arXiv subjects

Andrea J. Goldsmith

Publications and source records attributed to Andrea J. Goldsmith.

At least 37 records · Page 2Linked to original sources

arXiv2021

Learned Factor Graphs for Inference from Stationary Time Sequences

The design of methods for inference from time sequences has traditionally relied on statistical models that describe the relation between a latent desired sequence and the observed one. A broad family of model-based algorithms have been derived to carry out inference at controllable complexity using recursive computations over the factor graph representing the underlying distribution. An alternative model-agnostic approach utilizes machine learning (ML) methods. Here we propose a framework that combines model-based algorithms and data-driven ML tools for stationary time sequences. In the proposed approach, neural networks are developed to separately learn specific components of a factor graph describing the distribution of the time sequence, rather than the complete inference task. By exploiting stationary properties of this distribution, the resulting approach can be applied to sequences of varying temporal duration. Learned factor graph can be realized using compact neural networks that are trainable using small training sets, or alternatively, be used to improve upon existing deep inference systems. We present an inference algorithm based on learned stationary factor graphs, which learns to implement the sum-product scheme from labeled data, and can be applied to sequences of different lengths. Our experimental results demonstrate the ability of the proposed learned factor graphs to learn to carry out accurate inference from small training sets for sleep stage detection using the Sleep-EDF dataset, as well as for symbol detection in digital communications with unknown channels.

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arXiv2021

Interference Reduction in Virtual Cell Optimization

Virtual cell optimization clusters cells into neighborhoods and performs optimized resource allocation over each neighborhood. In prior works we proposed resource allocation schemes to mitigate the interference caused by transmissions in the same virtual cell. This work aims at mitigating both the interference caused by the transmissions of users in the same virtual cell and the interference between transmissions in different virtual cells. We propose a resource allocation technique that reduces the number of users that cannot achieve their constant guaranteed bit rate, i.e., the "unsatisfied users", in an uplink virtual cell system with cooperative decoding. The proposed scheme requires only the knowledge of the number of users each base station serves and relies on creating the interference graph between base stations at the edges of virtual cells. Allocation of frequency bands to users is based on the number of users each base station would serve in a non cooperative setup. We evaluate the performance of our scheme for a mmWave system. Our numerical results show that our scheme decreases the number of users in the system whose rate falls below the guaranteed rate, set to $128$kbps, $256$kbps or $512$kbps, when compared with our previously proposed optimization methods.

eess.SP↗

arXiv2021

Alternative Formulations for the Fluctuating Two-Ray Fading Model

We present two alternative formulations for the distribution of the fluctuating two-ray (FTR) fading model, which simplify its statistical characterization and subsequent use for performance evaluation. New expressions for the probability density function (PDF) and cumulative distribution function of the FTR model are obtained based on the observation that the FTR fading distribution is described, for arbitrary $m$, as an underlying Rician Shadowed (RS) distribution with continuously varying parameter $K$, while for the special case of $m$ being an integer, the FTR fading model is described in terms of a finite number of underlying squared Nakagami-$m$ distributions. It is shown that the chief statistics and any performance metric that are computed by averaging over the PDF of the FTR fading model can be expressed in terms of a finite-range integral over the corresponding statistic or performance metric for the RS (for arbitrary $m$) or the Nakagami-$m$ (for integer $m$) fading models, which have a simpler analytical characterization than the FTR model and for which many results are available in closed-form. New expressions for some Laplace-domain statistics of interest are also obtained; these are used to exemplify the practical relevance of this new formulation for performance analysis.

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arXiv2021

Model-Based Machine Learning for Communications

We present an introduction to model-based machine learning for communication systems. We begin by reviewing existing strategies for combining model-based algorithms and machine learning from a high level perspective, and compare them to the conventional deep learning approach which utilizes established deep neural network (DNN) architectures trained in an end-to-end manner. Then, we focus on symbol detection, which is one of the fundamental tasks of communication receivers. We show how the different strategies of conventional deep architectures, deep unfolding, and DNN-aided hybrid algorithms, can be applied to this problem. The last two approaches constitute a middle ground between purely model-based and solely DNN-based receivers. By focusing on this specific task, we highlight the advantages and drawbacks of each strategy, and present guidelines to facilitate the design of future model-based deep learning systems for communications.

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arXiv2021

The Rate-Distortion Risk in Estimation from Compressed Data

Consider the problem of estimating a latent signal from a lossy compressed version of the data when the compressor is agnostic to the relation between the signal and the data. This situation arises in a host of modern applications when data is transmitted or stored prior to determining the downstream inference task. Given a bitrate constraint and a distortion measure between the data and its compressed version, let us consider the joint distribution achieving Shannon's rate-distortion (RD) function. Given an estimator and a loss function associated with the downstream inference task, define the rate-distortion risk as the expected loss under the RD-achieving distribution. We provide general conditions under which the operational risk in estimating from the compressed data is asymptotically equivalent to the RD risk. The main theoretical tools to prove this equivalence are transportation-cost inequalities in conjunction with properties of compression codes achieving Shannon's RD function. Whenever such equivalence holds, a recipe for designing estimators from datasets undergoing lossy compression without specifying the actual compression technique emerges: design the estimator to minimize the RD risk. Our conditions simplified in the special cases of discrete memoryless or multivariate normal data. For these scenarios, we derive explicit expressions for the RD risk of several estimators and compare them to the optimal source coding performance associated with full knowledge of the relation between the latent signal and the data.

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arXiv2020

ViterbiNet: A Deep Learning Based Viterbi Algorithm for Symbol Detection

Symbol detection plays an important role in the implementation of digital receivers. In this work, we propose ViterbiNet, which is a data-driven symbol detector that does not require channel state information (CSI). ViterbiNet is obtained by integrating deep neural networks (DNNs) into the Viterbi algorithm. We identify the specific parts of the Viterbi algorithm that are channel-model-based, and design a DNN to implement only those computations, leaving the rest of the algorithm structure intact. We then propose a meta-learning based approach to train ViterbiNet online based on recent decisions, allowing the receiver to track dynamic channel conditions without requiring new training samples for every coherence block. Our numerical evaluations demonstrate that the performance of ViterbiNet, which is ignorant of the CSI, approaches that of the CSI-based Viterbi algorithm, and is capable of tracking time-varying channels without needing instantaneous CSI or additional training data. Moreover, unlike conventional Viterbi detection, ViterbiNet is robust to CSI uncertainty, and it can be reliably implemented in complex channel models with constrained computational burden. More broadly, our results demonstrate the conceptual benefit of designing communication systems to that integrate DNNs into established algorithms.

cs.LG↗

arXiv2020

Capacity scaling in a Non-coherent Wideband Massive SIMO Block Fading Channel

The scaling of coherent and non-coherent channel capacity is studied in a single-input multiple-output (SIMO) block Rayleigh fading channel as both the bandwidth and the number of receiver antennas go to infinity jointly with the transmit power fixed. The transmitter has no channel state information (CSI), while the receiver may have genie-provided CSI (coherent receiver), or the channel statistics only (non-coherent receiver). Our results show that if the available bandwidth is smaller than a threshold bandwidth which is proportional (up to leading order terms) to the square root of the number of antennas, there is no gap between the coherent capacity and the non-coherent capacity in terms of capacity scaling behavior. On the other hand, when the bandwidth is larger than this threshold, there is a capacity scaling gap. Since achievable rates using pilot symbols for channel estimation are subject to the non-coherent capacity bound, this work reveals that pilot-assisted coherent receivers in systems with a large number of receive antennas are unable to exploit excess spectrum above a given threshold for capacity gain.

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arXiv2020

Compressed Sensing Channel Estimation for OFDM with non-Gaussian Multipath Gains

This paper analyzes the impact of non-Gaussian multipath component (MPC) amplitude distributions on the performance of Compressed Sensing (CS) channel estimators for OFDM systems. The number of dominant MPCs that any CS algorithm needs to estimate in order to accurately represent the channel is characterized. This number relates to a Compressibility Index (CI) of the channel that depends on the fourth moment of the MPC amplitude distribution. A connection between the Mean Squared Error (MSE) of any CS estimation algorithm and the MPC amplitude distribution fourth moment is revealed that shows a smaller number of MPCs is needed to well-estimate channels when these components have large fourth moment amplitude gains. The analytical results are validated via simulations for channels with lognormal MPCs such as the NYU mmWave channel model. These simulations show that when the MPC amplitude distribution has a high fourth moment, the well known CS algorithm of Orthogonal Matching Pursuit performs almost identically to the Basis Pursuit De-Noising algorithm with a much lower computational cost.

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arXiv2020

Data-Driven Symbol Detection via Model-Based Machine Learning

The design of symbol detectors in digital communication systems has traditionally relied on statistical channel models that describe the relation between the transmitted symbols and the observed signal at the receiver. Here we review a data-driven framework to symbol detection design which combines machine learning (ML) and model-based algorithms. In this hybrid approach, well-known channel-model-based algorithms such as the Viterbi method, BCJR detection, and multiple-input multiple-output (MIMO) soft interference cancellation (SIC) are augmented with ML-based algorithms to remove their channel-model-dependence, allowing the receiver to learn to implement these algorithms solely from data. The resulting data-driven receivers are most suitable for systems where the underlying channel models are poorly understood, highly complex, or do not well-capture the underlying physics. Our approach is unique in that it only replaces the channel-model-based computations with dedicated neural networks that can be trained from a small amount of data, while keeping the general algorithm intact. Our results demonstrate that these techniques can yield near-optimal performance of model-based algorithms without knowing the exact channel input-output statistical relationship and in the presence of channel state information uncertainty.

eess.SP↗

arXiv2020

Data-Driven Factor Graphs for Deep Symbol Detection

Many important schemes in signal processing and communications, ranging from the BCJR algorithm to the Kalman filter, are instances of factor graph methods. This family of algorithms is based on recursive message passing-based computations carried out over graphical models, representing a factorization of the underlying statistics. Consequently, in order to implement these algorithms, one must have accurate knowledge of the statistical model of the considered signals. In this work we propose to implement factor graph methods in a data-driven manner. In particular, we propose to use machine learning (ML) tools to learn the factor graph, instead of the overall system task, which in turn is used for inference by message passing over the learned graph. We apply the proposed approach to learn the factor graph representing a finite-memory channel, demonstrating the resulting ability to implement BCJR detection in a data-driven fashion. We demonstrate that the proposed system, referred to as BCJRNet, learns to implement the BCJR algorithm from a small training set, and that the resulting receiver exhibits improved robustness to inaccurate training compared to the conventional channel-model-based receiver operating under the same level of uncertainty. Our results indicate that by utilizing ML tools to learn factor graphs from labeled data, one can implement a broad range of model-based algorithms, which traditionally require full knowledge of the underlying statistics, in a data-driven fashion.

stat.ML↗

arXiv2019

Virtual Cell Clustering with Optimal Resource Allocation to Maximize Capacity

This work proposes a new resource allocation optimization and network management framework for wireless networks using neighborhood-based optimization rather than fully centralized or fully decentralized methods. We propose hierarchical clustering with a minimax linkage criterion for the formation of the virtual cells. Once the virtual cells are formed, we consider two cooperation models: the interference coordination model and the coordinated multi-point decoding model. In the first model base stations in a virtual cell decode their signals independently, but allocate the communication resources cooperatively. In the second model base stations in the same virtual cell allocate the communication resources and decode their signals cooperatively. We address the resource allocation problem for each of these cooperation models. For the interference coordination model this problem is an NP-hard mixed-integer optimization problem whereas for the coordinated multi-point decoding model it is convex. Our numerical results indicate that proper design of the neighborhood-based optimization leads to significant gains in sum rate over fully decentralized optimization, yet may also have a significant sum rate penalty compared to fully centralized optimization. In particular, neighborhood-based optimization has a significant sum rate penalty compared to fully centralized optimization in the coordinated multi-point model, but not the interference coordination model.

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arXiv2019

Deep Neural Network Symbol Detection for Millimeter Wave Communications

This paper proposes to use a deep neural network (DNN)-based symbol detector for mmWave systems such that CSI acquisition can be bypassed. In particular, we consider a sliding bidirectional recurrent neural network (BRNN) architecture that is suitable for the long memory length of typical mmWave channels. The performance of the DNN detector is evaluated in comparison to that of the Viterbi detector. The results show that the performance of the DNN detector is close to that of the optimal Viterbi detector with perfect CSI, and that it outperforms the Viterbi algorithm with CSI estimation error. Further experiments show that the DNN detector is robust to a wide range of noise levels and varying channel conditions, and that a pretrained detector can be reliably applied to different mmWave channel realizations with minimal overhead.

eess.SP↗

arXiv2019

Optimal Resource Allocation for Cellular Networks with Virtual Cell Joint Decoding

This work presents a new resource allocation optimization framework for cellular networks using neighborhood-based optimization. Under this optimization framework resources are allocated within virtual cells encompassing several base-stations and the users within their coverage area. Incorporating the virtual cell concept enables the utilization of more sophisticated cooperative communication schemes such as coordinated multi-point decoding. We form the virtual cells using hierarchical clustering given a particular number of such cells. Once the virtual cells are formed, we consider a cooperative decoding scheme in which the base-stations in each virtual cell jointly decode the signals that they receive. We propose an iterative solution for the resource allocation problem resulting from the cooperative decoding within each virtual cell. Numerical results for the average system sum rate of our network design under hierarchical clustering are presented. These results indicate that virtual cells with neighborhood-based optimization leads to significant gains in sum rate over optimization within each cell, yet may also have a significant sum-rate penalty compared to fully-centralized optimization.

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arXiv2019

Virtual Cell Clustering with Optimal Resource Allocation to Maximize Cellular System Capacity

This work presents a new network optimization framework for cellular networks using neighborhood-based optimization. Under this optimization framework resources are allocated within virtual cells encompassing several base-stations and the users within their coverage areas. We form the virtual cells using hierarchical clustering with a minimax linkage criterion given a particular number of such cells. Once the virtual cells are formed, we consider an interference coordination model in which base-stations in a virtual cell jointly allocate the channels and power to users within the virtual cell. We propose two new schemes for solving this mixed integer NP-hard resource allocation problem. The first scheme transforms the problem into a continuous variables problem; the second scheme proposes a new channel allocation method and then alternately solves the channel allocation problem using this new method, and the power allocation problem. We evaluate the average system sum rate of these schemes for a variable number of virtual cells. These results quantify the sum-rate along a continuum of fully-centralized versus fully-distributed optimization for different clustering and resource allocation strategies. These results indicate that the penalty of fully-distributed optimization versus fully-centralized (cloud RAN) can be as high as 50%. However, if designed properly, a few base stations within a virtual cell using neighborhood-based optimization have almost the same performance as fully-centralized optimization.

cs.IT↗

arXiv2019

"Fog" Optimization via Virtual Cells in Cellular Network Resource Allocation

This work proposes a new resource allocation optimization framework for cellular networks using "fog" or neighborhood-based optimization rather than fully centralized or fully decentralized methods. In neighborhood-based optimization resources are allocated within virtual cells encompassing several base-stations and the users within their coverage area. As the number of base-stations within a virtual cell increases, the framework reverts to centralized optimization, and as this number decreases it reverts to decentralized optimization. We address two tasks that must be carried out in the fog optimization framework: forming the virtual cells and allocating the communication resources in each virtual cell effectively. We propose hierarchical clustering for the formation of the virtual cells given a particular number of such cells. Once the virtual cells are formed, we consider several optimization methods to solve the NP-hard joint channel access and power allocation problem within each virtual cell in order to maximize the sum rate of the entire system. We present numerical results for the system sum rate of each scheme under hierarchical clustering. Our results indicate that proper design of the fog optimization results in little degradation relative to centralized optimization even for a relatively large number of virtual cells. However, improper design leads to a significant decrease in sum rate relative to centralized optimization.

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arXiv2018

Sparse mmWave OFDM Channel Estimation Using Compressed Sensing in OFDM Systems

This paper proposes and analyzes a mmWave sparse channel estimation technique for OFDM systems that uses the Orthogonal Matching Pursuit (OMP) algorithm. This greedy algorithm retrieves one additional multipath component (MPC) per iteration until a stop condition is met. We obtain an analytical approximation for the OMP estimation error variance that grows with the number of retrieved MPCs (iterations). The OMP channel estimator error variance outperforms a classic maximum-likelihood (ML) non-sparse channel estimator by a factor of approximately $2\hat{L}/M$ where $\hat{L}$ is the number of retrieved MPCs (iterations) and $M$ the number of taps of the Discrete Equivalent Channel. When the MPC amplitude distribution is heavy-tailed, the channel power is concentrated in a subset of dominant MPCs. In this case OMP performs fewer iterations as it retrieves only these dominant large MPCs. Hence for this MPC amplitude distribution the estimation error advantage of OMP over ML is improved. In particular, for channels with MPCs that have lognormally-distributed amplitudes, the OMP estimator recovers approximately 5-15 dominant MPCs in typical mmWave channels, with 15-45 weak MPCs that remain undetected.

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arXiv2018

Orthogonal Time Frequency Space Modulation

This paper introduces a new two-dimensional modulation technique called Orthogonal Time Frequency Space (OTFS) modulation. OTFS has the novel and important feature of being designed in the delay-Doppler domain. When coupled with a suitable equalizer, OTFS modulation is able to exploit the full channel diversity over both time and frequency. Moreover, it converts the fading, time-varying wireless channel experienced by modulated signals such as OFDM into a time-independent channel with a complex channel gain that is essentially constant for all symbols. This design obviates the need for transmitter adaptation, and greatly simplifies system operation. The paper describes the basic operating principles of OTFS as well as a possible implementation as an overlay to current or anticipated standardized systems. OTFS is shown to provide significant performance improvement in systems with high Doppler, short packets, and/or large antenna array. In particular, simulation results indicate at least several dB of block error rate performance improvement for OTFS over OFDM in all of these settings.

cs.IT↗

arXiv2018

The Distortion-Rate Function of Sampled Wiener Processes

We consider the recovery of a continuous-time Wiener process from a quantized or lossy compressed version of its uniform samples under limited bitrate and sampling rate. We derive a closed form expression for the optimal tradeoff among sampling rate, bitrate, and quadratic distortion in this setting. This expression is given in terms of a reverse waterfilling formula over the asymptotic spectral distribution of a sequence of finite-rank operators associated with the optimal estimator of the Wiener process from its samples. We show that the ratio between this expression and the standard distortion rate function of the Wiener process, describing the optimal tradeoff between bitrate and distortion without a sampling constraint, is only a function of the number of bits per sample. For example using one bit per sample on average, the expected distortion is approximately 1.2 times the standard distortion rate function, indicating a performance loss of about 20% due to sampling. We next consider the distortion when the continuous-time process is estimated from the output of an encoder that is optimal with respect to the discrete-time samples. We show that while the latter is strictly greater than the distortion under optimal encoding, the ratio between the two does not exceed 1.027. We therefore conclude that nearly optimal performance is attained even if the encoder is unaware of the sampling rate and encodes the samples without taking into account the continuous-time underlying process.

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