Impact of Non-Linear High-Power Amplifiers on Cooperative Relaying Systems

In this paper, we investigate the impact of the high-power amplifier non-linear distortion on multiple relay systems by introducing the soft envelope limiter, traveling wave tube amplifier, and solid-state power amplifier to the relays. The system employs amplify-and-forward either fixed or variable gain relaying and uses the opportunistic relay selection with outdated channel state information to select the best relay. The results show that the performance loss is small at low rates; however, it is significant for high rates. In particular, the outage probability and the bit error rate are saturated by an irreducible floor at high rates. The same analysis is pursued for the capacity and shows that it is saturated by a detrimental ceiling as the average signal-to-noise ratio becomes higher. This result contrasts the case of the ideal hardware where the capacity grows indefinitely. Moreover, the results show that the capacity ceiling is proportional to the impairment's parameter and for some special cases the impaired systems practically operate in acceptable conditions. Closed-forms and high SNR asymptotes of the outage probability, the bit error rate, and the capacity are derived. Finally, analytical expressions are validated by the Monte Carlo simulation

Asymmetric RF/FSO Relaying with HPA non-Linearities and Feedback Delay Constraints

In this work, we investigate the performance of a dual-hop multiple relays system consisting of mixed Radio-Frequency (RF)/Free Space Optical (FSO) channels. The RF channels are subject to Rayleigh fading while the optical links experience the Double Generalized Gamma including atmospheric turbulence, path loss and the misalignment between the transmitter and the receiver aperture (also known as the pointing error). The FSO model also takes into account the receiver detection technique which could be either heterodyne or intensity modulation and direct detection. Partial Relay Selection with outdated Channel State Information is assumed based on the RF channels to select a relay and we also consider fixed and variable Amplify-and-Forward relaying schemes. In addition, we assume that the relays are affected by the high power amplifier non-linearities and herein we discuss two power amplifiers called Soft Envelope Limiter and Traveling Wave Tube Amplifier. Furthermore, novel closed-forms and tight upper bounds of the outage probability, the bit error probability, and the ergodic capacity are derived. Capitalizing on these performance, we derive the high SNR asymptotic to get engineering insights about the system gains such as the diversity and the coding gains. Finally, the mathematical expressions are validated using the Monte Carlo simulation

Adaptive Gradient Search Beamforming for Full-Duplex mmWave MIMO Systems

In this work, we present a framework analysis of full-duplex (FD) systems for Millimeter Wave (mmWave) analog architecture. Given that FD systems can double the ergodic capacity, such systems experience large losses caused by the loopback self-interference (SI). In addition, systems with analog architecture also suffer from other forms of losses mainly incurred by the constant amplitude (CA) constraint. For this purpose, we propose the projected Gradient Ascent algorithm to maximize the sum rate under the unit-norm and CA constraints. Unlike previous works, our approach achieves the best spectral efficiency while minimizing the losses incurred by the CA constraint. We also consider an adaptive step size to compensate for the perturbations that may affect the cost function during the optimization. The results will show that the proposed algorithm converges to the same optimal value for different initializations while the number of iterations required for the convergence changes for each case. In this context, we primarily consider the gradient search method for a two-nodes FD systems and then we extend the analysis for a dual-hop FD relaying systems. Finally, we evaluate the robustness of our method in terms of rate and outage probability and compare with previous approaches

Tractable Approach to MmWaves Cellular Analysis with FSO Backhauling under Feedback Delay and Hardware Limitations

In this work, we investigate the performance of a millimeter waves (mmWaves) cellular system with free space optical (FSO) backhauling. MmWave channels are subject to Nakagami-m fading while the optical links experience the Double Generalized Gamma including atmospheric turbulence, path loss and the misalignment between the transmitter and the receiver aperture (also known as the pointing errors). The FSO model also takes into account the receiver detection technique which could be either heterodyne or intensity modulation and direct detection (IM/DD). Each user equipment (UE) has to be associated to one serving base station (BS) based on the received signal strength (RSS) or Channel State Information (CSI). We assume partial relay selection (PRS) with CSI based on mmWaves channels to select the BS associated with the highest received CSI. Each serving BS decodes the received signal for denoising, converts it into modulated FSO signal, and then forwards it to the data center. Thereby, each BS can be viewed as a decode-and-forward (DF) relay. In practice, the relay hardware suffers from nonlinear high power amplification (HPA) impairments which, substantially degrade the system performance. In this work, we will discuss the impacts of three common HPA impairments named respectively, soft envelope limiter (SEL), traveling wave tube amplifier (TWTA), and solid state power amplifier (SSPA). Novel closed-forms and tight upper bounds of the outage probability, the probability of error, and the achievable rate are derived. Capitalizing on these performance, we derive the high SNR asymptotes to get engineering insights into the system gain such as the diversity order.Comment: arXiv admin note: substantial text overlap with arXiv:1901.0424

Zero-Forcing Max-Power Beamforming for Hybrid mmWave Full-Duplex MIMO Systems

Full-duplex (FD) systems gained enormous attention because of the potential to double the spectral efficiency. In the context of 5G technology, FD systems operating at millimeter-wave (mmWave) frequencies become one of the most promising solutions to further increase the spectral efficiency and reduce the latency. However, such systems are vulnerable to the self-interference (SI) that significantly degrades the performance. To overcome this shortcoming, analog-only beamforming techniques have been developed to mitigate the SI. Because of the huge power consumption, systems operating at mmWave frequencies beamform the power by only tunning the phase shifters while maintaining constant amplitudes. Such a hardware constraint, known as the constant amplitude (CA) constraint, severely limits the system performance. In this work, we propose a digital and analog hybrid beamforming design that completely eliminates the SI while substantially minimizing the losses imposed by the CA constraint. Further, we develop a fully-digital beamforming design and derive the upper bound for the spectral efficiency as benchmarking tools to quantify the losses of our proposed hybrid design

Mixed RF/FSO Cooperative Relaying Systems with Co-Channel Interference

In this paper, we provide a global framework analysis of a dual-hop mixed Radio Frequency (RF)/Free Space Optical (FSO) system with multiple branches/relays wherein the first and second hops, respectively, consist of RF and FSO channels. To cover various cases of fading, we propose generalized channels' models for RF and FSO links that follow the Nakagami-m and the Double Generalized Gamma (DGG) distributions, respectively. Moreover, we suggest Channel State Information (CSI)-assisted relaying or variable relaying gain based Amplifiy-and-Forward (AF) amplification. Partial relay selection with outdated CSI is assumed as a relay selection protocol based on the knowledge of the RF CSI. In order to derive the end-to-end Signal-to-Interference-plus-Noise Ratio (SINR) statistics such as the Cumulative Distribution Function (CDF), the Probability Density Function (PDF), the higher order moments, the amount of fading and the Moment Generating Function (MGF), the numerical values of the fading severity parameters are only valid for integer values. Based on these statistics, we derive closed-forms of the outage probability, the bit error probability, the ergodic capacity and the outage capacity in terms of Meijer-G, univariate, bivariate and trivariate Fox-H functions. Capitalizing on these expressions, we derive the asymptotic high SNR to unpack valuable engineering insights of the system performance. Monte Carlo simulation is used to confirm the analytical expressions

Partial Relay Selection For Hybrid RF/FSO Systems with Hardware Impairments

In this paper, we investigate the performance analysis of dual hop relaying system consisting of asymmetric Radio Frequency (RF)/Free Optical Space (FSO) links. The RF channels follow a Rayleigh distribution and the optical links are subject to Gamma-Gamma fading. We also introduce impairments to our model and we suggest Partial Relay Selection (PRS) protocol with Amplify-and-Forward (AF) fixed gain relaying. The benefits of employing optical communication with RF, is to increase the system transfer rate and thus improving the system bandwidth. Many previous research attempts assuming ideal hardware (source, relays, etc.) without impairments. In fact, this assumption is still valid for low-rate systems. However, these hardware impairments can no longer be neglected for high-rate systems in order to get consistent results. Novel analytical expressions of outage probability and ergodic capacity of our model are derived taking into account ideal and non-ideal hardware cases. Furthermore, we study the dependence of the outage probability and the system capacity considering, the effect of the correlation between the outdated CSI (Channel State Information) and the current source-relay link, the number of relays, the rank of the selected relay and the average optical Signal to Noise Ratio (SNR) over weak and strong atmospheric turbulence. We also demonstrate that for a non-ideal case, the end-to-end Signal to Noise plus Distortion Ratio (SNDR) has a certain ceiling for high SNR range. However, the SNDR grows infinitely for the ideal case and the ceiling caused by impairments no longer exists. Finally, numerical and simulation results are presented

Mixed RF/FSO Relaying Systems with Hardware Impairments

In this work, we provide a detailed analysis of a dual-hop fixed gain (FG) amplify-and-forward relaying system, consisting of a hybrid radio frequency (RF) and free-space optical (FSO) channels. We introduce an impairment model which is the soft envelope limiter (SEL). Additionally, we propose the partial relay selection (PRS) protocol with outdated channel state information (CSI) based on the knowledge of the RF channels in order to select one relay for the communication. Moreover, the RF channels of the first hop experience Rayleigh fading while we propose a unified fading model for the FSO channels, called the unified Gamma Gamma (GG), taking into account the atmospheric turbulence, the path loss and the misalignment between the transmitter and the receiver aperture also called the pointing error. Novel closed-forms of the outage probability (OP), the bit error probability (BEP) and the average ergodic capacity (EC) are derived in terms of Meijer-G and Fox-H functions. Capitalizing on these metrics, we also derive the asymptotical high signal-to-noise ratio (SNR) in order to get engineering insights into the impacts of the hardware impairments and the system parameters as well. Finally, using Monte Carlo simulations, we validate numerically the derived mathematical formulations.Comment: arXiv admin note: text overlap with arXiv:1901.0424

Rate and Power Adaptation for Multihop Regenerative Relaying Systems

In this work, we provide a global framework analysis of a multi-hop relaying systems wherein the transmitter (TX) communicates with the receiver (RX) through a set of intermediary relays deployed either in series or in parallel. Regenerative based relaying scheme is assumed such as the repetition-coded decoded-and-forward (DF) wherein the decoding is threshold-based. To reflect a wide range of fading, we introduce the generalized $H$-function (also termed as Fox-$H$ function) distribution model which enables the modeling of radio-frequency (RF) fading like Weibull and Gamma, as well as the free-space optic (FSO) such as the Double Generalized Gamma and M\'alaga fading. In this context, we introduce various power and rate adaptation policies based on the channel state information (CSI) availability at TX and RX. Finally, we address the effects of relaying topology, number of relays and fading model, etc, on the performance reliability of each link adaptation policy

Sub-6 GHz Microstrip Antenna: Design and Radiation Modeling

This paper presents a global framework analysis of a microstrip antenna design circularly polarized with an operating frequency of 5.80 GHz and a bandwidth of at least 500 MHz. We evaluate the optimal antenna parameters to design requirements. Capitalizing on these parameters, we simulate the radiation model of this antenna using the Finite Difference Time Domain (FDTD) technique assuming one, two, and three dimensions. The propagation medium is assumed to be a free space bounded by absorbing boundaries, and perfect matched layer (PML). The FDTD-1D is considered in free space while FDTD-2D and 3D are considered both in free space and in a free space-medium containing either dielectric sphere or cylinder in the center. In this case, we model the incident and the scattered electromagnetic fields reflected back from hitting the dielectric object. Moreover, the microstrip antenna radiates an electromagnetic pulse either in the middle or at one end of the medium and the sources considered are Gaussian pulse and plane wave. Finally, we provide the analytic solutions of the propagation models to confirm the accuracy of the FDTD simulation technique