Performance analysis of system with L‐branch selection combining over correlated Weibull fading channels in the presence of cochannel interference

In this paper, the performance of L‐branch selection combining receiver over correlated Weibull fading channels in the presence of correlated Weibull‐distributed cochannel interference is analyzed. Closed‐form expressions for probability density function and cumulative distribution function of the signal‐to‐interference ratio at the output of the selection combining receiver present main contribution of this paper. Numerical results are also presented to show the effects of various parameters as the fading severity, correlation and number of branches on outage probability. Copyright © 2009 John Wiley & Sons, Ltd.     

Performance analysis of system with selection combining over correlated Weibull fading channels in the presence of cochannel interference

Selection diversity based on the signal to interference ratio (SIR) is a very efficient technique that reduces fading and channel interference influence. In this paper, system performances of selection combining and correlated Weibull channels are analyzed. Fading between the diversity branches and between interferers is correlated and Weibull distributed. Very useful closed-form expressions are obtained for the output SIR's probability density function (PDF) and cumulative distribution function which is main contribution of this paper. Outage probability, the average output SIR, and the average error probability for coherent, noncoherent modulation are derived. Numerical results presented in this paper point out the effects of fading severity and correlation on the system performances.     

Enhanced switch combining for spatial diversity with a switch window over correlated Nakagami‐m fading channels

On the basis of a mixture of the selection combining and switch‐and‐stay combining schemes, the enhanced switch combining (ESC) scheme is proposed for antenna diversity over multiple correlated Nakagami‐m fading channels, where a switch window with upper and lower switch thresholds are used. Compared with the existing select‐and‐stay combining or switch with post‐examining, the ESC scheme reduces simultaneous multiantenna observations and hence saves processing time and energy from multibranch observations, while achieving matched receiver performance. Thus, ESC also has better performance than switch‐and‐examine combining (SEC). To assess the reduction of simultaneous observations, a dual‐observation rate is defined. Moreover, the ESC unifies some well‐known switch‐based combining schemes (for example selection combining, switch‐and‐stay combining, or SEC) in the sense that, by adjusting switch thresholds, these combining schemes become different special cases of ESC. The CDF, PDF, and moment generating function of the combined signal‐to‐noise ratio for ESC are derived for general fading channels. Then, the outage probability and the average BER of different binary modulations over correlated Nakagami‐m fading channels are evaluated. Numerical results from analysis and simulation are presented to demonstrate ESC performance. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance of generalized selection combining over Weibull fading channels

The literature is relatively sparse in performance analysis of diversity combining schemes over Weibull fading channels, despite the fact that the Weibull distribution is often found to be suitably fit for empirical fading channel measurements. In this paper, we capitalize on some interesting results due to Lieblein on the order statistics of Weibull random variables to derive exact closed‐form expressions for the combined average signal‐to‐noise ratio (SNR) as well as amount of fading (AF) at a generalized selection combining (GSC) output over Weibull fading channels. We also use some simple AF‐based mappings between the fading parameters of the Weibull distribution and those of the Nakagami, Rice, and Hoyt distributions to obtain the approximate but accurate average SNR and AF of GSC over these types of channels. The mathematical equations are validated and illustrated by some numerical examples for scenarios of practical interest. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance analysis of switch‐and‐examine diversity systems with interference and Rayleigh fading channels

This paper studies the behavior of the low‐complexity switch‐and‐examine diversity combining (SEC) and switch‐and‐examine diversity combining with post‐examine selection (SECps) antenna selection schemes with interference. In this paper, we first derive the cumulative distribution function (CDF) of the end‐to‐end (e2e) signal‐to‐interference plus noise ratio at the selection scheme combiner output. This CDF is then used to derive closed‐form expressions for the e2e outage and symbol error probabilities for the independent nonidentically distributed and independent identically distributed cases of diversity branches. In the analysis, the channels of the desired user and the interferers are assumed to follow Rayleigh distribution. Furthermore, to have more details about the system insights, the performance is evaluated at the high signal‐to‐noise ratio (SNR) values where the diversity order and coding gain are derived and analyzed. The derived analytical and asymptotic results are validated via a comparison with Monte‐Carlo simulations. Main findings show that with interference power does not scale with average SNR; the system can still achieve performance gain when more receive antennas are used. This happens at the values of switching threshold that are close to average SNR. Also, results illustrate that the interference is noticeably affecting the gain achieved in system performance when more antennas are used. Furthermore, findings show that the SECps selection scheme outperforms the conventional SEC scheme when more antennas are added with the switching threshold is much larger than the average SNR. Finally, findings show that the SEC and SECps antenna selection schemes are efficient for systems which operate at the range of low SNR values and this makes them attractive candidates to be implemented in the emerging mobile broadband communication systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Unified analysis of EGC diversity over Weibull fading channels

In this paper, the performance analysis based on PDF approach of an L ‐branch equal gain combiner (EGC) over independent and not necessarily identical Weibull fading channels is presented. Several closed‐form approximate expressions are derived in terms of only one Fox H‐function as PDF, cumulative distribution function, and moments of the EGC output Signal‐to‐noise ratio (SNR), outage probability, amount of fading, channel capacity, and the average symbol error rate for various digital modulation schemes. All results are illustrated and verified by simulations using computer algebra systems.     

Capacity of MIMO channels in the presence of co‐channel interference

This paper presents analytical results on the capacity of multiple‐input‐multiple‐output (MIMO) fading channels in the presence of co‐channel interference (CCI). We consider the scenario in which the desired and CCI users are all subject to Rayleigh fading. We assume that channel realizations of both the desired and CCI users are known at the receiver. Moreover, we consider the case where the transmitter does not have any CSI and as such equal‐power allocation among transmit antennas is used. Given this setup, we derive the moment generating function (MGF) and the mean of the mutual information (MI). We then study the complementary cumulative distribution function of the MI using a Gaussian approximation. Finally, we present and discuss numerical examples to illustrate the mathematical formalism and to show the effect of various parameters on the capacity of MIMO channels in the presence of CCI. Copyright © 2006 John Wiley & Sons, Ltd.     

OFDM-MQAM在相关Nakagami-m衰落信道上的性能分析

本文研究频率选择性相关Nakagami衰落信道上采用最大比合并(MRC)分集接收的正交频分多路复用M进制正交幅度调制(OFDM-MQAM)系统.使用矩生成函数(MGF)方法和高斯超几何函数、Appell超几何函数或Lauricella函数,推导任意衰落参数频率选择性相关Nakagami衰落信道上MRC分集接收的OFDM-MQAM系统的误符号率(SER)性能,获得了OFDM-MQAM误符号率的一个新的解析表达式.数值计算结果阐明了多径路径数、Nakagami衰落参数和信道脉冲响应抽头间的相关系数对OFDM-MQAM误符号率性能的影响.     

Switching rate and receiver performance of binary modulations with the selection‐and‐stay combining over independent and correlated Nakagami‐m fading channels

The dual‐branch selection‐and‐stay combining (SSTC) is analyzed for diversity reception on independent and correlated Nakagami‐m fading channels, where the conventional selection combining (SC) is employed only at the switching instance, and the receiver uses the selected branch till its signal‐to‐noise ratio (SNR) estimation is lower than a preset threshold. In this combining scheme, the receiver only needs to continuously estimate the SNR of the single selected branch. For the performance analysis of SSTC, the switching rate and the average bit error rates (BERs) of different binary coherent and non‐coherent modulations are evaluated. Numerical results based on the analysis and simulations are illustrated. According to the analysis and numerical results, the SSTC outperforms the existing switch‐and‐stay combining in the senses of the average BER and switching rate. Copyright © 2011 John Wiley & Sons, Ltd.     

Switch‐and‐examine combining with different new switch statistics for diversity over Rayleigh fading channels

Three schemes of multibranch switch‐and‐examine combining (MSEC) with switch statistics different from the signal‐to‐noise ratio used in the traditional MSEC are analyzed. For each diversity branch, with its fading factor a and low‐passed received signal r, the switch statistics for the three MSEC schemes considered in the paper are | r | , | ar | , and a linear combination of a and | r | , respectively. To illustrate the performances of the MSEC schemes, the average BER of each MSEC scheme with BPSK signaling is evaluated for independent and identically distributed Rayleigh fading channels. For performance optimization, the optimal switch thresholds of the MSEC schemes are obtained. Numerical results based on the analysis and simulations are presented for performance illustrations. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance and diversity analysis of decode‐and‐forward cooperative system over Nakagami‐m fading channels

In this paper, we derive the upper bound of bit‐error rate (BER) performance and diversity gain for a decode‐and‐forward (DF) cooperative system. Either maximal‐ratio combining (MRC) or cooperative MRC (C‐MRC) is employed at the receiver in the presence of independent, non‐identical Nakagami‐m fading. Both analytical and simulation results show that C‐MRC takes advantage of spatial diversity more efficiently and thus achieves the same or better performance and diversity order as compared to MRC. Copyright © 2009 John Wiley & Sons, Ltd.     

Unified BER and optimum threshold analysis of binary modulations in simple and cascaded Rayleigh fading channels with switched combining

Following a unified analytical framework, the bit error rate (BER) of several coherent and non‐coherent binary modulation schemes is derived for a switched diversity system. The two variants of switched combining that have been investigated are switch and stay combining and switch and examine combining. For channel modelling, at first a simple slow flat fading channel is assumed, where the amplitude attenuation obeys the Rayleigh distribution. Later the BER calculations are repeated for cascaded Rayleigh fading channel case. Rayleigh fading is the most popular model for electromagnetic signal propagation in wireless media when both or either of the transmitter/receiver is fixed. On the other hand, when both the transmitter and the receiver are mobile, a cascaded (or double) Rayleigh fading model is better suited. The applicability of these two models, namely simple and cascaded Rayleigh model, has been indicated by several theoretical studies and their suitability is established by various field measurements. In our paper, simple closed‐form BER expressions as a function of switching threshold have been found and optimum switching thresholds have been computed for both these models as well as for both types of diversity combining described earlier. The results presented in this paper can be very useful for communication system designers to analyze link quality of switched diversity assisted systems in various wireless environments. Copyright © 2010 John Wiley & Sons, Ltd.     

Comments on “Average LCR and AFD for SC diversity over correlated Weibull fading channels”

In a recent paper, two formulae for the average level crossing rate and fade duration at the output of dual-branch selection diversity receivers have been derived. In this short communication, some previously published works including results being in a more general setting are reviewed and compared.     

Performance analysis of multiple-antenna cooperative networks under Weibull fading

In wireless communications, cooperative relaying is well-known to enhance the overall system performance, but implementation and cost constraints stand against its wide deployment. This paper investigates the performance of cooperative relays with and without multiple antennas under independent and identically distributed (i.i.d.) Weibull faded channels in a two-hop wireless network. We consider the Weibull fading channel model due to its flexibility in describing the radio propagation environment more than the classical Rayleigh model. Our study relies on applying selection combining (SC) along with threshold decode and forward (TDF) protocol at the cooperative relays as a good compromise between cost and performance. In addition, maximal ratio combining (MRC) is used at the destination. We derive analytical expressions for the end-to-end (E2E) error performance of the network under such scenario and provide simulation results to confirm the validity of the obtained analytical expressions.     

BER performance of MQAM with L‐branch MRC diversity reception over correlated Nakagami‐m fading channels

Exact and closed form generalized expressions for bit error rate (BER) of M‐ary quadrature amplitude modulation (MQAM) with L‐branch maximal ratio combining (MRC) space diversity reception in fading channels are derived and analyzed. The fading channels are modeled as identical but correlated frequency‐nonselective slow Nakagami‐m fading channels corrupted by additive white Gaussian noise (AWGN). Analytical results obtained are in terms of few finite range integrals with an integrand composed of elementary functions. Because of their simple form, these analytical results readily allow numerical evaluation in cases of practical interest. The results are also general enough to include Nakagami‐m fading channels with and without correlation, no diversity system, Rayleigh fading channels with and without correlation, and AWGN as special cases. The numerical results for the case of 16QAM are shown graphically and also in tabular form in order to examine the effects of fading severity, order of diversity, and branch correlation on the BER performance. The two correlation models considered are constant correlation model and exponential correlation model. One may be interested to know how the BER of MQAM is related to symbol error rate (SER) of MQAM. Therefore, the BER results obtained in this paper are also compared with that obtained directly from the SER. It is expected that the analytical results presented in this paper will provide a convenient tool for design and analysis of a radio communication system with space diversity reception in uncorrelated and correlated fading environment. Copyright © 2002 John Wiley & Sons, Ltd.     

Performance evaluation of generalized selection diversity systems over Nakagami‐m fading channels

The generalized selection combining (GSC) scheme that adaptively combines a subset of M strongest paths out of L available diversity paths finds applications in several wideband receivers and broadband wireless communications. In this paper, exact closed‐form expressions for the moment generating function (MGF), the probability density function (PDF) and the cumulative density function (CDF) of the GSC(M, L) output signal‐to‐noise ratio (SNR) in independent and identically distributed (i.i.d) Nakagami‐m fading channels are derived while the fading index is a positive integer. These expressions hold for any M and L and provide a comprehensive framework for performance analysis including the derivation of closed‐form formulas for the average symbol error probability (ASEP) of a broad class of binary and M‐ary modulations, mean combined SNR and the outage probability of GSC(M, L) receiver structures. When the Nakagami‐m fading index is not an integer, the MGF of GSC(M, L) output SNR is derived as an (M − 1)‐fold infinite series. With this MGF, analytical expressions for both the outage probability and error rates can be readily obtained. An easily programmable recursive solution of the MGF of GSC(M, L) output SNR is also outlined for both the positive integer and noninteger fading severity index cases. Copyright © 2002 John Wiley & Sons, Ltd.     

Statistical analysis of co‐channel interference in wireless communications systems

Co‐channel interference is recognized as one of the major factors that limits the capacity and link quality of a wireless communications system. An appropriate understanding of the statistical behavior of the co‐channel interference is therefore required when analyzing and designing techniques that mitigate its undesired effects. The total co‐channel interference in a wireless communications system is usually modeled as the sum of lognormally distributed signals, and is generally assumed to be itself lognormally distributed. Based on this assumption, several methods for estimating the moments of the resulting lognormal distribution have been proposed. The accuracy of these methods has been studied in previous works, under the assumption of having all summand signals (individual interference signals) identically distributed. Such an assumption rarely holds in practical cases of emerging wireless communications systems, where co‐channel interference may stem from far‐away macrocells and nearby transmitters, causing the interference signals to have different moments. In this paper we present an analysis of the accuracy of two popular methods for computing the moments of a sum of lognormal random variables, namely Wilkinson's method and Schwartz and Yeh's method, for the general case when the summands have different mean values and standard deviations in decibel units. We show that Schwartz and Yeh's method provides better accuracy than Wilkinson's method and is virtually invariant with the difference of the mean values and standard deviations of the summands. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

Adaptive modulation and combining for bandwidth and power efficient communication over fading channels

Traditional fading mitigation techniques are designed relative to the worst‐case channel conditions, resulting in a poor utilization of the spectrum and the available power a good percentage of the time. In contrast, we introduce and investigate in this paper new adaptive modulation and diversity combining techniques that jointly select the most appropriate constellation size and the most suitable diversity branches in response to the channel variation and given a desired bit error rate (BER) requirement. Numerical results show that these newly proposed adaptive modulation and combining schemes can reduce considerably the average receiver channel estimation complexity as well as the power drain from the battery while offering high spectral efficiency and satisfying the desired outage probability and BER requirements. Copyright © 2006 John Wiley & Sons, Ltd.     

A general moment generating function for MRC diversity over fading channels with Gaussian channel gains

For maximal ratio combining (MRC) diversity over correlated fading channels with Gaussian channel gains, we utilize unitary diagonalization of the channel covariance matrix to decorrelate the physical channels into uncorrelated virtual channels to obtain the moment generating function (MGF) of the received signal‐to‐noise ratio (SNR). The MGF thus obtained has a compact form and can be universally applied to various popular fading models. In addition to the advantage of simple derivation procedure, this general MGF can be readily modified to express various scenarios of channel power distributions as well as joint fading models. To demonstrate these advantages, we use the generalized Ricean fading as a specific example to compare our derivation and our MGF expression with an existing work in the literature. Again, we present numerical simulations for MRC reception of binary phase shift keying (BPSK) signals over Nakagami fading to compare with existing results appearing in the literature. Copyright © 2006 John Wiley & Sons, Ltd.