On the bit error probability of QAM modulation

This paper presents some closed-form bit error probability expressions for coherent demodulation of both Gray coded and differentially decoded Gray coded QAM modulations in nonfading and frequency nonselective Rayleigh fading channels. These results demonstrate that as QAM constellation sizes get larger the BEP degradation due to differential encoding and decoding becomes negligible.     

A Moment-Generating Function (MGF) Derivative-Based Unified Analysis of Incoherent Diversity Reception of M-ary Orthogonal Signals over Independent and Correlated Fading Channels

Exact, closed-form, error probability expressions for noncoherent M-ary frequency-shift-keying (MFSK) systems that employ postdetection equal-gain diversity over Rayleigh, Rician, and Nakagami-m channels are derived using a Laplace derivative formula. Both independent and generically correlated fading cases are considered. For independent fading, closed-form solutions are also derived for both Nakagami-q fading (either with identical or dissimilar fading statistics) and mixed fading cases. Previous results are shown to be specific instances of our general expressions. In addition, a concise, derivative formula is derived for calculating the bit error rate of square-law detected multichannel binary differential phase-shift-keying (DPSK) signals. All of these expressions are applicable in many cases of practical interest and provide accurate predictions of the performance of both binary and M-ary orthogonal signaling over generalized fading channels with arbitrary parameters.     

Performance analysis of dual selection diversity in correlated Weibull fading channels

Ascertaining the importance of the dual selection combining (SC) receivers and the suitability of the Weibull model to describe mobile fading channels, we study the performance of a dual SC receiver over correlated Weibull fading channels with arbitrary parameters. Exact closed-form expressions are derived for the probability density function, the cumulative distribution function, and the moments of the output signal-to-noise ratio (SNR). Important performance criteria, such as average output SNR, amount of fading, outage probability, and average bit-error probability for several modulation schemes are studied. Furthermore, for these performance criteria, novel closed-form analytical expressions are derived. The proposed analysis is complemented by various performance evaluation results, including the effects of the input SNR's unbalancing, fading severity, and fading correlation on the overall system's performance. Computer simulation results have verified the validity and accuracy of the proposed analysis.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

Closed-form expressions for outage probability of decode-and-forward relaying over Nakagami-m fading channels

In this article, an exact closed-form expression is derived for outage probability of decode-and-forward (DF) cooperative communications over independent identically distributed Nakagami-m fading channels. Simulation results verify that the theoretical expressions for the outage probability are correct. The optimal power allocation based on the derived outage probability is also studied.     

Outage Probability and Average Channel Capacity of Amplify-and-Forward in Conventional Cooperative Communication Networks over Rayleigh Fading Channels

Performance of conventional cooperative communication networks using amplify-and-forward relay over independent and identically distributed Rayleigh fading channels is investigated in this paper. An expression for probability density function by using moment generating function is obtained. Further closed-form expressions of the outage probability and the average channel capacity are derived. The derived analytical results are compared with Monte Carlo simulations to confirm correctness of the derived expressions.     

Switched diversity receivers over generalized gamma fading channels

A versatile envelope distribution which generalizes several commonly used fading models is the generalized Gamma (GG) distribution. This letter deals with the performance analysis of switch and stay combining (SSC) receivers operating over not necessarily identical GG fading channels. For these receivers, novel analytical expressions for the moments of the output signal-to-noise ratio (SNR) (including average SNR and amount of fading), outage probability, average bit error probability (ABEP), and Shannon average spectral efficiency (ASE) are derived. Moreover, closed-form expressions are obtained for the optimal average SNR, ABEP, and ASE switching thresholds. Special cases of the derived expressions agree with known results.     

On the performance of selection decode-and-forward relay networks over Nakagami-m fading channels

In this paper, we present the performance of fixed decode-and-forward cooperative networks with relay selection over independent but not identically distributed Nakagamim fading channels, with integer values of the fading severity parameter m. Specifically, closed-form expressions for the symbol error probability and the outage probability are derived using the statistical characteristic of the signal-to-noise ratio. We also perform Monte-Carlo simulations to verify the analytical results.     

Linear diversity analyses for M-PSK in Rician fading channels

Symbol and bit error rates of M-ary differentially encoded/differentially decoded phase-shift keying (MDPSK) and coherent M-ary phase-shift keying (M-PSK) over slow, flat, Rician fading channels are derived when linear diversity combining is applied to combat degradation due to fading. These closed-form solutions are general enough to cover several cases of nondiversity, additive white Gaussian noise (the nonfading mode), Rayleigh fading, mixtures of Rayleigh and Rician fading (the mixed mode), and Rician fading. The results presented here can also be applied to predict the error-rate performance when recent transmit diversity techniques are employed. The solutions for the nonuniform fading profile are included as well. Error probabilities are graphically displayed for both modulation schemes.     

Error probability with incoherent diversity reception of FSKsignals transmitted over fast Rician fading channels

We compute the error performance of noncoherent detection receivers for FSK signals transmitted over fast frequency-flat Rician fading channels. Linearly time-varying fading models are used to derive closed-form expressions for the error probability of binary FSK signaling. Error bounds are established for the performance of M-ary orthogonal FSK. Simulation results are in excellent agreement with analytical predictions     

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.     

Performance analysis of spectrum sensing techniques over TWDP fading channels for CR based IoTs

In this paper, the performance of spectrum sensing techniques over two wave diffused power (TWDP) fading channels has been investigated for CR based IoT devices. The ubiquitous objects based on IoTs with cognitive capabilities are the future that would enable intelligent decisions to achieve any time, any place, interference-free and on-demand services. In this work, new closed-form expressions in terms of Marcum-Q function and Whittaker function for the spectrum detection probability over TWDP fading channels have been derived for different sensing techniques. The expressions are then used to optimize the decision threshold for IoT sensor nodes describing the optimal behavior of sensing over TWDP channels. The error probabability and Receiver Operating Characteristic (ROC) curves have been plotted and the operating point and limiting values of threshold for optimal performance have been identified. The performance loss of traditional energy detection (ED), cyclostationary based detection (CSD) and matched filtering detector (MFD) has been analyzed. The analytical results thus obtained are validated through monte-carlo simulations.     

混合衰落信道下选择中继译码转发的性能分析

蜂窝中继通信中基站到中继以及中继到移动台可以建模成混合衰落信道,即基站到中继的信道通常经历莱斯衰落,中继到移动台的信道通常经历瑞利衰落。该文研究混合衰落信道下协同通信系统中两跳译码转发方式的性能,首先通过分析推导了基于选择最佳中继的中断概率、误符号率以及误符号率的渐近线的闭式表达式,然后基于误符号率的渐近线给出了一种功率优化方法。蒙特卡洛仿真验证了理论公式,仿真结果显示优化功率分配的性能优于平均功率分配的性能。     

Performance analysis of mobile radio systems over composite fading/shadowing channels with co-located interference

This paper presents an analytical framework for performance evaluation of mobile radio systems operating in composite fading/shadowing channels in the presence of colocated co-channel interference. The desired user and the interferers are subject to Nakagami fading superimposed on gamma shadowing. The paper starts by presenting generic closed-form expressions for the signal-to-interference ratio (SIR) probability density function (pdf). From this pdf, closed-form expressions for the outage probability, the average bit error rate and the channel capacity are obtained in both cases of statistically identical interferers and multiple interferers with different parameters. The newly derived closed-form expressions of the aforementioned metrics allow us to easily assess the effects of the different channel and interference parameters. It turns out that the system performance metrics are predominantly affected by the fading parameters of the desired user, rather than by the fading parameters of the interferers.     

Some new results for integrals involving the generalized Marcum Q function and their application to performance evaluation over fading channels

This letter evaluates some new integrals whose integrand involves the generalized Marcum Q function, both of whose arguments are linear functions of the integration variable. The resulting closed-form expressions obtained for these integrals are then applied to the error probability evaluation of noncoherent and differentially coherent detection with postdetection equal gain combining over Rayleigh and Nakagami fading channels.     

Capacity of correlated nakagami-m fading channels with diversity combining techniques

We derive closed-form expressions for the capacity of dual-branch maximal ratio combining, equal gain combining, selection combining, and switch and stay combining (SSC) diversity systems over correlated Nakagami-m fading channels. Because the final capacity expressions contain infinite series, we truncate the series and present upper bounds on the truncation errors. We also derive an expression that can be used to numerically determine the optimum adaptive switching threshold for the capacity of a dual-branch SSC system over correlated Nakagami-m fading channels. However, a closed-form expression for the optimum adaptive switching threshold is derived for the case of independent branches. The corresponding expressions for Rayleigh fading are obtained as a special case of Nakagami-m fading. Finally, numerical examples are presented for illustration.     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

Secrecy Trade-off at the Physical Layer over Mixed Fading Multicast Channels Employing Antenna Diversity

This paper deals with the secrecy performance analysis of a multicast network over mixed fading scenarios in which a cluster of passive eavesdroppers is trying to overhear the secret transmission. Our key contribution is to prevent this malicious attack of the illegitimate receivers. Rayleigh/ Rician mixed fading channels are considered to model alternately the multicast/ eavesdropper and eavesdropper/ multicast channels as such mixed fading scenarios are often encountered in cellular communication where only one link (either multicast or eavesdropper) undergo a line-of-sight propagation path. At first, we derive the probability density functions for the single-input-multiple-output multicast scenarios and then the secrecy analysis is carried out by obtaining closed-form expressions for the performance matrices such as the probability of non-zero secrecy multicast capacity, ergodic secrecy multicast capacity, and secure outage probability for multicasting. The derived expressions are beneficial to investigate how the antenna diversity can combat the detrimental impact of fading as well as the number of multicast users and eavesdroppers, and improve the secrecy level to the acceptable limit. Moreover, the best secure scenario in terms of the secrecy parameters is obtained when the multicast channels undergo Rician fading whereas the eavesdropper channels experience Rayleigh fading. Finally, the analytical expressions are justified via the Monte-Carlo simulations.

     

Turbo 码在无信道状态信息的Nakagami 衰落信道中的性能分析

讨论了Turbo码在无法获取信道状态信息的移动通信系统中的纠错性能联合上界，提出无信道状态信息时，Nakagami慢衰落信道中成对差错概率的2个精确计算式和2个近似计算式。数值分析结果表明，成对差错概率的2个精确计算式的数值积分曲线完全吻合；封闭形式近似计算式的计算结果与精确值相近。仿真结果说明，理论联合上界在高信噪比处逼近仿真性能。所提出的性能分析式可快速有效地评估无信道状态信息的移动通信系统中Turbo码的性能。     

Effect of Channel Estimation Error on Bit Error Probability in OFDM Systems over Rayleigh and Ricean Fading Channels

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.