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Determining tractable analytical expressions for the probability density functions (PDFs) of correlated Rayleigh random variables (i.e., the multivariate Rayleigh joint PDF) is a longstanding problem in wireless communications. Recent results have reported simpler forms for the 3-D and 4-D Rayleigh joint PDFs. Yet, the new solutions are still mathematically complex. New representations for the general 3-D Rayleigh and the general 4-D Rayleigh fading PDFs are derived. An advantage of the new representations is that only a single-integral computation is needed to compute the 3-D Rayleigh PDF and only double integral computation is needed for the 4-D Rayleigh PDF, where the integrals are proper and definite on $[0,\pi )$ and {[0,2\pi )} , respectively. The new expressions for the 3-D and 4-D Rayleigh PDFs are used to determine several special, “best” placements in the 2-D plane for three and four antennas. Closed-form solutions are found for three antennas with two or three independent antenna pairs, and four antennas with four or five independent antenna pairs. [ABSTRACT FROM AUTHOR]

Packet collision is a well-known severe impairment in ALOHA-based networks and, more generally, in any random access network. As a consequence, several methodologies have been considered with the aim of lowering the resulting performance degradation. A novel multiuser detection scheme exploiting channel diversity to separate collided signals is proposed here to enable multiple packet reception capability in random access schemes. The performance of this approach is analytically derived and optimized in terms of network throughput, and compared with that of different alternatives. The overall performance in terms of throughput shows the effectiveness of the proposed scheme in different operating conditions. [ABSTRACT FROM AUTHOR]

The biproduct correlation coefficient matrix structure has gained acceptance and application in wireless communications. Yet, the set of correlation matrices that has this structure has not been fully identified. It is known that the positive equicorrelated matrix satisfies the biproduct condition, but little else is known. The set of admissible correlation matrices having the special biproduct structure is investigated. Constraints on the signs of the correlation coefficients that define the admissible set are revealed. Additional constraints on the magnitudes of the correlation coefficients for admissibilty are also identified. The set of matrices satisfying the required structure is much more restricted than previously thought. The constraints are shown to become increasingly restrictive as the dimension $N$ of the correlation matrix increases. The constraints also become more restrictive as the values of the correlation coefficients increase to approach 1. Previously, only the equicorrelated matrix has been identified as having the biproduct structure. Two additional correlation matrix structures satisfying the biproduct structure are identified. Tests that exclude a correlation matrix from having the biproduct structure are derived. [ABSTRACT FROM AUTHOR]

ABSTRACT 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. [ABSTRACT FROM AUTHOR]

An underlay cognitive multisource multirelay cooperative network is proposed and an analytical framework to evaluate the system performance is formulated. Under both maximum transmission power and interference power constraints, exact and asymptotic outage probabilities for proactive decode-and-forward relaying over Rayleigh fading channels are derived. Both multiuser diversity and cooperative diversity can be achieved with direct secondary links. [ABSTRACT FROM PUBLISHER]

The asymptotic performances of multibranch diversity reception systems employing the popular and important combining techniques over arbitrarily correlated Rician channels are studied. Based on an integral representation of the joint probability density function of multivariate Rician random variables with arbitrary correlations, closed-form expressions for asymptotic error rate and asymptotic outage probability are derived for multibranch receiver diversity receptions. The important diversity schemes studied are maximal ratio combining, equal gain combining, selection combining, and hybrid maximal ratio combining as well as hybrid equal gain combining. Numerical results indicate that these analytical solutions can provide accurate estimation of error rate and outage probability in large-signal-to-noise-ratio regimes. The analysis provides some important theoretical and practical results concerning the performance characteristics of multibranch diversity receivers operating on arbitrarily correlated Rician fading channels. [ABSTRACT FROM PUBLISHER]

A signal-plus-noise (S + N) energy selection combining (S + N-ESC) scheme and a weighted S + N-ESC scheme for binary phase shift keying (BPSK) signaling are studied. The S + N-ESC selects the branch with the maximum S + N energy for detection. The advantage of the S + N-ESC and the weighted S + N-ESC is that they require no explicit channel estimation for diversity branch selection. The bit error rate (BER) performances of the S + N-ESC and the weighted S + N-ESC are analyzed for BPSK signaling in independent and nonidentically distributed (i.n.d.) Rayleigh fading channels. We show that the average error rate performance of the S+N-ESC is the same as classical signal- to-noise ratio selection combining (SNR-SC), which requires the estimation of fading amplitudes for branch selection, in independent and identically distributed (i.i.d.) Rayleigh fading channels. We also show that the weighted S + N-ESC has the same BER performance as the classical SNR-SC for i.n.d. Rayleigh fading channels. [ABSTRACT FROM AUTHOR]

The effect of noise on the switching rate of a dual branch selection diversity combiner in noisy fading channels is examined. A closed-form solution is derived for independent and identically distributed (i.i.d.) and independent and non-identically distributed (i.n.d.) fading channels. The switching rate in noisy fading channels is compared to that in noise-free conditions. [ABSTRACT FROM AUTHOR]

Optimum selection combining using the maximum energy (OSC-ME) criterion for M-ary noncoherent frequency shift keying signaling in independent and nonidentically distributed fading channels is examined. A weighted maximum energy selection combining (WMESC) scheme is proposed and found to provide virtually the same symbol error probability as OSC-ME in Rician fading channels. The WMESC always provides power gain over the classical selection combining regardless of diversity order and signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

The switching rates of dual selection combining diversity and dual switch-and-stay combining diversity in Rayleigh, Rician and Nakagami-m (n-i half-integer or integer) fading are derived. Closed-form or single integral expressions are obtained for both the cases of balanced channels and unbalanced channels. [ABSTRACT FROM AUTHOR]

Asymptotic error rate expressions are derived for equal gain combining and selection combining on dual-branch correlated Rician channels. The asymptotic error rate performances of three popular, diversity combining techniques are compared and some insights are obtained. The impacts of various channel parameters on the asymptotic performances of these diversity combining techniques are studied comprehensively. Some previous observations on diversity performances on correlated Rician channels are unified and further extended. [ABSTRACT FROM AUTHOR]

The outage probability of maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise is derived when the branch gains of the desired user signal and interfering signals experience Rayleigh fading and have the same correlation matrix. Two special cases, when the correlation matrix is equicorrelated and when the correlation matrix has different eigenvalues, are considered for both the equal-power cochannel interference case and the unequal-power cochannel interference case. Further, the average bit-error rate of a coherent binary phase-shift keying (BPSK)-modulated cellular system using maximal ratio combining diversity in cochannel interference and correlated Rayleigh fading is derived. The effects of the average signal-to-noise ratio (SNR) and the average signal-power-to-interference-power ratio on the system performance are examined. [ABSTRACT FROM AUTHOR]

An exact closed-form expression for the average bit error rate (BER) of coherent BPSK using maximal ratio combining (MRC) with correlated branches in the presence of cochannel interference (CCI) and noise is derived. This expression is valid for an arbitrary correlation structure under the assumption that the branch gains of the desired user signal and interfering signals experience correlated Rayleigh fading with the same correlation eigenvector matrix. [ABSTRACT FROM AUTHOR]

The question of how many receiver antennas to employ in a diversity system operating in cochannel interference is examined. The long-term signal-power-to-interference-power ratio, the long-term signal amplitude to the square root of the interference power ratio, the average instantaneous signal-to-interference ratio, and the average bit-error rate of a maximal ratio combining diversity system in the presence of an arbitrary number of cochannel interferers are evaluated when the desired user signal and the interfering user signals are independent, and each of them experiences correlated Ricean fading at the receiver antennas. The best number of antennas required for a fixed-size antenna array to achieve a good compromise between system performance and system cost is investigated. The results show that, in general, the performance of a fixed-size antenna array containing the maximum number of independent antennas cannot be significantly improved by adding more than one additional antenna. Some special cases where particular gains can be achieved by adding additional correlated antennas are also discussed. [ABSTRACT FROM AUTHOR]

The exact performance of selection combining, hybrid selection/maximal-ratio combining (H-S/MRC), and threshold-based H-S/MRC in correlated Nakagami-m fading for positive integer values of fading parameter m, is analyzed for a particular correlation structure. This correlation model, though not general, is much more general than the equal-correlation case, and includes equal correlation as a special case. The symbol-error rate and outage probability of the three combining schemes are obtained by transforming the correlated branch gains into a set of conditionally independent branch gains. Numerical and simulation results show excellent agreement with theoretical results. [ABSTRACT FROM AUTHOR]

Time variation on fading channels hinders accurate channel estimation in differential space-time modulation and deteriorates the performance. Decision-feedback differential detection is studied for block differential space-time modulation, and compared with conventional differential space-time modulation. It is observed that the proposed scheme does not suffer effective fading bandwidth expansion, as does the conventional scheme. An improved effective signal-to-noise ratio approach is proposed for analyzing the performance of the proposed scheme in time-varying flat Rayleigh fading. Theoretical analysis and simulations show the improved performance of the proposed scheme over the conventional scheme. [ABSTRACT FROM AUTHOR]

An accurate approximation to the average symbol-error rate of hybrid selection/maximal-ratio combining (H-S/MRC) in correlated Nakagami-m fading with positive integer values of m is obtained by using a Green's matrix approximation. This approach is valid for different M-ary linear modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example. [ABSTRACT FROM AUTHOR]

The average symbol-error rate of threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) with correlated Nakagami-m fading channels is obtained for positive integer values of fading parameter m for a special correlation structure. An accurate approximate analysis of T-HS/MRC in arbitrarily correlated Nakagami-m fading channels is presented by using a Green matrix approximation. The derivation allows different M-ary linear modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example. [ABSTRACT FROM AUTHOR]

Lower and upper-bound expressions for the penalty of hybrid diversity used with any two-dimensional (2-D) signaling constellation with polygonal decision regions are derived. Using these bounds with well-known results for maximal ratio combining, the error probability performance of 2-D signaling with hybrid selection/maximal ratio combining can be approximated to a high accuracy. [ABSTRACT FROM AUTHOR]

A signal-plus-noise (S+N) energy selection diversity combining (S+N-ESC) scheme for M-ary phase shift keying (MPSK) in Rayleigh fading channels is mathematically analyzed. Also, the S+N-ESC scheme for MPSK and 16-quadrature amplitude modulation (16-QAM) signaling in Nakagami-m and Rician fading channels is studied by computer simulations. The S+N-ESC selects the branch with the maximum S+N energy for detection. The advantage of the S+N-ESC scheme is that it requires no explicit channel estimation for diversity branch selection. We show that the symbol error probability (SEP) of the S+N-ESC is the same as that of classical selection combining (SC) for MPSK signaling in independent and identically distributed (i.i.d.) Rayleigh fading channels. Also, we show that the SEP of a weighted S+N-ESC scheme is the same as that of classical SC for MPSK signaling in independent and nonidentically distributed (i.n.d.) Rayleigh fading channels. It is shown by computer simulations that the S+N-ESC scheme provides a smaller SEP than classical SC for MPSK signaling in nondispersive fading channels such as Nakagami-m fading channels with Nakagami parameter m > 1 and Rician fading channels with Rician parameter K > 0. On the other hand, the S+N-ESC scheme is shown by computer simulations to have a larger SEP than classical SC for 16-QAM signaling in Nakagami-m and Rician fading channels. [ABSTRACT FROM AUTHOR]