Performance of RAKE receivers in Nakagami fading channel witharbitrary fading parameters

A new expression for the bit error rate of RAKE receivers with either coherent or noncoherent/differentially coherent binary demodulation schemes in a Nakagami fading channel is derived. The analysis assumes an arbitrary number of diversity branches with arbitrary fading parameters     

Selection diversity for wireless communications in Nakagami-fadingwith arbitrary parameters

By means of analytical and numerical methods, the probability of error and the outage probability of a selection diversity RAKE receiver system employing direct sequence/code division multiple access (DS/CDMA) is derived. A noise-limited propagation environment is modeled as a Nakagami (1960)-fading channel with arbitrary fading parameters and unequal mean power at the receiver. New analytical expressions are derived for the average probability of error and outage probability. Binary detection schemes are considered including binary phase-shift keying (PSK) and frequency-shift keying (FSK). Both coherent and noncoherent detection is considered as well as identical and arbitrary fading. It is shown that the effect of arbitrary fading on system performance is significant and may not be ignored     

MRC performance for binary signals in Nakagami fading with generalbranch correlation

Exact expressions are derived for the performance of predetection maximal ratio combiner diversity reception with L correlated branches in Nakagami fading. Bit error rates are evaluated for both coherent and noncoherent binary phase-shift-keying and frequency-shift-keying signals, starting from the L-variate moment generating function of the random input power vector. The new formulation presented for the bit error rate, in which the covariance matrix of the fading at the L branches explicitly appears, allows arbitrary branch correlation to be taken into account for any diversity order in the case of identical fading severity on the branches. Results are presented for evaluation of the outage probability, for integer values of fading severity, as well as for the effect of the presence of unbalanced channels with arbitrary correlation     

On the error probability of binary and M-ary signals in Nakagami-m fading channels

In this letter, we present new closed-form formulas for the exact average symbol-error rate (SER) of binary and M-ary signals over Nakagami-m fading channels with arbitrary fading index m. Using the well-known moment generating function-based analysis approach, we express the average SER in terms of the higher transcendental functions such as the Gauss hypergeometric function, Appell hypergeometric function, or Lauricella function. The results are generally applicable to arbitrary real-valued m. Furthermore, with the aid of reduction formulas of hypergeometric functions, we show previously published results for Rayleigh fading (m=1) as special cases of our expressions.     

Another look at the performance of MRC schemes in Nakagami-m fading channels with arbitrary parameters

In this letter, we take a close look at the performance of maximal ratio combining (MRC) schemes operating in a flat-Nakagami-m fading environment with arbitrary fading parameters. We derive an expression for the probability density function (pdf) of the output signal-to-noise ratio (SNR) by expressing the moment generating function of the output SNR in the form of multiple Barnes-type contour integrals. By evaluating the inverse transform and converting the multiple contour integrals into infinite series, we are able to derive an expression for the pdf of the output SNR when the Nakagami fading parameters along the diversity branches take on real and arbitrary values. Consequently, the average bit-error rate can now be expressed in terms of Lauricella's multivariate hypergeometric function, which can be easily evaluated numerically. Special cases of the main results reduce to known results in the literature. The results, which apply to independent as well as correlated diversity branches, will be useful for predicting the system performances when the Nakagami fading parameters are real and arbitrary.     

Exact BER analysis of bandlimited BPSK with EGC and SC diversity in cochannel interference and Nakagami fading

Equal gain and selection combining for bandlimited binary phase-shift keying systems in Nakagami fading with cochannel interference are considered. Spectrum raised-cosine and Beaulieu-Tan-Damen pulse shapes are employed. Average bit error rates are derived for arbitrary orders of diversity and fading parameters. The computational complexity of the solution does not grow with the diversity order. Slow flat fading, asynchronous timing and independent fading gains are assumed.     

Selective decode-and-forward cooperation over Nakagami-m fading channels

The asymptotic performance analysis is presented for selective fixed decode-and-forward (DF) cooperation over independent but not identically distributed Nakagami-m fading channels. A tractable closed-form average bit error probability expression is derived at the high signal-tonoise ratio region. The presented expression is quite simple and general for cooperative systems with an arbitrary number of DF relays and fading environment with arbitrary values of severity parameters m ⩾ 0.5.     

Compact formulas for the average error performance of noncoherent m-ary orthogonal signals over generalized rician, nakagami-m, and nakagami-q fading channels with diversity reception

This paper derives exact expressions for the average error performance of M-ary orthogonal signals with noncoherent equal-gain diversity combining over nonidentical generalized Rician, Nakagami-m, Nakagami-g, and implicitly Rayleigh fading channels. The assumption of generalized distributed fading envelopes implies that the received average signal-to-noise ratios (SNRs) and/or the fading parameters can have arbitrary nonidentical values. The derived expressions are precisely given in terms of either one-fold integral or rapidly convergent infinite series, which can be readily evaluated numerically. In addition, they can be usefully used to study the impact of arbitrary correlation among diversity branches on the system average error performance.     

Performance of Optimum and Suboptimum Combining Diversity Reception for Binary and Quadrature DPSK Over Independent, Nonidentical Rayleigh Fading Channels

dThis paper is concerned with the error-performance analysis of binary and quadrature differential phase-shift keying with differential detection over the nonselective, Rayleigh fading channel with combining diversity reception. The diversity channels are independent, but have nonidentical statistics. The fading process in each channel is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. Both optimum diversity reception and suboptimum diversity reception are considered. Results available previously apply only to the case of second-order diversity and require numerical integration for their actual evaluation. Our results are more general in that the order of diversity is arbitrary. Moreover, the bit-error probability (BEP) result is obtained in an exact, closed-form expression which shows the behavior of the BEP as an explicit function of the one-symbol-interval fading correlation coefficient at the matched-filter output, the mean received signal-to-noise ratio per symbol per channel, and the order of diveristy.      

Unified analysis of practical selection diversity system indifferent fading environments

A general expression is presented for the bit error rate performance of a signal plus interference and noise (S+I) selection diversity system over generalised fading channels, including all possible conditions of signal strengths and arbitrary fading parameters     

The trivariate and quadrivariate weibull fading distributions with arbitrary correlation and their applications to diversity reception

The statistical characteristics of the trivariate and quadrivariate Weibull fading distribution with arbitrary correlation, non-identical fading parameters and average powers are analytically studied. Novel expressions for important joint statistics are derived using the Weibull power transformation. These expressions are used to evaluate the performance of selection combining (SC) and maximal ratio combining (MRC) diversity receivers in the presence of such fading channels.     

Mobile Communications Using Source-Selected Multi-Antenna AF Relays Over Dual-Hop Nakagami-{\varvec{m}} Channels

This paper presents a scheme for dual-hop amplify-and-forward multi-antenna, multi-relay selection over Nakagami-m fading channels. A source-selected best relay performs maximal ratio combining on received data, applies variable gain, and then uses beamforming to transmit to a destination device. Such a configuration is beneficial for end-to-end communication using single antenna mobile terminals with a multi-antenna relay infrastructure. Closed form expressions for performance metrics are derived that cater for arbitrary number of relays, arbitrary number of receive and transmit antennas and different fading parameters. Results are verified through simulation. Furthermore, the influence of multiple antennas, the effects of fading, power imbalance between hops, and the beneficial impact of additional relays are explored.     

Performance of 2-D RAKE receiver in a correlatedfrequency-selective Nakagami-fading

The bit error rate (BER) performance and the characteristics of a two-dimensional (2-D) RAKE receiver operating in a correlated frequency-selective Nakagami-fading environment are analyzed. Correlated fading between array elements whose fading statistics are identical across the same RAKE branch, as well as an arbitrary number of RAKE-branches with arbitrary finding statistics, are assumed. We derived an approximated signal-to-noise ratio (SNR) statistics for one RAKE branch with correlated multiple antennas, which is extended to that for multiple RAKE branches with arbitrary fading statistics, i.e., a 2-D RAKE receiver. The receiver's performance and characteristics are analyzed using the cumulative distribution function of the SNR at the 2-D RAKE receiver output and the BER under various conditions, Numerical results show that the improvement In performance of the 2-D RAKE receiver is brought about by the average SNR and diversity gains, which are identified by two parameters specifying the gamma distribution of SNR     

Efficient Nakagami-m fading channel Simulation

An efficient method for generating correlated Nakagami-m fading envelope samples is presented; this method is applicable for arbitrary values of the fading parameter m. The new method is compared to other methods used to generate Nakagami-m random variates. An accurate approximation to the inverse Nakagami-m cumulative distribution function, valid for all values of m, is derived. Uncertainties regarding the autocorrelation of the Nakagami-m fading process are discussed. The fading envelope autocorrelation is determined by simulation and asymptotic analysis.     

Performance analysis of SIR-based dual selection diversity over correlated Nakagami-m fading channels

Signal-to-interference-ratio (SIR)-based selection diversity is an efficient technique to mitigate fading and cochannel interference in wireless communications systems. An approach to the performance analysis of dual SIR-based selection diversity over correlated Nakagami-m fading channels with arbitrary parameters is presented. Useful formulae for the outage probability, the average output SIR, and the average error probability for coherent, noncoherent, and multilevel modulation schemes are derived. The main contribution of the paper is that, for the first time, the proposed analysis is carried out assuming correlated Nakagami-m fading with arbitrary parameters for both the desired signals and the cochannel interferers, which is the real scenario in practical dual selection diversity systems with insufficient antenna spacing. It is shown that the presented general results reduce to the specific ones for the independent fading case, previously published. Numerical and simulation results are also presented to show the effects of various parameters, such as the fading severity, input SIR unbalance, and level of correlation, to the system's performance.     

Performance of QDPSK signals with postdetection equal gaindiversity combining in arbitrarily correlated Nakagami-m fading channels

This letter derives a bit-error probability (BEP) expression for quadrature differential phase-shift keying (QDPSK) signals with post-detection equal gain combining (EGC) in additive white Gaussian noise and slow frequency-nonselective arbitrarily correlated Nakagami-m fading channels. Unlike previous work, the effects of arbitrary values of fading severity parameter m and the arbitrary correlation between the L diversity channels are considered. The derived expression can be easily computed via numerical integration routines, and hence, can be usefully exploited in the performance evaluation of digital mobile radio systems     

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.     

Outage and BER of MRC diversity in bandlimited micro-cellular systems with CCI

Maximal ratio combining for bandlimited BPSK in micro-cellular systems with cochannel interference is considered. A Nakagami/Rayleigh fading model is assumed. Spectrum raised-cosine and Beaulieu-Tan-Damen pulse shapes are employed. Exact closed-form expressions for outage probability with equal and different interferer powers are derived. An average bit error rate approximation is derived using a Gaussian assumption for the cochannel interference. Monte-Carlo simulation is used to validate the Gaussian assumption. The results are valid for arbitrary diversity order and desired user fading parameter. Slow flat fading, asynchronous timing and independent fading gains are assumed.     

Multicarrier channels with non-identical subcarrier fading distributions-analysis and adaptation

In this letter, the subcarrier fading distribution of multicarrier modulation (MCM) systems is derived based on channel-impulse response (CIR) information. Frequency-selective channels with arbitrary Rician-Rayleigh fading paths and inter-path correlations are considered. It is discovered that certain MCM channels experience different fading severity among the subcarriers. Motivated by this observation, a novel bit-loading cum power-control scheme that can achieve better spectral and power efficiency by adapting the subcarrier modulation parameters based on the long-term subcarrier fading statistics, instead of instantaneous channel state information, is proposed and studied.     

Further results on the bit error probabilities of MDPSK over thenonselective Rayleigh fading channel with diversity reception

This paper presents a fundamental approach for deriving the bit error probability of BDPSK and QDPSK over the nonselective Rayleigh fading channel for a receiver with an arbitrary IF filter, and for a fading process with an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The results generalize those published earlier which were restricted to matched filter reception and to a fading process with a small Doppler bandwidth compared to the symbol rate. This allows the error probability to be studied in the presence of varying degrees of ISI due to the bandlimitation of the received signal by the IF filter, and in the presence of fading fluctuations of various rates. The analytical approach presented is simple, and yet powerful in that it can handle the case of diversity reception. This is a great advantage over the alternative approach of using the distribution of the differential phase of the received signal over a symbol interval. The bit error probability results apply to both conventional BDPSK and QDPSK, as well as π/2-2DPSK and π/4-4DPSK, and allow the irreducible bit error probability as well as the SNR at which this irreducible value sets in to be studied as a function of the Doppler bandwidth and IF filter bandwidth. The computed results are applicable to the design of digital cellular mobile communication systems