An MGF-based performance analysis of generalized selectioncombining over Rayleigh fading channels

Using the notion of the “spacing” between ordered exponential random variables, a performance analysis of the generalized selection combining (GSC) diversity scheme over Rayleigh fading channels is presented and compared with that of the conventional maximal-ratio combining and selection combining schemes. Starting with the moment generating function (MGF) of the GSC output signal-to-noise ratio (SNR), we derive closed-form expressions for the average combined SNR, outage probability, and average error probability of a wide variety of modulation schemes operating over independently, identically distributed (i.i.d.) diversity paths. Because of their simple form, these expressions readily allow numerical evaluation for cases of practical interest. The results are also extended to the case of non-i.i.d. diversity paths     

SNR of generalized diversity selection combining with nonidenticalRayleigh fading statistics

A closed-form expression for the average signal-to-noise-ratio (SNR) of generalized diversity selection combining, using the m largest (in instantaneous SNR) diversity signals, for arbitrary m, assuming that the Rayleigh fading statistics on each diversity branch are identically, independently distributed (i.i.d.), already exists in the literature. In this paper, a similar closed-form expression, but for nonidentically distributed statistics, is derived, This expression specializes to known results, such as the average SNRs of maximal-ratio combining with either i.i.d. or non-i.i.d. diversity statistics and that of conventional selection combining (CSC) with i.i.d. diversity statistics. In addition, it provides, for the first time, a simple closed-form solution to the combined SNR of CSC with non-i.i.d. diversity statistics. Further, the closed-form solution for the SNR of selecting the m, largest diversity signals has negligible computational complexity     

Blind multipath separation and combining technique for signal recovery

To achieve better mitigation of both cochannel interference (CCI) and intersymbol interference, a new structure using generalized estimation of multipath signals in conjunction with maximal-ratio combining diversity for wireless communications over multipath channels is introduced. In this structure, the signal replicas received from multiple paths are first independently produced by a bank of blind spatial filters and then constructively combined by a diversity combining receiver for final signal estimate. The new scheme can be applied on single antenna array or between multiple antenna subarrays. It will be shown, from both theoretical analysis and numerical experiments, that the new scheme provides both space diversity gains and path diversity gains while suppressing the CCIs.     

Performance Analysis of Generalized Sort, Switch, and Examine Combining

Examples of low-complexity diversity combining schemes are, among others, the generalized selection combining (GSC) scheme and the generalized switch-and-examine combining (GSEC). In this paper, we propose a new low-complexity combining scheme, termed generalized sort-switch-and-examine combining (GSSEC), that, in a sense, can be considered as a hybrid GSC/GSEC scheme. A generic expression for the moment-generating function of the GSSEC output SNR in general independent, identically distributed fading channels is derived, and is then applied to the analysis of its error performance     

Pre-DFT combining space diversity assisted COFDM

A new pre-discrete Fourier transformation (DFT) combining diversity receiver is proposed for coded orthogonal frequency-division multiplexing systems and investigated in a frequency-selective fading channel. Although the post-DFT combining space diversity receiver is optimum in terms of maximizing the signal-to-noise ratio (SNR) after combining, it requires an increased number of DFT processors, which increases the computational complexity. Since the proposed pre-DFT combining receiver requires only one DFT processor, while achieving space diversity gain, the proposed scheme can drastically reduce the computational complexity. This paper derives the optimum diversity weights for the proposed receiver analytically, in order to maximize the SNR after combining. Computer simulation results show that the proposed scheme can reduce the computational complexity by tolerating a slight performance degradation     

分布反馈和外腔的双波长运转

通过分布反馈和外腔的联合运转,获得了独立调谐的双波长激光,并研究了两个振荡的模式竞争与相对起振时间的关系.     

Selection of diversity and modulation parameters for Nakagami fading channels to jointly satisfy outage and bit error requirements

Outage events occur when the instantaneous signal-to-noise ratio or bit error rate fall into an unacceptable operational regime. Outage performance analysis is traditionally carried out for diverse channel behaviors and transmission techniques, leaving the identification of unacceptable operational regime to user specified performance requirements. An alternative approach is taken in this work and an acceptable combination of system parameters are identified such that the user specified quality of service (QoS) constraints are satisfied. The QoS constraints are specified jointly in terms of outage probability, outage duration and probability of occurrence of errors during the outage event. This work presents inter-dependencies between the QoS constraints and modulation, diversity and signal parameters in closed form. The analysis assumes identically, independently distributed Nakagami interferers using maximal ratio diversity combining (MRC).     

End-to-end SER of MRT/MRC and SC in multi-hop wireless sensor networks

The purpose of this study is to express analytically the end-to-end (e2e) symbol error rate (SER) in multi-hop decode-and-forward relaying in wireless sensor networks. These may occur in independently distributed cascaded Nakagami-m fading channels that may or may not be identical. In this study, all sensor terminals show mobility and this study is possibly the first one that undertakes performance analysis of maximal ratio transmission/maximum ratio combining and selection combining diversity that enables a better system performance in a multi-hop wireless sensor transmission system. In this paper, the first step undertaken was to generate a closed-form expression of the probability distribution function (PDF), the cumulative distribution function, and the moment-generating function for the system being examined. This discovery helped in the evaluation of the eventual performance of the system as far as e2e SER is concerned. It also helped in determining the upper limits of SER expressions for high signal-to-noise ratios. In the next phase, the intended system was utilized in an accurate approximation of the PDF of the cascaded Rayleigh fading channels to compare the findings acquired thus with those derived by its use in the actual PDF of the cascaded Rayleigh fading channels. These analytical findings were then validated with the help of Monte-Carlo simulations.

     

Performance analysis of multibranch switched diversity systems

We investigate the performance of multibranch switched diversity systems. Specifically, we first derive generic formulas for the cumulative distribution function, probability density function, and moment-generating function of the combined signal power for both switch-and-stay combining (SSC) and switch-and-examine combining (SEC) schemes. We then capitalize on these expressions to obtain closed-form expressions for the outage probability and average error rate for various practical communication scenarios of interest. As a byproduct of our analysis we prove that for SSC with identically distributed and uniformly correlated branches, increasing the number of branches to more than two does not improve the performance, but the performance can be different in the case the branches are not identically distributed and/or not uniformly correlated. We also show that, in general, the SEC performance improves with additional branches. The mathematical formalism is illustrated with a number of selected numerical examples.     

Analysis of hybrid selection/maximal-ratio diversity combiners withGaussian errors

The paper examines the impact of Gaussian distributed weighting errors (in the channel gain estimates used for coherent combination) on both the output statistics of a hybrid selection/maximal-ratio (SC/MRC) receiver and the degradation of the average symbol-error rate (ASER) performance as compared with the ideal case. New expressions are derived for the probability density function, cumulative distribution function and moment generating function (MGF) of the coherent hybrid SC/MRC combiner output signal-to-noise ratio (SNR). The MGF is then used to derive exact, closed-form, ASER expressions for binary and M-ary modulations in conjunction a nonideal hybrid SC/MRC receiver in a Rayleigh fading environment. Results for both selection combining (SC) and maximal-ratio combining (MRC) are obtained as limiting cases. Additionally, the effect of the weighting errors on both the outage rate of error probability and the average combined SNR is investigated. These analytical results provide insights into the tradeoff between diversity gain and combination losses, in concert with increasing orders of diversity branches in an energy-sharing communication system     

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.     

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.     

Efficient performance evaluation for generalized selection combining on generalized fading channels

The authors propose an efficient moment generating function (MGF)-based method to evaluate the performance of generalized selection combining (GSC) over different fading channels. Employing a recently proposed method which is, however, only applicable to GSC diversity with independent and identically distributed branches, they derive a general MGF expression for the GSC output signal-to-noise ratio (SNR) for generalized fading channels, where the channel statistics in different diversity branches may be nonidentical or even distributed according to different distribution families. The resulting MGF expression is applicable to the analysis of the error probability, the outage probability, and the SNR statistics for GSC in a number of wireless communications scenarios with generalized fading. Numerical examples are presented to illustrate the application of the new analysis.     

Higher Order Capacity Statistics of Diversity Receivers

A statistical analysis for the channel capacity (CC) for several diversity receivers under optimal rate adaptation with constant transmit power is provided. Independent but not necessarily identically distributed Nakagami-m fading channels are considered. Specifically, the moments of the CC at the output of selection combining, maximal-ratio combining, and switched and stay combining are obtained, assuming integer-order fading parameters, while for the Rayleigh model the moments of the CC at the output of equal-gain combining and generalized-selection combining are derived in closed form. Using these formulas, a new performance criterion, namely as fading figure (FF) as well as the variance, skewness, and kurtosis, are studied. Our findings show that the FF improves with an increase of the signal-to-noise ratio (SNR), the fading parameters, and/or the diversity order. Also, unlike to the variance of the error probability, the variance of the CC is a monotonic function of the average input SNR.     

Diversity with distributed decisions combining for direct-sequenceCDMA in a shadowed Rician-fading land-mobile satellite channel

The performance of two diversity schemes with distributed decisions combining is analyzed and compared with that of the selection and maximal ratio-combining schemes for binary-phase shift keying (BPSK) direct-sequence code-division multiple access (DS-CDMA) in a shadowed Rician-fading land-mobile satellite channel. In the first scheme of distributed decisions combining, the combiner collects only the binary branch decisions to make the data decision. In the second scheme, the combiner makes the data decision using the branch decisions and the channel states. Both symmetrical and asymmetrical diversity branches are considered. Based on optimal likelihood ratio testing, a new data decision rule is devised for the detection of the spread-spectrum signals in the DS-CDMA system. Upper bounds are employed for the performance evaluation of the diversity combining schemes when the bit error probability is difficult to compute. Numerical results are presented for the satellite channel under light, average, and heavy shadowing     

Scaled Selection Combining for Adaptive Decode-and-Forward Relaying in Dissimilar Rayleigh Fading Channels

This paper enhances the conventional scaled selection combiner (SSC) for decode-and-forward (DF) relay networks using adaptive M-ary quadrature amplitude modulation (M-QAM) to improve the spectral efficiency. Compared with the conventional SSC designed for the combining of identically distributed diversity branches using the same modulation level, the improved SSC allows all diversity branches to choose different modulation levels according to the dissimilar channel conditions. Different scale factors are used for all diversity branches to reflect not only the performance degradation caused by possible erroneous relaying but also different error-resistance abilities of different levels QAM. We derive the bit-error-rate (BER) expressions for DF relay networks using SSC in a recursive way, with all channels conforming to independently and non-identically distributed (i.ni.d.) Rayleigh fading. Newton’s method is employed to obtain the numerical solutions of the optimal scale factors minimizing the BER, and the approximations of the optimal scale factors are derived in closed form for high SNRs. Theoretical analysis and simulation results show that the improved SSC can effectively combine diversity branches with different modulation levels, and for a DF cooperative network with N relay nodes, SSC achieves the full diversity gain of N+1 if for each branch its source-to-relay SNR is proportional to the (N+1)th power of its relay-to-destination SNR.     

SER and outage of threshold-based hybrid selection/maximal-ratio combining over generalized fading channels

The average symbol-error rate and outage probability of threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) in generalized fading environments are analyzed. A T-HS/MRC combiner chooses the combined branches according to a predetermined normalized threshold and the strength of the instantaneous signal-to-noise ratio (SNR) of each branch. Therefore, the number of combined branches is a random variable, rather than a fixed number, as in conventional hybrid selection/maximal-ratio combining (H-S/MRC). Using the moment generating function method, a unified analysis of T-HS/MRC over various slow and frequency-nonselective fading channels is presented. Both independent, identically distributed and independent, nonidentically distributed diversity branches are considered. The derivation allows different M-ary linear modulation schemes. The theory is illustrated using coherent M-ary phase-shift keying in Nakagami-m fading as an example. It is shown that previous published results are incorrect.     

Diversity reception over generalized-K (KG) fading channels

A detailed performance analysis for the most important diversity receivers operating over a composite fading channel modeled by the generalized-K (Kg) distribution is presented. The Kg distribution has been recently considered as a generic and versatile distribution for the accurate modeling of a great variety of short term fading in conjunction with long term fading (shadowing) channel conditions. For this relatively new composite fading model, expressions for important statistical metrics of maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC) and switch and stay combining (SSC) diversity receivers are derived. Using these expressions and by considering independent but not necessarily identical distributed fading channel conditions, performance criteria, such as average output signal-to-noise ratio, amount of fading and outage probability are obtained in closed form. Moreover, following the moments generating function (MGF) based approach for MRC and SSC receivers, and the Pade approximants method for SC and EGC receivers, the average bit error probability is studied. The proposed mathematical analysis is complemented by various performance evaluation results which demonstrate the accuracy of the theoretical approach.     

Performance analysis of TCM with generalized selection combining on Rayleigh fading channels

We derive the computational cutoff rate, R/sub 0/, for coherent trellis-coded modulation (TCM) schemes on independent identically distributed (i.i.d.) Rayleigh fading channels with (K, L) generalized selection combining (GSC) diversity, which combines the K paths with the largest instantaneous signal-to-noise ratios (SNR) among the L available diversity paths. The cutoff rate is shown to be a simple function of the moment generating function (MGF) of the SNR at the output of the (K, L) GSC receiver. We also derive the union bound on the bit error probability of TCM schemes with (K, L) GSC in the form of a simple, finite integral. The effectiveness of this bound is verified through simulations.     

Adaptive coded modulation with receive antenna diversity and imperfect channel knowledge at receiver and transmitter

Unifying and generalizing the works of Cai and Giannakis and Oien et al., the performance of an adaptive trellis-coded modulation system where receive antenna diversity is implemented by means of maximum ratio combining is analyzed and optimized. As in the work of Cai and Giannakis, the analysis is done in the presence of both estimation and prediction errors. Rayleigh fading on each subchannel is considered, with the estimation and prediction being performed independently on each subchannel. The system optimization process is done in such a way that the throughput is maximized under a bit-error-rate (BER) constraint. The numerical example employs a Jakes-fading spectrum and shows how the power should be distributed between pilot and data symbols and how often pilot symbols should be transmitted for maximum throughput under an instantaneous (with respect to the predicted channel) BER constraint.