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     

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.     

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     

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.     

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.     

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 coded communication systems on Nakagami fading channels with selection combining diversity

In this paper, we develop analytical tools for the performance analysis of coded, coherent communication systems on independent and identically distributed Nakagami-m fading channels with selection combining (SC) diversity. First, we derive an exact expression for the moment generation function (MGF) of the signal-to-noise ratio (SNR) of a code symbol at the output of the selection combiner. Next, based on Gauss-Chebyshev quadrature and Gauss-Laguerre quadrature rules, we propose a simple to compute, yet accurate, numerical solution for the pairwise error probability (PEP) of coded M-phase-shift keying (PSK) signals. Using the PEP expressions, we present the union bound-based bit-error performance of trellis-coded modulation schemes and turbo codes. Finally, we derive an exact expression for the computational cutoff rate of a coded system with M-PSK signaling and SC diversity, and show that the cutoff rate expression is a simple function of the MGF of the SNR at the output of the diversity combiner.     

Selection-and-stay combining on correlated Nakagami fading channels

Selection-and-stay combining (SSTC) is addressed and its outage probability is derived for dual-branch diversity on correlated Nakagami fading channels. In the SSTC scheme, the receiver uses the branch with a larger signal-to-noise ratio (SNR) until its SNR is lower than a preset threshold, and selection combining (SC) is used only at the switching instance. Numerical results from analyses and simulations are also presented.     

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.     

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     

MQAM Performance over Nakagami channels with diversity

This paper presents the error probability performance for M-ary quadrature amplitude modulation (mqam) signalling with L-branch diversity receiver over Nakagami fading channel. Both maximal ratio combining (mrc) and selection diversity combining (sdc) techniques are considered with reference to predetection diversity architecture, in the case of integer values of fading severity and independent fading. Average symbol error probability is analitycally derived in terms of finite sum of Gauss hypergeometric functions for balanced branches with identical values of the fading severity. In particular, performance analysis of sdc for mqam in Nakagami fading is new since it has not been presented in any previous work. Numerical results are presented allowing to identify those operational conditions in which diversity techniques can aid successfully in counteracting the effects of slow and nonselective short-term fading.     

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。     

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.     

Analytical level crossing rates and average fade durations for diversity techniques in Nakagami fading channels

The level crossing rates (LCRs) and average fade durations (AFDs) of a fading channel find diverse applications in the evaluation and design of wireless communication systems. Analytical expressions for these quantities are available in the literature for certain diversity reception techniques, but are generally limited to the Rayleigh fading channel, with few exceptions. Moreover, the methods employed are usually specific to a certain channel/diversity pair, and thus cannot be applied to all cases of interest. Using a unified methodology, we derive analytical expressions for the LCRs and AFDs for three diversity reception techniques and a general Nakagami (1960) fading channel. We provide novel analytical expressions for selection combining (SC) and equal-gain combining (EGC), and rederive in a more general manner the case of maximal-ratio combining (MRC). It is shown that our general results reduce to some specific cases previously published. These results are used to examine the effects of the diversity technique, the number of receiving branches and severity of the fading on the concerned quantities. It is observed that as the Nakagami m-parameter and the diversity order increase, the behavior of the combined received envelope for EGC follows closely the one for MRC, and distances itself from SC.     

Maximal-ratio combining over Nakagami fading channels with anarbitrary branch covariance matrix

The error probability of maximal ratio combiners (MRCs) in a correlated Nakagami environment with an arbitrary branch covariance matrix is not available in the literature although some work has been done for two special cases with constant and exponential correlations. Correlation structures of this type, though of theoretical interest, may not match to practical situations, even for an antenna array of a totally symmetrical configuration. In this paper, we tackle the general problem by virtue of characteristic functions, avoiding the difficulty of explicitly obtaining the probability density function (PDF) for the signal-to-noise ratio (SNR) at the MRC output. We derive a simple closed-form solution for arbitrarily correlated channels with an integral fading parameter and a solution in the form of a one-fold integral for a fading parameter of nonintegral values. Simple algorithms have also been developed for their efficient implementation. The formulas are then used to analyze two possible antenna configurations for a base station, ending up with some findings of interest to system design     

Bit error probability of MDPSK in Nakagami fading channels

A general formula for the bit error probability of M-ary DPSK transmission with equal gain combining diversity over frequency non-selective m-distributed Nakagami fading channels is derived. Simulations have shown that the analysis is efficient and accurate     

Outage probability of multihop transmission over Nakagami fading channels

We present a general analytical framework for the evaluation of the end-to-end outage probability of multihop wireless communication systems with nonregenerative relays over Nakagami fading channels. It is shown that the presented results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, we obtain a closed-form expression for the moment generating function of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and we then use this expression to calculate the outage probability via numerical inversion of the Laplace transform. Numerical examples show that regeneration is more crucial at low average SNR and for multihop systems with a large number of hops.     

Outage probabilities of diversity cellular systems with cochannelinterference in Nakagami fading

Analytical, closed-form expressions for cellular outage probabilities in generalized Nakagami fading are derived for three practical diversity combining schemes. The outage is defined as the probability that the signal-to-interference power ratio (SIR) is less than a power protection ratio. The analysis considers L-branch equal gain (EG), selection (SC), and switched (SW) diversity combining schemes. The analyses are not limited to a single interferer, but rather assume the presence of multiple independent cochannel interferers. Previous results have used some approximations to study the performance of the EG combiner. A precise method is used to analyze the performance of an L-branch EG combiner. Selection diversity combining using the total power algorithm, the desired power algorithm, and the signal-to-interference power algorithm is analyzed. The effects of diversity on the reuse factor and on the spectrum efficiency of cellular mobile radio systems are considered in detail. The results for the Rayleigh fading channel are obtained and presented as a special case of the generalized Nakagami fading model     

New analytical expressions for orthogonal, biorthogonal, and transorthogonal signaling in Nakagami fading channels with diversity reception

Analytical probability of error expressions are presented in this paper for orthogonal, biorthogonal, and transorthogonal signaling in slow Nakagami fading channels with diversity reception. These new probability of error expressions are exact, numerically efficient, and general for arbitrary signal dimension. The numerical results obtained will guide system engineers in determining the appropriate dimensionality of the orthogonal, biorthogonal, and transorthogonal signals. They will also be useful for deciding the suitable number of diversity branches used at the receiver to meet the design requirements in wireless fading environments.