M-ary NCFSK with S+N selection combining in Rician fading

The performances of general M-ary and binary orthogonal noncoherent frequency-shift keying signal-plus-noise (S+N) receiver structures in slow, flat Rician fading channels are examined. The fading on the diversity branches is assumed to be independent, but not necessarily identically distributed. For each receiver, a symbol-error probability expression is derived as a single integral with finite integration limits. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The results indicate that, unlike previously published results, the performance of S+N selection combining (SC) is not always superior to that of classical SC in fading and is dependent on the value of the signal-to-noise ratio (SNR), the modulation order, the diversity order, the multipath intensity profile, and the fading parameter. It is further shown that increasing the number of diversity branches in a S+N SC receiver does not necessarily decrease the probability of error if the system is operating in the low-SNR region. The performances of S+N SC schemes are also compared with the performances of equal-gain combining and square-law combining receivers.     

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     

SER of M-ary NCFSK with S + N Selection Combining in Nakagami Fading for Integer m

The performance of M-ary orthogonal noncoherent frequency-shift keying (NCFSK) with N branch signal-plus-noise (S + N) selection combining (SC) in Nakagami-m fading (m, integer) is studied. Both independent, identically distributed (i.i.d) and independent, nonidentically distributed (i.n.d) diversity branches are considered and two S + N SC receiver structures are examined. The performances of the S + N SC receivers are compared to those of classical SC and square-law combining (SLC) receivers. The effects of modulation order, fading parameter and the number of diversity branches on the performance of S + N SC are compared to the effects on the performances of classical SC and SLC. For example, it is shown that in an i.n.d fading channel, the value of signal-to-noise ratio (SNR) at which the error rate curves of classical SC and S + N SC cross, decreases as the modulation order, M, increases. Our results indicate that in i.n.d fading channels classical SC outperforms S + N SC for small ranges of SNR, while for moderate to large SNR values S + N SC has superior performance over classical SC. It is also shown that increasing the diversity order will increase the performance gap of S 4N SC over classical SC and over SLC in both i.i.d and i.n.d Nakagami-m fading channels     

Moment analysis of the equal gain combiner output in equally correlated fading channels

Moments of the multibranch equal gain combiner (EGC) output signal-to-noise ratio (SNR) are only known for independent fading channels or exponentially correlated Nakagami-m fading channels. In this paper, we derive the moments of the EGC output SNR in equally correlated Rayleigh, Rician, and Nakagami-m fading channels. Our moment expressions can be used to evaluate the outage and the average error rate as well as purely moments-based measures such as the average output SNR and the amount of fading as functions of the fading correlation. Numerical results that illustrate the effect of fading correlation on the distribution of the EGC output SNR are also provided.     

Bit-error-probability for noncoherent orthogonal signals in fadingwith optimum combining for correlated branch diversity

Due to the interest in wireless personal communications, there has been a lot of research on the performance of receivers with diversity. Most analyses assume the diversity branches are independent. This paper presents an analysis of the bit-error probability for receivers in which the diversity branches are correlated. Noncoherent orthogonal digital modulation (NCODM) with Rician and Rayleigh slow, nonselective fading models are assumed. Through the use of the diagonalization of quadratic forms, most of the calculations of the bit-error probability can be reduced to a two-dimensional numerical integration. For some cases for dual diversity, a closed-form expression for the error probability is given. A number of diversity combining laws, including square law and maximum likelihood, are considered. We find that Rician fading can be worse than Rayleigh fading in correlated diversity environments, a situation quite different from the independent diversity case. Also, for the Rayleigh fading model with correlated branch diversity, we find that an equal-weight, square-law combiner usually has the same error performance as the more complex maximum-likelihood combiner. However, this is not the case for a Rician fading model with the same correlation environment. Simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals     

Distribution functions of selection combiner output in equally correlated Rayleigh, Rician, and Nakagami-m fading channels

We develop a novel approach to derive the cumulative distribution functions (cdfs) of the selection-combining (SC) output signal-to-noise ratio (SNR) in equally correlated Rayleigh, Ricean, and Nakagami-m fading channels. We show that a set of equally correlated channel gains can be transformed into a set of conditionally independent channel gains. Single-fold integral expressions are, therefore, derived for the cdfs of the SC output SNR. Infinite series representations of the output cdfs are also provided. New expressions are applied to analyze the average error rate, the outage probability, and the output statistics of SC. Numerical and simulation results that illustrate the effect of fading correlation on the performance of L-branch SC in equally correlated fading channels are provided.     

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.     

Asymptotic analysis of multi‐branch EGC and SC over equally correlated Rician channels

Closed‐form asymptotic expressions for bit error rate and outage probability are derived for multi‐branch equal gain combining and selection combining receiver diversity over equally correlated Rician channels. Numerical results indicate that these analytical solutions can provide accurate estimation of bit error rate and outage probability in large signal‐to‐noise ratio regimes. The analytical results reveal some important insights into the performance characteristics of equal gain combining and selection combining diversity operating over equally correlated Rician fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Error probabilities of an FFH/BFSK self-normalizing receiver in aRician fading channel with multitone jamming

We derive the analytical bit-error rate (BER) expressions for a fast frequency-hopped binary frequency-shift keying self-normalizing receiver over a fading channel with the worst-case band multitone jamming (MTJ) and additive white Gaussian noise (AWGN). The desired signal and MTJ are assumed to undergo independent Rician fading and our analyses, validated with simulation results, show that the system performance is not sensitive to different types of MTJ fading conditions. The self-normalizing receiver is found to be superior to the linear-combining receiver when the signal amplitude does not experience severe fading, while the converse is true under Rayleigh fading signal conditions. Under a Rician fading channel and AWGN conditions, the worst-case MTJ and the worst-case partial-band noise jamming are shown to have similar effects on the BER performance of the self-normalizing receiver with diversity     

Closed‐Form Expressions for Selection Combining System Statistics over Correlated Generalized‐K Fading Channels in the Presence of Interference

This paper considers the effects of simultaneous correlated multipath fading and shadowing on the performances of a signal‐to‐interference ratio (SIR)‐based dual‐branch selection combining (SC) diversity receiver. This analysis includes the presence of cochannel interference. A generalized fading/shadowing channel model in an interference‐limited correlated fading environment is modeled by generalized‐K distribution. Closed‐form expressions are obtained for probability density function and cumulative distribution function of the SC output SIR, as well as for the outage probability. Based on this, the influence of various fading and shadowing parameter values and the correlation level on the outage probability is examined.     

Performance analysis of three-branch selection combining over arbitrarily correlated Rayleigh-fading channels

The recent literature has thoroughly treated two-branch selection combining (SC) over correlated Rayleigh fading and three-branch SC over exponentially correlated Rayleigh fading. However, a long-standing open problem involves the three-branch SC performance over arbitrarily correlated Rayleigh fading. We solve this problem completely by deriving new infinite series expressions for the cumulative distribution function, the probability density function, and the moment generating function (mgf) of the three-branch SC output signal-to-noise ratio (SNR). The output mgf can be used to derive the average symbol-error rate for any two-dimensional digital modulations. The outage probability and the higher moments of the SC output SNR are also derived. These analytical results are canonical, in that the three-branch SC performance is now completely solved for arbitrary correlation. Some previous results are shown to be special cases of our new results.     

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.     

A New Approach to Bivariate Hoyt Distribution and its Application in Performance Analysis of Dual-Diversity Receivers

Novel infinite series based expressions for the bivariate Hoyt distribution are derived. More specifically, expressions for the joint probability density function (JPDF) and the joint cumulative distribution function (JCDF) of two Hoyt fading envelopes are derived, and proposed for use in performance analyses of dual-branch diversity receivers operating over correlated Hoyt fading channels. Using these reasonably simple and mathematically tractable expressions, we evaluate the performance of a dual-branch selection combining (SC) diversity receiver in terms of the outage probability (P _out ) and the average bit error probability (ABEP) criteria. The ABEP performance is evaluated for binary differential phase-shift-keying (BDPSK) and binary non-coherent frequency-shift keying (BNFSK) modulation schemes.     

Performance analysis of dual selection diversity in correlated Weibull fading channels

Ascertaining the importance of the dual selection combining (SC) receivers and the suitability of the Weibull model to describe mobile fading channels, we study the performance of a dual SC receiver over correlated Weibull fading channels with arbitrary parameters. Exact closed-form expressions are derived for the probability density function, the cumulative distribution function, and the moments of the output signal-to-noise ratio (SNR). Important performance criteria, such as average output SNR, amount of fading, outage probability, and average bit-error probability for several modulation schemes are studied. Furthermore, for these performance criteria, novel closed-form analytical expressions are derived. The proposed analysis is complemented by various performance evaluation results, including the effects of the input SNR's unbalancing, fading severity, and fading correlation on the overall system's performance. Computer simulation results have verified the validity and accuracy of the proposed analysis.     

Analysis of MIMO MRT/SC Systems

Multiple-input multiple-output (MIMO) diversity systems with maximum ratio transmission at the transmitter and selection combining at the receiver (MRT/SC) are presented to obtain the tradeoff between the system performance and receiver complexity. Closed-form expressions for average symbol error rate (SER) in single-user scenario and average capacity in multi-user scenario are derived to get the performance of MIMO MRT/SC systems under independent and identically distributed (i.i.d.) Rayleigh fading. Our study shows that performance of MIMO MRT/SC systems outperforms that of MIMO space-time block coding systems. The analytical results are compared with the simulation results and a good agreement is obtained.     

Predetection Switched Combining in Correlated Rician Fading

The performance of dual-branch predetection switch-and-stay combining (SSC) in correlated Rician fading is considered in conjunction with several modulation formats. Analytical expressions are derived for the average symbol error rate (SER) of predetection SSC in correlated Rician fading. Switching thresholds that minimize the average SER are obtained. The impact of fading factor and the fading correlation on the performance of predetection SSC is studied. Analytical expressions for the output average signal-to-noise ratio (SNR) and the outage probability are derived. The validity of the analytical expressions are verified using Monte Carlo simulation.     

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.     

Performance of the noncoherent biquadratic and GLRT receivers overtwo-path channels with known amplitudes and Rayleigh fading

Noncoherent detection over Rayleigh fading diversity channels with known or perfectly estimated amplitudes is studied for binary, uniformly orthogonal signaling. The optimum receiver is well known, but is too difficult to implement. Hence, two suboptimal receivers are considered: the “biquadratic” receiver, optimum at low signal-to-noise ratios (SNR's), and the “bilinear” receiver (optimum at high SNR's) which is also a generalized likelihood ratio test (GLRT) receiver for this case. We analyze the performances of the two suboptimal receivers over two-path channels and compare them to the basic quadratic receiver. For this purpose we present a general method for computing the error probability that can be applied to any dual-diversity binary detection problem whenever the method of characteristic functions fails. We present the exact analytical expressions for the biquadratic receiver, and the numerically computed results for the GLRT receiver, in terms of the conditional, average and asymptotic error probabilities. It is shown that the two receivers are rather close in performance in most of the SNR ranges of interest     

Performance Analysis of Dual-Branch Selection Combining Over Correlated Rician Fading Channels for Desired Signal and Cochannel Interference

System performances of dual selection combining over fading channels are analyzed. Fading between the diversity branches and between interferences is correlated and Rician distributed. Infinite series expressions for the probability density function, and the cumulative distribution function of the output signal-to-interference ratio are derived, which is the main contribution of this paper. Outage probability and the average bit error probability for noncoherent modulation schemes are also presented. Numerical results, presented in this paper, point out the effects of fading severity and correlation on the system performances.