Outage probability and channel capacity for the Nth best relay selection AF relaying over INID Rayleigh fading channels

Cooperative diversity systems have recently been proposed as a way to form virtual antenna schemes without utilizing collocated multiple antennas. In this paper, we consider the Nth best opportunistic amplify‐and‐forward (AF) cooperative diversity systems. The AF type can be regarded as one on the basis of modified channel state information. Wireless channels between any pair of nodes (i.e., direct and dual hop links) are assumed quasi‐static independent and nonidentically distributed (INID) Rayleigh fading. The best opportunistic AF (OAF) scheme requires two phases of transmission. During the first phase, the source node transmits a signal to all relays and the destination. In the second phase, the best relay is only selected on the basis of highest signal‐to‐noise ratio (SNR) scheme to forward the source signal to the destination. Therefore, the indirect link (i.e., source‐selected relay destination) can give the highest received SNR. However, the best relay selection cannot be available so that we might choose the second, third, or generally the Nth best relay. In this paper, we derive the approximated outage probability and channel capacity for the Nth best OAF relay systems over INID Rayleigh fading channels. At first, the indirect link's received SNR is approximated as harmonic mean upper bound. With this information, we obtain the given relay's Nth best selection probability as the closed form. Finally, both outage probability and channel capacity are derived as the closed forms. Simulation results are finally presented to validate the analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Outage probability of opportunistic decode-and-forward relaying over Nakagami-m fading channels

In this article, the outage probability behavior of a relay network over Nakagami-m fading channels is analyzed. Both reactive and proactive opportunistic decode-and-forward (DAF) strategies are considered. The closed-form solutions to the outage probabilities on both opportunistic DAF strategies are derived. Simulation results conf'Lrrn the presented mathematical analysis.     

Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels

We consider spatial multiplexing systems in correlated multiple-input multiple-output (MIMO) fading channels with equal power allocated to each transmit antenna. Under this constraint, the number and subset of transmit antennas together with the transmit symbol constellations are determined assuming knowledge of the channel correlation matrices. We first consider a fixed data rate system and vary the number of transmit antennas and constellation such that the minimum margin in the signal-to-noise ratio (SNR) is maximized for linear and Vertical Bell Laboratories Layered Space-Time (V-BLAST) receivers. We also derive transmit antenna and constellation selection criteria for a successive interference cancellation receiver (SCR) with a fixed detection order and a variable number of bits transmitted on each substream. Compared with a system using all available antennas, performance results show significant gains using a subset of transmit antennas, even for independent fading channels. Finally, we select a subset of transmit antennas to maximize data rate given a minimum SNR margin. A lower bound on the maximum outage data rate is derived. The maximum outage data rate of the SCR receiver is seen to be close to the outage channel capacity.     

Diversity order of decode-and-forward MIMO relaying with transmit antenna selection

This article analyzes the diversity order of several proposed schemes, where the transmit antenna selection (TAS) strategies are combined with low-complexity decode-and-forward (DF) protocols in the multiple-input multiple-output (MIMO) relaying scenario. Although antenna selection is a suboptimal form of beamforming, it enjoys the advantages of tractable optimization and low feedback overhead. Specifically, this article proposes schemes that combine TAS strategies with fixed decode-and-forward (FDF) and selection decode-and-forward (SDF) protocols. Following that, the asymptotic expressions of outage probabilities are derived and the diversity order of the proposed schemes analyzed. These kinds of combination of transmit antenna selection strategies and low-complexity decode-and-forward protocols can achieve partial diversity order in the MIMO relaying scenario. The numerical simulations verify the analysis.     

Receive antenna selection for MIMO systems over correlated fading channels

In this letter, we propose a novel receive antenna selection algorithm based on cross entropy optimization to maximize the capacity over spatially correlated channels in multiple-input multiple-output (MIMO) wireless systems. The performance of the proposed algorithm is investigated and compared with the existing schemes. Simulation results show that our low complexity algorithm can achieve near-optimal results that converge to within 99% of the optimal results obtained by exhaustive search. In addition, the proposed algorithm achieves near-optimal results irrespective of the mutual relationship between the number of transmit and receive antennas, the statistical properties of the channel and the operating signal-to-noise ratio.     

Power allocation for bidirectional AF relaying over rayleigh fading channels

This letter presents two novel power allocation schemes for bidirectional amplify-and-forward (AF) relaying over Rayleigh fading channels through the exploitation of channel mean strength. The first scheme aims to maximize the upper bound of average sum rate, and the other aims to achieve the trade-off of outage probability between two terminals. Numerical results show considerable performance improvement in comparison with conventional power allocation approaches.     

Performance analysis of MIMO systems with antenna selection over quasi-static fading channels

We analyze the performance of multiple-input-multiple-output (MIMO) systems with antenna selection over quasi-static fading channels. The basic idea is that, for a given number of receive antennas, M, the receiver uses the best L out of the available M antennas where, typically, L相似文献   

Outage probability of cooperative relay networks in Nakagami-m fading channels

It is well known that the cooperation among nodes can improve the performance of a wireless network. In this letter we analyze the outage probability behaviour of a relay network in Nakagami-m fading channels. A closed-form solution for the outage probability is derived. When m=1, the results are applicable for Rayleigh fading. Computer simulations confirm the presented mathematical analysis     

Performance analysis of DF relaying multi-hop systems over log-normal fading channels

In this paper, we studied the end-to-end average bit error rate (BER) performance of decode-and-forward (DF) relaying multi-hop chain systems (MCSs) over log-normal fading channels. After specifying the distribution of the signal-to-noise rate for each hop, the analytical expression of the end-to-end average BER has been derived. The derived end-to-end average BER model can be used in the case that all the single-hops in the chain have different statistical behaviors, i.e., all links suffer various types of fadings, not limited to one type of fading. The comparisons between Monte Carlo simulation results and analytical results under various conditions verify the accuracy of the proposed model.     

Outage probability of multihop transmission over Nakagami fading channels

We present a general analytical framework for the evaluation of the end-to-end outage probability of multihop wireless communication systems with nonregenerative relays over Nakagami fading channels. It is shown that the presented results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, we obtain a closed-form expression for the moment generating function of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and we then use this expression to calculate the outage probability via numerical inversion of the Laplace transform. Numerical examples show that regeneration is more crucial at low average SNR and for multihop systems with a large number of hops.     

Outage probability of diversity systems over generalized fading channels

Outage probability is an important performance measure of communication systems operating over fading channels. Relying on a simple and accurate algorithm for the numerical inversion of the Laplace transforms of cumulative distribution functions, we develop a moment generating function-based numerical technique for the outage probability evaluation of maximal-ratio combining (MRC) and postdetection equal-gain combining (EGC) in generalized fading channels for which the fading in each diversity path need not be independent, identically distributed, nor even distributed according to the same family of distributions. The method is then extended to coherent EGC but only for the case of Nakagami-m fading channels. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the power delay profile and the fading correlation on the outage probability of MRC and EGC systems.     

Spatial modulation and physical layer network coding based bidirectional relay network with transmit antenna selection over Nakagami‐m fading channels

In this paper, a high data rate bidirectional relay network is proposed by combining the merits of spatial modulation (SM) and physical layer network coding. All nodes in the network are equipped with multiple antennas. Spatial modulation technique is used to reduce hardware complexity and interchannel interference by activating only one antenna at any time during transmission. In the proposed bidirectional relay network, transmit antennas are selected at the source nodes and relay node on the basis of the order statistics of channel power. It increases received signal power and provides a significant improvement in the outage performance. Also, the data rate of the proposed network is improved by physical layer network coding at the relay node. A closed form analytical expression for the outage probability of the network over Nakagami‐m fading channel is derived and validated by Monte Carlo simulations. In addition, asymptotic analysis is investigated at high signal‐to‐noise ratio region.The outage performance of the proposed network is compared with SM and physical layer network coding bidirectional relay network without transmit antenna selection and point‐to‐point SM. With approximate SNR≈1 dB difference between the two networks, the same data rate is achieved.     

Outage performance of two-hop multi-antenna co-operative relaying in rayleigh fading channel

Performance of co-operative relaying employing infrastructure based fixed relays having multiple antennas has been investigated. A closed-form expression of outage probability for such a system has been derived when the relay performs selection combining and the destination performs MRC combining of signals. The effect of relay placement on the system performance has also been studied.     

Secrecy performance analysis of AF relaying with relay selection scheme over Nakagami‐m fading channels

This paper investigates the secrecy outage probability (SOP) and intercept behavior for the amplify‐and‐forward network over Nakagami‐m fading channels. Relay selection schemes are evaluated. The optimal and suboptimal criterions require the instantaneous and statistical channel state information of the eavesdroppers' channels, respectively. The enhanced 2‐hop criterion needs the additional information of the target secrecy rate for relay selection. Theoretical analysis reveals that the diversity order of the SOP is dominated by the minimum fading figures of the source‐relay and relay‐destination channels, while that of the intercept probability depends on the fading figure of the relay‐destination channel. In the multirelay scenario, the optimal, suboptimal, and enhanced 2‐hop scheme achieve the same diversity orders of the SOP. For the intercept probability, the optimal and second‐hop relay selection schemes provide the same diversity order, while the diversity orders of the suboptimal and enhanced 2‐hop schemes are the same. Simulation results finally substantiate the accuracy of the theoretical analysis.     

Outage probability analysis of multi-hop relayed wireless networks over $$\alpha -\mu $$ fading channels

In this paper, we study the end-to-end outage probability performance of Amplify and Forward (AF) and Decode and Forward (DF) multi-hop wireless communication systems operating over independent but not necessarily identical \(\alpha -\mu \) fading channels. To this end, we derive an expression for the moment generating function of the reciprocal of the end-to-end signal-to-noise ratio, and then use this expression to evaluate the end-to-end outage probability of the AF system by numerically inverting the Laplace transform. We also derive an expression for the end-to-end outage probability of the DF system.     

Performance of antenna selection schemes in dual hop full-duplex decode-and-forward relaying over Nakagami-m fading channels

In this paper, we investigate the outage performance of several antenna selection (AS) schemes in dual hop full-duplex (FD) multiple-input multiple-output (MIMO) relay networks in which the relay adopts decode-and-forward (DF) protocol over Nakagami-m fading channels. In the network, the source (S), destination (D) and relay (R) are assumed to be equipped with multiple antennas. We assume that the line-of-sight component between S and D cannot be established due to the poor fading environment conditions. For signal transmission-reception during the training period, only a single antenna at each node is selected according to selection techniques, and then with the help of an error-free feedback channel the selected antenna index is sent to the related node. Outage probability (OP) expressions related to AS schemes are obtained in closed forms and asymptotic OPs are also derived in order to get more meaningful insights into OP and diversity behaviour. The theoretical results are verified by Monte Carlo simulations. We show that performance of the FD relay can be significantly improved by using selection techniques compared to half-duplex (HD), especially at low signal-to-noise ratio (SNR) region. In addition, results show that the performance floor level meaning zero diversity at high SNR region, which is also confirmed by asymptotic analysis and is an inherent disadvantage of FD relay, can be decreased. Moreover, it is shown that the FD relay with AS schemes outperforms HD as the target rate increases for a certain value of SNR and residual self-interference power.     

Space-time coding over correlated fading channels with antenna selection

In a previous paper by Bahceci et al., antenna selection ' for multiple-antenna transmission systems under the assumption that the subchannels between antenna pairs fade independently was studied. In this paper, the performance of such systems when the subchannels experience correlated fading is considered. It is assumed that the channel-state information (CSI) is available only at the receiver, the antenna selection is performed only at the receiver, and the selection is based on the instantaneous received signal power. The effects of channel correlations on the diversity and coding gain when the receiver system is a subset of the antennas are quantified. Theoretical results indicate that the correlations in the channel do not degrade the diversity order, provided that the channel is full rank. However, it does result in some performance loss in the coding gain.     

Outage probability and error rate analysis of full duplex relay in asymmetric fading channels

Full duplex (FD) technique has evolved as a viable solution to address the spectrum scarce issue. It has gained research interest for its potential to double the wireless link capacity and enhance spectral efficiency (SE). In this paper, the end-to-end performance of an amplify-and-forward full duplex relay(FDR) in asymmetric Rayleigh–Rician fading channels is explored, unlike the other works that assume symmetric fading conditions in both the links. The asymmetric or mixed fading channels properly model the realistic communication scenarios like satellite/terrestrial wireless communication systems. In this work, we consider that the source-relay link experiences Rayleigh fading and the relay-destination link experiences Rician fading. The novel exact and lower bound closed form analytical expressions for outage probability (OP) and bit error rate (BER) for the considered FD system are derived. Moreover, the effect of severity of fading and the amount of residual self-interference (RSI) on the performance of FDR are also studied. In addition, MC simulations are carried out to validate the results. It is observed that the performance metrics, OP and BER, are highly dependent on the severity of fading and the amount of RSI. Furthermore, it is found that typically at the SNR of 10 dB, an improvement of approximately 27.6% in OP is obtained. Also, our work offers appreciable SNR gain, for example, for a BER of 10⁻², an SNR improvement of around 11 dB is achieved. These findings have been compared with the mixed Rayleigh–Rician fading channel conditions considering only half duplex(HD) mode. These parameter metrics are helpful in analyzing the performance of FD in various communication scenarios such as LoS/NLoS conditions and hence pave the way for more realistic FDR.     

Outage probability of SC receiver over exponentially correlated K fading channels

A mathematical expression for the outage probability of a selection combining diversity receiver with an arbitrary number of input branches is presented for exponentially correlated K fading channels. Numerical and simulation results are plotted and the effect of correlation, number of diversity branches and fading parameter on the outage performance of the receiver is studied. Results suggest that a correlation coefficient less than 0.5 may be used in practice.