Search

This paper is concerned with multiple-input multiple-output (MIMO) wireless channel capacity, when the probability distribution of the channel matrix p(H) is not completely known to the transmitter and the receiver. The partial knowledge of a true probability distribution of the channel matrix p(H) is modelled by a relative entropy D(·∥·) such that D(p∥p nom)≤d, d≥0, where d is the distance from the so-called nominal channel matrix distribution p nom(H). The capacity of this compound channel is equal to the maximin of the mutual information, where the minimum is with respect to the channel matrix distribution, and the maximum is with respect to the covariance matrix of a transmitted signal. The existence of a minimizing probability distribution is proved, and the explicit formula for the minimizing distribution is derived in terms of the nominal distribution p nom(H) and parameter d. A number of properties of the mutual information, minimized over the set of channel distributions, are derived. Specifically, upper and lower bounds are derived for the minimized mutual information, while its convexity with respect to d is shown. In the case of the Rayleigh fading, an explicit formula for the capacity and the optimal transmit covariance matrix are derived. © 2009 IEEE. 55 8 3725 3734

In this paper, achievable rates for compound Gaussian multiple-input-multiple-output (MIMO) channels are derived. Two types of channels, modeled in the frequency domain, are considered when: 1) the channel frequency response matrix H belongs to a subset of H∞ normed linear space, and 2) the power spectral density (PSD) matrix of the Gaussian noise belongs to a subset of L1 space. The achievable rates of these two compound channels are related to the maximin of the mutual information rate. The minimum is with respect to the set of all possible H matrices or all possible PSD matrices of the noise. The maximum is with respect to all possible PSD matrices of the transmitted signal with bounded power. For the compound channel modeled by the set of H matrices, it is shown, under certain conditions, that the code for the worst case channel can be used for the whole class of channels. For the same model, the water-filling argument implies that the larger the set of matrices H, the smaller the bandwidth of the transmitted signal will be. For the second compound channel, the explicit relation between the maximizing PSD matrix of the transmitted signal and the minimizing PSD matrix of the noise is found. Two PSD matrices are related through a Riccati equation, which is always present in Kalman filtering and liner-quadratic Gaussian control problems. © 2009 IEEE. 55 4 1603 1617

In this work, we focus on the encoder, decoder, and controller design for jump linear systems over jump communication channels.The plant state information (PSI) and the channel state information (CSI) are assumed to be known at the both transmitter and the receiver ends. Both the PSI and the CSI are governed by a finite state Markov chain. The control and communication system is designed for the general vector observations over two different channels. One is assumed to be a vector channel, and the other one is a scalar channel. We design the optimal encoder, controller and decoder for both channels and the design scheme achieves the desired distortion. The rate distortions for both cases are also computed. © 2013 AACC American Automatic Control Council. 4239 4244

The paper introduces a new asymptotic series expansion for the mutual information of multiple-input multiple-output (MIMO) channels. The expansion approaches mutual information from below, and for low signal to noise ratio (SNR) first and second order terms give a tight lower bound. The low SNR approximation is used to derive a new water-filling power allocation at the transmitter for the case when the receiver and the transmitter have perfect channel state information. The low SNR approximation is also compared against existing approximations, while the new water-filling policy is related to minimum mean square decoding subject to power constraint. © 2010 IEEE. 15 3 329 331

As the CMOS semiconductor technology enters nanometer regime, interconnect processes must be compatible with device roadmaps and meet manufacturing targets at the specified wafer size. The resulting ubiquitous process variations cause errors in data delivering through interconnects. This paper proposes an Information Theory based design method to accommodate process variations. Different from the traditional delay based design metric, the current approach uses achievable rate to relate interconnect designs directly to communication applications. More specifically, the data communication over a typical interconnect, a bus, subject to process variations (uncertain bus), is defined as a communication problem under uncertainty. A data rate, called the achievable rate, is computed for such a bus, which represents the lower bound on the maximal data rate attainable over the bus. When a data rate applied over the bus is smaller than the achievable data rate, a reliable communication can be guaranteed regardless of process variations, i.e., a bit error rate arbitrarily close to zero is achievable. A single communication strategy to combat the process variations is proposed whose code rate is equal to the computed achievable rate. The simulations show that the variations in the interconnect resistivity could have the most harmful effect regarding the achievable rate reduction. Also, the simulations illustrate the importance of taking into account bus parasitic parameters correlations when measuring the influence of the process variations on the achievable rates. © 2006 IEEE. 19 3 397 410

The paper introduces an asymptotic series expansion for the mutual information of Multiple-Input Multiple-Output (MIMO) channels. For low signal to noise ratio (SNR) the first term of expansion approaches mutual information from below. Using the low SNR approximation a new water filling power allocation at the transmitter is derived when the receiver and the transmitter have perfect channel state information (CSITR). The low SNR approximation is related to existing approximation while the new water filling policy is related to minimum mean square decoding subject to power constraint. Finally, an upper bound for the outage probability at low SNR is presented. ©2010 IEEE.

Uncertainty is an intrinsic phenomenon in control of gene regulatory networks (GRNs). The presence of uncertainty is related to impreciseness of GRN models due to: (1) Errors caused by imperfection of measurement devices and (2) Models' inability to fully capture a complex structure of the GRN. Consequently, there is a discrepancy between actual behaviour of the GRN and what is predicted by its mathematical model. This can result in false control signals, which can drive a cell to an undesirable state. To address the problem of control under uncertainties, a risk-sensitive control paradigm is proposed. Robustness is accomplished by minimisation of the mean exponential cost as opposed to, for instance, minimisation of the mean square cost by risk-neutral controllers. The authors derive an optimal risk-sensitive controller when a GRN is modelled by a context-sensitive probabilistic Boolean network (CSPBN). By using a relation between the relative entropy and free-energy, a relative stability of the cost achieved by the risk-sensitive controller is demonstrated when the distribution of the CSPBN attractors is perturbed, as opposed to the cost of the risk-neutral controller that exhibits increase. The use of the relation between the relative entropy and free-energy to analyse the influence of a particular attractor on the robustness of the controller is studied. The efficiency of the risk-sensitive controller is tested for the CSPBN obtained from the study of malignant melanoma. © The Institution of Engineering and Technology. 3 4 279 295

This note is concerned with the control of continuous-time linear Gaussian systems over additive white noise wireless fading channels subject to capacity constraints. Necessary and sufficient conditions are derived, for bounded asymptotic and asymptotic observability and stabilizability in the mean square sense, for controlling such systems. For the case of a noiseless time-invariant system controlled over a continuous-time additive white Gaussian noise channel, the sufficient condition for stabilizability and observability states that the capacity of the channel C must satisfy C > Sigma{i;Re(lambdai(A))ges0} Re(lambdai(A)), where A is the system matrix and lambdai(A) denotes the eigenvalues of A. The necessary condition states that the channel capacity must satisfy C ges Sigma {i;Re(lambdai(A))ges0} Re(lambdai(A)). Further, it is shown that a separation principle holds between the design of the communication and the control subsystems, implying that the controller that would be optimal in the absence of the communication channel is also optimal for the problem of controlling the system over the communication channel.

This paper is concerned with the control of one dimensional continuous time linear Gaussian systems over additive white noise wireless fading channels subject to capacity constraints. Necessary and sufficient conditions are derived, for bounded asymptotic and asymptotic observability and stabillzability in the mean square sense, for controlling such systems. For the case of a noiseless time-invariant system controlled over a continuous time additive white Gaussian channel, the sufficient condition for stabilizability and observability states that the capacity of the channel, Ca, satisfies, Ca > [A]+, where A is the system coefficient and a]+ = a, if a ≥ 0 and [a+ = 0, if a < 0. Moreover, the necessary condition states that the channel capacity must satisfy C a ≥ |A|+. It is shown that a separation principle holds between the design of the communication and the control sub-systems, implying that the controller that would be optimal in the absence of the communication channel is also optimal for the problem of the controlling the system over the communication channel. © 2005 IEEE. 2005 3225 3230

We consider the problem of control of discrete-time partially-observed jump linear system over a noisy causal communication channel. Necessary conditions for observability and stabilizability in probability and r-th mean of a jump linear system driven by a Markov chain are derived. The methodology is information theoretic and it is based on an alternative definition of mutual information between two random processes which is restricted to a causal channel. Specifically, the self-mutual information is restricted to Radon-Nykodym Derivatives corresponding to causal channels. This gives rise to information capacity and rate distortion formulaes which involve causal operations, leading to a new set of data processing inequalities. © 2006 IEEE. 496 501

The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations (SDEs). The latter rapture the spatio-temporal variations of the communication link, as well as the randomness. This class of models is more realistic than the static models usually encountered in the literature. Under this scenario, average and probabilistic Quality of Service (QoS) measures are introduced to evaluate the performance of any control strategy by using Chernoff bounds. Moreover, the Chernoff bound is computed explicitly, while the solution of the stochastic optimal power control is obtained through pathwise optimization. The pathwise optimization can be solved using linear programming if predictable control strategies are introduced. Finally, if predictable control strategies do not hold, it is shown that the proposed power control problem reduces to particular convex optimizations. © 2005 IEEE. 51 12 4396 4401

This paper is concerned with the problem of defining, and computing the capacity of a continuous-time additive Gaussian noise communication channel when the true frequency response of the channel, and the power spectral density of the noise are not perfectly known, and the transmitted signal is a wide-sense stationary process constrained in power. The uncertainties of a true channel frequency response and power spectral density of the noise are described by weighted balls in the H ∞ space. In that way two sets are defined that describe the set of all possible channel frequency responses, and the set of all possible power spectral densities of the noise. The ball radii depend on the degree of uncertainty that one has about the true channel frequency response, and power spectral density of the noise. The channel capacity is defined as the max-min-min of a mutual information rate between transmitted, and received signals, where the first minimum is taken over the set of all possible noises, the second minimum is taken over the set of all possible channel frequency responses, and maximum is over the set of all possible power spectral densities of transmitted signal with constrained power. It is shown that such defined channel capacity, called robust capacity, is equal to the operational capacity that represents the theoretical maximum of all attainable rates over a given channel. ©2005 AACC. 3 1829 1834

This paper is concerned with the definition and computation of channel capacity of continuous time additive Gaussian channels, when the channel is subject to uncertainty, the noise power spectral density is known and the input signal is wide-sense stationary and constrained in power. The uncertainty description of the channel transfer function is described by the set of all channels which belong to a ball in a normed linear space, known as H ∞ space. Two uncertainty models are used that are borrowed from the control theory, additive, and multiplicative. The channel capacity, that we call robust capacity, is then defined as a maxi-min of mutual information rate in which the minimization is over the uncertainty set while the maximization is over all transmitted signals having finite power. An exact formulae for the robust capacity is derived. Part of the results include a modified version of the water-filling equation, describing how the optimal transmitter power depends on the channel uncertainty. The conditions are introduced under which the robust capacity is equivalent to operational capacity. Finally, an example is worked out to show the effect of uncertainty in case of the second order system. Copyright © 2005 IFAC. 16 111 116

This paper concerns the problem of defining, and computing the channel capacity of a continuous time additive white Gaussian noise channel when the true frequency response of the channel is not completely known to the transmitter, and receiver, and when a transmitted signal is a wide sense stationary process constrained in power. To represent the uncertainty of a true frequency response two basic uncertainty models are used that are borrowed from the control theory, additive, and multiplicative. Here, the true frequency response although unknown, belongs to a ball in a normed linear space. The radius of the ball is a function of frequency, and it depends on the size of the uncertainty. The channel capacity, called robust capacity is defined as a max-min of the mutual information rate, where the maximum is over all power spectral densities of the input signal with constrained power, and minimum is over the uncertainty set of frequency response. The robust capacity formula is explicitly computed describing how the channel uncertainty reduces the capacity. The water-filling formula is derived showing how the optimal transmitted power changes with uncertainty. At the end, it is shown that a channel coding theorem, and its converse under certain conditions imposed on the uncertainty set hold for the robust maximin capacity. 5 4880 4884

In this paper the problem of defining, and computing the capacity of a communication channel when the statistic of an additive noise is not fully known, is addressed. The communication channel is specified as a continuous time channel with the known transfer function, where the transmitted signal is constrained in power, and an additive Gaussian noise channel is assumed. The power spectral density of the noise although unknown belongs to a known set defined through the uncertainty of the filter the shapes the power spectral density of the noise. The channel capacity is defined as the max-min of mutual information rate between the transmitted, and received signals, where the infimum is taken over the set of all possible power spectral densities of the noise, and supremum is taken over all power spectral densities of transmitted signal with constrained power. It is shown that the so defined channel capacity is equal to the operational capacity that represents the supremum of all attainable rates over a given channel. 1 421 424

The objectives of this paper are twofold. First, to point out the significance of certain results on stochastic processes in computing the channel capacity for flat fading wireless channels. Second, to design an optimal encoding and decoding strategies for general sources, when the channel is perfectly known to both transmitter and receiver. We give an optimal encoding and decoding scheme with noiseless feedback achieving the channel capacity and consider the effect of feedback on decoding error. It turns out that the optimal encoding function has two parts; one part behaves as power control and the other part represents the decoding error. 4 4036 4041

The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations. Under this scenario, average and probabilistic Quality of Service (QoS) measures are introduced to evaluate the performance of any control strategy, while a solution of the stochastic optimal power control is obtained through pathwise optimization. The pathwise optimization can be solved using linear programming techniques. Several optimization problems are identified. 2 Journal Article 1049 1052

[This corrects the article DOI: 10.1371/journal.pgen.1000621.].