Performance of Two Dual-Branch Postdetection Switch-and-Stay Combining Schemes in Correlated Rayleigh and Rician Fading

The performance of binary frequency-shift keying (BFSK) and M-ary frequency shift keying (MFSK) with dual-branch postdetection switch-and-stay combining (SSC) in correlated Rayleigh and Rician fading is studied. Two postdetection SSC receivers are considered and the performances of noncoherent BFSK and MFSK are analyzed. Closed-form expressions are derived for the average bit-error rate (BER) of BFSK and MFSK with postdetection SSC in correlated Rayleigh and Rician fading. Optimum switching thresholds that minimize the average BER are obtained. Extensive Monte Carlo simulations are presented to test the validity of the analytical results. The performance of dual-branch postdetection SSC is compared with the performance of dual-branch predetection SSC. The effects of correlation, fading parameter, average fading power imbalance, and switching threshold on the performances of postdetection SSC receivers are examined     

Performance of S + N Selection Diversity Receivers in Correlated Rician and Rayleigh Fading

The performances of two signal-/?/wi-noise (S + N) selection diversity receivers employing noncoherent M-ary frequency shift keying (MFSK) in slow, flat, correlated Rayleigh and Rician fading channels are examined. The branches are assumed to be equally correlated for Rician fading. The correlation model for Rayleigh fading is more general than the equally correlated scenario and includes it as a special case. Analytical expressions are derived for the average symbol error rate (SER) and the average bit error rate (BER) of each receiver structure. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The performances of the S + N SC receivers are compared to the performance of the classical SC receiver. The effects of correlation, average fading power imbalance and diversity order on the performances of the S + N SC receivers are examined.     

Revised analyses of postdetection switched combining in Nakagami-m fading

In two recent papers, the performances of dual-branch postdetection switch-and-stay combining (SSC) for noncoherent orthogonal binary frequency-shift keying (BFSK) and noncoherent orthogonal M-ary frequency-shift keying (MFSK) operating in the presence of slow flat fading modeled by Rayleigh, Nakagami-m, and Rician distributions have been analyzed. In this paper, we show that these previous analyses for the Nakagami-m fading model, which are restricted to integer values of m, are incorrect, and we derive the correct bit-error rate (BER) performances of BFSK and MFSK with dual-branch SSC in Nakagami-m fading for all values of m. Optimum switching thresholds that minimize the BER of BFSK and MFSK with postdetection SSC in Nakagami-m fading are obtained. The performance of postdetection SSC is compared with the performance of predetection SSC, and it is shown that postdetection SSC outperforms predetection SSC for all values of signal-to-noise ratio (SNR). We also show that for a given BER, the performance gain of postdetection SSC over predetection SSC has been overestimated by several decibels in SNR in previous publications.     

Exact evaluation of maximal-ratio and equal-gain diversityreceivers for M-ary QAM on Nakagami fading channels

Exact integral expressions are derived for calculating the symbol-error rate (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on arbitrary Nakagami fading channel. Both maximal-ratio combining (MRC) (in independent and correlated fading) and equal-gain combining (EGC) predetection (in independent fading) diversity techniques have been considered. Exact closed-form SER expressions for two restricted Nakagami fading cases (MRC reception) are also derived. An exact analysis of EGC for MQAM has not been reported previously, despite its practical interest. Remarkably, the exact SER integrals can also be replaced by a finite-series approximation formula. A useful procedure for computing the confluent hypergeometric series is also presented     

Revised Analyses of Postdetection Switched Combining in Nakagami-$m$Fading

In two recent papers, the performance of dual-branch postdetection switch-and-stay combining (SSC) for noncoherent binary orthogonal frequency-shift keying (BFSK) and noncoherent$M$-ary orthogonal frequency-shift keying (MFSK) operating in the presence of slow flat fading modeled by Rayleigh, Nakagami-$m$, and Rician distributions have been analyzed. In this paper, we show that these previous analyses for the Nakagami-$m$fading model, which are restricted to integer values of$m$, are incorrect, and we derive the correct bit-error rate (BER) performances of BFSK and MFSK with dual-branch SSC in Nakagami-$m$fading for all values of$m$. Optimum switching thresholds that minimize the BER of BFSK and MFSK with postdetection SSC in Nakagami-$m$fading are obtained. The performance of postdetection SSC is compared with the performance of predetection SSC, and it is shown that postdetection SSC outperforms predetection SSC for all values of signal-to-noise ratio (SNR). We also show that for a given BER, the performance gain of postdetection SSC over predetection SSC has been overestimated by several decibels in SNR in previous publications.     

Particle swarm optimization–based power allocation for Alamouti amplify and forward relaying protocol

The performance of wireless communication systems is improved over flat fading channel by using Alamouti coding scheme, which provides the quality of diversity gain. In this paper, performance analysis of symbol error rate (SER) and particle swarm optimization (PSO)–based power allocation (PA) for Alamouti amplify and forward (AF) relaying protocol using maximum ratio combining (MRC) technique is presented. Analytical expression of SER upper bound and SER approximation is derived for Alamouti AF relaying protocol with quadrature phase shift keying (QPSK) modulation over Rayleigh fading channel and Rician fading channel. In addition, PSO‐based optimum PA factor is calculated on the basis of the minimum SER of proposed method. PSO‐based optimum PA gives 0.5 dB of improved signal‐to‐noise ratio (SNR) compared with the equal power allocation (EPA). The theoretical approximate SER result is compared with the simulated SER. The proposed protocol provides full diversity gain and reduces SER compared with the existing AF and decode and forward (DF) relaying protocols over Rayleigh fading channel and Rician fading channel.     

Revised analyses of postdetection switch-and-stay diversity in rician fading

The performances of dual-branch postdetection switch-and-stay combining (SSC) for noncoherent orthogonal binary frequency-shift keying and noncoherent orthogonal M-ary frequency-shift keying operating over slow, flat Rician fading channels are a topic of current interest. It is shown that recently published analyses obtain incorrect final results because some incorrect probability distribution parameters are used in the analyses. The previous results are corrected, and it is seen that the final results change significantly. The revised results are used to obtain optimum switching thresholds that minimize the average bit-error rate (BER) performance of these systems. Monte Carlo simulations are presented to verify the results, and it is shown that for a given BER, the signal-to-noise ratio difference of postdetection SSC and predetection SSC is much less than previously reported.     

Infinite-series representations associated with the bivariate rician distribution and their applications

Analytical expressions for the evaluation of the bivariate Rician cumulative distribution function (CDF), the covariance, and the characteristic function (CHF) are not known, despite their usefulness in wireless communications systems analysis. In this letter, motivated by the ability of the Rician model to describe fading in wireless communications, we derive infinite-series representations for the probability density function, the CDF, the covariance, and the CHF of two correlated Rician random variables. It is shown that the presented infinite-series expressions converge rapidly, and can be efficiently used to study several performance criteria for dual-diversity receivers operating over correlated Rician fading channels.     

Performance of decorrelating receivers in multipath Rician fading channels

This letter focuses on the performance analysis of the decorrelating receiver in multipath Rician faded CDMA channels. M-ary QAM scheme is employed to improve the spectral efficiency. Approximate expressions are first derived for the two performance indexes: the average symbol error rate (SER) and the average bit error rate (BER) when the decorrelating-first receiver perfectly knows the channel information of the user of interest. To achieve desirable closed-form expressions of the SER and the BER, we exploit results in large system analysis and make assumptions of a high signal-to-interference ratio (SIR) and/or a small Rician K-factor. To measure the receiver performance in the practical scenario, we further derive expressions to approximate the average SER and BER of the decorrelating-first scheme with channel uncertainty. Simulation results demonstrate that the analytical results can also be employed to evaluate the performance of the combining-first receiver.     

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

Closed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Performance Analysis of the Dual-Hop Asymmetric Fading Channel

In real wireless communication environments, it is highly likely that different channels associated with a relay network could experience different fading phenomena. In this paper, we investigate the end-to-end performance of a dualhop fixed gain relaying system when the source-relay and the relay-destination channels experience Rayleigh/Rician and Rician/Rayleigh fading scenarios respectively. Analytical expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio are derived and used to evaluate the outage probability and the average bit error probability of M-QAM modulations. Numerical and simulation results are presented to illustrate the impact of the Rician factor on the end-toend performance. Furthermore, these results confirm that the system exhibits an improved performance in a Rician/Rayleigh (source-relay link/relay-destination link) environment compared to a Rayleigh/Rician environment.     

Achievable Performance of Orthogonal STBC Over Spatially Correlated Rician Channels

The effect of spatial correlation on the performance of orthogonal space-time block codes (OSTBCs) over multiple-input-multiple-output (MIMO) Rician fading channels is studied. Asymptotic error-rate formulas for OSTBC with high average signal-to-noise ratios (ASNRs) over arbitrarily correlated Rician MIMO channels are derived in terms of the diversity and coding gains. Our results show that, in correlated fading, the phase vector phi of the channel line-of-sight (LOS) components affects the effective Rice K-factor at the OSTBC receiver output and, hence, may result in a coding gain that is significantly higher than that for independent Rician MIMO channels. Furthermore, when the channel covariance matrix is rank deficient and under some additional mild conditions, the error and outage probabilities of OSTBC achieve those in a nonfading additive-white-Gaussian-noise channel. For both cases of full-rank and rank-deficient channel covariance matrices, analytical expressions of optimal and worst case phase vectors phi, and exact upper and lower bounds of OSTBC performance are derived. These results provide new insights into the achievable performance of OSTBC over correlated Rician MIMO channels and, if incorporated into future multiple antenna systems design, will bring about significant performance enhancement     

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.     

Closed-form SER expressions for Star MQAM in frequency non-selective Rician and Nakagami- channels

The theoretical SER of star constellations (M-QAM) is calculated in frequency non-selective slowly fading channels, characterized by either Rician or Nakagami-m statistics and corrupted by AWGN. Closed form expressions for the average SERs for Star M-QAM are derived and analyzed, having the form of a single finite integral composed of elementary functions. Because of their simplicity, these expressions readily allow numerical evaluations in practical cases.     

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.     

Moments-based approach to the performance analysis of equal gain diversity in Nakagami-m fading

In this letter, an alternative moments-based approach for the performance analysis of an L-branch predetection equal gain combiner (EGC) over independent or correlated Nakagami-m fading channels is presented. Exact closed-form expressions are derived for the moments of the EGC output signal-to-noise ratio (SNR), while the corresponding moment-generating function (MGF) is accurately approximated with the aid of Pade/spl acute/ approximants theory. Important performance criteria are studied; the average output SNR, which is expressed in closed form both for independent and correlative fading and for arbitrary system parameters, the average symbol-error probability for several coherent, noncoherent, and multilevel modulation schemes, and the outage probability, which are both accurately approximated using the well-known MGF approach. The proposed mathematical analysis is illustrated by various numerical results, and computer simulations have been performed to verify the validity and the accuracy of the theoretical approach.     

Error probability of M-ary DPSK in fast Rician fading and lognormalshadowing

A new expression for the symbol error probability (SER) of M-ary DPSK in fast Rician fading, lognormal shadowing and Gaussian noise is derived. New SER curves are computed and the effects of K factor, fading bandwidth and shadowing spread on the error probability are analysed and discussed     

A Moment-Generating Function (MGF) Derivative-Based Unified Analysis of Incoherent Diversity Reception of M-ary Orthogonal Signals over Independent and Correlated Fading Channels

Exact, closed-form, error probability expressions for noncoherent M-ary frequency-shift-keying (MFSK) systems that employ postdetection equal-gain diversity over Rayleigh, Rician, and Nakagami-m channels are derived using a Laplace derivative formula. Both independent and generically correlated fading cases are considered. For independent fading, closed-form solutions are also derived for both Nakagami-q fading (either with identical or dissimilar fading statistics) and mixed fading cases. Previous results are shown to be specific instances of our general expressions. In addition, a concise, derivative formula is derived for calculating the bit error rate of square-law detected multichannel binary differential phase-shift-keying (DPSK) signals. All of these expressions are applicable in many cases of practical interest and provide accurate predictions of the performance of both binary and M-ary orthogonal signaling over generalized fading channels with arbitrary parameters.     

Analysis of SER of MIMO‐MRC systems with imperfect channel estimation in the presence of non‐Rayleigh CCIs

In this paper, we study the average symbol error rate (SER) for a multiple input multiple output (MIMO) maximal ratio combining (MRC) system with Rayleigh fading desired signal in the presence of non‐Rayleigh fading co‐channel interferers (CCIs) and additive white Gaussian noise (AWGN). To simulate the actual environments of wireless transmission, we assume that the transceiver only obtains imperfect channel estimation (ICE). For the cases of Nakagami and Rician fading CCIs, analytic expressions for the SER have been derived approximately by introducing the modified signal‐to‐interference and noise power ratio (SINR) that can be obtained by averaging the CCI term in the original SINR over the distribution of ICE of intended user. These formulas can provide important reference of design of MIMO diversity systems. Numerical simulations verify the effectiveness of these formulas. Copyright © 2010 John Wiley & Sons, Ltd.     

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.