Partial relay selection and energy detection for MCIM based dual-hop multiple DF relay network

SummaryThe performance of radio‐frequency (RF) networks where channels are modeled by an extended‐generalized‐K(EGK) distribution and consider significant phase errors during coherent detection at the receiver due to carrier‐phase‐synchronization‐mismatch is investigated in this work. The performance is evaluated for a single‐hop link and two‐hop amplify‐and‐forward (AF) and decode‐and‐forward (DF) relay‐assisted RF links. The EGK is a generalized distribution, which can model various fading conditions in millimeter (mm)‐wave wireless channels where transmission frequency is 60 GHz and above and takes into account non‐homogeneous propagation, interference effects in a multiuser transmission environment, multipath fading and shadowing effects. The average symbol error probability (ASEP) performance is evaluated for a single‐hop link when carrier is modulated using multilevel PSK modulation scheme. Based on the analytical results obtained for a single‐hop link, the mathematical analysis for the error performance in widely employed AF and DF relay‐assisted RF two‐hop networks is developed and ASEP is derived. To quantify the degradation in system performance introduced by phase errors, the reference‐carrier phase estimation loss for a single‐hop RF link is also evaluated. The obtained analytical results are also verified by numerical plots and depict the effects of various channel conditions existing over the RF link and phase synchronization errors.

We analyze the end-to-end error performance of Mary frequency shift keying (MFSK) with noncoherent detection over independent and non-identical flat Nakagami-m fading channels. A dual-hop relay transmission using amplify-and-forward (AF) protocol with average power scaling (APS) mechanism [1] is considered. Generalized closed-form expressions for the average symbol error probability (ASEP) of noncoherent MFSK has been obtained following the cumulative distribution function (CDF) approach. Moreover, we derive a simplified closed-form expression for the ASEP over high signal-to-noise ratio (SNR) over the source-relay link. Computer simulations are performed to validate our proposed mathematical analysis. The obtained error probability expressions will help the design of two-hop relay networks adopting MFSK in determining various system parameters such as the transmission power at the source and the gain factor at the relay.

In this paper, we analyze the performance of single relay selection cooperative wireless networks using decode-and-forward relaying. Under optimum relay selection, the expressions for asymptotic outage probability, average symbol error probability are derived over Nakagami-m fading channels. Then we improve the performance of the system through optimum power allocation based on asymptotic outage probability and asymptotic average symbol error probability. Our results are verified through comparison with Monte Carlo simulations.

In this paper, we investigate the performance of a dual-hop block fading cognitive radio network with underlay spectrum sharing over independent but not necessarily identically distributed (i.n.i.d.) Nakagami-$m$ fading channels. The primary network consists of a source and a destination. Depending on whether the secondary network which consists of two source nodes have a single relay for cooperation or multiple relays thereby employs opportunistic relay selection for cooperation and whether the two source nodes suffer from the primary users' (PU) interference, two cases are considered in this paper, which are referred to as Scenario (a) and Scenario (b), respectively. For the considered underlay spectrum sharing, the transmit power constraint of the proposed system is adjusted by interference limit on the primary network and the interference imposed by primary user (PU). The developed new analysis obtains new analytical results for the outage capacity (OC) and average symbol error probability (ASEP). In particular, for Scenario (a), tight lower bounds on the OC and ASEP of the secondary network are derived in closed-form. In addition, a closed from expression for the end-to-end OC of Scenario (a) is achieved. With regards to Scenario (b), a tight lower bound on the OC of the secondary network is derived in closed-form. All analytical results are corroborated using Monte Carlo simulation method.

Based on the Moment Generating Function (MGF), we derive closed form expressions for the Average Symbol Error Probability (ASEP) and the outage probability of the adaptive Decode and Forward (DF) relaying over independent and identical (i.i.d) Generalized-K channels for BPSK modulated signals. This kind of channel model includes jointly multipath fading and shadowing. It is very versatile and accurately approximates many of the commonly used channel models as Nakagami-m, Log-Normal distributions. Simulation results are discussed and proved to be in good agreement with our theoretical analysis.

In this paper, we focus on downlink zero forcing (ZF) beamforming design scheme for multiuser (MU) spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems. Based on the minimum average probability of symbol error (PSE), we give the optimal design method of the beamforming weight matrices. Furthermore, we derive the upper bound PSEs to evaluate the impact of channel feedback errors on the system performance. Comparison of the upper bounds of the average PSE for several schemes shows that the downlink ZF beamforming for multiuser spatial multiplexing MIMO schemes provide almost the same performance as the SU beamforming scheme.

Although relaying can be very beneficial for wireless systems, understanding which relaying schemes can achieve specific performance objectives under realistic fading is crucial. In this paper we present a general framework for modeling and evaluating the performance of dual-hop decode-and-forward (DF) relaying schemes over independent and not necessarily identically distributed (INID) Nakagami- fading channels. We obtain closed-form expressions for the statistics of the instantaneous output signal-to-noise ratio of repetitive transmission with selection diversity. Furthermore, we present a unified statistical overview of other three significant relaying schemes with DF, one based on repetitive transmission with maximal-ratio diversity and the other two based on relay selection (RS). To compare the considered schemes, we present closed-form and analytical expressions for the outage probability and the average symbol error probability under various modulation methods, respectively. Importantly, it is shown that when the channel state information for RS is perfect, RS-based schemes always outperform repetitive ones. Furthermore, when the direct link between the source and the destination nodes is sufficiently strong, relaying may not result in any gains, and it should be switched off.

In this paper, spatial modulation (SM) is used in a cooperative decode-and-forward (DF) cognitive radio system in order to enhance the overall spectral efficiency. In particular, a multi- antenna secondary transmitter communicates with a single antenna secondary receiver with the help of DF secondary relays in the presence of multiple primary users (PUs). To study the secondary system performance, we derive a closed-form expression for the average pairwise error probability (PEP) over Rayleigh fading channels assuming limited feedback from the PUs. A tight upper bounded average bit error rate is obtained using the PEP expression. Moreover, simple approximate expressions are obtained to get insights on the system diversity and estimation errors effects. Numerical results, which match simulations, show the effectiveness of SM in improving the overall secondary performance in the presence of channel estimation errors.

In this work, we derive exact closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular quadrature amplitude modulation (QAM) when used along with orthogonal space-time block coding (OSTBC) over independent but not necessarily identically distributed multiple-input multiple-output (MIMO) Nakagami-m fading channels. The derived SEP expressions account for diversity branches which may exhibit identical or distinctive power levels while their associated Nakagami indexes can take arbitrary real values not less than 1/2. Our work extends previous results pertaining to the performance analysis of OSTBC using M-ary rectangular QAM over Rayleigh fading channels and M-ary square QAM over Nakagami-m fading channels. For a MIMO diversity system with n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> transmit and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> receive antennas and a corresponding set of arbitrary real-valued Nakagami indexes, our rectangular QAM SEP results are expressed in terms of Lauricella's multivariate hypergeometric functions F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L)</sup> and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L + 1)</sup> where L = n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> is the total number of diversity branches.

An analytical expression of average Symbol Error Probability (ASEP) for general order rectangular QAM is derived for a dual hop cooperative diversity system where a source node communicate with a destination node directly and indirectly(through a single relay) over independent and not identical Nakagami-m fading channel. A pdf based approach is used to derive the expression considering sufficiently large end to end signal to noise ratio (SNR) for source-relay link. Numerically evaluated results are plotted and verified with simulation results.

We define a symbol transition matrix (STM) as a matrix whose entries are the symbol transition probabilities of a relay in a decode-and-forward (DF) relaying system. Using the STM as a state transition matrix of a discrete-time Markov chain, the source-to-destination STM is shown to be the product of intermediate STMs in multihop DF relaying systems. We show that the probability of correct decision at the destination is the trace of the source-to-destination STM divided by the modulation order. The symbol error probabilities (SEPs) of multihop DF relaying systems with any modulation scheme in any independent and nonidentically distributed (ind) channels are derived using the STM. For multihop DF relaying systems in independent and identically distributed (iid) channels, the eigenvalues of the single link STM are used to simplify the calculation of the SEP for any modulation scheme. Also, the SEP of multihop DF relaying systems with 16-quadrature amplitude modulation (QAM) signals in ind Rayleigh fading channels is derived using the STM. A relay advantage criterion is derived for multihop DF relaying systems in iid Nakagami-m fading channels with both the total transmitted energy and the source-to-destination distance fixed. The relay advantage criterion can be used for deciding whether putting more relays between the source and the destination increases or decreases the SEP.

This paper investigates the maximal ratio combining (MRC) performance of an amplify and forward (AF) relay system in Nakagami-m fading environments. The study considers a general scenario with distinct m fading parameters for the following three links, source to relay link, and source to destination link and relay to destination link. We derive new closed form expressions for the statistics of important performance metrics, including the moment generating function, outage probability, higher order moments of equivalent signal to noise ratio (SNR), ergodic capacity, and average symbol error probability (SEP) of common modulation types. In particular, we focus on analytical SEP expressions in the context of an additive white generalized Gaussian noise (AWGGN). As an active area of research, generalized noise receives much attention for its flexible model. However, analytical performance of modulation scheme in generalized noise type has not been found in open literature for AF relaying with MRC despite its practical usefulness. Without the help of analytical solutions, the SEP in generalized noise can only be obtained by a large number of repeated simulation experiments. Therefore, we present the general SEP expression by using special Fox’s H function. Simulation results verify the accuracy of our theoretical analysis and show that the diversity order of MRC criterion linearly depends upon Nakagami parameters of three links.

Cooperative communications can exploit the distributed spatial diversity to improve the multiple-link performance. In this paper, the average symbol error probability (SEP) is carefully investigated for the three-node relaying structure, in which the relaying protocol is amplify-and-forward, and the modulation scheme can be N-PSK or N-QAM. We first exploit the optimistic condition to derive the lower bound of SEP. This is the generalization of the existing Anghel-Kaveh formulation. Then, the upper bound is also provided based on the exponential approximation to the Bessel function. This bound turns out to be tighter than the Anghel-Kaveh upper bound. Numerical results are provided to confirm the analytical analysis.

The performance of dual-hop Decode-and-Forward relaying with relay selection (RS) is analyzed over Nakagami-m fading channels. Assuming that the direct source-to-destination link is active, closed-form expressions for the moment generating and the cumulative distribution functions of a RS-based cooperation scheme that utilizes maximal-ratio diversity at the destination are derived. These expressions are used to obtain the outage probability (OP) and average symbol error probability (ASEP) of this pure RS scheme as well as of a rate-selective one that utilizes RS only when it provides higher achievable rate than that of the direct transmission. Numerically evaluated results, verified by computer simulations, show that, although, in terms of ASEP, relaying is always beneficial, in terms of OP, it should be disabled whenever the direct link is strong.

This paper investigates a time-switching energy-harvesting system in which a source communicates with a destination via energy-constrained amplify-and-forward relays. To exploit the benefit of using multiple relays, we propose a relay scheduling called consecutive relay selection (CRS), which allows all relays to assist the source-to-destination communication, to improve the transmission efficiency of the time-switching policy. The partial relay selection (PRS) is examined for performance comparison. The selected relay in the PRS protocol is considered in two cases: in one, it is selected based on the first-hop channel gains (PRS-1 protocol), and in the other, it is selected based on the second-hop channel gains (PRS-2 protocol). For performance evaluation, the analytical expressions of the outage probability and throughput for Nakagami-m fading channel are derived. Our results show that the CRS protocol outperforms the PRS protocol in terms of throughput, the PRS-1 protocol achieves better performance than the PRS-2 protocol. Moreover, we discuss the effects of various key system parameters on system performance, such as the energy-harvesting ratio, source transmission rate, and locations of relays, to provide insights into the various design choices.