Symbol error rate analysis and power allocation for hybrid cooperation in Rayleigh fading environment

In this paper, the impact of diversity order on symbol error rate (SER) performance is investigated for the cooperative amplify-and-forward (AF) multiple-input-and-multiple-output (MIMO) relaying system under the average power scaling (APS) constraints. Furthermore, the optimal power allocation (OPA) scheme is proposed based on the criterion of maximizing signal-to-noise-ratio (SNR). Through the SER analysis and numerical results, it can be shown that the diversity order in AF MIMO relaying system under APS is M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> (the number of transmitting antennas) when uniform power allocation (UPA) is adopted. Given M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> receiving antennas at the relay nodes, the proposed novel OPA scheme can not only reduce the SER but also improve the diversity order efficiently up to M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> even when M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> = 1.

Cooperative communications is a promising technology to improve the performance of wireless sensor networks. In this paper, a dual-hop wireless cooperative network with opportunistic amplify-and-forward relaying is investigated over independent and non-identically distributed Nakagami-m fading channels. Due to the complicated form of the probability density function of the instantaneous signal-to-noise ratio (SNR), the symbol error rate and outage probability expressions are difficult to obtain in closed form. Taking advantage of Maclaurin series expansion of the probability density function of the output instantaneous SNR, we present the asymptotic symbol error rate and outage probability expressions at medium and high SNR regions, and the optimal power allocation scheme between the source and opportunistic relay is also proposed to minimize the outage probability. Simulation results demonstrate that the derived symbol error rate and outage probability matches well with the Monte-Carlo simulations. In addition, it is verified that the optimal power allocation scheme outperforms the equal power allocation scheme in terms of outage probability.

This paper presents the symbol error rate (SER) vs. signal-to-noise (SNR) ratio performance of OFDM system with QAM modulation. It has been observed that the optimal power allocation between pilot and information symbols can improve the performance gain by 2.3 dB relative to the equal power allocation between pilot and information symbols, for a system with N=3D512 sub-carriers, and a channel with L=3D40 taps. The SER performance is then compared with Rayleigh-faded as well as Rician-faded channels. It has been further concluded that the SER vs. SNR performance graph in Rayleigh-faded channel environment is better than that in Rician-faded channel. This idea implies that in OFDM case, the SER vs. SNR performance is better in scattered rich channel environments. The SER vs. SNR performance graph is degraded by equal magnitude for both equal-power and optimal-power cases, which implies that the difference between the equal-power and optimal power case is independent of the channel fading model being used. It is also observed that by varying the standard-deviation of the channel, the SER vs. SNR performance graph is not going to be affected if the channel is considered Rayleigh-faded.

Aiming at the cooperative communication system with directional antenna, this paper has studied the SER (Symbol Error Rate) performance under AF (Amplify-and-Forward protocol). The model of AF cooperative communication system using directional antenna was firstly established to deduce the closed-form expression of SER in this model as well as the upper limit of SER. Then, the OPA (Optimum Power Allocation) was also analysed on the purpose of minimising SER. Combining specific simulation numerical values, SER performance of established model was thoroughly researched in this paper. Simulation results demonstrate that system SER obviously decreases by adopting cooperative communication system with directional transmitting and directional receiving. Each node's directional gain, channel quality and power allocation method all have great influence on system's overall performance. And the OPA is also proved to be superior to EPA (Equal Power Allocation).

Cooperative wireless communication has been newly proposed in wireless communication systems for discovering the inherent spatial diversity in relay channels. The Amplify- and-Forward (AF) cooperation protocols with multiple relays have not been sufficiently examined; however, it has a low complexity in terms of application. Through this article, we evaluate a cooperative diversity technique whereby a source broadcasts some data to a destination with the assistance of multiple relay nodes with AF protocols, by taking into account the challenge of allocating power to be able to increase the total capacity of AF and also enhance resource utilization. We analyse the optimality of how much the power should really be allocated at the source as well as relays system by optimizing the symbol error rate (SER) performance in a useful method on the basis of Rayleigh and Nakagami- m fading. Firstly, we derive a closed-form SER formulation for MPSK signal making use of the idea of moment generating function (MGF) and some statistical approximations in high signal to noise ratio (SNR) for the system under studied. We therefore determine a tight corresponding lower bound, which converges to the identical limit the same as the theoretical upper bound, after that develops an optimal power allocation (OPA) strategy with mean channel gains over Rayleigh and also Nakagami- m fading to reduce the SER. Simulation results prove that our approach using Nakagami- m fading outperforms the (OPA) using Raleigh fading scheme and is tight with the theoretical approximation based on the SER upper bound in high SNR for a different number of relays .  Index Terms—Wireless communication, amplify-and-forward, symbol error rate, Nakagami- m fading, power allocation.

The performance analysis of multi-hop MIMO free space optical communications with space–time block codes over exponentiated Weibull fading channels

Aiming at the cooperative communication system with directional antenna, this paper has studied the SER (Symbol Error Rate) performance under AF (Amplify-and-Forward protocol). The model of AF cooperative communication system using directional antenna was firstly established to deduce the closed-form expression of SER in this model as well as the upper limit of SER. Then, the OPA (Optimum Power Allocation) was also analysed on the purpose of minimising SER. Combining specific simulation numerical values, SER performance of established model was thoroughly researched in this paper. Simulation results demonstrate that system SER obviously decreases by adopting cooperative communication system with directional transmitting and directional receiving. Each node's directional gain, channel quality and power allocation method all have great influence on system's overall performance. And the OPA is also proved to be superior to EPA (Equal Power Allocation).

In this paper, we analyse the symbol error rate (SER) performance of adaptive relay selection schemes (ARS) in a general dual-hop multiple-relay network. Specifically, we provide a closed-form SER expression for ARS which is tight over the whole signal-to-noise ratio (SNR) region. In addition, the derived SER can be readily extended to conventional relay selection schemes, i.e. amplify-and-forward relay selection (AF-RS), perfect decode-and-forward relay selection (PDF-RS), adaptive decode-and-forward relay selection (ADF-RS), and cooperative-maximum-ratio-combining decode-and-forward relay selection (CDF-RS). Transmit power allocation based on the simplified SER is presented to improve the system performance. The analytical results are verified by computer simulations.

The recently proposed intelligent reflecting surface (IRS) is considered as a promising technology to combat the propagation distance problem in the future communications. However, due to the lack of quantitative analysis and IRS selection scheme from the perspective of symbol error rate (SER) performance, the performance analysis method of asymptotically tight approximation SER is proposed. Firstly, a communication system model aided by an IRS is established. Then, through the reasonable reconstruction between the reflection coefficient and the link coefficient of IRS, the SNR on the forwarding link of IRS satisfies the harmonic mean form. Finally, based on the calculation method of moment generating function (MGF), the asymptotically tight approximation SER formula of the system with simple structure is derived. The simulation results show that, the asymptotically tight approximation SER formula can accurately describe the system SER performance under the low SNR condition. Before the number of IRS reflection unit increases to a certain value, the system SER performance can be effectively improved. Compared with the AF multi-relay system, IRS aided system has the slightly better SER performance only in the case of low SNR. Our work will provide the important theoretical basis for the IRS selection in practical communications.

In this paper, we consider a dual-hop wireless cooperative network with amplify-and-forward (AF) relaying. The output signal-to-noise ratio (SNR) at the destination of the AF cooperative networks is in the form of the sum of harmonic mean of the source-relay channel SNR and the relay-destination channel SNR. Instead of deriving the exact probability density function (PDF) of the output SNR, we study the series expansion of this PDF around zero. This result is then applied to evaluate the performance of the AF cooperative systems over Nakagami-m fading channels, and closed-form high-SNR approximations of the average symbol error rate (SER) and the outage probability are derived. Next, we investigate the optimal power allocation (OPA) among the source node and the relays to minimize the approximate SER as well as the outage probability. It is shown that the optimal power allocation depends on the channel mparameters and the ratio of the source-relay channel gain to the relay-destination gain. In addition to the optimal power allocation, we also propose a low complexity sub-optimal power allocation (SubOPA) scheme. The performance improvement with optimal and sub-optimal power allocation is analyzed and validated by numeric results. It is shown that equal power allocation is near optimal when the relays are close to the source, while significant performance improvement is observed by both the optimal and sub-optimal power allocation schemes when the relays are close to the destination.

Spatial modulation (SM) is a multiple input multiple output (MIMO) wireless communication system that gives better spectral efficiency without costing extra bandwith for the same signal constellation size. In an SM MIMO system with $$N_t$$Nt transmitting antennas, spectral efficiency increases by $$log_2(N_t)$$log2(Nt). The superior performance of SM systems over other MIMO systems like Alamouti Space-Time Block Codes and Vertical Bell Laboratories Layered Space-Time is already reported in the literature. In this paper, we analyzed the symbol error rate (SER) performance of an SM system in generalized $$\eta-\mu $$?-μ and $$\kappa - \mu $$?-μ fading channels for several modulation schemes. A closed form expression for approximate SER is derived using moment generating function (MGF) approach and the results are validated using Monte Carlo simulations. The approximate SER expression obtained in this communication is applicable for any fading channels whose MGF is known. The SER analysis over generalized fading channels can be easily deduced to various classical fading channels like Rayleigh, Rician, Nakagami-m and Nakagami-q fading channels by choosing appropriate values of $$\kappa $$?, $$\mu $$μ and $$\eta $$?.

In this paper, the Symbol Error Rate (SER) performance formulation which suited to multi-node amplify-and-forward cooperative communication M-PSK constellation systems with the mean channel gains is derived. Firstly, the closed-form theory symbol error rate formulation with M-PSK modulation is derived. Then, a Low Bound (LB) is established to show the asymptotic performance of the cooperation protocol which tightens the theory SER under the both low and high Signal to Noise Ratio (SNR) conditions. Thirdly, the optimal power allocation algorithm for multi-node cooperative communication systems which minimizes the SER performance based on the Low Bound (LB) is formulated. SER comparison between the proposed approximate optimal power allocation method and the traditional Equal Power Allocation (EPA) method, the SER performance for the approximate optimal power allocation is better than the EPA's, especially under the channel conditions which the relay nodes are near the middle locations between the source and destination node or near the destination node.

ABSTRACTIn this paper, we derive expressions for exact, approximate, and asymptotic symbol error rate (SER) of transmit antenna selection with maximal ratio combining (TAS/MRC) multiple input multiple output (MIMO) systems for several modulation schemes. We have assumed independent and identically distributed η − µ fading channels. We use a moment generating function (MGF) based approach to derive the expressions of SER. The expression for approximate SER is derived by approximating Q Function as a sum of exponentials. The expressions of SER are in the form of sum of converging infinite series for all values of fading parameters. The analytical expressions derived in this paper are also applicable to the SER performance analysis of TAS with selection combining at receiver (TAS/SC) systems. The analytical results are validated by comparing them with the results of extensive Monte Carlo simulations for different values of fading parameters. Finally, the SER performance of TAS/MRC systems and TAS/SC systems has been compared and superiority of TAS/MRC systems over TAS/SC systems has been demonstrated.

In this paper we study the statistical properties of the Signal to Noise Ratio (SNR) of the dual-hop relaying link in a cooperative wireless communication system in the presence of channel estimation errors for Decode and Forward (DF) relaying protocol. Then for assessment of the system performance the Symbol Error Rate (SER) is considered. Two approaches are introduced for SER calculation from which the second one results in a closed form solution. Finally the second approach is used to find an optimum power allocation scheme for transmission of pilot and data symbols at the source and the relay terminals that results in minimizing the SER and considerable amount of power saving. Also Monte Carlo simulation is used to confirm the accuracy of the derived expressions.

Dual-hop cooperative Multiple-Input Multiple-Output (MIMO) network with multi-relay cooperative communication is introduced. Power allocation problem with Amplify-and-Forward (AF) and Selective Decode-and-Forward (SDF) strategies in multi-node scenario are formulated and solved respectively. Optimal power allocation schemes that maximize system capacity with AF strategy are presented. In addition, optimal power allocation methods that minimize asymptotic Symbol Error Rate (SER) with SDF cooperative protocol in multi-node scenario are also proposed. Furthermore, performance comparisons are provided in terms of system capacity and approximate SER. Numerical and simulation results confirm our theoretical analysis. It is revealed that, maximum system capacity could be obtained when powers are allocated optimally with AF protocol, while minimization of system’s SER could also be achieved with optimum power allocation in SDF strategy. In multi-node scenario, those optimal power allocation algorithms are superior to conventional equal power allocation schemes.