Analysis of switched diversity systems on generalized-fadingchannels

The performances of switched diversity systems operating on generalized (Nakagami)-fading channels are analyzed using a discrete-time model. The average bit error rate (BER) of binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Nakagami-fading channels is derived. Closed-form expressions that can be used to determine optimum switching thresholds (in a minimum error rate sense) are also derived. In addition, the use of optimum fixed thresholds is considered. It is found that a considerable amount of diversity gain can be obtained using an optimum fixed (rather than adaptive) switching threshold. Results are obtained for both independent and correlated Nakagami-fading branch signals. The effects of fading severity and the correlation coefficient on both the BER and on the optimum switching threshold are investigated. It is shown that useful diversity gain can be obtained with power correlation coefficients as high as 0.9 when the fading is strong. The results for a Rayleigh channel are obtained and presented as a special case of generalized-fading model     

Performance of DSWC diversity system using suboptimum adaptive switching threshold in independent and correlated nakagami‐m fading channels

The use of dual switched combining (DSWC) diversity reception scheme, for combating the detrimental effects of fading on digital transmissions, is popular due to its simpler implementation. The performance of switched diversity strategy is dependent on the selection of the switching threshold. But, for the analysis and design of the DSWC diversity system, the closed form analytical solution for optimum adaptive switching threshold is not possible for most of the modulation schemes in correlated fading environment. This letter presents an approximate, but simple and closed form, generic expression for adaptive switching threshold, called in this case as suboptimum adaptive switching threshold, in independent and correlated Nakagami‐m fading channels for a wide range of binary and M‐ary modulation schemes. It is shown that the average symbol error rate (ASER) performance obtained using this suboptimum adaptive switching threshold is almost same as obtained using optimum adaptive switching threshold. Copyright © 2005 John Wiley & Sons, Ltd.     

Switched Dual Diversity Reception of M-ary DPSK Signals on Nakagami Fading Channels

The paper deals with dual diversity reception of M-ary differential phase-shift keying modulated signals in the presence of additive white Gaussian noise and Nakagami-distributed slow and nonselective fading. The performance of a switched diversity system is analysed and compared to that of the predetection selection diversity combining scheme. The general case of correlated diversity branches is considered, without restrictions on the fading severity parameter. Average symbol error rate formulas are analytically derived in terms of integral expressions that can be easily computed via numerical integration routines. Moreover, the numerical evaluation of the optimum switching threshold is carried out and the influence of the fading severity parameter, the branch correlation, and the cardinality of the symbol alphabet is analysed. Finally, three fixed switching threshold strategies that allow to obtain a satisfactory diversity gain are considered.     

BER analysis of arbitrary QAM for MRC diversity with imperfect channel estimation in generalized ricean fading channels

Imperfect channel estimation (ICE) can severely degrade the bit error rate (BER) of digital modulations with maximum ratio combining (MRC) diversity reception. The resulting performance analysis problem in its most general setting has not been addressed before. In this paper, the effect of ICE on the BER of an arbitrary square/rectangular Gray-coded quadratic amplitude modulation (QAM) in generalized Ricean fading channels when MRC reception is employed is analyzed. A general expression for the bit error probability of an arbitrary square/rectangular QAM scheme is first derived. This general formula requires a number of conditional probabilities, which is derived in closed form for independent and nonidentically distributed (i.n.d.) Rayleigh-fading channels with MRC and ICE. An efficient numerical method is also presented to compute the conditional probabilities for i.n.d. and correlated Ricean fading. In addition, extensive Monte Carlo simulations that agree excellently with the analytical results are presented.     

Unified BER and optimum threshold analysis of binary modulations in simple and cascaded Rayleigh fading channels with switched combining

Following a unified analytical framework, the bit error rate (BER) of several coherent and non‐coherent binary modulation schemes is derived for a switched diversity system. The two variants of switched combining that have been investigated are switch and stay combining and switch and examine combining. For channel modelling, at first a simple slow flat fading channel is assumed, where the amplitude attenuation obeys the Rayleigh distribution. Later the BER calculations are repeated for cascaded Rayleigh fading channel case. Rayleigh fading is the most popular model for electromagnetic signal propagation in wireless media when both or either of the transmitter/receiver is fixed. On the other hand, when both the transmitter and the receiver are mobile, a cascaded (or double) Rayleigh fading model is better suited. The applicability of these two models, namely simple and cascaded Rayleigh model, has been indicated by several theoretical studies and their suitability is established by various field measurements. In our paper, simple closed‐form BER expressions as a function of switching threshold have been found and optimum switching thresholds have been computed for both these models as well as for both types of diversity combining described earlier. The results presented in this paper can be very useful for communication system designers to analyze link quality of switched diversity assisted systems in various wireless environments. Copyright © 2010 John Wiley & Sons, Ltd.     

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     

Capacity of correlated nakagami-m fading channels with diversity combining techniques

We derive closed-form expressions for the capacity of dual-branch maximal ratio combining, equal gain combining, selection combining, and switch and stay combining (SSC) diversity systems over correlated Nakagami-m fading channels. Because the final capacity expressions contain infinite series, we truncate the series and present upper bounds on the truncation errors. We also derive an expression that can be used to numerically determine the optimum adaptive switching threshold for the capacity of a dual-branch SSC system over correlated Nakagami-m fading channels. However, a closed-form expression for the optimum adaptive switching threshold is derived for the case of independent branches. The corresponding expressions for Rayleigh fading are obtained as a special case of Nakagami-m fading. Finally, numerical examples are presented for illustration.     

Unified analysis of switched diversity systems in independent andcorrelated fading channels

The moment generating function (MGF) of the signal power at the output of dual-branch switch-and-stay selection diversity (SSD) combiners is derived. The first-order derivative of the MGF with respect to the switching threshold is also derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The MGF yields the performance (bit or symbol error probability) of a broad class of coherent, differentially coherent and noncoherent digital modulation formats with SSD reception. The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases. For independent and identically distributed diversity branches, the optimal switching threshold in closed form is derived for three generic forms of the conditional error probability. For correlated Rayleigh or Nakagami-m fading with identical branches, the optimal switching threshold in closed form is derived for the noncoherent binary modulation formats. We show previously published results as special cases of our unified expression. Selected numerical examples are presented and discussed     

Switching rate and receiver performance of binary modulations with the selection‐and‐stay combining over independent and correlated Nakagami‐m fading channels

The dual‐branch selection‐and‐stay combining (SSTC) is analyzed for diversity reception on independent and correlated Nakagami‐m fading channels, where the conventional selection combining (SC) is employed only at the switching instance, and the receiver uses the selected branch till its signal‐to‐noise ratio (SNR) estimation is lower than a preset threshold. In this combining scheme, the receiver only needs to continuously estimate the SNR of the single selected branch. For the performance analysis of SSTC, the switching rate and the average bit error rates (BERs) of different binary coherent and non‐coherent modulations are evaluated. Numerical results based on the analysis and simulations are illustrated. According to the analysis and numerical results, the SSTC outperforms the existing switch‐and‐stay combining in the senses of the average BER and switching rate. Copyright © 2011 John Wiley & Sons, Ltd.     

Precise Outage Analysis of Selection Diversity and Switched Diversity in Bandlimited Microcellular Systems With Cochannel Interference

Precise outage probability performance analysis of a microcellular system with selection and switched diversities is considered. The microcellular system is assumed to follow a flat, slow Nakagami/Rayleigh fading model wherein the fading channels from the desired transmitter to all the receiver antennas are independent and identically distributed Nakagami channels, and all the fading channels for the interfering signals are independent, identically distributed Rayleigh channels. Three selection and switching criteria, namely, desired signal power, signal-to-interference power ratio, and total output power are considered. Unlike previous results, the system model under investigation takes into account the pulse shaping, the random delays, and the phase offsets of the interfering users. Two Nyquist pulse shapes, spectrum-raised-cosine and Beaulieu-Tan-Damen pulse shapes, are considered. Analytical outage probability expressions are derived for an arbitrary number of interferers, arbitrary diversity order, and arbitrary value of desired user fading parameter. The outage performances of the selection criteria are compared. The optimum switching thresholds for different switching criteria are formulated.     

BER performance of MQAM with L‐branch MRC diversity reception over correlated Nakagami‐m fading channels

Exact and closed form generalized expressions for bit error rate (BER) of M‐ary quadrature amplitude modulation (MQAM) with L‐branch maximal ratio combining (MRC) space diversity reception in fading channels are derived and analyzed. The fading channels are modeled as identical but correlated frequency‐nonselective slow Nakagami‐m fading channels corrupted by additive white Gaussian noise (AWGN). Analytical results obtained are in terms of few finite range integrals with an integrand composed of elementary functions. Because of their simple form, these analytical results readily allow numerical evaluation in cases of practical interest. The results are also general enough to include Nakagami‐m fading channels with and without correlation, no diversity system, Rayleigh fading channels with and without correlation, and AWGN as special cases. The numerical results for the case of 16QAM are shown graphically and also in tabular form in order to examine the effects of fading severity, order of diversity, and branch correlation on the BER performance. The two correlation models considered are constant correlation model and exponential correlation model. One may be interested to know how the BER of MQAM is related to symbol error rate (SER) of MQAM. Therefore, the BER results obtained in this paper are also compared with that obtained directly from the SER. It is expected that the analytical results presented in this paper will provide a convenient tool for design and analysis of a radio communication system with space diversity reception in uncorrelated and correlated fading environment. Copyright © 2002 John Wiley & Sons, Ltd.     

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     

Performance of Dual Branch SSC Receiver in Correlated <Emphasis Type="Italic">α</Emphasis>-<Emphasis Type="Italic">μ</Emphasis> Fading Channels

In this paper, the performance analysis of dual branch switch and stay combining (SSC) receivers operating over correlated and identically distributed (i.d.) α-μ fading channels is presented. Assuming this diversity technique, infinite series expressions with fast converging properties are derived for the probability density function (pdf), cumulative distribution function (cdf) and the moments of the output envelope. The proposed analysis is used for evaluating the important performance criteria, such as the outage probability, the mean square output envelope, the amount of fading and the average bit error probability (ABEP). The effects of fading severity, branch correlation and optimum choice of switching threshold are considered and numerically presented. Monte Carlo simulations confirm the validity and accuracy of the derived analytical expressions.     

Closed‐form analysis of multibranch switched diversity with noncoherent and differentially coherent detection

Exact closed‐form analytical expressions are derived for the average bit error probability of multibranch switched diversity systems over independent and identically Nakagami‐m distributed fading channels. Practical schemes that use noncoherent or differentially coherent symbol detection are considered. The general bit error probability expression derived in this paper includes as particular cases the following signaling formats: orthogonal binary signaling, correlated binary signaling, differential phase‐shift keying, and differential quadrature phase‐shift keying. Finally, we apply our analytical results to study the impact of the switching threshold selection on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Switched-diversity FSK in frequency-selective Rayleigh fading

This paper presents the measured performance of a 64 kbit/s switched-diversity FSK receiver subjected to simulated frequency-selective Rayleigh fading. The single receiver input is switched between two, three, or four uncorrelated Rayleigh-fading signals whenever the instantaneous receiver output falls below a threshold. The optimum level of this threshold relative to the mean signal level is relatively insensitive to frequency selectivity and vehicle speed. A nearly optimum threshold may be determined using an AGC amplifier and fixed comparator. Switched diversity is a powerful tool for combating frequency selectivity and Rayleigh fading. Two-branch switched diversity can achieve 10^-2BER, with 6 dB lower SNR than that needed without diversity. In the absence of frequency selectivity, two-branch switched diversity can perform within 3 dB SNR of maximal-ratio diversity and within 1 dB of selection diversity. Switched diversity can achieve BER's lower than the irreducible single-channel BER produced by frequency selectivity. Four-branch switched diversity typically requires 4 dB lower SNR to achieve a given BER than does two-branch switched diversity.     

Switched-Diversity FSK in Frequency-Selective Rayleigh Fading

This paper presents the measured performance of a 64 kbit/s switched-diversity FSK receiver subjected to simulated frequency-selective Rayleigh fading. The single receiver input is switched between two, three, or four uncorrelated Rayleigh-fading signals whenever the instantaneous receiver output falls below a threshold. The optimum level of this threshold relative to the mean signal level is relatively insensitive to frequency selectivity and vehicle speed. A nearly optimum threshold may be determined using an AGC amplifier and fixed comparator. Switched diversity is a powerful tool for combating frequency selectivity and Rayleigh fading. Two-branch switched diversity can achieve 10^-2BER, with 6 dB lower SNR than that needed without diversity. In the absence of frequency selectivity, two-branch switched diversity can perform within 3 dB SNR of maximal-ratio diversity and within 1 dB of selection diversity. Switched diversity can achieve BER's lower than the irreducible single-channel BER produced by frequency selectivity. Four-branch switched diversity typically requires 4 dB lower SNR to achieve a given BER than does two-branch switched diversity.     

Optimal maximal ratio combining with correlated diversity branches

It is proved that a maximal ratio combiner operating on correlated branches and weighting the branch signals as though they were independent is optimal. It is also proved that performance measures of maximal ratio combining operating with correlated Rayleigh or Ricean fading input branches are identical to performance measures of an equivalent diversity system operating with independent and, in general, unbalanced inputs     

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 switched diversity TCM-MPSK systems on Nakagami fadingchannels

Space diversity reception and forward-error correction coding are powerful techniques to combat multipath fading encountered in mobile radio communications. In this paper, we analyze the performance of a discrete-time switched diversity system using trellis-coded modulation multiple phase-shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami (1960) fading channels. Analytical upper bounds using the transfer function bounding technique are obtained and illustrated by several numerical examples. A simple integral expression for calculating the exact pairwise error probability is presented. The use of optimum adaptive and fixed switching thresholds is considered. Monte Carlo simulation results, which are more indicative of the exact system performance, are also given     

BER Performance of Free-Space Optical Transmission with Spatial Diversity

Free space optical (FSO) communications is a cost-effective and high bandwidth access technique, which has been receiving growing attention with recent commercialization successes. A major impairment in FSO links is the turbulence- induced fading which severely degrades the link performance. To mitigate turbulence-induced fading and, therefore, to improve the error rate performance, spatial diversity can be used over FSO links which involves the deployment of multiple laser transmitters/receivers. In this paper, we investigate the bit error rate (BER) performance of FSO links with spatial diversity over log- normal atmospheric turbulence fading channels, assuming both independent and correlated channels among transmitter/receiver apertures. Our analytical derivations build upon an approximation to the sum of correlated log-normal random variables. The derived BER expressions quantify the effect of spatial diversity and possible spatial correlations in a log-normal channel.