Switched diversity on microcellular Ricean channels

The performances of switched dual diversity systems operating on independent and correlated Ricean fading channels are analyzed using a discrete time model. The average bit error rate (BER) of the discrete time switched diversity system using binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Ricean fading channels is derived. A closed form expression that gives the optimum switching threshold in a minimum error rate sense is derived for the case of independent branch signals. Results for the optimum switching threshold for the case of correlated branch signals, obtained numerically, are also presented. Results using selection diversity combining are obtained for comparison. The effects of fading severity on both the BER and on the optimum switching threshold are investigated. The Ricean fading model may be used to model both the microcellular radio environment and the mobile satellite fading channel. Hence, the results of the paper are useful for both of these areas     

Variable‐rate adaptive modulation with optimum switching thresholds for cooperative systems with relay selection

In this paper, the performance of variable‐rate adaptive modulation schemes in the amplify‐and‐forward cooperative systems with relay selection is analyzed over Rayleigh fading channels. We consider constant power and discrete‐rate adaptive multi‐level modulation techniques. The switching levels required for discrete‐rate adaptive modulation have been determined for two schemes, namely fixed switching levels and optimum switching levels, both respecting a target bit error rate requirements, where in the later scheme, the switching levels are optimally determined in a way that the average spectral efficiency of the system is maximized. Two M‐ary modulation schemes, namely quadrature amplitude modulation and phase shift keying, are considered. Closed‐form expressions are derived for three performance metrics, namely average spectral efficiency, outage probability, and average bit error rate, for two cases: independent and identically distributed fading relay links and independent and non‐identically distributed links. It is shown that, compared with using fixed switching levels, employing optimum switching levels provides a slight improvement in the spectral efficiency and moderate improvements in the signal‐to‐noise ratio gain and in the outage probability of the system. It is also shown that compared with the independent and identically distributed links, independent and non‐identically distributed relay links yield a slight increase in the signal‐to‐noise ratio gain and a slight decrease in the diversity order of the system. Copyright © 2011 John Wiley & Sons, Ltd.     

Unified analysis of switched diversity systems in independent andcorrelated fading channels

The moment generating function (MGF) of the signal power at the output of dual-branch switch-and-stay selection diversity (SSD) combiners is derived. The first-order derivative of the MGF with respect to the switching threshold is also derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The MGF yields the performance (bit or symbol error probability) of a broad class of coherent, differentially coherent and noncoherent digital modulation formats with SSD reception. The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases. For independent and identically distributed diversity branches, the optimal switching threshold in closed form is derived for three generic forms of the conditional error probability. For correlated Rayleigh or Nakagami-m fading with identical branches, the optimal switching threshold in closed form is derived for the noncoherent binary modulation formats. We show previously published results as special cases of our unified expression. Selected numerical examples are presented and discussed     

Performance analysis of dual switched diversity over correlated Weibull fading channels with co‐channel interference

This paper studies the performance of switch and stay combining (SSC) diversity in the presence of co‐channel interference over correlated Weibull fading channels. SSC diversity based on signal‐to‐interference ratio (SIR) is a low‐complexity and a very efficient technique that reduces fading and co‐channel interference influence. New closed‐form expressions for the probability density function and cumulative distribution function of the output SIR's are derived. These formulas are used in a detailed analysis of the average output SIR and outage probability. The influence of fading severity and correlation coefficient on the optimum switching threshold and system performance is investigated. Monte Carlo simulations are performed to verify obtained theoretical results and determine average bit error rate in detecting binary phase‐shift keying (BPSK), differential BPSK and quadrature amplitude modulation signals. Copyright © 2011 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.     

Analysis of switched diversity TCM-MPSK systems on Nakagami fadingchannels

Space diversity reception and forward-error correction coding are powerful techniques to combat multipath fading encountered in mobile radio communications. In this paper, we analyze the performance of a discrete-time switched diversity system using trellis-coded modulation multiple phase-shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami (1960) fading channels. Analytical upper bounds using the transfer function bounding technique are obtained and illustrated by several numerical examples. A simple integral expression for calculating the exact pairwise error probability is presented. The use of optimum adaptive and fixed switching thresholds is considered. Monte Carlo simulation results, which are more indicative of the exact system performance, are also given     

Closed‐form analysis of multibranch switched diversity with noncoherent and differentially coherent detection

Exact closed‐form analytical expressions are derived for the average bit error probability of multibranch switched diversity systems over independent and identically Nakagami‐m distributed fading channels. Practical schemes that use noncoherent or differentially coherent symbol detection are considered. The general bit error probability expression derived in this paper includes as particular cases the following signaling formats: orthogonal binary signaling, correlated binary signaling, differential phase‐shift keying, and differential quadrature phase‐shift keying. Finally, we apply our analytical results to study the impact of the switching threshold selection on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of switched diversity systems on generalized-fadingchannels

The performances of switched diversity systems operating on generalized (Nakagami)-fading channels are analyzed using a discrete-time model. The average bit error rate (BER) of binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Nakagami-fading channels is derived. Closed-form expressions that can be used to determine optimum switching thresholds (in a minimum error rate sense) are also derived. In addition, the use of optimum fixed thresholds is considered. It is found that a considerable amount of diversity gain can be obtained using an optimum fixed (rather than adaptive) switching threshold. Results are obtained for both independent and correlated Nakagami-fading branch signals. The effects of fading severity and the correlation coefficient on both the BER and on the optimum switching threshold are investigated. It is shown that useful diversity gain can be obtained with power correlation coefficients as high as 0.9 when the fading is strong. The results for a Rayleigh channel are obtained and presented as a special case of generalized-fading model     

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

Closed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

自适应调制的最优调制模式转换

根据信道条件采用自适应调制技术是解决衰落问题的有效手段,同时也可以有效提高误比特率性能或平均吞吐量.本文在无线衰落信道条件下采用方形正交振幅调制方式,以一般的恒功率自适应调制模型为基础,推导出了平均误比特率和平均吞吐量的一种近似的表述形式,并在平均误比特率的约束条件下,为了获得最大可能的吞吐量,利用Lagrangian最优化方法得出了调制模式的最佳转换等级,且通过仿真表明,采用了这种最佳转换等级模式的自适应调制方式,在保持恒定的平均误比特率的条件下表现出了优越的性能.     

Diversity combining for coherent and differential M-PSK in fading and class-A impulsive noise

In this paper, optimum and suboptimum diversity combining schemes for coherent and differential M-ary phase-shift keying (M-PSK) transmission impaired by general Ricean fading and impulsive Class-A noise are derived and analyzed. The proposed suboptimum coherent combining (SCC) and suboptimum noncoherent combining (SNC) schemes yield similar performance as the corresponding optimum combining schemes but require a lower computational complexity. In addition, the novel SCC and SNC strategies achieve large performance gains over conventional maximum ratio combining (MRC) and equal gain combining (EGC), respectively. For MRC and EGC, respectively, we also provide a performance analysis for coherent and differential M-PSK transmissions over general Ricean fading channels with Class-A noise. Furthermore, tight performance upper bounds for the proposed optimum and suboptimum combining schemes are derived.     

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.     

Switched Dual Diversity Reception of M-ary DPSK Signals on Nakagami Fading Channels

The paper deals with dual diversity reception of M-ary differential phase-shift keying modulated signals in the presence of additive white Gaussian noise and Nakagami-distributed slow and nonselective fading. The performance of a switched diversity system is analysed and compared to that of the predetection selection diversity combining scheme. The general case of correlated diversity branches is considered, without restrictions on the fading severity parameter. Average symbol error rate formulas are analytically derived in terms of integral expressions that can be easily computed via numerical integration routines. Moreover, the numerical evaluation of the optimum switching threshold is carried out and the influence of the fading severity parameter, the branch correlation, and the cardinality of the symbol alphabet is analysed. Finally, three fixed switching threshold strategies that allow to obtain a satisfactory diversity gain are considered.     

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.     

采用两条支路分集接收的相关瑞利衰落信道容量

本文研究采用两条支路最大比合并(MRC)或选择合并(SC)分集接收的相关瑞利衰落信道理论容量推导恒定发射功率自适应M进制正交幅度调制(M-QAM)的频谱效率,并将它们与独立同分布瑞利信道理论容量进行比较,其结果对收发信机之间无视距分量路径、接收机上分集天线之间的距离小于半个波长的无线通信系统设计具有指导作用.     

Performance analysis of cooperative network over Nakagami and Rician fading channels

This paper presents an analysis on the performance of single‐relay and multiple fixed‐relay cooperative network. The relay nodes operate in amplify‐and‐forward (AF) mode and transmit the signal through orthogonal channels. We consider maximal‐ratio combining at the destination to get the spatial diversity by adding the received signals coherently. The closed‐form moment‐generating function (MGF) for the total equivalent signal‐to‐noise ratio (SNR) is derived. The exact expressions of symbol‐error rate, outage capacity, and outage probability are obtained using the closed‐form MGF for single‐relay and multiple‐relay cooperative network with M‐ary phase shift keying (M‐PSK) and M‐ary quadrature amplitude modulation (M‐QAM) over independent and non‐identical Nakagami‐m channels and Rician fading channels. The approximated closed‐form expression of ergodic capacity is derived for both Nakagami‐m and Rician fading channels. The performance of the system is analyzed at various relay locations. The theoretical results are then compared with the simulation results obtained for binary PSK, quadrature PSK, and 16‐QAM modulation schemes to verify the analysis. Here, the expressions derived can be easily and more efficiently used to compute the performance parameters than doing Monte Carlo simulations. It is shown that cooperation is significant only for low K values for Rician by plotting cooperation gain versus K. The results show that the cooperative network performs best when the relay is located in the middle of source to destination link, at lower SNR values, and the performance of the system is worst if the relay is located closer to the source than to the destination. Copyright © 2013 John Wiley & Sons, Ltd.     

Reference-based dual switch and stay diversity systems over correlated Nakagami fading channels

We provide new generic and exact analytical results for the performance of nonideal reference-based dual predetection switch and stay diversity systems in receiving M-ary digitally modulated signals in the presence of additive white Gaussian noise and correlated slow and nonselective Nakagami-m fading channels. Pilot-tone-aided, pilot-symbol-aided, and differential detection (DD) reference-based systems are considered. The impact of symbol alphabet cardinality, normalized distance between antennas, fading severity, and normalized Doppler frequency on the performance of these systems is analyzed. Optimum switching threshold and optimum pilot-to-signal power ratio as a function of channel fading characteristics, normalized distance between antennas, and modulation type are determined. Furthermore, some fixed switching strategies - minimum cost strategy, fixed average strategy, and midpoint strategy - that allow one to obtain diversity gain with a reduced complexity receiver are considered.     

Performance analysis of joint switched diversity and adaptive modulation

In this paper, a simple and practical system based on a switched diversity scheme with adaptive modulation is presented. This system provides a reduced number of channel estimation while offering the optimum spectral efficiency given by a selection diversity system. In addition, the switching threshold is easily manipulated so as to make an efficient use of the tradeoff between spectral efficiency and channel estimation overhead. An extension of switched diversity into a multiuser scheduling is later also considered. This switch-based multiuser access scheme results in a lower average feedback load than that for the optimal selection-based multiuser scheme. Numerical results show that we can obtain a trade-off between spectral efficiency and the feedback load by choosing the switching threshold appropriately.     

Linear Diversity Analysis for M‐ary Square Quadrature Amplitude Modulation over Nakagami Fading Channels

We derive and analyze the exact closed‐form expression for the average bit error probability (BEP) of M‐ary square quadrature amplitude modulation (QAM) for diversity reception in frequency‐nonselective Nakagami fading. A maximal ratio combining (MRC) diversity technique with independent or correlated fading cases are considered. Numerical results demonstrate error performance improvement with the use of MRC diversity reception. The presented new expressions offer a convenient way to evaluate the performance of M‐ary square QAM with an MRC diversity combiner for various cases of practical interest.