Non-identical Nakagami-m Fading Channels Research Articles

CSIN-assisted AF dual-hop relaying communication systems over imperfect Nagakami-[formula omitted] fading channels: Exact error performance

Relaying-based communication techniques are promising for current and future wireless systems. Amplify-and-forward (AF) relaying is more attractive due to the low cost and simplicity in its relay implementation. As compared to other AF schemes, the channel-state-information (CSI)-and-noise (CSIN)-assisted one is optimal and practically recommended. However, up to this moment, the exact symbol error rate (SER) performance of CSIN-assisted AF dual-hop relaying systems has been analytically derived only for Rayleigh fading environments, while for other more generic fading models, including Nakagami-m, it has been computed either approximately or via long-running time computer simulations. Thus, in this paper, we consider a CSIN-assisted AF dual-hop relaying system with independent and non-identical Nakagami-m fading channels and derive a new expression for its exact SER performance under the effect of imperfect channel estimation. The derived expression includes infinite series that can truncate quickly using a few terms, requires short computational time as compare to simulation, shows perfect matching with the simulation results, and offers remarkable accuracy enhancement over its approximate peer derived in literature. In addition, it helps in demonstrating some useful insights into the system’s realistic error performance considering different system and fading severity conditions. For example, results show that the system’s exact SER performance is dominated by the worse fading hop, does not change when the system’s two fading hops exchange their fading conditions, and improves faster with the per symbol average SNR when the fading severity conditions are better.

Outage probability analysis and optimal transmit power allocation for multi-hop full duplex relay network over Nakagami-m fading channels

This paper investigates the outage probability and rate performance of multi-hop full duplex (FD) and half duplex (HD) decode-and-forward (DF)-based relay networks. First of all, we derive new closed form equation for the end-to-end outage probability of multi-hop FDR system taking into account the inter-relay interference (IRI), i.e., interference caused by simultaneous transmissions by the nodes in non-orthogonal frequency bands, and the residual self-interference (RSI) present at the full duplex relay (FDR) nodes, in independent non-identical Nakagami-m fading channels. We also derive an approximate expression for the outage probability which is found to be highly accurate. Further, we provide an asymptotic expression as well, for Rayleigh fading channels. Furthermore, we derive exact and approximate expression for the outage probability of multi-hop spectral efficient HDR network that employ two-phase relaying. We then consider optimal power allocation (OPA) for multi-hop FDR and HDR networks that maximizes the end-to-end transmission rate with individual peak power constraint at the nodes. Since the optimization problem is non-convex, we develop an efficient, low-complex and fast-converging iterative algorithm for power allocation based on sequential convex programming. Secondly, we consider OPA for multi-hop FDR and HDR networks that minimizes the end-to-end outage probability with individual peak power constraints at the nodes. We devise geometric programming (GP) to obtain the OPA vector. The results demonstrate that OPA can significantly improve the outage and end-to-end rate performance of both FDR and HDR networks as compared to uniform power allocation policy. The results from the analytical model are validated by extensive Monte Carlo 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.

HSSEC strategy for decode‐and‐forward‐relaying systems over Nakagami‐ m fading channels

Distributed switched diversity combining has drawn significant attention in the recent past due to its low-complexity nature in terms of channel state information requirement at the receiving end to achieve full diversity order. In this study, the authors propose a hybrid selection and switch-and-examine combining (HSSEC) scheme, which is a combination of selection combining and SEC schemes, for a multi-relay decode-and-forward system to improve the performance of distributed switched diversity combining schemes proposed in the literature. Furthermore, the performance of HSSEC scheme is investigated over non-identical Nakagami-m fading channels. Average end-to-end symbol error probability (SEP) expression is derived for M-ary phase-shift keying signalling, and in addition asymptotic SEP expression is also derived to analyse diversity order. From the derived asymptotic expression, it is inferred that the HSSEC scheme attains full diversity order over Nakagami-m fading channels, except for the case when threshold signal-to-noise ratio (SNR) is very much lesser than the average SNR. Furthermore, exact outage probability expression is derived for the HSSEC scheme. Finally, in the numerical results, the outage and SEP performances are compared with other schemes proposed in the literature.

Performance Analysis of Decode–Amplify-and-Forward Scheme used in Relay-based Cooperative Spectrum Sensing in Cognitive Radio Network

In this paper we have analyzed performance of relay based Cognitive Radio (CR) networks. Later on we present a scheme for cooperative spectrum sensing known as DetectAmplify-and-Forward (DAF). This technique is having the capacity of sensing over non-identical Nakagami-m fading channels. We have also introduced an advanced statistical approach to derive a new relation in order to calculate the average false alarm probability and average detection probability. In subsequent section it is also proved that a small number of reliable cognitive radios are enough to achieve practical detection level in cooperative spectrum sensing instead of incorporating all CRs. The simulation results shows improvement in detection accuracy and reduction in bandwidth requirement of the relaying links by abstaining from the heavily faded relays in the DAF scheme

Diversity and delay performance of max link selection relay cooperation systems over non-identical Nakagami-m fading channels

The work focuses on the max link selection (MLS) schemes of buffer-aided relaying over the independent and non-identically distributed (i.ni.d) Nakagami-m fading channels in terms of outage probability, average packet delay, and improved diversity-delay trade-off schemes. By modeling the transition of buffer states as a Markov chain, we first obtain the outage probability and average packet delays for MLS schemes, which are given with closed-form expressions. The achieved results show that the i.ni.d fading channels impose severe loss in the diversity and coding gains of MLS schemes. Especially, when the disparity among the channel powers is very large, the diversity order provided by the MLS schemes is less than the ones provided by the traditional best relay selection (T-BRS) and max-max link selection (MMLS) schemes even if the buffers’ size is large enough. For the average packet delay of MLS schemes, our results show that they are impacted by the transmit power and the fading severity factors. In general, in the low transmit power, the average packet delays are varying with the transmit power. However, in the high transmit power, the average packet delays approach the stationary values. Besides of this, it is also achieved that the i.ni.d fading makes the average packet delays of MLS schemes at all relays are different. When the powers of relay-destination links are greater than the ones of source-relay links, the average packet delays can be reduced evidently. Motivated by the observations, a weight-based MLS (W-MLS) diversity-delay trade-off scheme is proposed. The proposed W-MLS diversity-delay trade-off schemes not only have the low packet delays at all relays but also provide enough diversity and coding gains over T-BRS and MMML, which can overcome the performance loss caused by non-identical distribution on MLS schemes.

Performance Analysis of Relay-Based Cooperative Spectrum Sensing in Cognitive Radio Networks Over Non-Identical Nakagami-<named-content content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="TeX">$m$</tex-math></inline-formula></named-content> Channels

This paper provides performance analysis of relay-based cognitive radio (CR) networks and presents a detect-amplify-and-forward (DAF) relaying strategy for cooperative spectrum sensing over non-identical Nakagami-m fading channels. An advanced statistical approach is introduced to derive new exact closed-form expressions for average false alarm probability and average detection probability. We also introduce a novel approximation to alleviate the computational complexity of the proposed models. This paper points out the inconsistency of several assumptions that are typically used for performance analysis of CR networks and reveals that channel fading on the relaying links yields similar performance degradations as on the sensing channel. The study also shows that it is not necessary to incorporate all CRs in the cooperative process and that a small number of reliable radios are enough to achieve practical detection level. Compared with the amplify-and-forward strategy, refraining the heavily faded relays in the DAF strategy improves the detection accuracy and reduces the bandwidth requirement of the relaying links. The presented analysis could lead to intuitive system design guidelines for CR networks impaired with non-identical faded channels.

Outage Probability of Decode-and-Forward Relaying Systems with Efficient Partial Relay Selection in Nakagami Fading Channels

Recently, efficient partial relay selection (e-PRS) was proposed as an enhanced version of PRS. In comparing e-PRS, PRS, and the best relay selection (BRS), there is a tradeoff between complexity and performance; that is, the complexity for PRS, e-PRS, and BRS is low to high, respectively, but vice versa for performance. In this paper, we study the outage probability for e-PRS in decode-and-forward (DF) relaying systems over non-identical Nakagami-m fading channels, where the fading parameter m is an integer. In particular, we provide closed-form expressions of the exact outage probability and asymptotic outage probability for e-PRS in DF relaying systems. Numerical results show that e-PRS achieves similar outage performance to that of BRS for a low or medium signal-to-noise ratio, a high fading parameter, a small number of relays, and a large difference between the average channel powers for the first and the second hops.

Outage Performance of CRNs with Best Relay Selection in Dependent Nonidentical Distributed Nakagami-m Channels

The outage performance with best relay selection is proposed for cognitive relay networks with multiple primary users in independent nonidentical distributed Nakagami-m fading channels. Specifically, we take the interference temperature and fading severity into consideration. Exact closed-form expression of outage probability is derived. Based on the exact closed-form expression, we can evaluate the impact of interference temperature, fading severity, number of relays, and number of primary users on the secondary network. Finally, the effects of fading severity, number of relays, number of primary users, and interference temperature on the system performance are examined through some representative numerical plots, and the Monte Carlo results match perfectly with theory results which validates our theory analysis.

Performance Evaluation and Optimization of Dual-Hop Communication over Nakagami-m Fading Channels in the Presence of Co-Channel Interferences

The performance of dual-hop communication over independent and non-identical Nakagami-m fading channels in the presence of co-channel interference is investigated. Specifically, an upper-bound of the equivalent signal-to-interference-plus-noise ratio (SINR) at the destination is introduced. Then, the cumulative distribution function (CDF) and the probability density function (PDF) of the upper bounded SINR are obtained. Moreover, simple, yet general, asymptotic expression for the error probability is presented and discussed. Besides, with the goal to minimize the asymptotic average error probability of the system under study, we investigate three optimization schemes, namely, adaptive power allocation under fixed location for the relay, optimal relay positioning with fixed power allocation, and joint optimization of the power allocation and relay location under transmit power constraint. Results show that optimum power allocation brings only coding gain, while the optimum relay location scheme yields diversity gains as well.

Performance analysis of multi-antenna relay networks with imperfect channel estimation

Abstract In this paper, we present the performance of multi-antenna selective combining decode-and-forward (SC-DF) relay networks over independent but non-identical Nakagami-m fading channels with imperfect channel estimation. The outage probability, moment generating function (MGF) and symbol error probability (SEP) will be derived in closed-form using the SNR statistical characteristics. To make the analysis trackable, we have derived the MGF and SEP for integer values of fading severity, m . Also, to make the relations more simple, we develop high signal to noise ratio (SNR) analysis for the performance metrics of our system. Subsequently, we propose optimal and adaptive power allocation algorithms along with the equal power allocation method. Finally, for comparison with analytical formulas, we perform some Monte-Carlo simulations.

Performance analysis of joint single transmit and receive antenna selection in non-identical Nakagami-m fading channels

In this study, joint single transmit and receive antenna selection systems are examined for independent but non-identically distributed flat Nakagami-m fading channels. Exact bit/symbol error rate expressions are derived for binary and M-ary signals by using the conventional probability density function-based analysis method and the moment generating function based analysis method for arbitrary and integer values of the fading parameters, respectively. Upper bounds are obtained in order to show that the investigated systems achieve full diversity order at high SNRs. Also, outage probability analysis has been carried out for examining system capacity. Theoretical results are validated by Monte Carlo simulations.

Multi-branch decode-and-forward cooperative diversity networks performance analysis over Nakagami-m fading channels

In this study, the performances analysis of cooperative-diversity networks using adaptive decode-and-forward (DF) relaying over independent non-identical flat Nakagami-m fading channels is investigated. The authors derive exact and approximate closed-form expressions for the error probability, outage probability and average channel capacity, and analyse their dependence on the channel parameters. In adaptive DF relaying, among M relays that can participate, only C relays (C≤M), with good channels to the source, DF (retransmit) the source information to the destination. Then, the destination combines the direct and the indirect signals using maximum ratio combining technique. The authors derive a closed-form expression for the the moment generating function of the total signal-to-noise ratio (SNR) at the destination node. Then, the authors find an exact closed-form expression for the probability density function (PDF) of the total SNR at the destination. This PDF is used to derive the exact closed-form expressions of the performance metrics. Such closed-form solutions are highly desirable because they allow for rapid and efficient evaluation of system performance. Since exact expressions are complicated, the authors have introduced simple approximate expressions for the error and outage probabilities where these expressions explicitly show the diversity order. Computer simulations are used to validate our analytical results. Results show the significant performance improvement because of the use of the adaptive DF cooperative diversity. Also, results indicate that increasing the number of relays will not always decrease the outage probability.

Performance of Amplify-and-Forward Cooperative Communications with the N^{th} Best-Relay Selection Scheme over Nakagami-m Fading Channels

This letter derives the asymptotic symbol error rate (SER) of amplify-and-forward (AF) cooperative communications with the Nth best-relay scheme over independent and non-identical Nakagami-m fading channels. The diversity gain has been analyzed and examined as well. Simulation and numerical evaluation show the tightness of such an approximation in the high SNR regions and the accuracy of our theoretical analysis.

Unified Error Analysis of Dual-Hop Relay Link in Nakagami-m Fading Channels

Using the unified expression as devised by Wojnar, an analytical framework is presented to determine the end-to-end error performance of coherent and non-coherent binary modulation schemes with dual-hop relay transmission in amplify-and-forward (AF) mode under average power scaling (APS) and instantaneous power scaling (IPS) constraints and operating over independent, non-identical flat Nakagami-m fading channels. Generalized closed-form expressions for the bit error probability (BEP) have been obtained following the cumulative distribution function (cdf)-based approach for a dual-hop relay link with single antenna nodes. Moreover, we derive a unified closed-form solution for the BEP when selection combining (SC) is employed at the IPS based multi-antenna relay to diversity process the signals.

Modeling and Performance Analysis of Multihop Cooperative Wireless Networks

In this paper, we develop a cross-layer analytical framework for studying the performance of reliable relaying schemes in multihop cooperative diversity systems. A generalized signaling model over independent nonidentical Nakagami-m fading channels is assumed, and mathematical expressions for end-to-end throughput rate, spectral efficiency, and latency distribution are derived. The proposed framework can capture the effect of correlated packet errors caused by cooperative retransmission attempts and, thus, adequately evaluate the network performance. Using the framework, the performance of automatic-repeat-request-based relaying schemes is demonstrated over a range of network conditions and system parameters. It is shown that tradeoffs are necessary among network robustness, throughput rate, spectral efficiency, and latency variability.

Performance of cooperative diversity using Equal Gain Combining (EGC) over Nakagami-m fading channels

Cooperative diversity is a promising technology for future wireless networks. In this paper, we derive exact closed-form expressions for the average bit error rate (BER) and outage probability (Pout) for differential equal gain combining (EGC) in cooperative diversity networks. The considered network uses amplify-and-forward relaying over independent non-identical Nakagami-m fading channels. The performance metrics (BER and Pout) are derived using the moment generating function (MGF) method. Furthermore, we found (in terms of MGF) the SNR moments, the average signal-to-noise ratio (SNR) and amount of fading. Numerical results show that the differential EGC can benefit from the path-loss reduction and outperform the traditional multiple-input single output (MISO) system. Also, numerical results show that the performance of the differential EGC is comparable to the maximum ratio combining (MRC) performance.

Outage performance of cooperative relaying with dissimilar Nakagami-m interferers in Nakagami-m fading

The authors investigate the outage performance for decode-and-forward relaying schemes in the presence of dissimilar Nakagami-m interferers under non-identical Nakagami-m fading channels. A closed-form expression for the outage probability is derived under this scenario. Simulation results demonstrate our theoretical solutions.

Closed-form error analysis of the non-identical Nakagami-m relay fading channel

We present closed-form expressions for the average bit error probability (ABEP) of BPSK, QPSK and M-QAM of an amplify-and-forward average power scaling dual-hop relay transmission, over non-identical Nakagami-m fading channels, with integer values of m. Additionally, we evaluate in closed-form the ABEP under sufficiently large signal-to-noise ratio for the source-relay link, valid for arbitrary rn. Numerical and simulation results show the validity of the proposed mathematical analysis and point out the effect of the two hops unbalanced fading conditions on the error performance.

Performance Analysis Of Cooperative Relaying In Nakagami-M Fading Channels

This paper is concerned with the analysis of exact symbol error probability (SEP) for cooperative diversity using amplify-and-forward (AF) relaying over independent and non-identical Nakagami-m fading channels. The mathematical formulations for Probability Density Function (pdf) and Moment Generating Function (MGF) of a cooperative link have been derived for calculating symbol error probability with well-known MGF based approach taking M-ary Phase Shift Keying (MPSK) signals as input. The numerical results obtained from this research have been compared with different fading conditions. It is observed that the existence of the diversity link in a relay network plays a dominating role in error performance. Keywords: Symbol Error Probability; Probability Density Function; Moment Generating Function; Nakagami-m fading. DOI: http://dx.doi.org/10.3329/diujst.v6i2.9338 DIUJST 2011; 6(2): 1-5