On the Capacity of SWIPT Systems with a Nonlinear Energy Harvesting Circuit

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.Comment: 7 pages, 4 figures, submitted for possible conference publicatio

Memristor models for machine learning

In the quest for alternatives to traditional CMOS, it is being suggested that digital computing efficiency and power can be improved by matching the precision to the application. Many applications do not need the high precision that is being used today. In particular, large gains in area- and power efficiency could be achieved by dedicated analog realizations of approximate computing engines. In this work, we explore the use of memristor networks for analog approximate computation, based on a machine learning framework called reservoir computing. Most experimental investigations on the dynamics of memristors focus on their nonvolatile behavior. Hence, the volatility that is present in the developed technologies is usually unwanted and it is not included in simulation models. In contrast, in reservoir computing, volatility is not only desirable but necessary. Therefore, in this work, we propose two different ways to incorporate it into memristor simulation models. The first is an extension of Strukov's model and the second is an equivalent Wiener model approximation. We analyze and compare the dynamical properties of these models and discuss their implications for the memory and the nonlinear processing capacity of memristor networks. Our results indicate that device variability, increasingly causing problems in traditional computer design, is an asset in the context of reservoir computing. We conclude that, although both models could lead to useful memristor based reservoir computing systems, their computational performance will differ. Therefore, experimental modeling research is required for the development of accurate volatile memristor models.Comment: 4 figures, no tables. Submitted to neural computatio

A quantum mechanical version of Price's theorem for Gaussian states

This paper is concerned with integro-differential identities which are known in statistical signal processing as Price's theorem for expectations of nonlinear functions of jointly Gaussian random variables. We revisit these relations for classical variables by using the Frechet differentiation with respect to covariance matrices, and then show that Price's theorem carries over to a quantum mechanical setting. The quantum counterpart of the theorem is established for Gaussian quantum states in the framework of the Weyl functional calculus for quantum variables satisfying the Heisenberg canonical commutation relations. The quantum mechanical version of Price's theorem relates the Frechet derivative of the generalized moment of such variables with respect to the real part of their quantum covariance matrix with other moments. As an illustrative example, we consider these relations for quadratic-exponential moments which are relevant to risk-sensitive quantum control.Comment: 11 pages, to appear in the Proceedings of the Australian Control Conference, 17-18 November 2014, Canberra, Australi

Probabilistic analysis of a differential equation for linear programming

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are i.i.d. Gaussian variables, we compute the distribution of the convergence rate to the attracting fixed point. Using the framework of Random Matrix Theory, we derive a simple expression for this distribution in the asymptotic limit of large problem size. In this limit, we find that the distribution of the convergence rate is a scaling function, namely it is a function of one variable that is a combination of three parameters: the number of variables, the number of constraints and the convergence rate, rather than a function of these parameters separately. We also estimate numerically the distribution of computation times, namely the time required to reach a vicinity of the attracting fixed point, and find that it is also a scaling function. Using the problem size dependence of the distribution functions, we derive high probability bounds on the convergence rates and on the computation times.Comment: 1+37 pages, latex, 5 eps figures. Version accepted for publication in the Journal of Complexity. Changes made: Presentation reorganized for clarity, expanded discussion of measure of complexity in the non-asymptotic regime (added a new section