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     

Error analysis of noncoherent M-ary FSK with postdetection EGC overcorrelated Nakagami and Rician channels

We analyze the performance for the noncoherent reception of M-ary orthogonal frequency shift keying with postdetection equal gain combining over a correlated fading channel. Two kinds of correlated fading statistics are considered: (1) Nakagami fading in which the diversity branches can have unequal signal-to-noise ratios (SNRs) as well as different m-parameters and (2) Rician fading in which the diversity branches can have unequal SNRs. Using the characteristic function of the combiner output SNR, closed-form expressions for the symbol error probability are obtained     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

Performance of Single and Multichannel Coherent Reception under Rician Fading

In the present work, simple closed-form series solutions for the average error rate of several coherent modulation schemes such as, binary phase shift keying (BPSK), binary frequency shift keying (BFSK), differential binary phase shift keying (DBPSK), quadrature phase shift keying (QPSK), offset-QPSK, minimum shift keying (MSK), and square M-ary quadrature amplitude modulation (M-QAM), operating over frequency non-selective slow Rician fading channel and corrupted by additive white Gaussian noise (AWGN) are derived. Further, to improve the link quality, receiver antenna space diversity is considered, where multiple independent and identically distributed (i.i.d.) as well as uncorrelated signal replicas are combined before successive demodulation. The proposed linear predetection combiner follows optimum maximal ratio combining (MRC) algorithm. Starting from a novel unified expression of conditional error probability the error rates are analysed using probability density function (pdf) based approach. The derived end expressions, consisting of rapidly converging infinite series summations of Gauss hypergeometric function, are accurate, free from any numerical integration and general enough, as it encompasses as special situations, some cases of non-diversity, non-fading AWGN and Rayleigh fading. Symbol or, bit error probabilities (SEP/BEP) are graphically displayed against signal to noise ratio (SNR) per bit per channel for all the digital modulation schemes stated above with different values of diversity order L and varying values of the channel specular-to-scatter ratio or, the Rician parameter K, as found from the measured statistics of mobile and indoor wireless channels. In addition, to examine the dependence of error rate performance of M-QAM on the constellation size M, numerical results are plotted for various values of M. Selected simulation results are also provided to verify the analytical deductions. The series solutions presented in current text realize a trade-off between precision and complexity and offers valuable insight into the performance evaluation over a fading channel in a unified manner.     

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     

Dual MRC diversity reception of TCM-MPSK signals over Nakagamifading channels

Space diversity reception and forward error correction coding are powerful techniques for combating the multipath fading encountered in mobile radio communications. In this Letter, the authors analyse the performance of a dual maximal ratio combining (MRC) diversity system using trellis coded modulation-multiple phase shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami fading channels. An alternative exact derivation is introduced for the pairwise error probability, used in calculating average bit error rate analytical upper bounds     

Effect of channel estimation errors on MRC diversity in Rician fading channels

We study the effect of imperfect channel estimation (ICE) on the performance of M-ary phase shift keying (M-PSK) with maximum ratio combining (MRC) in generalized Rician fading channels. First, we derive the error probability formulas for M-PSK with MRC and ICE in arbitrary Rician fading channels. Furthermore, we derive the effective receiver output signal-to-noise ratio (SNR) statistics and the outage probability, and analytically quantify the average SNR loss of M-PSK caused by ICE, assuming independent diversity branches. Finally, we point out a major approximation in a popular approach used in the literature to evaluate the adverse effect of ICE.     

Dual predetection SC diversity reception of TCM-MPSK signals overNakagami fading channels

Space diversity reception and forward error correction coding are powerful techniques for combatting multipath fading encountered in mobile radio communications. The authors analyse the performance of a dual predetection selection combining (SC) diversity system using trellis coded modulation-multiple phase shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami fading channels. An alternative exact derivation for the pairwise error probability, used in calculating average bit error rate analytical upper bounds, is introduced     

Performance Analysis of System with Micro- and Macrodiversity Reception in Correlated Gamma Shadowed Rician Fading Channels

In this paper, the performance of wireless system employing microdiversity to mitigate the effects of short-term fading and macrodiversity to reduce long-term fading (shadowing) effects is studied. The system model assumes implementation of maximal-ratio combining (MRC) at the microlevel and selection combining (SC) at the macrolevel. The received signal envelope follows a Rician distribution and it also suffers gamma shadowing. Novel expressions for the probability density function (PDF), cumulative distribution function (CDF), and moment-generating function (MGF) of the output signal-to-noise ratio (SNR) are obtained. Several useful performance criteria, such as the moments of the output SNR and outage probability are analytically derived. Moreover, the average bit error probability (ABEP) for noncoherent binary differential phase-shift keying (BDPSK) is calculated using the MGF based approach while the ABEP for coherent binary phase-shift keying (BPSK) is studied by averaging the conditional bit error probability over the PDF. Numerical results are graphically presented to show the effects of various system parameters to the system performance, as well as the enhancement due to use of the combination of micro- and macrodiversity. Some of numerical results are complemented by equivalent computer simulated results which validate the accuracy of the proposed analysis. The agreement between the Rician-gamma and Rician-lognormal fading model is also established.     

Analyzing GPS signals to investigate path diversity effects of non‐geostationary orbit satellite communication systems

The concept behind path diversity is that a user who can access several satellites simultaneously will be able to communicate more effectively than a user who could only access one. The success of this method depends on the environment, the satellite constellation, and diversity combining technology. This paper explores the path diversity effects of non‐geostationary orbit (NGO) satellite personal communication services, for different degrees of user mobility, under various scenarios, using the constellation of the global positioning system (GPS). Measurements are taken near downtown Taipei. Three types of mobilities (fixed‐point, pedestrian, and vehicular) are examined, and the switch diversity and maximum ratio combining method are applied to determine the path diversity gain and calculate bit error probability. The error probability performance of applying diversity schemes in coherent binary phase shift keying (BPSK) and non‐coherent differential phase shift keying (DPSK) modulations over Rician fading channels are also analysed and evaluated by using the characteristic function method. The results show that fading can be significantly reduced and diversity greatly increased. A significant diversity gain and improvement in bit error rate (BER) can be expected in all cases by simply applying switch diversity scheme. Besides, for the maximum ratio combining method, the results imply that summing two satellite signals suffices to increase diversity and improve the bit error rate performance. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of hybrid selection/maximal-ratio combining in correlated Nakagami fading

We present an analysis of a hybrid selection/maximal-ratio combining diversity system over an evenly correlated slow frequency-nonselective Nakagami fading channel, where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same, and all average branch signal-to-noise ratios (SNRs) are equal. In this system, the L branches with the largest instantaneous SNR out of N available branches are selected and combined using maximal-ratio combining. From the joint characteristic function (cf) of the instantaneous branch SNRs, we obtain an expression for the cf of the combiner output SNR as a series of elementary cfs. The expression can be conveniently used to obtain the symbol error probability of coherent detection of different M-ary modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.     

Diversity MPSK receivers in cochannel interference

The performance of M-ary phase shift keying (MPSK) in the presence of cochannel interference in microcellular radio environments is analyzed. Average bit error rates (BER) of MPSK using both dual-branch equal gain combining (EGG) and dual-branch selection combining (SC) are derived assuming that the desired signal experiences frequency-nonselective Ricean or Nakagami fading and the multiple interferers experience independent frequency-nonselective Rayleigh fading. Nyquist pulses are used, and perfect coherent detection is assumed at the receiver. The accuracy of the Gaussian interference approximation for diversity receivers is also assessed     

Quadrature space shift keying performance with dual‐hop AF relay over mixed fading

Quadrature space shift keying (QSSK) modulation combined with cooperative relaying improves the reliability in communication and enhances the overall spectral efficiency. Here, QSSK scheme is analyzed for multiple‐input multiple‐output (MIMO) wireless communication system with dual‐hop amplify‐and‐forward (AF) relaying systems over asymmetric mixed Rayleigh/Rician and symmetric Nakagami‐m/Nakagami‐m fading channels. Analytical expressions for cumulative distribution function (CDF) of the end‐to‐end signal‐to‐noise ratio are derived and used to evaluate the average bit error probability (ABEP) of QSSK modulation in mixed asymmetric and symmetric fading channels. The obtained ABEP expression is in the form of Whittaker function, which can be numerically evaluated using its numerical or series representation. Numerical and simulation results are presented to illustrate the impact of fading parameters on the system performance.     

Performance analysis of generalized-faded coherent PSK channels with equal-gain combining and carrier phase error

A new method is developed to analyze the performance of partially coherent PSK systems in wireless channels with equal-gain combining diversity receiver. Two performance criteria are considered: the average bit error probability and the probability distribution of the combiner SNR (SNR reliability). Tikhonov-distributed phase error processes are assumed and generalized fading channels including Rayleigh, Rician, and Nakagami-m are investigated. We evaluate the detection loss suffered by the carrier recovery for different SNR reliability levels when BPSK and QPSK systems are used in wireless channels. The analysis is based on a convergent infinite series for the distribution of the sum of random variables. The convergence rate of the proposed series is investigated and the analytical results are presented along with providing results obtained by simulation.     

Precise BER analysis of dual-channel reception of QPSK in Nakagami fading and cochannel interference

A precise bit error rate analysis is performed for bandwidth-efficient dual-channel quadrature phase shift keying in Nakagami fading with Nakagami-faded asynchronous interfering signals. In contrast to previous works, the analysis accounts for the dependencies between the quadrature carriers owing to nonRayleigh fading and cochannel interference. The impact of the interfering users' fading severities on the desired user bit error rate is investigated. A comparison of the bit error performance for binary phase shift keying and quadrature phase shift keying is given.     

An error probability formula for noncoherent orthogonal binary FSKwith dual diversity on correlated Rician channels

We derive a novel error probability formula for noncoherent detection of orthogonal binary frequency-shift keying with dual diversity and equal gain combining in the presence of slow, correlated, Rician time-selective fading. Numerical results indicate that: (1) fading correlation may produce a substantial performance loss and (2) the error performance of the noncoherent detector improves uniformly as the intensity of the line-of-sight signal component increases     

An approximate analytical framework for performance analysis of equal gain combining technique over independent Nakagami,Rician and Weibull fading channels

In this paper, an approximate analytical method for performance analysis of equal gain combiner (EGC) receiver over independent Nakagami and Rician fading channels is presented. We use a convergent infinite series approach which makes it possible to describe the probability of error of EGC receiver in the form of an infinite series. In this paper, we develop a new approximation method for computation of the required coefficients in this series which lets us to derive simple analytical closed-form expressions with good accuracy compared with the exact results existing in the literatures. Our proposed approximation method only needs the mean and the variance of the fading envelope, which are known for various fading distributions, and hence, bypasses the required integration over the fading envelope distribution while computing the required coefficients. This feature lets us to extend our approximation method for performance analysis of EGC receiver over independent Weibull fading channels where the required integration has not any closed-form or tabulated solutions. To give an application of our developed method, we analyze the probability of error of an EGC receiver for binary, coherent PSK (CPSK) modulation over independent Nakagami, Rician and weibull fading channels and study the effect of the fading conditions on the system performance.     

Effect of Microdiversity and Macrodiversity on Average Bit Error Probability in Gamma‐Shadowed Rician Fading Channels

In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma‐shadowed Rician fading channels for a binary differential phase‐shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment‐generating function (MGF) are derived. The average bit error probability can be calculated by averaging the conditional bit error probability over the PDF or using the MGF‐based approach. Numerical results are graphically presented to show the effects of macrodiversity, correlation, number of diversity branches, and severity of both fading and shadowing.     

On the performance of rate 1/2 convolutional codes with QPSK onRician fading channels

Consideration is given to the bit error probability performance of rate 1/2 convolutional codes in conjunction with quaternary phase shift keying (QPSK) modulation and maximum-likelihood Viterbi decoding on fully interleaved Rician fading channels. Applying the generating function union bounding approach, an asymptotically tight analytic upper bound on the bit error probability performance is developed under the assumption of using the Viterbi decoder with perfect fading amplitude measurement. Bit error probability performance of constraint length K=3-7 codes with QPSK is numerically evaluated using the developed bound. Tightness of the bound is examined by means of computer simulation. The influence of perfect amplitude measurement on the performance of the Viterbi decoder is observed. A performance comparison with rate 1/2 codes with binary phase shift keying (BPSK) is provided     

CDF and MGF based analysis over Rayleigh TWDP shadowed fading channel for indoor communication

Recently, the two-wave with diffuse power (TWDP) distribution has been extensively used to model the shadowing in multipath-faded/shadowed indoor environment. In this article, novel expressions for joint moments, mean, second moment, variance and cumulative distribution function for Rayleigh TWDP shadowed fading model are derived. By using the derived expression of mean and variance, the expression for amount of fading is obtained. Also, the outage probability, moment generating function and average bit error rate (ABER) for various modulation schemes namely binary phase shift keying (BPSK), binary frequency shift keying (BFSK), minimum shift keying (MSK), differentially coherent phase shift keying (DCPSK) and non-coherent frequency shift keying (NCFSK) are calculated. The derived expressions for cumulative distribution function, outage probability and ABER are presented in analytical format and have been numerically evaluated. Moreover, the numerical results of ABER using MSK and DPSK modulation schemes is compare with results of Rayleigh Gamma composite fading model. The study shows that better outage probability (0.01) is observed at 40dB average signal to noise ratio (SNR) with 5dB lowest threshold SNR, however, at higher threshold SNR (>5dB) with fixed average SNR (40dB), poor outage probability performance are obtained. Further, at higher shadowing (10dB), for fixed average SNR (15dB), minimum error probability (10^?4) is observe, while at lower shadowing (less than 10dB), higher error probability (greater than 10^?4) is observed that represents poor BER performance.