Performance Analysis of Hybrid Cooperation in Asymmetric Fading Channels

Cooperative diversity enables single antenna transmitter in a multi-user or relay environment to share the antennas so as to achieve diversity gain. In this work, the cooperative communication system with distributed Alamouti code is investigated, where amplify-and-forward (AF), adaptive decode-and-forward (DF) or hybrid AF/DF are used at the relay, with both Rayleigh fading and path loss effect introduced into channel model. The following results are derived by utilizing the moment generating function (MGF) of end-to-end output signal- to-noise ratio (SNR). For AF protocol, when the relay is near the destination, the approximative closed-form symbol error rate (SER) of M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM) are derived, and approximative analytical SER expression is given for binary phase shift keying (BPSK) as an example. For adaptive DF protocol, the closed-form SER of M-PSK and M-QAM are derived, and analytical SER expression is presented for BPSK. Furthermore, the optimal relay location of adaptive DF protocol with BPSK signal is derived through analytical analysis. Finally, the Monte-Carlo simulations are performed to get the optimal relay location of other scenarios and verify all the analytical results.

In this paper, symbol-error-rate (SER) performance analysis and optimum power allocation are provided for uncoded cooperative communications in wireless networks with either decode-and-forward (DF) or amplify-and-forward (AF) cooperation protocol, in which source and relay send information to destination through orthogonal channels. In case of the DF cooperation systems, closed-form SER formulation is provided for uncoded cooperation systems with PSK and QAM signals. Moreover, an SER upper bound as well as an approximation are established to show the asymptotic performance of the DF cooperation systems, where the SER approximation is asymptotically tight at high signal-to-noise ratio (SNR). Based on the asymptotically tight SER approximation, an optimum power allocation is determined for the DF cooperation systems. In case of the AF cooperation systems, we obtain at first a simple closed-form moment generating function (MGF) expression for the harmonic mean to avoid the hypergeometric functions as commonly used in the literature. By taking advantage of the simple MGF expression, we obtain a closed-form SER performance analysis for the AF cooperation systems with PSK and QAM signals. Moreover, an SER approximation is also established which is asymptotically tight at high SNR. Based on the asymptotically tight SER approximation, an optimum power allocation is determined for the AF cooperation systems. In both the DF and AF cooperation systems, it turns out that an equal power strategy is good, but in general not optimum in cooperative communications. The optimum power allocation depends on the channel link quality. An interesting result is that in case that all channel links are available, the optimum power allocation does not depend on the direct link between source and destination, it depends only on the channel links related to the relay. Finally, we compare the performance of the cooperation systems with either DF or AF protocol. It is shown that the performance of a systems with the DF cooperation protocol is better than that with the AF protocol. However, the performance gain varies with different modulation types and channel conditions, and the gain is limited. For example, in case of BPSK modulation, the performance gain cannot be larger than 2.4 dB; and for QPSK modulation, it cannot be larger than 1.2 dB. Extensive simulation results are provided to validate the theoretical analysis.

In this paper, the performance of amplify-and-forward (AF) cooperative diversity is analyzed over asymmetric fading channels. The source---relay and the relay---destination links experience Rayleigh fading while the source---destination link is subject to generalized Gamma fading. First, the probability density function (PDF) and the moment generating function (MGF) of the source---relay---destination link and the MGF of the source---destination link are derived. Then, the symbol error rate (SER) is determined based on the MGF of the total end-to-end signal-to-noise ratio (SNR). Moreover, the SER performance of N-relay assisted AF cooperative diversity is illustrated for M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM). Based on the derived MGF expressions, the numerical results are obtained by varying the modulation types and channel parameters for different scenarios.

This paper first analyzes the symbol error rate (SER) performance of the space-time network coding (STNC) over independent but not necessarily identically distributed (i.n.i.d) Nakagami-m fading channels, where multiple sources transmit information symbols to a destination through multiple helping amplify-and-forward (AF) relays. The exact expressions of the overall end-to-end received signal-to-noise ratio (SNR) via multiple STNC-AF relays and its moment generating function (MGF) are derived. Based on these results, the closed-form expression of STNC-AF for the SER with M-ary phase-shift keying and M-ary quadrature-amplitude modulation (QAM) modulations are then presented by adopting the unified MGF method. Furthermore, an approximate SER expression with low computational complexity is also given. In order to observe the performance limit, the diversity order and the nonorthogonality of STNC codes are discussed. Simulation results demonstrate our analytical results and it is illustrated that the diversity order of the STNC with multiple AF relay nodes is a sum function of the fading index of the direct link and the minimal fading indices of the multiple two-hop links.

Average symbol error rate and outage probability of DS-CDMA systems with AF relaying over asymmetric fading channels

Performance analysis of an up-link cooperative diversity system is investigated; sharing of the two ordered best relays over Rayleigh flat fading channel is introduced to establish full diversity order for both users. The two users are competing for the same best relay, so assigning the best relay for one user, and the next-best relay for the other shows different diversity orders. The relays are ordered based on the end-to-end signal to noise ratio (SNR) of the source-relay-destination links. In this sense, relay selection is examined under different criteria. Mainly, the ordered best relay, the ordered next-best relay, and equally sharing the two best ordered relays. To this end, analytical expression, for the moment generating function (MGF) is derived, and used to find the probability density function (PDF), and the cumulative density function of the end-to-end SNR for decode and forward (DF) sharing scenario. Furthermore, the MGF of the upper bound of the end-to-end SNR for amplify and forward (AF) sharing scenario is also derived. Sharing the two ordered best relays shows better performance in the bit error probability (BEP) than using the next-best relay alone in DF relay systems, while exploiting the full diversity of the system. Sharing of the two ordered best relays in AF relay systems shows better BEP performance than using the best relay alone. Distributed space time block coding and distributed beamforming (BF) scenarios at the relays that utilize the bandwidth more efficiently are also explored. It is found that the BEP performance of the two ordered best relays distributed BF with equal power allocation for AF (at high SNR) and DF (for all SNRs) schemes outperforms the BEP performance of the best ordered relay alone. The BEP performance for the DF distributed BF scheme with equal power allocation approaches the BEP performance of the optimum power assignment under global power sum constraint. Numerical simulations are used to validate the analysis.

SummaryThe performance of wireless communication systems is improved over flat fading channel by using Alamouti coding scheme, which provides the quality of diversity gain. In this paper, performance analysis of symbol error rate (SER) and particle swarm optimization (PSO)–based power allocation (PA) for Alamouti amplify and forward (AF) relaying protocol using maximum ratio combining (MRC) technique is presented. Analytical expression of SER upper bound and SER approximation is derived for Alamouti AF relaying protocol with quadrature phase shift keying (QPSK) modulation over Rayleigh fading channel and Rician fading channel. In addition, PSO‐based optimum PA factor is calculated on the basis of the minimum SER of proposed method. PSO‐based optimum PA gives 0.5 dB of improved signal‐to‐noise ratio (SNR) compared with the equal power allocation (EPA). The theoretical approximate SER result is compared with the simulated SER. The proposed protocol provides full diversity gain and reduces SER compared with the existing AF and decode and forward (DF) relaying protocols over Rayleigh fading channel and Rician fading channel.

In this paper, we analyze the performance of multi-hop multi-branch amplify-and-forward (AF) networks over generalized fading channels. Using the moment generating function (MGF)-based approach, we develop general expressions for the outage probability and symbol-error rate (SER) performance of the system with maximal ratio combining (MRC) receiver. The MGF-based approach relies on numerical integration. To gain insights into system performance, we therefore investigate the asymptotic outage and SER performance of the system with MRC and selection combining (SC) receiver at the destination. In particular, we develop the asymptotic statistics of the end-to-end signal-to-noise ratio (SNR) of an AF multi-hop link. We further derive the cumulative density function of the sum of the individual end-to-end SNRs, received from different diversity paths for MRC receiver. We also study the power allocation problem in a multi-hop multi-branch system with MRC receiver. In generalized Gamma fading environments, we seek to find the power allocation strategy that maximizes the SNR at the destination subject to a total power constraint. By means of simulations, we validate our theoretical developments and verify the efficiency of our proposed power allocation in improving the received SNR compared to a generic cooperative system with no power allocation. We also conclude that our asymptotic expressions for the outage probability and SER match the simulations very well in medium-to-high-SNR regime.

Cooperative communications technique receive a lot of interest, to combat frequency selectivity fading of wireless channels. Cooperative protocols are used to increase the total capacity, Signal to Noise Ratio (SNR) and reduced the Symbol Error Rate (SER) in wireless communication systems. The performance of Particle Swarm Optimization (PSO) based Power Allocation (PA) for Proposed Hybrid Decode and Forward (DF)/Amplify and Forward (AF) Relaying Protocol using Maximal Ratio Combining (MRC) technique with Mary-Phase Shift Keying (M-PSK) Modulation over Rayleigh fading and Rician fading is presented in this paper. The results are compared with exiting AF and DF relaying protocols. Hybrid DF/AF Relaying Protocol achieves reduced SER compared to the existing AF and DF relaying protocol.

In this paper investigates the performance, analysis of amplify and forward (AF) cooperative networks with the relay selection over  Nakagami-m and Rayleigh fading channels and  M-ary phase shift keying (MPSK) modulations. New closed form expressions are derived for the general cases of Rayleigh and Nakagami-m fading channels. cumulative density function (CDF), probability density function (PDF) of the end –to - end signal –to – nois ratio (SNR) of a dual-hop opportunistic AF relaying system, moment generating function (MGF), symbol error rate (SER) and outage probability (Pout). and the first closed-form study for opportunistic AF relaying system where the best node is selected from a number of candidate intermediate nodes to relay the data signal between the source and the destination. Simulation results reveal that the PDF , CDF, Pout and SER performance downgrades either the m parameter or the number of relays increases. Our simulations compared between Rayleigh and Nakagami-m links for a different number of relays. In addition, different modulation techniques are examined to show the effect of the modulation scheme which was used over Rayleigh and Nakagami-m fading channels on the cooperative networks. The obtained results proved the impact of m parameters, relay selection and modulation index on the pout and SER performance.

In this paper, we analyze a subcarrier intensity modulation (SIM) based relayed free space optical (FSO) system assuming independent but not necessarily identically distributed (i.n.i.d) Gamma-Gamma turbulence channels. System employs a channel-state-information-assisted (CSI-assisted) amplify and forward (AF) relay. We derive the moment generating function (MGF) of the end-to-end signal to noise ratio (SNR) of the system and using the novel MGF, accurate closed-form expressions for capacity under different adaptive transmission schemes such as optimal rate adaptation (ORA) and channel inversion with fixed rate (CIFR) are derived. Further, we derive closed form expression for average symbol error rate (SER) of M-ary phase shift keying (MPSK) modulation schemes in terms of Meijer's G-function.

In fading wireless channels, relays are used with the aim of achieving diversity and thus overall performance gain. In cooperative relay networks, various forwarding techniques like amplify and forward (AF) and decode and forward (DF) are used at the relay for better throughput and improved BER performance than traditional multihop systems. In a power constrained environment, the performance can be further improved by using an optimal power allocation strategy. The relative position of the relay with respect to the source and destination also has an immense effect on the efficacy of the relay.;We position the relay at various positions in a planar grid, with the position of source and destination being fixed, and we investigate the effect that the positioning of the relay has on a relaying system. We use our three terminal model to optimize the power allocation under total transmit power constraint, to maximize the instantaneous signal-to-noise ratio (SNR) at destination, and thus achieve improved throughput and BER performance, while using AF and DF protocols. We evaluate the performance of our system for both coherent and noncoherent modulation in a Rayleigh block fading channel. Quadrature phase shift keying (QPSK) is used in the coherent case and 4-Frequency shift keying (4-FSK) is used in the noncoherent case.;Previous works involving power allocation schemes have mainly concentrated on optimizing information theoretic quantities like capacity and outage probability. We derive expressions for instantaneous SNR using our model and optimize the power allocation based on that, with the final aim of achieving improved uncoded BER. Analytical expressions of the instantaneous SNR at the destination are derived for both AF and DF. These expressions are numerically optimized to obtain an optimum power allocation strategy for each position of the relay in both the AF and DF schemes using coherent or noncoherent detection.;We compare the performance of the AF and DF protocols based on their positional BER and throughput at different received SNR and notice that our power optimized schemes outperform existing power control schemes at certain areas. Finally we also identify the shape and area of the regions where relaying would provide performance gains for both the protocols at different received SNRs.

In this paper, we investigate the performance of Decode and Forward (DF) in multiple relay networks. We consider a cooperative diversity system where a source sends information to the destination with the aid of multi relay working in DF relaying protocol and investigate the Optimal Power Allocation (OPA) at both the source and the relay nodes. By taking advantage of the moment generating function (MGF), a closed form expression for the symbol error rate (SER) and signal to noise ratio (SNR) for both, M-Phase Shift Keying (MPSK) and M-Quadrature Amplitude Modulation (MQAM) signals has been derived to illustrate the asymptotic performance of the DF system where the approximation SER is tight at high SNR. Results show that the proposed system, based on SER lower bound is tight to the theoretical SER upper bound, and the suggested OPA outperforms the equal power allocation (EPA) and at different number of relays. DOI: http://dx.doi.org/10.11591/telkomnika.v15i1.8037

In this study, we analyse the error performance of decode and forward (DF) and amplify and forward (AF) multi-way relay networks (MWRNs). The authors consider a MWRN with pair-wise data exchange protocol using binary phase shift keying (BPSK) modulation in both additive white Gaussian noise (AWGN) and Rayleigh fading channels. The authors quantify the possible error events in an L-user DF or AF MWRN and derive accurate asymptotic bounds on the probability for the general case that a user incorrectly decodes the messages of exactly k (k ∈ [1, L − 1]) users. They show that at high signal-to-noise ratio (SNR), the higher order error events (k ≥ 3) are less probable in AF MWRN, but all error events are equally probable in a DF MWRN. They derive the average BER of a user in a DF or AF MWRN in both AWGN and Rayleigh fading channels under high SNR conditions. Simulation results validate the correctness of the derived expressions. The authors results show that at medium to high SNR, DF MWRN provides better error performance than AF MWRN in AWGN channels even with a large number of users (e.g. L = 100). Whereas, AF MWRN outperforms DF MWRN in Rayleigh fading channels even for much smaller number of users (e.g. L > 10).

In this paper, we consider a single-relay-based decode-and-forward (DF) cooperative multiple-input multiple-output (MIMO) system in which the source, the relay, and the destination are equipped with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{s}$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{r}$</tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{d}$</tex-math></inline-formula> antennas, respectively. We propose a joint antenna and path selection scheme, which jointly selects the single-transmit and single-receive antenna pairs, along with the selection of either a direct path that consists of source–destination channels or a cooperative path that consists of source–relay and relay–destination channels. The proposed selection scheme is based on the maximization of minimum of maximums (max-min-max) criterion of instantaneous signal-to-noise ratio (SNR). The analysis in this paper is based on the assumptions that all the channels follow independent Rayleigh fading. A closed-form expression of the symbol error rate (SER) for the proposed scheme in a cooperative MIMO system with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$</tex-math></inline-formula> -ary phase-shift keying is derived. We extract the analytical diversity order from the derived SER and show that the proposed selection scheme achieves the diversity order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{s}N_{d}+N_{r}\mathrm{min}(N_{s},N_{d})$</tex-math></inline-formula> in the considered cooperative MIMO system. Closed-form expressions of bandwidth efficiency (BE) and ergodic capacity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(C_{t})$</tex-math></inline-formula> are derived for the proposed scheme. An optimized selection parameter from the specific set of values is numerically evaluated by maximizing a heuristic utility function <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(C_{t}\times \mbox{BE}/\mbox{SER})$</tex-math></inline-formula> . By using the already-gathered information about the maximum instantaneous SNR of every hop, a power adaptation scheme that maximizes the instantaneous SNR in the cooperative path is proposed and analyzed. The proposed power adaptation scheme, which is applied only in the event of selection of a cooperative path, outperforms the uniform-power-distribution-based DF cooperative MIMO system.