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Alex Dytso - One of the best experts on this subject based on the ideXlab platform.
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the capacity achieving Distribution for the amplitude constrained additive gaussian channel an upper bound on the number of mass points
IEEE Transactions on Information Theory, 2020Co-Authors: Alex Dytso, Vincent H Poor, Semih Yagli, Shlomo Shamai ShitzAbstract:This paper studies an $n$ -dimensional additive Gaussian noise channel with a peak-power-constrained Input. It is well known that, in this case, when $n=1$ the capacity-achieving Input Distribution is discrete with finitely many mass points, and when $n>1$ the capacity-achieving Input Distribution is supported on finitely many concentric shells. However, due to the previous proof technique, not even a bound on the exact number of mass points/shells was available. This paper provides an alternative proof of the finiteness of the number mass points/shells of the capacity-achieving Input Distribution while producing the first firm bounds on the number of mass points and shells, paving an alternative way for approaching many such problems. The first main result of this paper is an order tight implicit bound which shows that the number of mass points in the capacity-achieving Input Distribution is within a factor of two from the number of zeros of the downward shifted capacity-achieving output probability density function. Next, this implicit bound is utilized to provide a first firm upper on the support size of optimal Input Distribution, an $O(\mathsf {A}^{2})$ upper bound where $\mathsf {A}$ denotes the constraint on the Input amplitude. The second main result of this paper generalizes the first one to the case when $n>1$ , showing that, for each and every dimension $n\ge 1$ , the number of shells that the optimal Input Distribution contains is $O(\mathsf {A}^{2})$ . Finally, the third main result of this paper reconsiders the case $n=1$ with an additional average power constraint, demonstrating a similar $O(\mathsf {A}^{2})$ bound.
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mmse bounds for additive noise channels under kullback leibler divergence constraints on the Input Distribution
IEEE Transactions on Signal Processing, 2019Co-Authors: Alex Dytso, Abdelhak M. Zoubir, Michael Faus, Vincent H PoorAbstract:Upper and lower bounds on the minimum mean square error for additive noise channels are derived when the Input Distribution is constrained to be close to a Gaussian reference Distribution in terms of the Kullback–Leibler divergence. The upper bound is tight and is attained by a Gaussian Distribution whose mean is identical to that of the reference Distribution and whose covariance matrix is defined implicitly via a system of non-linear equations. The estimator that attains the upper bound is identified as a minimax optimal estimator that is robust against deviations from the assumed prior. The lower bound provides an alternative to well-known inequalities in estimation and information theory—such as the Cramer–Rao lower bound, Stam's inequality, or the entropy power inequality—that is potentially tighter and defined for a larger class of Input Distributions. Several examples of applications in signal processing and information theory illustrate the usefulness of the proposed bounds in practice.
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an upper bound on the number of mass points in the capacity achieving Distribution for the amplitude constrained additive gaussian channel
International Symposium on Information Theory, 2019Co-Authors: Semih Yagli, Alex Dytso, Vincent H Poor, Shlomo Shamai ShitzAbstract:This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained Input. It is well known that, in this case, the capacity-achieving Input Distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of shells of the optimal Input Distribution nor a bound on it was available.This paper provides an alternative proof of the finiteness of the number shells of the capacity-achieving Input Distribution and produces the first firm upper bound on the number of shells, paving an alternative way for approaching many such problems. In particular, for every dimension n, it is shown that the number of shells is given by O(A2) where A is the constraint on the Input amplitude. Moreover, this paper also provides bounds on the number of points for the case of n = 1 with an additional power constraint.
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amplitude constrained mimo channels properties of optimal Input Distributions and bounds on the capacity
Entropy, 2019Co-Authors: Alex Dytso, Vincent H Poor, Mario Goldenbaum, Shlomo ShamaiAbstract:In this work, the capacity of multiple-Input multiple-output channels that are subject to constraints on the support of the Input is studied. The paper consists of two parts. The first part focuses on the general structure of capacity-achieving Input Distributions. Known results are surveyed and several new results are provided. With regard to the latter, it is shown that the support of a capacity-achieving Input Distribution is a small set in both a topological and a measure theoretical sense. Moreover, explicit conditions on the channel Input space and the channel matrix are found such that the support of a capacity-achieving Input Distribution is concentrated on the boundary of the Input space only. The second part of this paper surveys known bounds on the capacity and provides several novel upper and lower bounds for channels with arbitrary constraints on the support of the channel Input symbols. As an immediate practical application, the special case of multiple-Input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap to the capacity if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the regime of high amplitudes, it is shown that the capacity scales linearly with the minimum between the number of transmit and receive antennas, similar to the case of average power-constrained Inputs.
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the capacity achieving Distribution for the amplitude constrained additive gaussian channel an upper bound on the number of mass points
arXiv: Information Theory, 2019Co-Authors: Alex Dytso, Vincent H Poor, Semih Yagli, Shlomo ShamaiAbstract:This paper studies an $n$-dimensional additive Gaussian noise channel with a peak-power-constrained Input. It is well known that, in this case, when $n=1$ the capacity-achieving Input Distribution is discrete with finitely many mass points, and when $n>1$ the capacity-achieving Input Distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of mass points/shells of the optimal Input Distribution nor a bound on it was available. This paper provides an alternative proof of the finiteness of the number mass points/shells of the capacity-achieving Input Distribution and produces the first firm bounds on the number of mass points and shells, paving an alternative way for approaching many such problems. Roughly, the paper consists of three parts. The first part considers the case of $n=1$. The first result, in this part, shows that the number of mass points in the capacity-achieving Input Distribution is within a factor of two from the downward shifted capacity-achieving output probability density function (pdf). The second result, by showing a bound on the number of zeros of the downward shifted capacity-achieving output pdf, provides a first firm upper on the number of mass points. Specifically, it is shown that the number of mass points is given by $O(\mathsf{A}^2)$ where $\mathsf{A}$ is the constraint on the Input amplitude. The second part generalizes the results of the first part to the case of $n>1$. In particular, for every dimension $n>1$, it is shown that the number of shells is given by $O(\mathsf{A}^2)$ where $\mathsf{A}$ is the constraint on the Input amplitude. Finally, the third part provides bounds on the number of points for the case of $n=1$ with an additional power constraint.
Shlomo Shamai Shitz - One of the best experts on this subject based on the ideXlab platform.
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the capacity achieving Distribution for the amplitude constrained additive gaussian channel an upper bound on the number of mass points
IEEE Transactions on Information Theory, 2020Co-Authors: Alex Dytso, Vincent H Poor, Semih Yagli, Shlomo Shamai ShitzAbstract:This paper studies an $n$ -dimensional additive Gaussian noise channel with a peak-power-constrained Input. It is well known that, in this case, when $n=1$ the capacity-achieving Input Distribution is discrete with finitely many mass points, and when $n>1$ the capacity-achieving Input Distribution is supported on finitely many concentric shells. However, due to the previous proof technique, not even a bound on the exact number of mass points/shells was available. This paper provides an alternative proof of the finiteness of the number mass points/shells of the capacity-achieving Input Distribution while producing the first firm bounds on the number of mass points and shells, paving an alternative way for approaching many such problems. The first main result of this paper is an order tight implicit bound which shows that the number of mass points in the capacity-achieving Input Distribution is within a factor of two from the number of zeros of the downward shifted capacity-achieving output probability density function. Next, this implicit bound is utilized to provide a first firm upper on the support size of optimal Input Distribution, an $O(\mathsf {A}^{2})$ upper bound where $\mathsf {A}$ denotes the constraint on the Input amplitude. The second main result of this paper generalizes the first one to the case when $n>1$ , showing that, for each and every dimension $n\ge 1$ , the number of shells that the optimal Input Distribution contains is $O(\mathsf {A}^{2})$ . Finally, the third main result of this paper reconsiders the case $n=1$ with an additional average power constraint, demonstrating a similar $O(\mathsf {A}^{2})$ bound.
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an upper bound on the number of mass points in the capacity achieving Distribution for the amplitude constrained additive gaussian channel
International Symposium on Information Theory, 2019Co-Authors: Semih Yagli, Alex Dytso, Vincent H Poor, Shlomo Shamai ShitzAbstract:This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained Input. It is well known that, in this case, the capacity-achieving Input Distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of shells of the optimal Input Distribution nor a bound on it was available.This paper provides an alternative proof of the finiteness of the number shells of the capacity-achieving Input Distribution and produces the first firm upper bound on the number of shells, paving an alternative way for approaching many such problems. In particular, for every dimension n, it is shown that the number of shells is given by O(A2) where A is the constraint on the Input amplitude. Moreover, this paper also provides bounds on the number of points for the case of n = 1 with an additional power constraint.
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on the capacity of the peak power constrained vector gaussian channel an estimation theoretic perspective
IEEE Transactions on Information Theory, 2019Co-Authors: Alex Dytso, Vincent H Poor, Shlomo Shamai ShitzAbstract:This paper studies the capacity of an $n$ -dimensional vector Gaussian noise channel subject to the constraint that an Input must lie in the ball of radius $R$ centered at the origin. It is known that in this setting, the optimizing Input Distribution is supported on a finite number of concentric spheres. However, the number, the positions, and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint $R$ , such that the Input Distribution supported on a single sphere is optimal. The maximum $\bar {R}_{n}$ , such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that $\bar {R}_{n}$ scales as $\sqrt {n}$ and the exact limit of $\frac {\bar {R}_{n}}{\sqrt {n}}$ is found.
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capacity of the vector gaussian channel in the small amplitude regime
Information Theory Workshop, 2018Co-Authors: Alex Dytso, Vincent H Poor, Shlomo Shamai ShitzAbstract:This paper studies the capacity of an n-dimensional vector Gaussian noise channel subject to the constraint that an Input must lie in the ball of radius R centered at the origin. It is known that in this setting the optimizing Input Distribution is supported on a finite number of concentric spheres. However, the number, the positions and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint R such that the Input Distribution supported on a single sphere is optimal. The maximum $\overline{R}_{n}$, such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that $\overline{R}_{n}$ scales as $\sqrt{n}$ and the exact limit of $\overline{R}_{n}\overline{\sqrt{n}}$ is found.
Vincent H Poor - One of the best experts on this subject based on the ideXlab platform.
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the capacity achieving Distribution for the amplitude constrained additive gaussian channel an upper bound on the number of mass points
IEEE Transactions on Information Theory, 2020Co-Authors: Alex Dytso, Vincent H Poor, Semih Yagli, Shlomo Shamai ShitzAbstract:This paper studies an $n$ -dimensional additive Gaussian noise channel with a peak-power-constrained Input. It is well known that, in this case, when $n=1$ the capacity-achieving Input Distribution is discrete with finitely many mass points, and when $n>1$ the capacity-achieving Input Distribution is supported on finitely many concentric shells. However, due to the previous proof technique, not even a bound on the exact number of mass points/shells was available. This paper provides an alternative proof of the finiteness of the number mass points/shells of the capacity-achieving Input Distribution while producing the first firm bounds on the number of mass points and shells, paving an alternative way for approaching many such problems. The first main result of this paper is an order tight implicit bound which shows that the number of mass points in the capacity-achieving Input Distribution is within a factor of two from the number of zeros of the downward shifted capacity-achieving output probability density function. Next, this implicit bound is utilized to provide a first firm upper on the support size of optimal Input Distribution, an $O(\mathsf {A}^{2})$ upper bound where $\mathsf {A}$ denotes the constraint on the Input amplitude. The second main result of this paper generalizes the first one to the case when $n>1$ , showing that, for each and every dimension $n\ge 1$ , the number of shells that the optimal Input Distribution contains is $O(\mathsf {A}^{2})$ . Finally, the third main result of this paper reconsiders the case $n=1$ with an additional average power constraint, demonstrating a similar $O(\mathsf {A}^{2})$ bound.
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mmse bounds for additive noise channels under kullback leibler divergence constraints on the Input Distribution
IEEE Transactions on Signal Processing, 2019Co-Authors: Alex Dytso, Abdelhak M. Zoubir, Michael Faus, Vincent H PoorAbstract:Upper and lower bounds on the minimum mean square error for additive noise channels are derived when the Input Distribution is constrained to be close to a Gaussian reference Distribution in terms of the Kullback–Leibler divergence. The upper bound is tight and is attained by a Gaussian Distribution whose mean is identical to that of the reference Distribution and whose covariance matrix is defined implicitly via a system of non-linear equations. The estimator that attains the upper bound is identified as a minimax optimal estimator that is robust against deviations from the assumed prior. The lower bound provides an alternative to well-known inequalities in estimation and information theory—such as the Cramer–Rao lower bound, Stam's inequality, or the entropy power inequality—that is potentially tighter and defined for a larger class of Input Distributions. Several examples of applications in signal processing and information theory illustrate the usefulness of the proposed bounds in practice.
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an upper bound on the number of mass points in the capacity achieving Distribution for the amplitude constrained additive gaussian channel
International Symposium on Information Theory, 2019Co-Authors: Semih Yagli, Alex Dytso, Vincent H Poor, Shlomo Shamai ShitzAbstract:This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained Input. It is well known that, in this case, the capacity-achieving Input Distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of shells of the optimal Input Distribution nor a bound on it was available.This paper provides an alternative proof of the finiteness of the number shells of the capacity-achieving Input Distribution and produces the first firm upper bound on the number of shells, paving an alternative way for approaching many such problems. In particular, for every dimension n, it is shown that the number of shells is given by O(A2) where A is the constraint on the Input amplitude. Moreover, this paper also provides bounds on the number of points for the case of n = 1 with an additional power constraint.
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amplitude constrained mimo channels properties of optimal Input Distributions and bounds on the capacity
Entropy, 2019Co-Authors: Alex Dytso, Vincent H Poor, Mario Goldenbaum, Shlomo ShamaiAbstract:In this work, the capacity of multiple-Input multiple-output channels that are subject to constraints on the support of the Input is studied. The paper consists of two parts. The first part focuses on the general structure of capacity-achieving Input Distributions. Known results are surveyed and several new results are provided. With regard to the latter, it is shown that the support of a capacity-achieving Input Distribution is a small set in both a topological and a measure theoretical sense. Moreover, explicit conditions on the channel Input space and the channel matrix are found such that the support of a capacity-achieving Input Distribution is concentrated on the boundary of the Input space only. The second part of this paper surveys known bounds on the capacity and provides several novel upper and lower bounds for channels with arbitrary constraints on the support of the channel Input symbols. As an immediate practical application, the special case of multiple-Input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap to the capacity if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the regime of high amplitudes, it is shown that the capacity scales linearly with the minimum between the number of transmit and receive antennas, similar to the case of average power-constrained Inputs.
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the capacity achieving Distribution for the amplitude constrained additive gaussian channel an upper bound on the number of mass points
arXiv: Information Theory, 2019Co-Authors: Alex Dytso, Vincent H Poor, Semih Yagli, Shlomo ShamaiAbstract:This paper studies an $n$-dimensional additive Gaussian noise channel with a peak-power-constrained Input. It is well known that, in this case, when $n=1$ the capacity-achieving Input Distribution is discrete with finitely many mass points, and when $n>1$ the capacity-achieving Input Distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of mass points/shells of the optimal Input Distribution nor a bound on it was available. This paper provides an alternative proof of the finiteness of the number mass points/shells of the capacity-achieving Input Distribution and produces the first firm bounds on the number of mass points and shells, paving an alternative way for approaching many such problems. Roughly, the paper consists of three parts. The first part considers the case of $n=1$. The first result, in this part, shows that the number of mass points in the capacity-achieving Input Distribution is within a factor of two from the downward shifted capacity-achieving output probability density function (pdf). The second result, by showing a bound on the number of zeros of the downward shifted capacity-achieving output pdf, provides a first firm upper on the number of mass points. Specifically, it is shown that the number of mass points is given by $O(\mathsf{A}^2)$ where $\mathsf{A}$ is the constraint on the Input amplitude. The second part generalizes the results of the first part to the case of $n>1$. In particular, for every dimension $n>1$, it is shown that the number of shells is given by $O(\mathsf{A}^2)$ where $\mathsf{A}$ is the constraint on the Input amplitude. Finally, the third part provides bounds on the number of points for the case of $n=1$ with an additional power constraint.
Steve Hranilovic - One of the best experts on this subject based on the ideXlab platform.
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channel capacity and non uniform signalling for free space optical intensity channels
IEEE Journal on Selected Areas in Communications, 2009Co-Authors: A A Farid, Steve HranilovicAbstract:This work considers the design of capacity-approaching, non-uniform optical intensity signalling in the presence of average and peak amplitude constraints. Although it is known that the capacity-achieving Input Distribution is discrete with a finite number of mass points, finding it requires complex non-linear optimization at every SNR. In this work, a simple expression for a capacity-approaching Distribution is derived via source entropy maximization. The resulting mutual information using the derived discrete non-uniform Input Distribution is negligibly far away from the channel capacity. The computation of this Distribution is substantially less complex than previous optimization approaches and can be easily computed at different SNRs. A practical algorithm for non-uniform optical intensity signalling is presented using multi-level coding followed by a mapper and multi-stage decoding at the receiver. The proposed signalling is simulated on free-space optical channels and outage capacity is analyzed. A significant gain in both rate and probability of outage is achieved compared to uniform signalling, especially in the case of channels corrupted by fog.
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capacity achieving probability measure of an Input bounded vector gaussian channel
International Symposium on Information Theory, 2003Co-Authors: Terence Chan, Steve Hranilovic, Frank R KschischangAbstract:A discrete-time memoryless additive vector Gaussian noise channel subject to average cost constraints and an Input-bounded constraint is con- sidered. The necessary and sufficient condition for an Input Distribution to be capacity achieving is derived, and the capacity achieving Distribution is shown to be "discrete" in nature.
Robert Schober - One of the best experts on this subject based on the ideXlab platform.
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conditional capacity and transmit signal design for swipt systems with multiple nonlinear energy harvesting receivers
IEEE Transactions on Communications, 2020Co-Authors: Rania Morsi, Vahid Jamali, Amelie Hagelauer, Robert SchoberAbstract:In this paper, we study information-theoretic limits for simultaneous wireless information and power transfer (SWIPT) systems employing practical nonlinear radio frequency (RF) energy harvesting (EH) receivers (Rxs). In particular, we consider a SWIPT system with one transmitter that broadcasts a common signal to an information decoding (ID) Rx and multiple EH Rxs. Owing to the nonlinearity of the EH Rxs’ circuitry, the efficiency of wireless power transfer depends on the waveform of the transmitted signal. We aim to answer the following fundamental question: What is the optimal Input Distribution of the transmit signal waveform that maximizes the information transfer rate at the ID Rx conditioned on individual minimum required direct-current (DC) powers to be harvested at the EH Rxs? Specifically, we study the conditional capacity problem of a SWIPT system impaired by additive white Gaussian noise subject to average-power (AP) and peak-power (PP) constraints at the transmitter and nonlinear EH constraints at the EH Rxs. To this end, we develop a novel nonlinear EH model that captures the saturation of the harvested DC power by taking into account not only the forward current of the rectifying diode but also the reverse breakdown current. Then, we derive a novel semi-closed-form expression for the harvested DC power, which simplifies to closed form for low Input RF powers. The derived analytical expressions are shown to closely match circuit simulation results. We solve the conditional capacity problem for real- and complex-valued signalling and prove that the optimal Input Distribution that maximizes the rate-energy (R-E) region is unique and discrete with a finite number of mass points. Furthermore, we show that, for the considered nonlinear EH model and a given AP constraint, the boundary of the R-E region saturates for high PP constraints due to the saturation of the harvested DC power for high Input RF powers. In addition, we devise a suboptimal Input Distribution whose R-E tradeoff performance is close to optimal. All theoretical findings are verified by numerical evaluations.
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conditional capacity and transmit signal design for swipt systems with multiple nonlinear energy harvesting receivers
arXiv: Information Theory, 2019Co-Authors: Rania Morsi, Vahid Jamali, Amelie Hagelauer, Robert SchoberAbstract:We study information-theoretic limits for simultaneous wireless information and power transfer (SWIPT) systems employing nonlinear radio frequency (RF) energy harvesting (EH) receivers (Rxs). In particular, we consider a SWIPT system with one transmitter that broadcasts a common signal to an information decoding (ID) Rx and multiple EH Rxs. Owing to the nonlinearity of the EH Rxs' circuitry, the efficiency of wireless power transfer depends on the waveform of the transmitted signal. We aim to answer the following fundamental question: What is the optimal Input Distribution of the transmit signal waveform that maximizes the information transfer rate at the ID Rx conditioned on individual minimum required direct-current (DC) powers to be harvested at the EH Rxs? Specifically, we study the conditional capacity problem of a SWIPT system impaired by additive white Gaussian noise subject to average-power (AP) and peak power (PP) constraints at the transmitter and nonlinear EH constraints at the EH Rxs. To this end, we develop a novel nonlinear EH model that captures the saturation of the harvested DC power by taking into account the reverse breakdown current of the rectifying diode. We derive a novel semiclosed-form expression for the harvested DC power, which simplifies to closed form for low Input RF powers. The derived analytical expressions are shown to closely match circuit simulation results. We solve the conditional capacity problem for real- and complex-valued signalling and prove that the optimal Input Distribution that maximizes the rate-energy (R-E) region is unique and discrete with a finite number of mass points. Furthermore, we show that the boundary of the R-E region saturates for high PP constraints due to the saturation of the harvested DC power for high Input RF powers. In addition, we devise a suboptimal Input Distribution whose R-E tradeoff performance is close to optimal.
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on the capacity of swipt systems with a nonlinear energy harvesting circuit
International Conference on Communications, 2018Co-Authors: Rania Morsi, Vahid Jamali, Robert SchoberAbstract:In this paper, we study information-theoretic limits for simultaneous wireless information and power transfer (SWIPT) systems employing a practical nonlinear radio frequency (RF) energy harvesting (EH) receiver. In particular, we consider a three-node system with one transmitter that broadcasts a common signal to separated information decoding (ID) and EH receivers. Owing to the nonlinearity of the EH receiver circuit, the efficiency of wireless power transfer depends significantly on the waveform of the transmitted signal. In this paper, we aim to answer the following fundamental question: What is the optimal Input Distribution of the transmit waveform that maximizes the rate of the ID receiver for a given required harvested power at the EH receiver? In particular, we study the capacity of a SWIPT system impaired by additive white Gaussian noise (AWGN) under average-power (AP) and peak-power (PP) constraints at the transmitter and an EH constraint at the EH receiver. Using Hermite polynomial bases, we prove that the optimal capacityachieving Input Distribution that maximizes the rate-energy region is unique and discrete with a finite number of mass points. Our numerical results show that the rate-energy region is enlarged for a larger PP constraint and that the rate loss of the considered SWIPT system compared to the AWGN channel without EH receiver is reduced by increasing the AP budget.
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on the capacity of swipt systems with a nonlinear energy harvesting circuit
arXiv: Information Theory, 2017Co-Authors: Rania Morsi, Vahid Jamali, Robert SchoberAbstract:In this paper, we study information-theoretic limits for simultaneous wireless information and power transfer (SWIPT) systems employing a practical nonlinear radio frequency (RF) energy harvesting (EH) receiver. In particular, we consider a three-node system with one transmitter that broadcasts a common signal to separated information decoding (ID) and EH receivers. Owing to the nonlinearity of the EH receiver circuit, the efficiency of wireless power transfer depends significantly on the waveform of the transmitted signal. In this paper, we aim to answer the following fundamental question: What is the optimal Input Distribution of the transmit waveform that maximizes the rate of the ID receiver for a given required harvested power at the EH receiver? In particular, we study the capacity of a SWIPT system impaired by additive white Gaussian noise (AWGN) under average-power (AP) and peak-power (PP) constraints at the transmitter and an EH constraint at the EH receiver. Using Hermite polynomial bases, we prove that the optimal capacity-achieving Input Distribution that maximizes the rate-energy region is unique and discrete with a finite number of mass points. Furthermore, we show that the optimal Input Distribution for the same problem without PP constraint is discrete whenever the EH constraint is active and continuous zero-mean Gaussian, otherwise. Our numerical results show that the rate-energy region is enlarged for a larger PP constraint and that the rate loss of the considered SWIPT system compared to the AWGN channel without EH receiver is reduced by increasing the AP budget.
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capacity of the gaussian two hop full duplex relay channel with residual self interference
IEEE Transactions on Communications, 2017Co-Authors: Nikola Zlatanov, Erik Sippel, Vahid Jamali, Robert SchoberAbstract:In this paper, we investigate the capacity of the Gaussian two-hop full-duplex (FD) relay channel with residual self-interference. This channel is comprised of a source, an FD relay, and a destination, where a direct source-destination link does not exist and the FD relay is impaired by residual self-interference. We adopt the worst case linear self-interference model with respect to the channel capacity, and model the residual self-interference as a Gaussian random variable whose variance depends on the amplitude of the transmit symbol of the relay. For this channel, we derive the capacity and propose an explicit capacity-achieving coding scheme. Thereby, we show that the optimal Input Distribution at the source is Gaussian and its variance depends on the amplitude of the transmit symbol of the relay. On the other hand, the optimal Input Distribution at the relay is discrete or Gaussian, where the latter case occurs only when the relay-destination link is the bottleneck link. The derived capacity converges to the capacity of the two-hop ideal FD relay channel without self-interference and to the capacity of the two-hop half-duplex (HD) relay channel in the limiting cases when the residual self-interference is zero and infinite, respectively. Our numerical results show that significant performance gains are achieved with the proposed capacity-achieving coding scheme compared with the achievable rates of conventional HD relaying and/or conventional FD relaying.
