Performance analysis of a variable‐gain amplify‐and‐forward relayed mixed RF‐FSO system

In this work, an amplify‐and‐forward variable‐gain relayed mixed RF‐FSO system is studied. The considered dual‐hop system consists of a radio frequency (RF) link followed by a free space optical (FSO) channel. The RF link is affected by short‐term multipath fading and long‐term shadowing effects and is assumed to follow the generalized‐K fading distribution that approximates accurately several important distributions often used to model communication channels. The FSO channel experiences fading caused by atmospheric turbulence that is modeled by the gamma‐gamma distribution characterizing moderate and strong turbulence conditions. The FSO channel also suffers path loss and pointing error induced misalignment fading. The performance of the considered system is analyzed under the collective influence of distribution shaping parameters, pointing errors that result in misalignment fading, atmospheric turbulence, and path loss. The moment‐generating function of the Signal power to noise power ratio measured end‐to‐end for this system is derived. The cumulative distribution function for the Signal power to noise power ratio present between the source and destination receiver is also evaluated. Further, we investigate the error and outage performance and the average channel capacity for this system. The analytical expressions in closed form for the outage probability, symbol and bit error rate considering different modulation schemes and channel capacity are also derived. The mathematical expressions obtained are also demonstrated by numerical plots.     

Performance of joint transmit and receive antenna selection in dual hop amplify‐and‐forward relay network over Nakagami‐m fading channels

In this paper, performance of joint transmit and receive antenna selection in each hop of dual hop amplify‐and‐forward relay network is analyzed over flat and asymmetric Nakagami‐m fading channels. In the network, source, relay, and destination are equipped with multiple antennas. By considering relay location, we derive exact closed‐form cumulative distribution function, moment generating function, moments of end‐to‐end signal‐to‐noise ratio and closed form symbol error probability expressions for fixed and channel state information‐based relay gains. We also derive the asymptotical outage probability and symbol error probability expressions to obtain diversity order and array gain of the network. Analytical results are validated by the Monte Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance evaluation of HDAF relaying systems for pilot and data symbol burst transmission over quasi‐static Rayleigh fading channels

This paper analyzes averaged symbol error probabilities of burst transmission consisting of pilot and data symbols for hybrid adaptive decode‐or‐amplify‐forward (HDAF) relaying systems. Under the assumption of quasi‐static Rayleigh fading channels with independent and non‐identically distribution, we consider a channel estimation scheme based on pilot symbols and show how channel estimation error affects received signal‐to‐noise ratio (SNR) and symbol error probability (SEP). Firstly, all the possible detection error‐events are presented for all the relay nodes, and their probabilities are derived as forms related with data symbol burst transmission. For the given error event, we analyze the conditional SEP as an exact form and then, the averaged SEP (ASEP) is approximately derived as a closed‐form. The simulation results verify that our derived ASEP expression is accurate over all the regions of SNR. Utilizing the proposed expressions, we can evaluate ASEP performance of HDAF relay systems easily and fast. Copyright © 2015 John Wiley & Sons, Ltd.     

An Improved Approximation for the Gaussian Q-Function

We present a novel, simple and tight approximation for the Gaussian Q-function and its integer powers. Compared to other known closed-form approximations, an accuracy improvement is achieved over the whole range of positive arguments. The results can be efficiently applied in the evaluation of the symbol error probability (SEP) of digital modulations in the presence of additive white Gaussian noise (AWGN) and the average SEP (ASEP) over fading channels. As an example we evaluate in closed-form the ASEP of differentially encoded QPSK in Nakagami-m fading.     

Impact of co‐channel interference on performance of dual‐hop wireless ad hoc networks over α−μ fading channels

In this work, we investigate the performance of a dual‐hop cooperative network over α?μ fading channels with the presence of co‐channel interference (CCI) at both the relay and destination nodes. Amplify‐and‐forward (AF) relaying is considered in the relay node. The upper bound of the signal‐to‐interference‐plus‐noise ratio (SINR) of the dual‐hop relay link is used to determine the system performance. The probability density function (PDF) and the cumulative distribution function (CDF) of the upper bound of the SINR are analyzed. The system performance is determined in terms of the outage and error probabilities. Numerical results are used to present the performance analysis of the system.     

Performance of asynchronous slow frequency-hop multiple-accessnetworks with MFSK modulation

The performance of asynchronous slow frequency-hop spread-spectrum multiple-access networks where each user transmits L, M-ary symbols per hop using M-ary frequency-shift keying (FSK) modulation with noncoherent demodulation is investigated. Expressions for the decision variables are derived for a given multiple FSK (MFSK) symbol within a hop hit by K' interfering users under additive white Gaussian noise and Rayleigh fading channel models. For the special case when M=2, an accurate analytic approximation for the average error probability is derived as a function of L and K' and semianalytic Monte Carlo simulations are performed to estimate the probability of error for M larger than 2. The results are used to investigate the dependence of the average symbol error probability on L and M. Finally, the effect of enforcing phase transition between the MFSK symbols within a hop is investigated     

SER Analysis of QAM with Space Diversity in Rayleigh Fading Channels

This paper derives the symbol error probability for quadrature amplitude modulation(QAM) with L-fold space diversity in Rayleigh fading channels. Two combining techniques, maximal ratio combining(MRC) and selection combining(SC), are considered. The formula for MRC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an additive white Gaussian noise(AWGN) channel over a chi-square distribution with 2L degrees of freedom. The obtained formula overcomes the limitations of the earlier work, which has been limited only to deriving the symbol error rate(SER) of QAM with two branch MRC space diversity. The formula for SC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an AWGN channel over the distribution of the maximum signal-to-noise ratio among all of the diversity channels for SC space diversity. No analysis for QAM with SC space diversity has been reported yet. Analytical results show that the probability of error decreases with the order of diversity. We can also see that the incremental diversity gain per additional branch decreases as the number of branches becomes larger. On the other hand, the performance of 16 QAM with MRC becomes much better than that of SC as the number of branches becomes larger. By giving the order of diversity, L, and the number of signal points, M, we have been able to obtain the SER performance of QAM with general space diversity. These results can be used to determine the order of diversity to achieve the desired SER in land mobile communication system employing QAM modulation.     

A simplified exact expression of SEP for cross QAM in AWGN channel from M × N rectangular QAM and its usefulness in Nakagami-m fading channel

This paper derives a simple exact expression of symbol error probability (SEP) for general order cross QAM constellation in the presence of additive white Gaussian noise (AWGN) channel. The key idea is to obtain this novel expression from a simple analysis of the corresponding rectangular QAM. The analysis of the expression involves simple one dimensional Gaussian Q functions unlike other complex SEP expressions. A simple tight bound approximation of the proposed exact SEP is also given, which provides performance improvement over the existing SEP approximations, particularly for low signal to noise ratios (SNRs). Also, with the help of simulation results, we show that the proposed approximation is in excellent agreement with the exact SEP curve. Moreover, the proposed expressions prove to be useful for accurate estimation of the SEP in Nakagami-m fading channel, including the special case of Rayleigh fading (m = 1).     

End‐to‐end performance of transmit antenna selection and generalized selection combining in dual‐hop amplify‐and‐forward relay network in the presence of feedback errors

In this paper, end‐to‐end performance of transmit antenna selection (TAS) and generalized selection combining (GSC) is studied in a dual‐hop amplify‐and‐forward relay network over flat Rayleigh fading channels. In the system, source and destination equipped with multiple antennas, communicate by the help of single relay equipped with single antenna. Source‐destination link is not available. TAS is used for transmission at the source, and GSC is used for reception at the destination. By considering the relay location and the presence of error in feedback channel from the relay to the source, we derive closed‐form outage probability, moment generating function and moments of end‐to‐end signal‐to‐noise ratio, and closed‐form symbol error probability (SEP) expressions for channel state information (CSI)‐based and fixed relay gains. The diversity order and array gain of the network are obtained for both CSI‐based and fixed relay gains by deriving asymptotical outage probability and SEP expressions. The analytical results are validated by the Monte Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Bit error probability of the M‐QAM scheme under η‐μ fading and impulsive noise in a communication system using spatial diversity

This paper presents a new and exact expression for the bit error probability (BEP) of the square M‐ary quadrature amplitude modulation (M‐QAM) scheme, with the channel under double gated additive white Gaussian noise (G²AWGN) and η‐μ fading in a communication system using the spatial diversity technique. The expression for the BEP is written in terms of the Appell function. The BEP curves are presented under different values of the number of branches of the maximum ratio combining (MRC) receiver, order of the constellation M, and parameters that characterize mathematically the channel, corroborated by simulations performed with Monte Carlo method.     

Improved auxiliary particle filter‐based synchronization of chaotic Colpitts circuit and its application to secure communication

In this paper, we propose a synchronization scheme based on an improved auxiliary particle filter (IAPF) for chaotic Colpitts circuit and conduct an experimental study on the synchronization performance with application to secure communications. Specifically, with the synchronization scheme, when the chaotic signals generated by an analog Colpitts circuit are transmitted through a nonideal channel, the distorted signals are processed digitally by the novelly designed IAPF at the receiver, in order to obtain the synchronized signals of the transmitter circuit. Experimental results indicate that synchronization can be achieved over both the additive white Gaussian noise channel and the multipath fading channel with low signal‐to‐noise ratio, even if there exist severe circuit parameter mismatches between the transmitter and the receiver. Furthermore, a chaos‐masking secure communication system is constructed and verified over both the additive white Gaussian noise channel and the multipath fading channel, and the bit error rate is evaluated versus different signal‐to‐noise ratios and symbol periods. It is shown that the achievable bit error rate can reach the order of magnitude of 10 ^{− 4} without error correction coding techniques. In addition, security analysis demonstrates that the proposed chaotic secure communication system is resistant to the brute‐force attack. Copyright © 2013 John Wiley & Sons, Ltd.     

Physical layer security for dual‐hop FSO/RF system using generalized ΓΓ/η−μ fading channels

We investigate the physical layer security of decode‐and‐forward–relayed free space optics (FSO)/radio frequency (RF) communication system. In this network, the eavesdropper exists after relay node and overhears RF transmission. Further, FSO being a line‐of‐sight transmission is assumed to be secure from eavesdroppers. Here, we have the Gamma‐Gamma (ΓΓ) distribution for FSO link and generalized η?μ distribution for RF link. The security for information transmission to the legitimate user in the presence of an eavesdropper is measured in terms of secrecy capacity and secrecy outage probability. Deriving the probability density function and cumulative distribution function of end‐to‐end signal‐to‐noise ratio, the closed‐form expressions for security parameters are achieved. The numerical analysis of the proposed system is done under the influence of atmospheric turbulence effects and various fading conditions. The results have been verified through simulation.     

Error rate and outage of dual‐hop DF relay system with selection combining over Rice fading

Performance of dual‐hop decode‐and‐forward relay system with selection‐combining receiver is analyzed over Rice fading channels. The following closed‐form expressions of performance metrics are derived: moment generating function for selection‐combining receiver output signal‐to‐noise ratio, exact average bit error rate of noncoherent modulations, approximate average symbol error rate for coherent modulations, and outage probability. We also obtain simple asymptotic expressions for moment generating function, exact average bit error rate, average symbol error rate, and outage probability, which are useful to characterize the diversity order and the coding gain. The optimal power allocation analysis suggests that the optimal power allocation factor is independent of total signal‐to‐noise ratio and source‐to‐destination link fading parameters. The accuracy of the obtained analytical expressions are supported by computer simulation results.     

Noncentral F-Distribution for an M-ary Phase Shift Keying Wedge-Shaped Region

This letter presents an alternative analytical expression for computing the probability of an M-ary phase shift keying (MPSK) wedge-shaped region in an additive white Gaussian noise channel. The expression is represented by the cumulative distribution function of known noncentral F-distribution. Computer simulation results demonstrate the validity of our analytical expression for the exact computation of the symbol error probability of an MPSK system with phase error.     

Phase noise sensitivity analysis of lattice constellation

Based on the assumption of large number of constellation points and high signal-to-noise ratio (SNR), phase noise sensitivity of lattice constellation is analyzed. The upper bound of symbol error rate (SER) in additive white Gaussian noise (AWGN) channel is derived from pairwise error probability. For small phase noise, phase noise channel is transformed to AWGN channel. With the aid of Wiener model, the obtained upper bound can be extended to phase noise channel. The proposed upper bound can be used as performance criterion to analyze the sensitivity of phase noise in multi-dimensional lattice constellation. Simulation results show that with the same normalized spectral efficiency, higher dimensional lattice constellations are more sensitive than lower ones in phase noise channel. It is also shown that with the same dimension of constellation, larger normalized spectral efficiency means more performance loss in phase noise channel.     

脉冲噪声对空时分组码性能影响的研究

该文对脉冲及非高斯噪声环境下空时分组码(STBC)性能进行了研究。采用脉冲和高斯加性混合噪声模型,利用矩母函数(MGF)分析方法,通过建立多发单收(MISO)近似等效模型,推导出Rayleigh衰落信道下MISO空时分组码误符号率(SER)闭式表达式的渐近解。在此基础上,对于不同脉冲噪声发生概率、脉冲噪声与高斯噪声功率比条件下STBC的性能进行了分析。结果表明,即使在高信噪比情况下,混合噪声也将会使STBC系统性能显著降低。蒙特卡洛仿真结果验证了SER闭式解的有效性。     

Design and analysis of a fast frequency-hopped DBPSK communicationsystem. I. Error performance in AWGN plus partial-band noisejamming

The purpose of the paper is to present the design and performance analysis of a fast frequency-hopped (FFH) spread spectrum communication system employing differential binary phase-shifted-keying (DBPSK) modulation and differentially coherent demodulation. The receiver utilizes a hop time tracking loop to “lock” the hop clock. The authors present an analysis of the average bit error probability of the overall system when it is operating in additive white Gaussian noise plus partial-band noise jamming. The effect of channel phase distortion is also studied     

A unified framework for performance evaluation over generalized fading channels

In this paper, we present a unified framework to analyze the performance of the average bit error probability (BEP) and the outage probability over generalized fading channels. Specifically, we assume that the probability density function (PDF) of the instantaneous signal-to-noise ratio \(\zeta \) is given by the product of: power function, exponential function, and the modified Bessel function of the first kind, i.e., \(f_{\zeta }(\zeta )=\zeta ^{\lambda -1}exp\left( -a\zeta ^{\beta }\right) I_{v}\left( b\zeta ^{\beta }\right) \). Based on this PDF, we obtain a novel closed-form expression for the average BEP over such channels perturbed by an additive white generalized Gaussian noise (AWGGN). Note that other well-known noise types can be deduced from the AWGGN as special cases such as Gaussian noise, Laplacian noise, and impulsive noise. Furthermore, we obtain a novel closed-form expression for the outage probability. As an example of such channels, and without loss of generality, we analyze the performance of the average BEP and the outage probability over the \(\eta \)–\(\mu \) fading channels. Analytical results accompanied with Monte-Carlo simulations are provided to validate our analysis.     

Closed-Form Expressions for the Exact Symbol Error Probability of 32-Cross-QAM in AWGN and in Slow Nakagami Fading

Novel closed-form exact expressions for the average symbol error probability of 32-cross-QAM in an additive white Gaussian noise channel and in a slow, flat Nakagami fading channel with L-branch maximal ratio combining diversity are derived     

Performance Analysis of the Double-Antenna SDC System Over <Emphasis Type="Italic">N</Emphasis>-Nakagami Fading Channels

The performance of the double-antenna switched diversity combining (SDC) system over N-Nakagami fading channels is investigated in this paper. Based on the method of the probability density function of the signal-to-noise ratio, the exact expressions for the channel capacity and average symbol error probability (ASEP) are derived. Then the channel capacity and ASEP performance under different conditions is evaluated through numerical simulations to verify the analysis. The simulation results showed that the performance of the double-antenna SDC system is improved with the fading coefficient increased, but the level of improvement is declined as the number of cascaded components increased.