arXiv subjects

Andrea Goldsmith

Publications and source records attributed to Andrea Goldsmith.

At least 37 records · Page 2Linked to original sources

arXiv2020

Rethinking Modulation and Detection for High Doppler Channels

We present two modulation and detection techniques that are designed to allow for efficient equalization for channels that exhibit an arbitrary Doppler spread but no delay spread. These techniques are based on principles similar to techniques designed for time-invariant delay spread channels (e.g., Orthogonal Frequency Division Multiplexing or OFDM) and have the same computational complexity. Through numerical simulations, we show that effective equalization is possible for channels that exhibit a high Doppler spread and even a modest delay spread, whereas equalized OFDM exhibits a strictly worse performance in these environments. Our results indicate that, in rapidly time-varying channels, such as those found in high-mobility or mmWave deployments, new modulation coupled with appropriate channel estimation and equalization techniques may significantly outperform modulation and detection schemes that are designed for static or slowly time varying multipath channels.

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arXiv2019

Diffusive Molecular Communications with Reactive Molecules: Channel Modeling and Signal Design

This paper focuses on molecular communication (MC) systems using two types of signaling molecules which may participate in a reversible bimolecular reaction in the channel. The motivation for studying these MC systems is that they can realize the concept of constructive and destructive signal superposition, which leads to favorable properties such as inter-symbol interference (ISI) reduction and avoiding environmental contamination due to continuous release of signaling molecules into the channel. This work first presents a general formulation for binary modulation schemes that employ two types of signaling molecules and proposes several modulation schemes as special cases. Moreover, two types of receivers are considered: a receiver that is able to observe both types of signaling molecules (2TM), and a simpler receiver that can observe only one type of signaling molecules (1TM). For both of these receivers, the maximum likelihood (ML) detector for general binary modulation is derived under the assumption that the detector has perfect knowledge of the ISI-causing sequence. In addition, two suboptimal detectors of different complexity are proposed, namely an ML-based detector that employs an estimate of the ISI-causing sequence and a detector that neglects the effect of ISI. The proposed detectors, except for the detector that neglects ISI for the 2TM receiver, require knowledge of the channel response (CR) of the considered MC system. Moreover, the CR is needed for performance evaluation of all proposed detectors. However, deriving the CR of MC systems with reactive signaling molecules is challenging since the underlying partial differential equations that describe the reaction-diffusion mechanism are coupled and non-linear. Therefore, we develop an algorithm for efficient computation of the CR and validate its accuracy via particle-based simulation.

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arXiv2019

Low Noise Non-Linear Equalization Using Neural Networks and Belief Propagation

Nonlinearities can be introduced into communication systems by the physical components such as the power amplifier, or during signal propagation through a nonlinear channel. These nonlinearities can be compensated by a nonlinear equalizer at the receiver side. The nonlinear equalizer also operates on the additive noise, which can lead to noise enhancement. In this work we evaluate this trade-off between distortion reduction and noise-enhancement via nonlinear equalization techniques. We first, evaluate the trade-off between nonlinearity compensation and noise enhancement for the Volterra equalizer, and propose a method to determine the training SNR that optimizes this performance trade-off. We then propose a new approach for nonlinear equalization that alternates between neural networks (NNs) for nonlinearity compensation, and belief propagation (BP) for noise removal. This new approach achieves a 0.6 dB gain compared to the Volterra equalizer with the optimal training SNR, and a 1.7 dB gain compared to a system with no nonlinearity compensation.

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arXiv2019

Fast Blind MIMO Decoding through Vertex Hopping

We present an algorithm that efficiently performs blind decoding of MIMO signals. That is, given no channel state information (CSI) at either the transmitter or receiver, our algorithm takes a block of samples and returns an estimate of the underlying data symbols. In prior work, the problem of blind decoding was formulated as a non-convex optimization problem. In this work, we present an algorithm that efficiently solves this non-convex problem in practical settings. This algorithm leverages concepts of linear and mixed-integer linear programming. Empirically, we show that our technique has an error performance close to that of zero-forcing with perfect CSI at the receiver. Initial estimates of the runtime of the algorithm presented in this work suggest that the real-time blind decoding of MIMO signals is possible for even modest-sized MIMO systems.

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arXiv2018

Communication System Design and Analysis for Asynchronous Molecular Timing Channels

Two new asynchronous modulation techniques for molecular timing (MT) channels are proposed. One based on modulating information on the time between two consecutive releases of indistinguishable information particles, and one based on using distinguishable particles. For comparison, we consider the synchronized modulation scheme where information is encoded in the time of release and decoded from the time of arrival of particles. We show that all three modulation techniques result in a system that can be modeled as an additive noise channel, and we derive the expression for the probability density function of the noise. Next, we focus on binary communication and derive the associated optimal detection rules for each modulation. Since the noise associated with these modulations has an infinite variance, geometric power is used as a measure for the noise power, and we derive an expression for the geometric SNR (G-SNR) for each modulation scheme. Numerical evaluations indicate that for these systems the bit error rate (BER) is constant at a given G-SNR, similar to the relation between BER and SNR in additive Gaussian noise channels. We also demonstrate that the asynchronous modulation based on two distinguishable particles can achieve a BER performance close to the synchronized modulation scheme.

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arXiv2018

Distributed Convex Optimization With Limited Communications

In this paper, a distributed convex optimization algorithm, termed \emph{distributed coordinate dual averaging} (DCDA) algorithm, is proposed. The DCDA algorithm addresses the scenario of a large distributed optimization problem with limited communication among nodes in the network. Currently known distributed subgradient methods, such as the distributed dual averaging or the distributed alternating direction method of multipliers algorithms, assume that nodes can exchange messages of large cardinality. Such network communication capabilities are not valid in many scenarios of practical relevance. In the DCDA algorithm, on the other hand, communication of each coordinate of the optimization variable is restricted over time. For the proposed algorithm, we bound the rate of convergence under different communication protocols and network architectures. We also consider the extensions to the case of imperfect gradient knowledge and the case in which transmitted messages are corrupted by additive noise or are quantized. Relevant numerical simulations are also provided.

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arXiv2018

Neural Network Detection of Data Sequences in Communication Systems

We consider detection based on deep learning, and show it is possible to train detectors that perform well without any knowledge of the underlying channel models. Moreover, when the channel model is known, we demonstrate that it is possible to train detectors that do not require channel state information (CSI). In particular, a technique we call a sliding bidirectional recurrent neural network (SBRNN) is proposed for detection where, after training, the detector estimates the data in real-time as the signal stream arrives at the receiver. We evaluate this algorithm, as well as other neural network (NN) architectures, using the Poisson channel model, which is applicable to both optical and molecular communication systems. In addition, we also evaluate the performance of this detection method applied to data sent over a molecular communication platform, where the channel model is difficult to model analytically. We show that SBRNN is computationally efficient, and can perform detection under various channel conditions without knowing the underlying channel model. We also demonstrate that the bit error rate (BER) performance of the proposed SBRNN detector is better than that of a Viterbi detector with imperfect CSI as well as that of other NN detectors that have been previously proposed. Finally, we show that the SBRNN can perform well in rapidly changing channels, where the coherence time is on the order of a single symbol duration.

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arXiv2018

Capacity Limits of Diffusion-Based Molecular Timing Channels

This work introduces capacity limits for molecular timing (MT) channels, where information is modulated in the release timing of small information particles, and decoded from the time of arrivals at the receiver. It is shown that the random time of arrival can be represented as an additive noise channel, and for the diffusion-based MT (DBMT) channel this noise is distributed according to the Lévy distribution. Lower and upper bounds on the capacity of the DBMT channel are derived for the case where the delay associated with the propagation of the information particles in the channel is finite, namely, when the information particles dissipate after a finite time interval. For the case where a single particle is released per channel use, these bounds are shown to be tight. When the transmitter simultaneously releases a large number of particles, the detector at the receiver may not be able to precisely detect the arrival time of all the particles. Therefore, two alternative models are considered: detection based on the particle that arrives first, or detection based on the average arrival times. Tight lower and upper bounds are derived for these two models. It is shown that by controlling the maximal delay of the information particles, the capacity can increase poly-logarithmically with the number of released particles. As each particle takes a random independent path, this diversity of paths is analogous to receiver diversity and can be used to considerably increase the achievable data rates.

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arXiv2018

Deep Learning for Joint Source-Channel Coding of Text

We consider the problem of joint source and channel coding of structured data such as natural language over a noisy channel. The typical approach to this problem in both theory and practice involves performing source coding to first compress the text and then channel coding to add robustness for the transmission across the channel. This approach is optimal in terms of minimizing end-to-end distortion with arbitrarily large block lengths of both the source and channel codes when transmission is over discrete memoryless channels. However, the optimality of this approach is no longer ensured for documents of finite length and limitations on the length of the encoding. We will show in this scenario that we can achieve lower word error rates by developing a deep learning based encoder and decoder. While the approach of separate source and channel coding would minimize bit error rates, our approach preserves semantic information of sentences by first embedding sentences in a semantic space where sentences closer in meaning are located closer together, and then performing joint source and channel coding on these embeddings.

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arXiv2018

Sliding Bidirectional Recurrent Neural Networks for Sequence Detection in Communication Systems

The design and analysis of communication systems typically rely on the development of mathematical models that describe the underlying communication channel. However, in some systems, such as molecular communication systems where chemical signals are used for transfer of information, the underlying channel models are unknown. In these scenarios, a completely new approach to design and analysis is required. In this work, we focus on one important aspect of communication systems, the detection algorithms, and demonstrate that by using tools from deep learning, it is possible to train detectors that perform well without any knowledge of the underlying channel models. We propose a technique we call sliding bidirectional recurrent neural network (SBRNN) for real-time sequence detection. We evaluate this algorithm using experimental data that is collected by a chemical communication platform, where the channel model is unknown and difficult to model analytically. We show that deep learning algorithms perform significantly better than a detector proposed in previous works, and the SBRNN outperforms other techniques considered in this work.

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arXiv2018

Ranking Causal Influence of Financial Markets via Directed Information Graphs

A non-parametric method for ranking stock indices according to their mutual causal influences is presented. Under the assumption that indices reflect the underlying economy of a country, such a ranking indicates which countries exert the most economic influence in an examined subset of the global economy. The proposed method represents the indices as nodes in a directed graph, where the edges' weights are estimates of the pair-wise causal influences, quantified using the directed information functional. This method facilitates using a relatively small number of samples from each index. The indices are then ranked according to their net-flow in the estimated graph (sum of the incoming weights subtracted from the sum of outgoing weights). Daily and minute-by-minute data from nine indices (three from Asia, three from Europe and three from the US) were analyzed. The analysis of daily data indicates that the US indices are the most influential, which is consistent with intuition that the indices representing larger economies usually exert more influence. Yet, it is also shown that an index representing a small economy can strongly influence an index representing a large economy if the smaller economy is indicative of a larger phenomenon. Finally, it is shown that while inter-region interactions can be captured using daily data, intra-region interactions require more frequent samples.

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arXiv2018

Exploiting Diversity in Molecular Timing Channels via Order Statistics

We study diversity in one-shot communication over molecular timing channels. We consider a channel model where the transmitter simultaneously releases a large number of information particles, while the information is encoded in the time of release. The receiver decodes the information based on the random time of arrival of the information particles. The random propagation is characterized by the general class of right-sided unimodal densities. We characterize the asymptotic exponential decrease rate of the probability of error as a function of the number of released particles, and denote this quantity as the system diversity gain. Four types of detectors are considered: the maximum-likelihood (ML) detector, a linear detector, a detector that is based on the first arrival (FA) among all the transmitted particles, and a detector based on the last arrival (LA). When the density characterizing the random propagation is supported over a large interval, we show that the simple FA detector achieves a diversity gain very close to that of the ML detector. On the other hand, when the density characterizing the random propagation is supported over a small interval, we show that the simple LA detector achieves a diversity gain very close to that of the ML detector.

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arXiv2017

Diffusive Molecular Communications with Reactive Signaling

This paper focuses on molecular communication (MC) systems where the signaling molecules may participate in a reversible bimolecular reaction in the channel. The motivation for studying these MC systems is that they can realize the concept of constructive and destructive signal superposition, which leads to favorable properties such as inter-symbol interference (ISI) reduction and avoiding environmental contamination due to continuous release of molecules into the channel. This work first derives the maximum likelihood (ML) detector for a binary MC system with reactive signaling molecules under the assumption that the detector has perfect knowledge of the ISI. The performance of this genie-aided ML detector yields an upper bound on the performance of any practical detector. In addition, two suboptimal detectors of different complexity are proposed. The proposed ML detector as well as one of the suboptimal detectors require the channel response (CR) of the considered MC system. Moreover, the CR is needed for the performance evaluation of all proposed detectors. However, analyzing MC with reactive signaling is challenging since the underlying partial differential equations that describe the reaction-diffusion mechanism are coupled and non-linear. Therefore, an algorithm is developed in this paper for efficient computation of the CR to any arbitrary transmit symbol sequence. The accuracy of this algorithm is validated via particle-based simulation. Simulation results using the developed CR algorithm show that the performance of the proposed suboptimal detectors can approach that of the genie- aided ML detector. Moreover, these results show that MC systems with reactive signaling have superior performance relative to those with non-reactive signaling due to the reduction of ISI enabled by the chemical reactions.

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arXiv2017

Diversity gain of one-shot communication over molecular timing channels

We study diversity in one-shot communication over molecular timing channels. In the considered channel model the transmitter simultaneously releases a large number of information particles, where the information is encoded in the time of release. The receiver decodes the information based on the random time of arrival of the information particles. We characterize the asymptotic exponential decrease rate of the probability of error as a function of the number of released particles. We denote this quantity as the system diversity gain, as it depends both on the number of particles transmitted as well as the receiver detection method. Three types of detectors are considered: the maximumlikelihood (ML) detector, a linear detector, and a detector that is based on the first arrival (FA) among all the transmitted particles. We show that for random propagation characterized by right-sided unimodal densities with zero mode, the FA detector is equivalent to the ML detector, and significantly outperforms the linear detector. Moreover, even for densities with positive mode, the diversity gain achieved by the FA detector is very close to that achieved by the ML detector and much higher than the gain achieved by the linear detector.

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arXiv2017

Optimal Detection for Diffusion-Based Molecular Timing Channels

This work studies optimal detection for communication over diffusion-based molecular timing (DBMT) channels. The transmitter simultaneously releases multiple information particles, where the information is encoded in the time of release. The receiver decodes the transmitted information based on the random time of arrival of the information particles, which is modeled as an additive noise channel. For a DBMT channel without flow, this noise follows the Lévy distribution. Under this channel model, the maximum-likelihood (ML) detector is derived and shown to have high computational complexity. It is also shown that under ML detection, releasing multiple particles improves performance, while for any additive channel with $α$-stable noise where $α<1$ (such as the DBMT channel), under linear processing at the receiver, releasing multiple particles degrades performance relative to releasing a single particle. Hence, a new low-complexity detector, which is based on the first arrival (FA) among all the transmitted particles, is proposed. It is shown that for a small number of released particles, the performance of the FA detector is very close to that of the ML detector. On the other hand, error exponent analysis shows that the performance of the two detectors differ when the number of released particles is large.

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arXiv2017

Detection Algorithms for Communication Systems Using Deep Learning

The design and analysis of communication systems typically rely on the development of mathematical models that describe the underlying communication channel, which dictates the relationship between the transmitted and the received signals. However, in some systems, such as molecular communication systems where chemical signals are used for transfer of information, it is not possible to accurately model this relationship. In these scenarios, because of the lack of mathematical channel models, a completely new approach to design and analysis is required. In this work, we focus on one important aspect of communication systems, the detection algorithms, and demonstrate that by borrowing tools from deep learning, it is possible to train detectors that perform well, without any knowledge of the underlying channel models. We evaluate these algorithms using experimental data that is collected by a chemical communication platform, where the channel model is unknown and difficult to model analytically. We show that deep learning algorithms perform significantly better than a simple detector that was used in previous works, which also did not assume any knowledge of the channel.

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arXiv2017

Non-Coherent Detection for Diffusive Molecular Communications

We study non-coherent detection schemes for molecular communication (MC) systems that do not require knowledge of the channel state information (CSI). In particular, we first derive the optimal maximum likelihood (ML) multiple-symbol (MS) detector for MC systems. As a special case of the optimal MS detector, we show that the optimal ML symbol-by-symbol (SS) detector can be equivalently written in the form of a threshold-based detector, where the optimal decision threshold is constant and depends only on the statistics of the MC channel. The main challenge of the MS detector is the complexity associated with the calculation of the optimal detection metric. To overcome this issue, we propose an approximate MS detection metric which can be expressed in closed form. To reduce complexity even further, we develop a non-coherent decision-feedback (DF) detector and a suboptimal blind detector. Finally, we derive analytical expressions for the bit error rate (BER) of the optimal SS detector, as well as upper and lower bounds for the BER of the optimal MS detector. Simulation results confirm the analysis and reveal the effectiveness of the proposed optimal and suboptimal detection schemes compared to a benchmark scheme that assumes perfect CSI knowledge, particularly when the number of observations used for detection is sufficiently large.

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arXiv2017

Compress-and-Estimate Source Coding for a Vector Gaussian Source

We consider the remote vector source coding problem in which a vector Gaussian source is to be estimated from noisy linear measurements. For this problem, we derive the performance of the compress-and-estimate (CE) coding scheme and compare it to the optimal performance. In the CE coding scheme, the remote encoder compresses the noisy source observations so as to minimize the local distortion measure, independent from the joint distribution between the source and the observations. In reconstruction, the decoder estimates the original source realization from the lossy-compressed noisy observations. For the CE coding in the Gaussian vector case, we show that, if the code rate is less than a threshold, then the CE coding scheme attains the same performance as the optimal coding scheme. We also introduce lower and upper bounds for the performance gap above this threshold. In addition, an example with two observations and two sources is studied to illustrate the behavior of the performance gap.

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