A new closed-form of ASEP and channel capacity with MRC and selection combining over Inverse Gaussian shadowing

This paper analyse and investigate the performance of communication system with maximal ratio combining (MRC) and selection combining (SC) over Inverse Gaussian (IG) fading distribution. All formats of coherent and non-coherent modulation schemes are considered and novel analytical expressions of average symbol error probability (ASEP) with diversity are derived. Gamma and IG fading distributions are popularly used as a mathematically less complex solution to lognormal in the open literature. Hence, we provide a comparative analysis between IG and gamma fading with the aim to provide a quantitative measure of the difference between the two distributions in the context of ASEP. Moreover, the novel closed-form expressions of channel capacity under transmission schemes such as optimal rate adaptation (ORA) and channel inversion fixed rate (CIFR) are derived and analysed with MRC and SC diversity over IG fading. The analytical results have been validated with the Monte Carlo simulations and the exact numerical results.     

最大比合并接收系统在n-Rayleigh信道下的性能分析

在n-Rayleigh信道下,研究了MRC(Maximal Ratio Combining)合并接收系统的平均码字错误率(ASEP)性能。基于矩生成函数(MGF)的方法,推导了MRC接收系统在n-Rayleigh衰落信道上采用M进制相移键控(MPSK),M进制正交幅度调制(MQAM)和M进制脉冲幅度调制(MPAM)等几种M进制数字调制方式的ASEP的计算式。然后在不同条件下,仿真了系统的ASEP性能,仿真值与理论值相一致,理论分析的正确性得到了证明。分析结果表明:分集支路数和衰弱因子对系统的ASEP性能有重要影响。     

Performance analysis of shadowed-Rice fading channel with cooperative spectrum sensing

In this paper, the performance analysis of wireless communication system over shadowed-Rice (SR) composite fading channel has been investigated and analysed. The unified analytical expressions of the average symbol error probability (ASEP) for several coherent and non-coherent modulation schemes separately with different constellation sizes are derived for composite fading channel under two different fade mitigation methods, with maximal ratio combining (MRC) microdiversity (Method 1) and MRC applied over the composite fading channel (Method 2). Furthermore, an asymptotic analysis is carried out and a closed-form expression of the ASEP with Method 2 is presented. Analytical expressions of the corresponding average probability of energy detection (PD) are formulated for both the methods. Finally, the derived PD expression is utilised to analyse the performance of cooperative system assuming erroneous feedback channel. Analysis of optimisation of detection threshold as well as number of cognitive users to minimise the total error rate is also carried out. The closed-form expressions are validated by comparing them with exact numerical results and Monte Carlo simulation.     

Equal-gain and maximal-ratio combining over nonidentical Weibull fading channels

We study the performance of L-branch equal-gain combining (EGC) and maximal-ratio combining (MRC) receivers operating over nonidentical Weibull-fading channels. Closed-form expressions are derived for the moments of the signal-to-noise ratio (SNR) at the output of the combiner and significant performance criteria, for both independent and correlative fading, such as average output SNR, amount of fading and spectral efficiency at the low power regime, are studied. We also evaluate the outage and the average symbol error probability (ASEP) for several coherent and noncoherent modulation schemes, using a closed-form expression for the moment-generating function (mgf) of the output SNR for MRC receivers and the Pade/spl acute/ approximation to the mgf for EGC receivers. The ASEP of dual-branch EGC and MRC receivers is also obtained in correlative fading. The proposed mathematical analysis is complimented by various numerical results, which point out the effects of fading severity and correlation on the overall system performance. Computer simulations are also performed to verify the validity and the accuracy of the proposed theoretical approach.     

New Analytical Expressions for ASEP of Modulation Techniques with Diversity Over Lognormal Fading Channels with Application to Interference-Limited Environment

In this paper, the analytical expressions of the average symbol error probability (ASEP) for both coherent and non-coherent modulation formats with diversity schemes such as maximal ratio combining (MRC), equal-gain combining (EGC), and selection combining (SC) over the lognormal (LN) distribution assuming independent and identically distributed (i.i.d.) channels have been derived. The functions involving LN distribution are simplified using the Gauss–Hermit and Gaussian Quadrature integration. Furthermore, the effect of the diversity order and constellation size on the error probability has been examined extensively under various shadowing conditions such as infrequent light, average, and frequent heavy shadowing. As an application, the derived results are used to analyze the performance of the communication systems over the interference-limited environment. The impact of the number of interferers on important performance metrics such as the outage probability, the ASEP, and the channel capacity has been examined. The accuracy of the analytical results are validated by comparing them with the exact numerical results and Monte Carlo simulations. The analytical expressions are simple and easily implementable in software package such as MATLAB. The proposed analytical expressions are supposed to be a vital tool in areas such as IEEE 802.15.3a wireless communication system, indoor environment, radio channel effect by body worn devices, ultra-wideband indoor channel.     

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.     

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.     

Pairwise codeword error probability for coded atmospheric optical communication systems

In atmospheric optical channels ,turbulence affects theperformance of I M/DDatmospheric optical communica-tion systems seriously,especiallyinthe range of 1kmormore.Using error-control code (error-correcting code orchannel code) it can be i mproved remarka…     

Performance analysis of maximum ratio combining with imperfect channel estimation in the presence of cochannel interferences

In this paper, we analyze the performance of maximum ratio combining (MRC) systems with imperfect channel estimation in the presence of cochannel interference (CCI) with an arbitrary power interference-to-noise ratio (INR). The maximum combining weights are the imperfect estimates of the desired user's fading channel coefficients and are assumed to be complex Gaussian distributed. The quantified measure for estimation error is the correlation coefficient between the true fading channel coefficients and their estimates. Exact closedform expressions are derived for the probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR), as well as performance metrics including outage probability and the average symbol error probability (ASEP) for some modulation formats. Simulation results demonstrate the accuracy of our theoretic analysis.     

Performance comparison of dual‐hop hybrid decode‐or‐amplify‐forward relay schemes for M‐ary quadrature amplitude modulation burst transmission over Rayleigh fading channels

This paper shows the analytical performance expressions of M‐ary quadrature amplitude modulation burst symbol transmission for hybrid decode‐or‐amplify‐forward (HDAF) relay schemes over quasi‐static Rayleigh‐fading channels. First, we derive the probability density function of the received instantaneous signal‐to‐noise ratio as the simplified form, which is related to all the possible occurrence probabilities of error‐events for M‐ary quadrature amplitude modulation burst transmission. On the basis of the derived probability density function, we express average bit error probability, average symbol error probability, and average burst error rate as closed forms, which can be also applied to both amplify‐and‐forward and adaptive decode‐and‐forward (ADF) schemes. The analysis and simulation results show that HDAF scheme for burst transmission can achieve the performance of ADF scheme with symbol‐by‐symbol transmission, which is the achievable lower bound. Furthermore, the outage probability, the normalized channel capacity, and the goodput performance are also derived as closed forms. The analysis shows the superiority of HDAF scheme to ADF scheme. Comparison with simulations confirms that the derived analytical expressions are accurate over all signal‐to‐noise ratio regions and for different numbers of relays and modulation orders.     

Closed form expressions for ABER and capacity over EGK fading channel in presence of CCI

Goal of next generation wireless communication system is to achieve very high data rate. Femto-cell is one of the possibilities to achieve the above target. However, co-channel interference (CCI) is the important concern in femto-cell. This paper presents closed form expressions for average bit error rate (ABER) and capacity for different adaptive schemes under extended generalised-K (EGK) fading channel in the presence of CCI. A novel conditional unified expression (C_UE) is derived, which results different conditional error probability and normalised average capacity. Using C_UE, a generic expression for ABER is obtained. In addition, closed form expressions for ABER for different modulation schemes under EGK fading channel in presence of CCI are also derived. Further, it is shown that generic ABER expression results into ABER of different modulation schemes. Besides, the closed form expressions of capacity for different adaptive schemes under EGK in presence of CCI are derived. Finally, analytical and simulated results are obtained with excellent agreement.     

Exact Performance Analysis of Dual-Branch Coherent Equal-Gain Combining in Nakagami- $m$, Rician, and Hoyt Fading

The exact symbol error rates (SERs) of several M-ary modulation schemes are obtained in a unified manner for mobile radio receivers employing dual-branch coherent equal-gain combining (EGC), where the received signals on each branch follow either similar or different fading distributions. Specifically, the cases considered are Nakagami-m, Rice, and Hoyt fading on both branches, but with not necessarily identical parameters, and mixed Nakagami-m/Rice and Nakagami-m/Hoyt fading; only the integer or half-integer values of the Nakagami-parameter are considered. While the previous exact expressions for the SERs of general M-ary modulations with L-branch EGC contained double integrals, the error probability expressions derived in this paper for the case of L=2 contain only a single integral. In addition, the derived probability distributions also allow the direct obtaining of other useful performance measures, such as the exact level crossing rates, average fade durations, and outage probabilities.     

Performance analysis of QAM in amplify-and-forward cooperative communication networks over Rayleigh fading channels

Performance analysis of quadrature amplitude modulation (QAM) schemes for cooperative amplify-and-forward (AF) dual-hop relaying system over independent and identically distributed (i.i.d.) Rayleigh fading channels are presented in this paper. Specifically, we derive closed-form lower-bound expressions of average symbol error rate (ASER) for general order rectangular QAM (RQAM) and cross QAM (XQAM) using well-known moment generating function (MGF) based approach with maximal ratio combining (MRC) scheme. Further, using best relay selection scheme (BRS), we also derive an ASER expression for XQAM. Numerical and simulated results are compared to validate the correctness of derived expressions. Furthermore, comparative analysis of RQAM and XQAM schemes is discussed which confirms that XQAM is better alternative over RQAM for transmission of odd number of bits per symbol for the considered system model. We also compare the ASER performance for MRC and BRS schemes in terms of SNR gain using different XQAM constellations. Moreover, the impact of system parameters on ASER is also highlighted.     

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.     

Average Error Performance of M-ary Modulation Schemes in Nakagami-q (Hoyt) Fading Channels

Presented are exact-form expressions for the average error performance of various coherent, differentially coherent, and noncoherent modulation schemes in Nakagami-q (Hoyt) fading channels. The expressions are given in terms of the Lauricella hypergeometric function, F_D ⁽ⁿ⁾; for nges1, which can be evaluated numerically using its integral or converging series representation. It is shown that the derived expressions reduce to some existing results for Rayleigh fading as special cases     

Probability of error analysis of digital partial responsecontinuous phase modulation with noncoherent detection in mobile radiochannels

An analysis is presented of noncoherent detection of constant-envelope digital partial-response continuous-phase modulation (PRCPM) in fast Rayleigh fading that characterizes land mobile radio channels. Closed-form expressions for the probability of error are derived for limiter discriminator detection, and both 1- and 2-bit differential detection. Numerical results are presented for cases of practical interest to researchers and designers of land mobile radio systems. The expressions derived for the probability of error are general and can be used for all PRCPM schemes     

Closed‐form solutions to SEP integrals over generalized fading distributions η−μ and κ−μ using approximate computing

The fading channels often involve complex expressions, when it comes to computing the integrals required for performance evaluation of various digital modulation schemes. In this paper, usefulness of exponential‐based approximations to the Gaussian‐Q function in computing these integrals is discussed. We present generic symbol error probability (SEP) expressions over η?μ and κ?μ fading distributions, which can be tailored for any digital modulation technique using different approximations. The resulting expressions thus obtained comprise only elementary mathematical functions thereby avoiding complex evaluations of hypergeometric functions. We explore all the exponential‐based approximations proposed till date and conclude that apart from being mathematically simple, they also lead to accurate expressions for performance analysis of various digital modulation schemes.     

不同调制方式下高斯信道容量的计算

计算不同调制方式下的信道容量对实际通信系统的信道编译码设计具有重要的理论意义。首先从Shannon信息论出发,介绍了平稳无记忆连续信道与加性白高斯噪声信道容量的定义。接着利用互信息与微分熵的相互关系,推导了几种常用的不同调制方式下高斯信道的容量,并给出了相应的信道容量闭合计算表达式。通过将电力卫星通信信道模拟为高斯信道,对采用无速率信道编码联合不同调制方式的卫星通信进行了数值仿真。仿真结果显示,通过推导得到的闭合表达式计算信道容量,能对实际卫星通信的编码速率、译码启动条件的确定起到很好的理论指导作用。     

On the Error Performance of <Emphasis Type="Italic">M</Emphasis>-ary Modulation Schemes on Rician–Nakagami Fading Channels

This paper presents exact expressions for the average error performance of various M-ary modulation schemes over Rician–Nakagami fading channels. The expressions for average symbol error probability (SEP) are given in terms of Lauricella’s multivariate hypergeometric function, which can be evaluated numerically using its integral or converging series representation. Furthermore, we show that the derived expressions include some previously published results for Rayleigh fading as special cases.     

瑞利衰落信道下DCSK系统性能分析

差分混沌键控(DCSK)是一种非相干调制技术,其输出信号具有固有的宽频特性。在各种混沌键控数字调制方案中,DCSK调制有着最优的抗噪声性能。文中在文献[4]的基础上,进一步分析了DCSK在瑞利衰落信道下的系统性能,推导出误码率公式,并通过计算机仿真实验验证了该理论分析的正确性。