Simultaneous transmission of information and power over a point-to-point flat-fading complex Additive White Gaussian Noise (AWGN) channel is studied. In contrast with the literature that relies on an inaccurate linear model of the energy harvester, an experimentally-validated nonlinear model is considered. A general form of the delivered Direct Current (DC) power in terms of system baseband parameters is derived, which demonstrates the dependency of the delivered DC power on higher order statistics of the channel input distribution. The optimization problem of maximizing Rate-Power (R-P) region is studied. Assuming that the Channel gain is available at both the receiver and the transmitter, and constraining to independent and identically distributed (i.i.d.) channel inputs determined only by their first and second moment statistics, an inner bound for the general problem is obtained. Notably, as a consequence of the harvester nonlinearity, the studied inner bound exhibits a tradeoff between the delivered power and the rate of received information. It is shown that the tradeoff-characterizing input distribution is with mean zero and with asymmetric power allocations to the real and imaginary dimensions. DRAFT rate and delivered power. Just to name a few, frequency-selective channel [2], MIMO broadcasting [3], interference channel [4], [5], relaying [6], [7].One of the major efforts in a Simultaneous Wireless Information and Power Transfer (SWIPT) architecture is to increase the Direct-Current (DC) power at the output of the harvester without increasing transmit power. The harvester, known as rectenna, is composed of a rectifier 1 followed by a low-pass filter.In [8], [9], it is shown that the RF-to-DC conversion efficiency is a function of rectenna's structure, as well as its input waveform. Accordingly, in order to maximize rectenna's DC power output, a systematic waveform design is crucial to make the best use of an available RF spectrum. In [9], an analytical model for rectenna's output is introduced via the Taylor expansion of the diode characteristic function. As one of the main conclusions, it is shown that the rectifier's nonlinearity is key to design efficient wireless powered systems. The design of an efficient SWIPT architecture fundamentally relies on designing an efficient Wireless Power Transfer (WPT) structure as an important building block of SWIPT. The SWIPT literature has so far focused on the linear model of the rectifier, e.g., [2]-[7], whereas, it is expected that considering nonlinearity effect changes the SWIPT design, signalling and architecture significantly. Indeed, in [10],[11], the design of SWIPT waveforms is studied accounting for rectenna's nonlinearity with a power splitter at the receiver. It is shown that superposing deterministic multisines (for power transfer purposes) with Orthogonal Frequency Division Multiplexing (OFDM) symbols modulated with Circularly Symmetric Complex Gaussian (CSCG) zero-mean inputs (for information purposes) enlarges the Rate-Power (R-P) region, compared ...
Nonlinear energy harvesters (EH) behave differently depending on the range of their input power. In the literature, different models have been proposed mainly for relatively small and large input power regimes of an EH. Due to the complexity of the proposed nonlinear models, obtaining analytical optimal or well performing signal designs have been extremely challenging. Relying on the proposed models in the literature, the learning problem of modulation design for simultaneous wireless information-power transfer (SWIPT) over a point-to-point link is studied. Joint optimization of the transmitter and the receiver is implemented using neural network (NN)-based autoencoders. The results reveal that for relatively small channel input powers, as the power demand increases at the receiver, one of the symbols is shot away from the origin while the remaining symbols approach zero amplitude. In the very extreme case of merely receiver power demand, the modulations are in the form of On-Off keying signalling with a low probability of the On signal. On the other side, for relatively large channel input powers, it is observed that as the receiver power demand increases, a number of symbols approach zero amplitude, whereas the others (more than one symbol) get equally high amplitudes but with different phases. In the extreme scenario of merely receiver power demand, the modulation resembles multiple On-Off keying signalling with different phases.
This paper considers the zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel with a one-bit analog-to-digital converter (ADC) front end. The optimization of the encoder and decoder is tackled under both the mean squared error (MSE) distortion and the outage distortion criteria with an average power constraint. For MSE distortion, the optimal transceiver is identified over the space of symmetric encoders. This result demonstrates that the linear encoder, which is optimal with a full-precision front end, approaches optimality only in the low signal-to-noise ratio (SNR) regime; while, digital transmission is optimal in the high SNR regime. For the outage distortion criterion, the structure of the optimal encoder and decoder are obtained. In particular, it is shown that the encoder mapping is piecewise constant and can take only two opposite values when it is non-zero. Index Terms-Joint source channel coding, zero-delay transmis- sion, average distortion, outage distortion, one-bit ADC
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.
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