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

Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we focus on the frequency-resolved logarithmic perturbation model to study the coherence properties of NLI. Based on this study, we devise an NLI mitigation strategy which exploits the synergic effect of phase and polarization noise compensation (PPN) and subcarrier multiplexing with symbol-rate optimization. This synergy persists even for high-order modulation alphabets and Gaussian symbols. A particle method for the computation of the resulting achievable information rate and spectral efficiency (SE) is presented and employed to lower-bound the channel capacity. The dependence of the SE on the link length, amplifier spacing, and presence or absence of inline dispersion compensation is studied. Single-polarization and dual-polarization scenarios with either independent or joint processing of the two polarizations are considered. Numerical results show that, in links with ideal distributed amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or, in alternative, the system reach can be doubled at a given SE) with respect to single-carrier systems without PPN mitigation. The gain is lower with lumped amplification, increases with the number of spans, decreases with the span length, and is further reduced by in-line dispersion compensation. For instance, considering a dispersion-unmanaged link with lumped amplification and an amplifier spacing of 60 km, the SE after 80 spans can be be increased from 4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%) for a fixed SE.Comment: Submitted to Journal of Lightwave Technolog

Optical Time-Frequency Packing: Principles, Design, Implementation, and Experimental Demonstration

Time-frequency packing (TFP) transmission provides the highest achievable spectral efficiency with a constrained symbol alphabet and detector complexity. In this work, the application of the TFP technique to fiber-optic systems is investigated and experimentally demonstrated. The main theoretical aspects, design guidelines, and implementation issues are discussed, focusing on those aspects which are peculiar to TFP systems. In particular, adaptive compensation of propagation impairments, matched filtering, and maximum a posteriori probability detection are obtained by a combination of a butterfly equalizer and four 8-state parallel Bahl-Cocke-Jelinek-Raviv (BCJR) detectors. A novel algorithm that ensures adaptive equalization, channel estimation, and a proper distribution of tasks between the equalizer and BCJR detectors is proposed. A set of irregular low-density parity-check codes with different rates is designed to operate at low error rates and approach the spectral efficiency limit achievable by TFP at different signal-to-noise ratios. An experimental demonstration of the designed system is finally provided with five dual-polarization QPSK-modulated optical carriers, densely packed in a 100 GHz bandwidth, employing a recirculating loop to test the performance of the system at different transmission distances.Comment: This paper has been accepted for publication in the IEEE/OSA Journal of Lightwave Technolog

Capacity -based parameter optimization of bandwidth constrained CPM

Continuous phase modulation (CPM) is an attractive modulation choice for bandwidth limited systems due to its small side lobes, fast spectral decay and the ability to be noncoherently detected. Furthermore, the constant envelope property of CPM permits highly power efficient amplification. The design of bit-interleaved coded continuous phase modulation is characterized by the code rate, modulation order, modulation index, and pulse shape. This dissertation outlines a methodology for determining the optimal values of these parameters under bandwidth and receiver complexity constraints. The cost function used to drive the optimization is the information-theoretic minimum ratio of energy-per-bit to noise-spectral density found by evaluating the constrained channel capacity. The capacity can be reliably estimated using Monte Carlo integration. A search for optimal parameters is conducted over a range of coded CPM parameters, bandwidth efficiencies, and channels. Results are presented for a system employing a trellis-based coherent detector. To constrain complexity and allow any modulation index to be considered, a soft output differential phase detector has also been developed.;Building upon the capacity results, extrinsic information transfer (EXIT) charts are used to analyze a system that iterates between demodulation and decoding. Convergence thresholds are determined for the iterative system for different outer convolutional codes, alphabet sizes, modulation indices and constellation mappings. These are used to identify the code and modulation parameters with the best energy efficiency at different spectral efficiencies for the AWGN channel. Finally, bit error rate curves are presented to corroborate the capacity and EXIT chart designs

Iterative Joint Channel Estimation and Multi-User Detection for Multiple-Antenna Aided OFDM Systems

Multiple-Input-Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems have recently attracted substantial research interest. However, compared to Single-Input-Single-Output (SISO) systems, channel estimation in the MIMO scenario becomes more challenging, owing to the increased number of independent transmitter-receiver links to be estimated. In the context of the Bell LAyered Space-Time architecture (BLAST) or Space Division Multiple Access (SDMA) multi-user MIMO OFDM systems, none of the known channel estimation techniques allows the number of users to be higher than the number of receiver antennas, which is often referred to as a “rank-deficient” scenario, owing to the constraint imposed by the rank of the MIMO channel matrix. Against this background, in this paper we propose a new Genetic Algorithm (GA) assisted iterative Joint Channel Estimation and Multi-User Detection (GA-JCEMUD) approach for multi-user MIMO SDMA-OFDM systems, which provides an effective solution to the multi-user MIMO channel estimation problem in the above-mentioned rank-deficient scenario. Furthermore, the GAs invoked in the data detection literature can only provide a hard-decision output for the Forward Error Correction (FEC) or channel decoder, which inevitably limits the system’s achievable performance. By contrast, our proposed GA is capable of providing “soft” outputs and hence it becomes capable of achieving an improved performance with the aid of FEC decoders. A range of simulation results are provided to demonstrate the superiority of the proposed scheme. Index Terms—Channel estimation, genetic algorithm, multiple-input-multiple-output, multi-user detection, orthogonal frequency division multiplexing, space division multiple access