Optimal Scheduling of Reliability-Constrained Relaying System under Outdated CSI in the Finite Blocklength Regime

Under the assumption of outdated channel state information (CSI) at the source, we consider the finite blocklength (FBL) throughput of a two-hop relaying system. Previous work has considered this setting so far only for the infinite blocklength case, where decoding can be arbitrarily reliable as long as operating below the Shannon limit. In contrast, in the FBL regime residual decoding errors can not be avoided even when transmitting below the Shannon limit. This makes the scheduling problem at the source more vulnerable to transmission errors, where we investigate the trade-off between the choice of so called scheduling weights to avoid transmission errors and the resulting coding rate. We show that the corresponding maximization of the throughput under a reliability constraint can be solved efficiently by iterative algorithms. Nevertheless, the optimal solution requires a recomputation of the scheduling weights prior to each transmission. Thus, we also study heuristics relying on choosing the scheduling weights only once. Through numerical analysis, we first provide insights on the structure of the throughout under different scheduling weights and channel correlation coefficients. We then turn to the comparison of the optimal scheduling with the heuristic and show that the performance gap between them is only significant for relay systems with high average signal-to-noise ratios (SNR) on the backhaul and relaying link. In particular, the optimal scheduling scheme provides most value in case that the data transmission is subject to strict reliability constraints, justifying the significant additional computational burden.Comment: 24 pages, 8 figures, IEEE TWC submissio

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

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

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

On Secure Mixed RF-FSO Systems With TAS and Imperfect CSI

In this work, we analyze the secrecy outage performance of a dual-hop relay system composed of multiple-input-multiple-output radio-frequency (RF) links and a free-space optical (FSO) link while a multiple-antenna eavesdropper wiretaps the confidential information by decoding the received signals from the resource node. The channel state information (CSI) of the RF and FSO links is considered to be outdated. We propose three transmit antenna selection (TAS) schemes to enhance the secrecy performance of the considered systems. The secrecy outage performance with different TAS schemes is analyzed and the effects of misalignment and detection technology on the secrecy outage performance of mixed systems are studied. We derive the closed-form expressions for probability density function (PDF) and cumulative distribution function (CDF) over M\'alaga channel with imperfect CSI. Then the closed-form expressions for the CDF and PDF of the equivalent signal-to-noise ratio (SNR) at the legitimate receiver over Nakagami-$m$ and M\'alaga channels are derived. Furthermore, the lower bound of the secrecy outage probability (SOP) with different TAS schemes are derived. Besides, the asymptotic results for SOP are investigated by exploiting the unfolding of Meijer's $G$-function when the electrical SNR of FSO link approaches infinity. Finally, Monte-Carlo simulation results are presented to testify the correctness of the proposed analysis. The results illustrate that the outdated CSI shows a strong effect on the secrecy outage performance. In addition, increasing the number of antennas at the source cannot significantly enhance the secrecy performance of the considered systems.Comment: 14 pages, to appear in the IEEE Transactions on Communication

Outage Probability Analysis of Selective-Decode and Forward Cooperative Wireless Network over Time Varying Fading Channels with Node Mobility and Imperfect CSI Condition

In this work, we explore the outage probability (OP) analysis of selective decode and forward (SDF) cooperation protocol employing multiple-input multipleoutput (MIMO) orthogonal space-time block-code (OSTBC) over time varying Rayleigh fading channel conditions with imperfect channel state information (CSI) and mobile nodes. The closed-form expressions of the per-block average OP, probability distribution function (PDF) of sum of independent and identically distributed (i.i.d.) Gamma random variables (RVs), and cumulative distribution function (CDF) are derived and used to investigate the performance of the relaying network. A mathematical framework is developed to derive the optimal source-relay power allocation factors. It is shown that source node mobility affects the per-block average OP performance more significantly than the destination node mobility. Nevertheless, in other node mobility situations, cooperative systems are constrained by an error floor with a higher signal to noise ratio (SNR) regimes. Simulation results show that the equal power allocation is the only possible optimal solution when source to relay link is stronger than the relay to destination link. Also, we allocate almost all the power to the source node when source to relay link is weaker than the relay to destination link. Simulation results also show that OP simulated plots are in close agreement with the OP analytic plots at high SNR regimes

Security-Reliability Trade-off Analysis of Multi-Relay Aided Decode-and-Forward Cooperation Systems

We consider a cooperative wireless network comprised of a source, a destination and multiple relays operating in the presence of an eavesdropper, which attempts to tap the source-destination transmission. We propose multi-relay selection scheme for protecting the source against eavesdropping. More specifically, multi-relay selection allows multiple relays to simultaneously forward the source's transmission to the destination, differing from the conventional single-relay selection where only the best relay is chosen to assist the transmission from the source to destination. For the purpose of comparison, we consider the classic direct transmission and single-relay selection as benchmark schemes. We derive closed-form expressions of the intercept probability and outage probability for the direct transmission as well as for the single-relay and multi-relay selection schemes over Rayleigh fading channels. It is demonstrated that as the outage requirement is relaxed, the intercept performance of the three schemes improves and vice versa, implying that there is a \emph{security versus reliability trade-off} (SRT). We also show that both the single-relay and multi-relay selection schemes outperform the direct transmission in terms of SRT, demonstrating the advantage of the relay selection schemes for protecting the source's transmission against the eavesdropping attacks. Finally, upon increasing the number of relays, the SRTs of both the single-relay and multi-relay selection schemes improve significantly and as expected, multi-relay selection outperforms single-relay selection.Comment: 8 pages, IEEE Transactions on Vehicular Technology, 201

A Buffer-aided Successive Opportunistic Relay Selection Scheme with Power Adaptation and Inter-Relay Interference Cancellation for Cooperative Diversity Systems

In this paper we consider a simple cooperative network consisting of a source, a destination and a cluster of decode-and-forward half-duplex relays. At each time-slot, the source and (possibly) one of the relays transmit a packet to another relay and the destination, respectively, resulting in inter-relay interference (IRI). In this work, with the aid of buffers at the relays, we mitigate the detrimental effect of IRI through interference cancellation. More specifically, we propose the min-power scheme that minimizes the total energy expenditure per time slot under an IRI cancellation scheme. Apart from minimizing the energy expenditure, the min-power selection scheme, also provides better throughput and lower outage probability than existing works in the literature. It is the first time that interference cancellation is combined with buffer-aided relays and power adaptation to mitigate the IRI and minimize the energy expenditure. The new relay selection policy is analyzed in terms of outage probability and diversity, by modeling the evolution of the relay buffers as a Markov Chain (MC). We construct the state transition matrix of the MC, and hence obtain the steady state with which we can characterize the outage probability. The proposed scheme outperforms relevant state-of-the-art relay selection schemes in terms of throughput, diversity and energy efficiency, as demonstrated via examples.Comment: Preliminary results of this article have been presented in the IEEE International Symposium on Personal Indoor and Mobile Radio Communications, 8-11 September, 2013, London, United Kingdo

Performance of Opportunistic Fixed Gain Bidirectional Relaying With Outdated CSI

This paper studies the impact of using outdated channel state information for relay selection on the performance of a network where two sources communicate with each other via fixed-gain amplifyand- forward relays. For a Rayleigh faded channel, closed-form expressions for the outage probability, moment generating function and symbol error rate are derived. Simulations results are also presented to corroborate the derived analytical results. It is shown that adding relays does not improve the performance if the channel is substantially outdated. Furthermore, relay location is also taken into consideration and it is shown that the performance can be improved by placing the relay closer to the source whose channel is more outdated