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the dependence of the outage probability and the system capacity considering, the effect of the correlation between the outdated CSI (Channel State Information) and the current source-relay link, the number of relays, the rank of the selected relay and the average optical Signal to Noise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 Additionally, we propose the partial relay selection (PRS) protocol with outdated channel state information (CSI) based on the knowledge of the RF channels in order to select one relay for the communication.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

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

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

Hybrid Rayleigh and Double-Weibull over Impaired RF/FSO System with Outdated CSI

In this work, we present a global framework of a dual-hop RF/FSO system with multiple relays operating at the mode of amplify-and-forward (AF) with fixed gain. Partial relay selection (PRS) protocol with outdated channel state information (CSI) is assumed since the channels of the first hop are time-varying. The optical irradiance of the second hop are subject to the Double-Weibull model while the RF channels of the first hop experience the Rayleigh fading. The signal reception is achieved either by heterodyne or intensity modulation and direct detection (IM/DD). In addition, we introduce an aggregate model of hardware impairments to the source (S) and the relays since they are not perfect nodes. In order to quantify the impairment impact on the system, we derive closed-form, approximate, upper bound and high signal-to-noise ratio (SNR) asymptotic of the outage probability (OP) and the ergodic capacity (EC). Finally, analytical and numerical results are in agreement using Monte Carlo simulation

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

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

Aggregate Hardware Impairments Over Mixed RF/FSO Relaying Systems With Outdated CSI

In this paper, we propose a dual-hop RF (Radio-Frequency)/FSO (Free-Space Optical) system with multiple relays employing the Decode-and-Forward (DF) and Amplify-and-Forward (AF) with a Fixed Gain (FG) relaying scheme. The RF channels are subject to a Rayleigh distribution while the optical links experience a unified fading model emcopassing the atmospheric turbulence that follows the M\'alaga distribution (or also called the $\mathcal{M}$-distribution), the atmospheric path loss and the pointing error. Partial relay selection (PRS) with outdated channel state information (CSI) is proposed to select the candidate relay to forward the signal to the destination. At the reception, the detection of the signal can be achieved following either heterodyne or Intensity Modulation and Direct Detection (IM/DD). Many previous attempts neglected the impact of the hardware impairments and assumed ideal hardware. This assumption makes sense for low data rate systems but it would no longer be valid for high data rate systems. In this work, we propose a general model of hardware impairment to get insight into quantifying its effects on the system performance. We will demonstrate that the hardware impairments have small impact on the system performance for low signal-to-noise ratio (SNR), but it can be destructive at high SNR values. Furthermore analytical expressions and upper bounds are derived for the outage probability and ergodic capacity while the symbol error probability is obtained through the numerical integration method. Capitalizing on these metrics, we also derive the high SNR asymptotes to get valuable insight into the system gains such as the diversity and the coding gains. Finally, analytical and numerical results are presented and validated by Monte Carlo simulation