Combining Diversity System Research Articles

Novel Expressions for Ricean Sum Distributions and Densities

This letter provides exact expressions for the sum statistics of independent and identically distributed Ricean random variables. More precisely, we derive new compact, fast, and manageable solutions for both the probability density function and the cumulative distribution function of the considered sum. Numerical results verified the validity of our expressions. In particular, our solutions present a faster and efficient way to evaluate the exact Ricean sum, overcoming the traditional multi-fold Brennan’s integral approach. In order to show the wide applicability of our expressions, we evaluate the performance of an $N$ -branch equal-gain combining diversity system over Ricean fading channels. More specifically, we derive exact and closed-form asymptotic expressions for the outage probability.

Fifth Generation promising integrated full loaded MIMO space‐time spreading‐aided‐orthogonal frequency code division multiple access system

The optimisation of a communication system becomes a difficult objective if distinct techniques are utilised to resolve different problems of the same system. Accordingly, the main target of future mobile communication systems (e.g. fifth generation) is to integrate different techniques under a unified framework for the optimisation purpose. This study proposes a downlink air interface that targets maximum capacity and bit error rate (BER) performance enhancement. The proposed system is an integration of a full loaded multi-code transmission orthogonal frequency code division multiple access and space-time spreading that exploits transmit diversity needed for BER enhancement and data rate optimisation. Further BER improvement was achieved through applying an effective iterative interference cancellation in the space domain combined with multi-code interference suppression algorithm at the receiver. The authors present a system performance analysis in addition to simulation results for the proposed system. The BER performance improvement was emphasised through comparing the proposed system with a similar system that uses joint iterative detection. Finally, the effect of frequency domain spreading factor with different number of iteration loops was investigated for further BER system performance enhancement. The achieved BER performance outperforms the maximal ratio receive combining diversity system performance with 1Tx and 8Rx.

On-glass automotive diversity antenna and LNA design for S-band satellite digital radio

Selection combining diversity system with antennas mounted on windshield and backlite of a vehicle is proposed for satellite digital audio radio applications. Standalone exterior mount antennas on metallic vehicles perform well for satellite digital audio radio applications, but for composite body vehicles or interior mount antennas, antenna performance becomes a real issue. Proposed on-glass two-antenna diversity is one solution for such applications. The antenna correlation is calculated using the S-parameters of the antennas and found to be very low due to many wavelengths separation between the antennas. Design of low noise amplifier, which has sub 1 dB noise figure and good P1dB due to strong cellular signals, is also detailed. A diversity receiver is described and ride tests are performed to assess the performance of the diversity system in real-time, under weak satellite signal environment which is regarded as the most challenging reception condition.

Performance analysis of switch and stay combining diversity system over κ–μ fading channels

This paper studies important performance measures for a dual-branch switch and stay combining (SSC) diversity system over κ–μ fading channels. In particular, an expression for the moments of the output signal-to-noise ratio (SNR) is obtained in three different forms: in terms of an infinite series, a single finite-range integral and the Nuttall Q-function, where the moments expression is utilized to obtained expressions for the average output SNR, and amount of fading. An expression for the outage probability is also derived with SSC. Furthermore, the moment-generating function (MGF) is derived in terms of an infinite series, a single finite-range integral and the generalized Marcum Q-function, which is applied to derive an expression for the average bit error rate (BER) for various coherent modulation schemes. The BER for non-coherent detection is also derived. The infinite series in the final expressions are truncated and upper bounds on the truncation errors are obtained. Closed-form expressions for the optimum switching threshold are also derived. The corresponding expressions for Rician fading, and Nakagami-m fading are presented as special cases of κ–μ fading. Finally, numerical and simulation results are offered for illustration purposes.

Terrain based system design and SNR variability prediction in multi-hop transparent relay transmission systems

The challenging issue of assessing the impact of fading distribution and hop count on the system performance of multi hop transparent cooperative network for indoor as well as outdoor communications is addressed in this article. As the received signal fluctuations depend on the compound channel variations, a cost effective link design and power budget of fixed relaying systems based on the evaluated terrain dependent statistical properties are presented. Subsequently, hop count selection and theoretical prediction of variability of signal-to-noise-ratio (SNR) are performed in a particular application scenario. The proposed approach eliminates the need for continuous monitoring of the time varying SNR on each branch of the receiver diversity system. The impact of hop count on the bit error rate performance of the designed system, under two different per-hop distributions–Nakagami-m and Weibull, which can adequately characterise the terrain fading effects on empirical data–are also studied using simulations. The effectiveness of the derived metrics in selecting appropriate branches of sufficient channel quality in selection combining diversity systems are also investigated.

Uniform bounds of first‐order Marcum Q ‐function

A new expression of the generalised Marcum Q-function is obtained in terms of incomplete cylindrical function. Based on the new representation, new lower and upper bounds of the first-order Marcum Q-function are formulated. The bounds are represented in terms of the error and modified Bessel functions. Unlike the existing bounds, the tightness of the new bounds is maintained over the entire range of arguments of the Marcum Q-function, which is numerically and theoretically demonstrated. To show the usefulness of the formulated bound, the upper and lower of a generic integral is formulated in the performance analysis of an antenna diversity system under a Nakagami fading channel. The uniform tightness of the bound of the integral is also observed. Then, the authors consider the average bit error rate (ABER) probability of the equal gain combining diversity system in the fading channel, which show that the proposed bound can estimate very tight bound of the ABER probability.

Superanalysis of Optimum Combining with Application to Femtocell Networks

A femtocell technology-towards the deployment of small-cell networks-is a key enabler for improving indoor coverage and throughput per network area at a low cost in future wireless networks. However, these small-cell networking inevitably increases cochannel interference due to aggressive (even uncontrolled) reuse of spectral resources. One of the attractive approaches to alleviating the cochannel interference is a multiple-antenna technique for which accurately characterizing the effects of interference is crucial but challenging. To elucidate this important problem, we analyze the performance of interference rejection diversity combining, often called the optimum combining, in an uplink two-tier femtocell network. Specifically, we consider that a single-antenna femtocell user (transmitter) communicates with a closed femtocell access point (receiver) with multiple antennas in the presence of single-antenna cochannel interferers from co-tier (femtocells) and cross-tier (macrocell) networks. We introduce a new mathematical methodology to analyze the average symbol error probability of optimum combining diversity systems in Rayleigh fading, accounting for multiple unequal-power interferers, each is spatially correlated across receiving antennas. The analysis resorts to the so-called Berezin's supermathematics that treats both commuting and Grassmann anticommuting variables on an equal footing. This powerful supermathematical framework enables us to quantify the cross- and co-tier interference effects in terms of interference power heterogeneity and spatial correlation.

Performance of dual-branch selection combining diversity systems in non-identical Nakagami- q (Hoyt) fading channels

Motivated by the low-complexity to implement a dual-branch selection combining system, which is a practical method to improve the performance of a communication system subject to fading, this work studies important performance measures for that system over independent but non-identically distributed Nakagami-q fading channels. In particular, a novel closed-form expression is derived for the moments of the output signal-to-noise ratio (SNR), which is utilised to obtain expressions for the average output SNR, and amount of fading. An expression for the outage probability is also obtained in a closed-form. Furthermore, novel expressions for the channel capacity are derived for two adaptive transmission schemes: the optimal rate adaptation with constant power and channel inversion with fixed rate. The corresponding expressions for one-sided Gaussian and Rayleigh fading are obtained as special cases of Nakagami-q fading. Finally, numerical examples are presented for illustration.

Performance analysis of rectangular quadrature amplitude modulation with combined arbitrary transmit antenna selection and receive maximal ratio combining in Nakagami- m fading

The average symbol error probability (SEP) performance of arbitrary rectangular quadrature amplitude modulation in the context of arbitrarily ordered transmit antenna selection and receive maximal ratio combining diversity system is analysed. The channel gains are assumed to follow Nakagami-m fading distribution with in general arbitrary fading parameters. Exact expressions for the average SEP performance are derived for the general case of unequal in-phase and quadrature decision distances as well as distinct in-phase and quadrature modulation orders. The results generalise many previous case studies, and can be used to investigate the impact of various diversity-combining schemes and different modulation and channel parameters on the system average SEP performance.

Accurate closed‐form approximations for the performance of equal gain combining diversity systems in Nakagami fading channels

AbstractAccurate closed‐form approximations for the distribution and density of the signal envelope at the output of L‐branch equal gain combining (EGC) receivers in Nakagami fading channels are derived. These expressions are used to analyse the probability of error of an L‐branch predetection EGC diversity system operating in different fading conditions. Coherent and noncoherent binary signalling as well as coherent M‐ary signalling are considered. In addition, a closed‐form expression for the outage probability of these systems is derived. These closed‐form expressions permit rapid evaluation of the performance of EGC diversity systems without resorting to numerical integration as required by previous solutions. Copyright © 2008 John Wiley & Sons, Ltd.

Efficient bit error probability expression and very tight bound for maximal ratio combining diversity systems over Rayleigh fading channel

Bit Error Probability (BEP) provides a fundamental performance measure for wireless diversity systems. This paper presents two new exact BEP expressions for Maximal Ratio Combining (MRC) diversity systems. One BEP expression takes a closed form, while the other is derived by treating the squared-sum of Rayleigh random variables as an Erlang variable. Due to the fact that the extant bounds are loose and could not properly characterize the error performance of MRC diversity systems, this paper presents a very tight bound. The numerical analysis shows that the new derived BEP expressions coincide with the extant expressions, and that the new approximation tightly bounds the accurate BEP.

On the Maximum Number of Receiver Diversity Antennas That Can Be Usefully Deployed in a Cochannel Interference Dominated Environment

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.

Error rates of M-ary signals with. Multichannel reception in Nakagami-m fading channels

In this letter, we present closed. form expressions for the exact average symbol-error rate (SER) of M-ary modulations with multichannel reception over Nakagami-m fading channels. The derived expressions extend already available results for the nondiversity case, to maximal-ratio combining-(MRC) and postdetection equal-gain combining (EGC) diversity systems. The average SERs are given in terms of Lauricella's multivariate hypergeometric function FD (n) . This function exhibits a finite integral representation that can be used for fast and accurate numerical computation of the derived expressions

Channel Capacity of Adaptive Transmission With Maximal Ratio Combining in Correlated Rayleigh Fading

We derive closed-form expressions for the single-user capacity of maximal ratio combining diversity systems taking into account the effect of correlation between the different branches. We consider a Rayleigh fading channel with two kinds of correlation: 1) equal branch signal-to-noise ratios (SNRs) and the same correlation between any pair of branches and 2) unequal branch SNRs and arbitrary correlation between branches such that the eigenvalues of the branch covariance matrix are all distinct. Three adaptive transmission schemes are analyzed: 1) optimal simultaneous power and rate adaptation; 2) optimal rate adaptation with constant transmit power; and 3) channel inversion with fixed rate.

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.

Approximation of SNR statistics for MRC diversitysystemsin arbitrarily correlated Nakagami fading channels

An approximated probability density function is presented for the SNR in maximal ratio combining diversity systems with an arbitrary number of diversity branches in an arbitrarily correlated Nakagami fading environment. Comparisons between the exact and approximated distribution show good agreement over wide ranges of correlation coefficients.

Outage probability of cellular radio systems using maximal ratio combining in the presence of multiple interferers

In mobile radio systems, antenna diversity is used to combat fading and reduce the impact of cochannel interference. We derived a new expression for probability density functions of the signal-to-interference-plus-noise ratio and apply it to analyze the outage probability (OTP) for a maximal ratio combining diversity system when multiple cochannel interferers are present. Numerical results showing the impact of the number of antenna elements, the number of cochannel interferers, and signal-to-noise ratio on the OTP are presented. Simulation results validating the analytical results are also presented.