On Capacity-Achieving Distributions for Complex AWGN Channels Under Nonlinear Power Constraints and their Applications to SWIPT

Abstract

The capacity of a complex and discrete time memoryless Additive White Gaussian Noise (AWGN) channel under three constraints, namely, input average power, input amplitude and delivered power at the output is studied.The delivered power constraint is modelled as a linear combination of even-moment statistics of the channel input being larger than a threshold. It is shown that the capacity of an AWGN channel under transmit average power and receiver delivered power constraints is the same as the capacity of an AWGN channel under an average power constraint, however, depending on the two constraints, it can be either achieved (via Circular Symmetric Complex Gaussian (CSCG) input) or arbitrarily approached (via time sharing between inputs with high amount of information, e.g. CSCG, and inputs with high amount of power, exhibiting a low probability of high amplitude signals). As an application, a simultaneous wireless information and power transfer (SWIPT) problem is studied, where an experimentally-validated nonlinear model of the harvester is used. It is shown that the delivered power depends on higher order statistics of the channel input. Two inner bounds, one based on complex Gaussian inputs and the other based on convexifying the optimization probability space, are obtained for the Rate-Power (RP) region. For Gaussian inputs, the optimal inputs are zero mean and a tradeoff between information and power is recognized by considering asymmetric power allocations between Inphase and Quadrature subchannels. Through numerical algorithms, it is observed that the numerically obtained input (NOI) distributions attain larger RP region compared to Gaussian input counterparts. The benefits of the newly developed and optimized input distributions are also confirmed and validated through realistic circuit simulations. The results reveal the crucial role played by the energy harvester nonlinearity on SWIPT and provide new engineering guidelines on how to exploit this nonlinearity in the design of SWIPT modulation, signal and architecture.

Signal and System Design for Wireless Power Transfer : Prototype, Experiment and Validation

“…In contrast to the multisine waveform that is deterministic, energy modulation carries information due to the randomness inherent from the modulation. However the modulation is designed in such a way that it maximizes the harvested DC power [19]. In its simplest form, M = 1, N = 1, and the transmit signal ω n,m (t) at time t on carrier frequency f 0 can be written as…”

“…Note that the performance could be improved by designing a circuit that is robust to diode breakdown and copes with high peak voltages (see discussions in [17], [28] and references therein). Remark 4: Energy modulation is not only important for improving WPT efficiency but plays a major role in simultaneous wireless information and power transmission (SWIPT) systems [18], [19]. These studies are beneficial to choose a modulation scheme for SWIPT that is as efficient as possible for information and power delivery.…”

“…Beamforming, waveform, modulation and transmit diversity performance have been analyzed using circuit simulations and results have been contrasted with the theory (using z DC scaling laws). Readers are referred to [9] and [10] for waveform and beamforming, to [19] for modulation and to [20] for transmit diversity. In all cases, circuit simulations confirm the benefits of the four signal strategies.…”

“…For instance, a real Gaussian modulation offers a higher harvested DC power than a circularly symmetric complex Gaussian modulation [18]. A new modulation scheme based on flash signalling has recently been introduced in [19]. It exploits the rectifier nonlinearity by transmitting signals of very high amplitudes with low probability.…”

“…{ω} ∼ N (0, 2P )) [18], and the recently proposed flash signalling [19] characterized by a uniformly distributed phase φ over [0, 2π) and the amplitude distributed according to the following probability mass function…”