is proposed for solving this problem in a general setting. Besides, we derive the Cramér-Rao Bound (CRB) and discuss the effects of quantization and the optimal choice of the ADC characteristic. Numerical and analytical analysis reveals that reliable estimation may still be possible even when the quantization is very coarse.
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