Crossing rates and fade durations for diversity-combining schemes over ?-? fading channels

This paper derives exact expressions for the level crossing rate and average fade duration of multibranch pure-selection, equal-gain, and maximal-ratio combiners operating over independent non-identical alpha-mu (also called generalized Gamma or Stacy) fading channels. The derived expressions are in closed form for pure-selection combining and in integral form for equal-gain and maximal-ratio combining. For the two latter schemes, accurate closed-form approximations are then provided. The analytical results are validated by reducing the general expressions to known particular cases and, more generally, by means of simulation. Numerical examples are also given to illustrate the high accuracy of the proposed closed-form approximations.     

Average level crossing rate and average fade duration of low-ordermaximal ratio diversity with unbalanced channels

The average level crossing rate and average fade duration of a maximal ratio diversity combiner, operating on independent, unequal power Rayleigh fading branches in isotropic scattering, are derived in closed-form for dual-branch diversity, and as definite integrals for threefold and fourfold diversity     

Level crossing rate and average fade duration of MRC and EGC diversity in Ricean fading

The average level crossing rate and average fade duration of the output signal of a maximal ratio combiner (MRC) and equal gain combiner (EGC), operating on independent Ricean fading input branch signals, are derived. Exact, closed-form results are obtained for MRC diversity, while precise expressions for EGC diversity are presented with an infinite series method. The results are valid for an arbitrary number of independent, identically distributed diversity branches, isotropic scattering, and a specular component perpendicular to the line of motion of the mobile.     

Path diversity for DS-SSMA communications in Nakagami fading channels

Average error probability and outage probability for an asynchronous direct sequence spread spectrum multiple access communications through slow nonselective Nakagami fading channels are evaluated for nondiversity and diversity receptions. Using the Gauss quadrature rule, the moments of the self-interference and the multiple access interferences are used to evaluate average error probability and outage probability. Combining the diversity technique and error correcting codes, comparisons between the uncoded nondiversity DS-SSMA system and that of the coded diversity system are shown for the Gold Code of codelength 127. Using fourth-order diversity and the Reed-Solomon code, the maximum achievable number of users is 12 percent of the codelength for Rayleigh fading, when the average probability is 10^–3. The corresponding outage probability is less than 5 percent. Performance comparisons between Rician and Nakagami fading channels are made. Since the system is interference limited, the performance seems to show no significant difference for the two fading channel models when the number of users is large.     

Post-detection diversity Nakagami fading channels with correlatedbranches

We derive a closed-form expression for the performance of the post-detection product detector combiner (PDC) operating on L correlated branches in Nakagami (1960) fading. We consider the 2-DPSK signaling scheme and nonselective slow fading. The average bit error rate (BER) obtained with this scheme is compared to the ideal predetection MRC, showing limited loss. Moreover, the post-detection PDC is shown to outperform the selection diversity combiner (SDC) under the considered case of Nakagami fading     

Analysis of selection diversity on Nakagami fading channels

A theoretical framework to evaluate the performance of different pre-detection diversity techniques in various mobile radio environments is developed     

Average level crossing rate and average fade duration of selectiondiversity

The average level crossing rate and average fade duration of the output signal envelope of a selection diversity combiner, operating on independent, but nonidentical fading input branch signals are derived. The exact closed-form results are valid for arbitrary diversity order, and are obtained for Rayleigh, Ricean, and Nakagami fading input signals     

Level crossing rate and average fade duration of the double nakagami-m random process and application in MIMO keyhole fading channels

We present novel exact expressions and accurate closed-form approximations for the level crossing rate (LCR) and the average fade duration (AFD) of the double Nakagami-m random process. These results are used to study the second order statistics of multiple input multiple output (MIMO) keyhole fading channels with space-time block coding. Numerical and computer simulation examples validate the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.     

Analysis of equal gain diversity on Nakagami fading channels

An infinite series for the complementary probability distribution function (CDF) of the signal-to-noise ratio (SNR) at the output of L -branch equal-gain (EG) diversity combiners in Nakagami (1960) fading channels is derived. The bit error rate for a matched filter receiver is analyzed for the L-branch EG combiner and different fading parameters. Both coherent phase shift keying (CPSK) and differential coherent phase shift keying (DCPSK) are considered. The effects of gain unbalance between branches on the probability distribution of the SNR and on the bit error rates are investigated. Bit error rate results are also obtained for coherent and noncoherent reception of frequency shift keying (FSK). The effects of gain unbalances on FSK modulations are also investigated. Bit error rates for EG combining on Rayleigh fading channels are obtained for L>2. These results are presented as a special case of the more generalized Nakagami fading model     

Level crossing rate and average fade duration of the select-and-hold policy of selection diversity combining in a Rayleigh fading channel

The select-and-hold policy (SAH) is a general form of selection diversity combining (SDC). In this letter, we provide closed-form expressions for average level crossing rate and average fade duration for Nth-order SAH-SDC. The diversity branches are assumed to be independent and identical Rayleigh fading channels. A useful guideline for choice of the holding time is also obtained.     

On the average crossing rates in selection diversity

This letter presents new results on the average crossing rate of the combined signal of a selection diversity in Rayleigh fading channels. Exact closed-form expressions are derived for the inphase zero crossing rate, inphase rate of maxima, phase zero crossing rate, and the instantaneous frequency zero crossing rate of the output of the selection combiner. The utility of the new theoretical formulas, validated by Monte Carlo simulations, are briefly discussed as well     

Fast simulation of diversity Nakagami fading channels using finite-state Markov models

We designed a multi-channel Nakagami fading simulator by modeling the received combined signal-to-noise ratio as a finite-state Markov chain, following a previously proposed approach. Our model generates directly the error process at the output of a diversity receiver and can emulate selection, maximal-ratio, and equal-gain combining. As the order of diversity increases, the savings in computational complexity improve linearly with respect to a traditional waveform simulator. The level crossing rates of the simulated envelope are shown to be very close to their theoretical values. The simulator's performance is also evaluated in terms of the accuracy of the obtained bit error rates, for both uncoded and coded systems. The simulator speeds up the performance evaluation of high-rate communication links where a high number of samples is needed.     

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.     

Improved-performance noncoherent weighted-coefficients diversity combiner for DPSK and NC-FSK signals in nonidentical Nakagami fading channels

It is well-known that noncoherent equal-gain combining (NC-EGC) is the simplest combining technique for noncoherent and differentially coherent communication systems. However, for nonidentical Nakagami-m channels (channels having nonuniform multipath intensity profile (MIP) and/or arbitrary non-integer fading parameters), the use of NC-EGC has three main disadvantages. First, its performance serves as a lossy upper bound to that of the optimum diversity combiner. Second, it results in complicated expressions for the system average error performance. Third, it incurs noncoherent combining loss (does not aid the use of diversity) at relatively low average signal-to-noise ratio (SNR). In this letter, we propose a modified version of the NC-EGC, which is a noncoherent combiner with weighting coefficients, to overcome the disadvantages of the conventional one. We show that this alternative combiner does provide improvements over the conventional N.C-EGC for all values of average SNRs, it does not incur any noncoherent combining loss, and it leads to a design of the receiver whose average error performance can be evaluated easily.     

Approximation of SNR statistics for MRC diversity systems inarbitrarily correlated Nakagami fading channels

An approximated probability density function is presented for the SNR in maximal ratio combining diversity systems with an arbitrary number of diversity branches in an arbitrarily correlated Nakagami fading environment. Comparisons between the exact and approximated distribution show good agreement over wide ranges of correlation coefficients     

Combining PSA fading estimation techniques for TCM and diversity reception in Rician fading channels

In this paper, a novel pilot‐symbol‐aided (PSA) technique is proposed for fading estimation in the land mobile satellite fading channels. The proposed technique combines the fading estimates obtained from a bandwidth‐efficient technique and a conventional technique according to the signal‐to‐noise ratios (SNRs) of the fading estimates. To enhance the transmission quality, trellis‐coded modulation (TCM) and diversity reception are employed in the system, and the combined estimates are subsequently used to correct the channel fading effects, to weight the signals from different diversity branches, and to provide channel state information to the Viterbi decoder. Monte Carlo computer simulation has been used to study the bit‐error‐rate (BER) performance of the proposed technique on trellis‐coded 16‐ary quadrature amplitude modulation in the frequency non‐selective Rician fading channels. Results have shown that the proposed PSA technique requires a very low bandwidth redundancy to provide satisfactory BER performance at low SNRs, and thus is suitable for use with TCM and diversity reception to achieve both bandwidth and power‐efficient transmission. Copyright © 2002 John Wiley & Sons, Ltd.     

Simulation of Nakagami fading channels with arbitrary cross-correlation and fading parameters

Nakagami fading model is widely used in modeling wireless communication systems. In this paper, we present methods to generate Nakagami fading signals with arbitrary cross-correlation and fading parameters by taking the square root of correlated Gamma random variables (RVs) with the corresponding shape parameters. To generate correlated Gamma RVs with different noninteger values of m-parameters, two methods, namely the decomposition method and Sim's method, are proposed. The former is more flexible and efficient. The latter is mathematically exact but carries constraints on the permissible simulation parameters. Simulations show that both methods produce outputs that match well with the specifications.     

Nakagami信道的中断容量分析

本文讨论了Nakagami-m衰落信道系统的中断容量性能,在发射端未知信道信息,接收端的信道估计存在误差时,给出了计算中断容量上界和下界的表达式,它们是接收端的估计误差和信道参数的函数,仿真结果表明随着估计误差的增大中断容量的上界和下界同时降低,但是中断容量的下界随着信道参数的增大而增大,上界随着信道参数的增大而减小。     

New results on the BER of switched diversity combining over Nakagami fading channels

New closed-form bit error rate (BER) expressions are derived for multibranch switched combining (SWC) systems with independent Nakagami faded diversity branches having integer Nakagami 717-parameters. Constellations considered include BPSK, M-PSK, M-PAM and M-QAM. The analysis is also applicable to the generalized hierarchical PAM and QAM modulation formats.