Variable-gain Amplify-and-forward Research Articles

Capacity and outage performance of multiple AF relays based cooperative OFDM-QIM system

In this paper, we propose a multiple amplify-and-forward (AF) relays based cooperative orthogonal frequency division multiplexing (OFDM) with quadrature index modulation (C-OFDM-QIM) system to enhance the spectral efficiency and the transmission reliability, where two independent subcarrier subsets are activated to convey the real and imaginary symbol vectors, respectively, and the per-subcarrier relay selection (RS) scheme is adopted to select the relay with the maximum end-to-end signal-to-noise ratio (SNR) for each active subcarrier. Both fixed-gain AF and variable-gain AF protocols are investigated at the selected relays. Based on the order statistics and the max-flow min-cut theory, the closed-form average outage probability (AOP) and the average capacity are derived, respectively. Numerical results demonstrate that the theoretical AOP is correct and accurate and the proposed C-OFDM-QIM system outperforms the traditional cooperative OFDM with index modulation (C-OFDM-IM) system in the spectral efficiency, the outage performance, and the average capacity.

On the Performance Analysis of Higher Order QAM Schemes Over Mixed RF/FSO Systems

In this work, the performance of a dual-hop variable gain amplify-and-forward (AF) mixed radio frequency (RF)/free space optics (FSO) system is analyzed in details. As variable gain AF relay network is considered, processing delay results in outdated channel state information (CSI) during amplification at the relay. For general applicability, the RF link is modeled with the generalized Nakagami-m fading. The FSO link is modeled with the Gamma-Gamma distribution which is affected with the atmospheric turbulence and pointing error impairments, and both the intensity modulation with direct detection (IM/DD) and heterodyne detection are employed at the FSO receiver. In this context, analytical expressions of outage probability and ergodic capacity are derived in terms of Meijer-G function and extended generalized bivariate Meijer-G function. For diversity order, asymptotic outage probability expression is also derived. Further, cumulative distribution function based generalized average symbol error rate expressions for various quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived in terms of Meijer-G function. Furthermore, a detailed comparative study of various modulation schemes is presented and the impact of pointing error, atmospheric turbulence, outdated CSI, and Nakagami-m parameter are highlighted on the system performance. Finally, all the analytical results are verified through Monte-Carlo simulations.

Performance Analysis of Dual-Hop Relaying With I/Q Imbalance and Additive Hardware Impairment

Hardware impairment is common in practical transceivers. This work analyzes the impact of hardware impairment on the performance of dual-hop relaying. In the analysis, both multiplicative I/Q imbalance and additive hardware impairment are considered at all nodes. The outage probabilities of amplify-and-forward (AF) and decode-and-forward (DF) relaying schemes are derived. The AF scheme includes both fixed-gain AF and variable-gain AF. Optimum maximum likelihood detectors are obtained. Numerical results are presented to show the effects of hardware impairment on relaying performances.

Green Relaying With Power-Efficient Amplification Factors Over Nakagami-${m}$ Frequency-Selective Fading Channels

In this paper, a power-efficient amplification factor (PEAF) is proposed for reducing the power consumption of the relay station and improving the overall system performance in dual-hop amplify-and-forward (AF) relay networks. In comparison to the conventional amplification factor, the PEAF is designed by minimizing the total transmission power whereas maintaining the required quality of service. Moreover, in accordance with the PEAF scheme, exact closed-form expressions of the probability density function and the cumulative distribution function of the received signal-to-noise ratio are derived with one-way and two-way relaying over Nakagami- ${m}$ frequency-selective fading channels. Monte Carlo simulation is executed to verify these mathematical expressions. Simulation results show that the relay system with the proposed PEAF possesses a lower outage probability and higher energy efficiency in comparison with counterparts of the conventional variable-gain AF relaying.

OFDM With Index Modulation Assisted by Multiple Amplify-and-Forward Relays

A multi-relay assisted orthogonal frequency division multiplexing system with index modulation is proposed in this letter, assuming that amplify-and-forward (AF) relaying protocol is adopted at relays. Two commonly used AF protocols are considered: 1) fixed-gain AF and 2) variable-gain AF relaying protocols. To utilize relays in an efficient manner, we also employ two multi-carrier relay selection schemes termed bulk and per-subcarrier relay selection in the proposed system. We analyze the outage performance of the proposed system and derive closed-form expressions of the average outage probabilities (AOPs) for all cases with different AF relaying protocols and multi-carrier relay selection schemes. In addition, we obtain the asymptotic expressions of AOPs in the high signal-to-noise ratio region, by which it is proven that the full diversity gain equaling the number of relays is attainable.

Exact error rate analysis of two-hop AF Rayleigh fading cooperative systems with variable amplification gain

A careful exploration of literature confirms that exact symbol-error-rate (SER) performance of amplify-and-forward (AF) wireless cooperative communication systems with variable amplification gain has not been analyzed before; even for simple models with single relay (i.e, two-hop systems) and Rayleigh fading channels. The main source of this mathematical intractability is the appearance of the modified Bessel function of the second type Kν(·) in the statistics of these systems end-to-end SNR. Here, however, we aim at filling this literature gap by proposing a novel theoretical method that helps in examining, for the first time, the exact SER performance of two-hop AF systems, where, as a case study, we assume Rayleigh quasi-static fading environment with perfect channel estimation. Specifically, we derive two new exact expressions for the system’s SER performance, which involve rapidly convergent infinite summation(s) and efficiently computable special functions. Furthermore, for the same system, we obtain new approximate closed-form SER expression, which outperforms its literature counterpart. The obtained analytical results are useful to gain insight about the actual error performance of variable gain AF systems. The presented methodologies can form a generic framework for exact SER performance evaluation of other variable gain AF cooperative system models.

An Improved Variational Inference Approach to Iterative OFDM Receiver Design for Superimposed Training-Based AF Relay Networks

Using variational Bayesian approximation (VBA), we propose a general framework for joint channel estimation, demodulation, and decoding in an orthogonal frequency-division multiplexing (OFDM) amplify-and-forward (AF) relay network. AF relaying is adopted due to its simplicity and ease of implementation, and both cases of fixed- and variable-gain AF protocols are addressed. Unlike the classical approach where a number of subcarriers are solely dedicated to pilots, partial data-dependent superimposed training is considered here, which preserves the spectral efficiency. Assuming a bit-interleaved coded modulation OFDM system at the source, a modified formulation of VBA is proposed, which is, in fact, a Bayesian framework of turbo data detection of OFDM under channel estimation errors. More precisely, by an appropriate exploitation of the inherent “soft” information on channel and data available from the VBA formalism, we derive a modified iterative receiver, which reduces the impact of channel uncertainty by averaging the “soft data decision” over the posterior distribution of the unknown channel at each decoding iteration. The proposed modified VBA approach is contrasted to the conventional VBA and to the mismatched VBA approach, where, in the latter, the unknown channel is just replaced by its imperfect estimate. We show that conventional and mismatched VBA are suboptimal and can be viewed as a particular case of the proposed VBA method. In addition, we show that the VBA approach makes a nice connection between the classical techniques such as pilot-only channel estimation and the expectation–maximization algorithm, which can be viewed as a special case of VBA. By comparison with state-of-the-art VBA-based estimators through numerical analysis, we highlight the superiority of our modified VBA method and demonstrate a notable performance improvement in terms of the bit error rate.

Energy Detection in Multi-user Relay Networks

In this correspondence, detection performance of an energy detector is evaluated in multi-user relay networks equipped with single amplify-and-forward (AF) relay. The relay network is assumed to be operating over independent and identically distributed, flat Rayleigh fading channels. New expressions for average detection probability are derived for both fixed-gain and variable-gain AF relays. Furthermore, truncation error bounds are also evaluated for the respective expressions because the derived average detection probability expressions were in the form of infinite summation series. In the end, the accuracy of the derived expressions is validated with the help of simulations .

Outage performance of fixed-gain and variable-gain AF full-duplex relaying in non-identical Nakagami-m fading channels

We investigate outage performance of fixed-gain and variable-gain amplify-and-forward (AF) full-duplex (FD) relaying systems under residual loop-interference (LI) in non-identical Nakagami-m fading channels. New exact outage probability expressions are derived analytically in a single-integral form by using the cumulative distribution function approach. Moreover, tight lower-bound and asymptotic outage probability expressions are derived in closed-form for the evaluated systems. It is shown that the fixed-gain AF-FD relaying outperforms the variable-gain AF-FD relaying when LI power and/or signal-to-noise ratio increase. The analytical results are verified by Monte-Carlo simulations.

Exploiting Direct Links in Multiuser Multirelay SWIPT Cooperative Networks With Opportunistic Scheduling

In this paper, we analyze the downlink outage performance of opportunistic scheduling in dual-hop cooperative networks consisting of one source, multiple radio-frequency energy harvesting relays, and multiple destinations. To this end, two low-complexity, suboptimal, yet efficient, relay-destination selection schemes are proposed, namely direct links plus opportunistic channel state information (CSI)-based selection (DOS) scheme and direct links plus partial CSI-based selection (DPS) scheme. Considering three relaying strategies, i.e., decode-and-forward (DF), variable-gain amplify-and-forward (VG-AF), and fixed-gain amplify-and-forward (FG-AF), the performance analysis in terms of outage probability (OP) is carried out for each selection scheme. For the DF and VG-AF strategies, exact analytical expressions and tight closed-form approximate expressions for the OP are derived. For the FG-AF strategy, an exact closed-form expression for the OP is provided. Additionally, we propose a gradient-based search method to find the optimal values of the power-splitting ratio that minimizes the attained OPs. The developed analysis is corroborated through Monte Carlo simulation. Comparisons with the optimal joint selection scheme are performed and it is shown that the proposed schemes significantly reduce the amount of channel estimations while achieving comparable outage performance. In addition, regardless of relaying strategy used, numerical results show that the DOS scheme achieves full diversity gain, i.e., $M+K$ , and the DPS scheme achieves the diversity gain of $M+1$ , where $M$ and $K$ are the numbers of destinations and relays, respectively.

An Equivalence Principle for OFDM-Based Combined Bulk/Per-Subcarrier Relay Selection over Equally Spatially Correlated Channels

In this paper, we propose a novel relay selection scheme for orthogonal frequency-division multiplexing systems by combining conventional bulk and per-subcarrier selection schemes and analyze its outage performance over equally spatially correlated channels. Specifically, the combined selection scheme selects only two relays at the first attempt and performs per-subcarrier selection over these two relays. We analyze the asymptotic outage performance of the combined selection scheme in the high signal-to-noise ratio (SNR) region and prove a generalized theorem. This theorem states that the combined selection can achieve an optimal outage probability equivalent to the per-subcarrier selection at a high SNR without using the full set of available relays for selection. This unique property is termed the equivalence principle , and it holds for all correlation conditions. To explore this principle, we consider three examples: decode-and-forward, fixed-gain amplify-and-forward (AF), and variable-gain AF relay systems. Furthermore, two extended applications, i.e., antenna selection and branch selection, are also considered to reveal the feasibility and the expandability of the equivalence principle. Our analysis is verified by Monte Carlo simulations. The proposed combined selection and the proved theorem provide a general and feasible solution to the tradeoff between system complexity and outage performance when relay selection is applied.

Design of distributed collaborative space‐time block codes for two‐way relaying networks

Utilising the recently-developed unique factorisation of signals and distributed Alamouti coding, a distributed collaborative space-time block code design is presented for a two-way amplify-and-forward (AF) relaying network, where all nodes are equipped with a single antenna. Two asymptotic pairwise error probability (PEP) formulae are firstly derived for both fixed-gain AF and variable-gain AF over Rayleigh channels with the maximum-likelihood detector. Then, subject to the constraints on a fixed transmission bit rate and unity average transmission energy, the optimal constellation combinations with the optimal coefficients are attained by minimising the dominant term of PEP. It is shown that the PEP and the average block error rate of the newly-designed code are superior to those of the conventional distributed Alamouti code while the prior still has linear-decoding complexity.

Lifetime Analysis of a Two-Hop Amplify-and-Forward Opportunistic Wireless Relay Network

An expression is derived for the probability mass function (PMF) of the relay transmit power in a variable gain amplify-and-forward (VG-AF) opportunistic wireless relay network (OWRN). The PMF is used to calculate the average relay transmit power. An expression is also obtained for evaluating the transition probabilities between energy states in a Markov chain model of the OWRN. This model is used to compute the average OWRN lifetime for a small number of relays, allowable transmit power levels, and low initial relay energy levels. Unfortunately, the computational complexity of this approach becomes prohibitive as the number of relays, transmit power levels, and initial energy levels increase. A low-complexity method, based on an existing expression and the average relay transmit power, is used to estimate the average network lifetime. The method is shown to yield very accurate results for practical initial relay energy levels.

Asymptotic SEP Analysis of Two-Way Relaying Networks With Distributed Alamouti Codes

Asymptotic symbol error probability (SEP) performance with an optimal maximum likelihood (ML) receiver and square quadrature amplitude modulation (QAM) constellations is investigated for two-way amplify-and-forward (AF) half-duplex relaying networks employing distributed Alamouti space-time block codes (DASTCs) recently proposed by Duong By developing a novel strategy to particularly deal with some specific Gaussian integrals, two asymptotic SEP formulas are derived for both fixed- and variable-gain AF protocols. These analytic results reveal that, when the signal-to-noise ratio (SNR) is large, the diversity gain for the variable-gain AF is 2, whereas the diversity gain function for the fixed-gain AF is proportional to SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> ln SNR.

Analysis of Instantaneous Power Distributions for Non-Regenerative and Regenerative Relaying Signals

In this paper, we analyze the instantaneous power distributions of the transmitting signals at the relay in the non-regenerative and regenerative cooperation scenarios with linear modulation. We study the following four relay function scenarios: fixed gain amplify and forward (AF) relay, variable gain AF relay, estimate and forward (EF) relay, and decode and forward (DF) relay. The analytical results show that the transmitting signals from non-regenerative relaying tend to suffer from high peak power, which is even prohibitive when the power amplifier (PA) efficiency at the relay is of primary concern.