Maximal Ratio Combining Diversity Research Articles

Bit error rate analysis of MRC diversity receiver over shadowed Beaulieu‐Xie fading channels for mmWave communications

SummaryThis paper presents the performance of maximum ratio combining (MRC) diversity receiver over shadowed Beaulieu‐Xie (SBX) fading model. The SBX model is used to characterise wireless communication environments that include multiple numbers of line‐of‐sight (LOS) and non‐line‐of‐sight (NLOS) signals. The probability density function (PDF) of the MRC scheme over the SBX channel has been derived. The PDF‐based approach has been used to calculate the outage performance and average bit error rate of several modulation schemes for coherent and non‐coherent signals. It has also been shown how the diversity orders and the fading channel's parameters affect the system's performance. To authenticate the evaluated expressions, Monte‐Carlo simulation results are used for validation. The SBX model is used to characterise wireless communication environments that include multiple numbers of LOS and NLOS signals.

Performance Evaluation of Maximum Ratio Combining Diversity Technology and Traditional System Based on Comprehensive Noise Analysis in Underwater Wireless Optical Communication

The maximum ratio combining (MRC) diversity technology has shown outstanding performance in overcoming the adverse effects of underwater wireless optical communication (UWOC) systems. However, its actual performance gain will be affected by the detection area and noise, which requires an in-depth analysis. In this paper, on the basis of fully considering the noises in the UWOC system, the performance of the MRC diversity technology is fairly and comprehensively studied by comparing it with two single-input–single-output (SISO) systems using a small aperture detection (SAD) scheme or a large-aperture detection (LAD) scheme through a Monte Carlo simulation and a formula analysis. The results show that the traditional belief that the MRC diversity scheme has consistently outperformed SISO systems may be misleading. When the thermal noise is dominant and the background noise is small, the LAD scheme performs better than the MRC diversity scheme with the same detection area. And in other cases, the MRC diversity scheme with the same detection area is always superior to the SISO systems. The conclusions obtained in this paper have a guiding significance for the practical application of UWOC.

Analytical framework for the performance of energy detectors over α‐μ fading model with MRC diversity

SummaryThe advancements towards the 5G technology are significantly reliant on the effective utilization of the radio spectrum. The scarcity of the spectrum is a barrier to the employment of emergent wireless multimedia. The cognitive radio (CR) technology has materialized as a reassuring remedy to the present problem of spectral scarcity. This study explores the statistical characterization of energy detector‐based cognitive radio device alongside diversity reception. The analysis is carried out with the postulation that the transmitting signal encounters fading, characterized by α‐μ fading channel. Initially, we present a PDF expression of the α‐μ fading model when subjected to maximal ratio combining (MRC) diversity reception. Utilizing this expression, the closed‐form expression of the average probability of detection (Pd) and the average area under the receiver operating characteristics curve (AUC) are derived in the terms of Fox's H function. The detection threshold has been optimized to improve the detection performance by curtailing the probability of error. Additionally, asymptotic results for Pd with various diversity combining cases are also obtained under high signal‐to‐noise‐ratio (SNR) regime. Furthermore, the result of Pd is applied to explore the execution of cooperative spectrum sensing (CSS) with diversity reception. The accuracy and validation of the presented results are assured by comparison with the Monte Carlo simulation.

Performance analysis of downlink NOMA system with diversity combining schemes over [formula omitted]–[formula omitted] fading channel

A novel downlink multiuser non-orthogonal multiple access (NOMA) system is proposed in which diversity combining techniques are employed at each user. In particular, selection combining (SC), equal gain combining (EGC), and maximum ratio combining (MRC) diversity techniques are adopted by each user to improve the performance of the system. The outage and sum-rate analysis of the proposed system are presented for L branch diversity combiner over η–μ fading channel with imperfect successive interference cancellation (SIC). In addition, an exact closed-form expression for the probability density function (PDF) of signal-to-noise ratio (SNR) at the output of equal gain combiner is derived using Laplace transform approach for η–μ fading channel. The proposed system completely outperforms the conventional NOMA system and among the proposed schemes, NOMA with MRC diversity has the best performance, as expected. The outage performance of the proposed NOMA system is compared with that of orthogonal multiple access (OMA) system. The theoretical results are verified with the simulation results.

Performance Analysis of Dynamic Downlink PPP Cellular Networks Over Generalized Fading Channels With MRC Diversity

This paper proposes novel and generalized expressions to characterize the performance of modern cellular networks under realistic user mobility behavior. The η-μ distribution is employed to derive the received power probability density function, the average bit error rate for different modulation schemes, and the coverage probability assuming a Poisson point process spatial distribution of base stations in downlink. The user is assumed to experience fading with Maximum Ratio Combining (MRC) and move according to a random way-point mobility model. The proposed expressions are applicable to different widely-used fading environments, such as Rayleigh and Nakagami-m as particular cases, by an appropriate selection of the η-μ parameters. Monte Carlo simulation was used to show the validity of the proposed expressions. The generalized expressions allow the system designer to quantify the effects of user mobility on the cellular network performance, in different propagation environments, and network topologies as a function of the number of base stations and MRC branches.

Secrecy Outage Performance of Cognitive Radio Network with Selection Combining at Eavesdropper

Background: Based on the idea of cooperative communication, recently a lot of attention has been drawn to cooperative spectrum access for the secure information transmission in a Cognitive Radio Network (CRN). Security is one of the most important aspects of these networks, as due to their open and dynamic nature, they are extremely vulnerable to malicious behavior. Cooperative cognitive radio has emerged as a dynamic spectrum access technique, where an unlicensed (secondary) user is allowed to simultaneously access the licensed channels dedicated to a Primary User (PU), as long as the Quality of Service (QoS) of primary communication is not affected. Method: This paper investigates the secrecy outage performance of threshold-based cognitive decode-andforward relay network, with interference constraints from primary licensed user. Threshold-based relaying is considered where; the source message is successfully decoded by the relay, only if the received SNR satisfies the particular threshold. Outage probability expressions have been derived for the worst-case scenario, where only the eavesdropper can achieve the advantage of diversity. The Selection Combining (SC) diversity scheme is employed only at the secondary eavesdropper. Results: The system secrecy performance is better for SC diversity scheme at the eavesdropper than Maximal Ratio Combining (MRC) diversity scheme, as MRC has better diversity performance than SC. We have shown that the improvement in desired secrecy rate, predetermined threshold, eavesdropper channel quality and interference constraints affect the secrecy performance of the cognitive radio system. The outage probability decreases accordingly with an increase in the maximum tolerable interference level at primary destination. The outage probability of Optimal relay Selection (OS) scheme is derived for a multi-relay system, when either the Instantaneous Channel State Information (ICSI) or the Statistical Channel State Information (SCSI) is available. We have shown that the secrecy performance of the OS with ICSI of the system is better than with SCSI. Also, the OS improves the performance of the multi-relay system, when the number of relays is increased. Conclusion: The secrecy outage probability of threshold-based DF underlay cognitive relay network is evaluated. Both interference and maximum transmit power constraints are considered at secondary source and secondary relay. Also, the relay can successfully decode the message, only if it meets the pre-defined threshold. We have investigated the performance of MRC and SC diversity schemes at the secondary eavesdropper and have shown that the system secrecy performance is better for SC than MRC, as MRC has better diversity performance than SC. We have shown that the system secrecy performance is significantly affected by the required secrecy rate, pre-defined threshold, interference constraints and choice of diversity scheme (MRC/SC) at the eavesdropper. The outage probability of OS scheme is derived for a multi-relay system, when either the ICSI or the SCSI is available. We have shown that the secrecy performance of the OS with ICSI of the system is better than with SCSI. Also, the OS improves the performance of the multi-relay system, when the number of relays is increased.

On the Distribution of the Sum of Málaga-$\mathcal {M}$ Random Variables and Applications

In this paper, a very accurate approximation method for the statistics of the sum of Malaga- $\mathcal {M}$ random variates with pointing error (MRVs) is proposed. In particular, the probability density function of MRV is approximated by a Fox's $H$ -function through the moment-based approach. Then, the respective moment-generating function of the sum of $N$ MRVs is provided, based on which the average symbol error rate is evaluated for an $N$ -branch maximal-ratio combining (MRC) receiver. The retrieved results show that the proposed approximate results match accurately with the exact simulated ones. Additionally, the results show that the achievable diversity order increases as a function of the number of MRC diversity branches.

Average bit error rate of the direct receive-diversity free-space optical system over correlated non-Kolmogorov turbulence fading channels

The average bit error rate (BER) performance of direct single-input multiple-output (SIMO) free-space optical link over correlated non-Kolmogorov turbulence fading channels is studied. In particular, the new closed-form expressions of BER performance of maximal ratio combining (MRC) and equal gain combining (EGC) receive-diversity systems are derived by α-μ distribution approximation method. The influence of both spectral power law and the channel correlation on the BER performance of MRC and EGC diversity systems is systematically investigated and compared. Monte Carlo simulation results are also presented to illustrate the validity of the proposed approach. We will help to investigate the fading correlation in spatial diversity systems and provide useful information for the design of the diversity system.

Efficient Turbo Inter Leaver Based MIMO OFDM System For Low Complexity Outdoor Communication

An arrangement of multiple antennas in both the receiver and transmitter called Multiple Input and Multiple Output (MIMO). The Orthogonal Frequency Division Multiplexing (OFDM) is enabled in MIMO system for high data wireless communications. Combination of both MIMO and OFDM Access (OFDMA) is a growing technology in next generation communication systems. In this work, the Bit Error Rate (BER) performance of MIMO-OFDMA is analyzed with Orthogonal Space Time Block Code (OSTBC), Maximum Ratio Combining (MRC) and Turbo coding scheme over flat fading channel are named as MIMO-MRC-OFDMA. OSTBC is a transmit diversity scheme, which is utilized for delivering an efficient transmission with high peak data rates that significantly improves the capacity of communication systems. Successively, the MRC diversity solves transmit and receive diversity from an OSTBC. MRC approach is applied in the receiving end for summing and weighing the received signals from the multiple paths. Besides, turbo coding scheme is utilized for error correction in a given code rate. The proposed system performance is evaluated in light of BER by varying the number of receive and transmit antennas such as 2×2, 2×4, 4×2 and 4×4.

Complete solutions for the outage probability of maximal ratio combining diversity on Nakagami‐ m fading channels with unequal power branches valid for integer m

Maximal ratio combining (MRC) diversity is fundamental in wireless communication theory and widely implemented in practice. There are limited results in the theory for the probability density function (PDF) of MRC diversity on Nakagami channels when the branches have unequal powers. In addition to being restricted, the known solutions are complex and in some cases unwieldy. Novel, complete solutions for the PDF of MRC signal-to-noise ratio (SNR), valid for integer values of the Nakagami fading parameter m and arbitrary branch powers, are derived. In addition to being solutions for the unsolved cases, the new solutions give different and much simpler expressions for the known restricted cases than previous solutions. The effects of branch channel power imbalances on the PDF of MRC and on the outage probability are investigated quantitatively. The new solutions are used to derive asymptotic large SNR performance measures for MRC diversity with unequal branch powers, insights not obtainable from previous solutions. The new solutions are used to derive intuitive simple approximations for the densities and distributions of MRC output signal power and amplitude, as well as for the outage probability. The approximations are shown to have excellent accuracies for power imbalances <;30% and good accuracies for power imbalances <;60%.

New approximate and asymptotic closed-form expressions for the outage probability and the average BER of MIMO-FSO system with MRC diversity technique over Gamma–Gamma fading channels with generalized pointing errors

This paper studies the outage probability (OP) and the average bit-error rate (BER) of multiple-input multiple-output (MIMO) free-space optical (FSO) system with maximal ratio combining (MRC) diversity technique over Gamma–Gamma (GG) fading channels with generalized pointing errors modeled by the Beckmann distribution. A new approximate closed-form probability density function (PDF) at high signal-to-noise ratio (SNR) for MRC scheme is derived by inverse Laplace transformation method. Based on the developed PDF, new approximate and asymptotic closed-form expressions for the OP and the average BER are derived, respectively. Then, the OP and the average BER performance of the MIMO-FSO system with MRC scheme at high SNR are analyzed with different parameters, including number of transmitters and receivers, receiver aperture sizes, nonzero boresight, and different jitters. Finally, numerical results and Monte Carlo simulations corroborate the accuracy of the derived approximate and asymptotic expressions over a wide range of SNR.

Performance analysis of repeated index modulation for OFDM with MRC and SC diversity under imperfect CSI

In this paper, we conduct the investigation into the performance of repeated index modulation-orthogonal frequency division multiplexing (RIM-OFDM) system with spatial diversity comprising the maximal ratio combining (MRC) and selection combining (SC). The considered systems, abbreviated as RIM-OFDM-MRC and RIM-OFDM-SC, are successful in exploiting both the frequency and spatial diversities to provide improvement in the error performance of the conventional IM-OFDM system with diversity reception. We find out the closed-form expressions for the index and symbol error probabilities of RIM-OFDM-MRC and RIM-OFDM-SC under a variety of different channel conditions. We also carry out asymptotic analysis in order to examine the system behavior under influences of system parameters and the imperfection in channel state information (CSI). Performance evaluation through both theoretical and simulation results demonstrates the significant performance improvement of our systems in comparison with the conventional IM-OFDM using MRC/SC even when channel estimation errors occur at the receiver.

MGF-Based Analysis of Spectrum Sensing Over $K-\mu$ Fading Channels for 5G Cognitive Networks

With the development of wireless communication techniques, higher spectrum efficiency is being pursued for the fifth generation (5G) mobile communication. Cognitive radio (CR) has attracted much attention from industry and academia due to its ability to improve spectrum efficiency. In 5G CR networks, the most important function is spectrum sensing (SS). However, SS performance deteriorates seriously for single-antenna signal detection. To improve spectrum efficiency, multiple-antenna (MA) signal-detection techniques have been proposed to improve SS performance by taking advantage of MA diversity reception. In this paper, we propose an MGF-based method for performance analysis of SS over $k-\mu $ channels for 5G CR networks. The expressions of the average detection probabilities are derived in closed form for cases of SA signal detection and MA signal detection. For MA signal detection, we mainly consider maximal ratio combining (MRC) and square law combining (SLC) diversity reception scheme over the $k-\mu $ fading channel. The improvement in detection performance is quantified for the MRC and SLC schemes. The simulation results show that the MRC and SLC diversity reception ( $L>1$ ) schemes achieve significant sensing diversity gains compared with that in the SA case.

Simplified approximations to the average of some useful forms of Gaussian Q functions with MRC diversity reception over Nakagami-q and Rician fading channels and their applications

In this paper, using an accurate exponential based approximation on the Gaussian Q function, the simplified novel approximations to the average of some useful forms of Gaussian Q functions, with maximal-ratio combining (MRC) diversity reception, over independent but not necessarily identical Nakagami-q (Hoyt) and Rician fading channels are proposed. The results proved to be useful in accurate estimation of the symbol error probability (SEP) for various digital modulation schemes like cross-QAM, triangular-QAM (TQAM), rectangular-QAM and square-QAM (SQAM), over the same fading statistics. Asymptotic expressions of the proposed approximations are also derived in this paper. Various simulation results are provided to verify the accuracy and significance of the proposed work.

A new closed-form of ASEP and channel capacity with MRC and selection combining over Inverse Gaussian shadowing

This paper analyse and investigate the performance of communication system with maximal ratio combining (MRC) and selection combining (SC) over Inverse Gaussian (IG) fading distribution. All formats of coherent and non-coherent modulation schemes are considered and novel analytical expressions of average symbol error probability (ASEP) with diversity are derived. Gamma and IG fading distributions are popularly used as a mathematically less complex solution to lognormal in the open literature. Hence, we provide a comparative analysis between IG and gamma fading with the aim to provide a quantitative measure of the difference between the two distributions in the context of ASEP. Moreover, the novel closed-form expressions of channel capacity under transmission schemes such as optimal rate adaptation (ORA) and channel inversion fixed rate (CIFR) are derived and analysed with MRC and SC diversity over IG fading. The analytical results have been validated with the Monte Carlo simulations and the exact numerical results.

Capacity of dual-branch MRC system over correlated Nakagami-m fading channels with non-identical fading parameters and imbalanced average SNRs

We present the closed-form expressions for the capacity with correlated, non-identical fading parameters and imbalanced average SNRs (Signal-to-Noise Ratios) of dual-branch MRC (Maximal Ratio Combining) diversity system over Nakagami-m fading channels. This capacity is evaluated for ORA (Optimum Rate Adaptation with constant transmit power) and CIFR (Channel Inversion with Fixed Rate) schemes. Numerical results have been presented and compared with the available capacity results of ORA and CIFR schemes in the literature. The effect of different practical constraints, e.g. non-identical fading parameters, fade correlation and level of imbalanced in average SNRs on the channel capacity of the systems, is analysed.

Performance Analysis of 32-QAPM System with MRC Diversity in Rician Fading Channel

In this study, the performance of a 32-quadrature amplitude position modulation (QAPM) system is analyzed under a Rician fading channel condition when the maximal ratio combining (MRC) diversity technique is used in the receiver. The fading channel is modeled as a frequency non-selective slow Rician fading channel corrupted by additive white Gaussian noise (AWGN). QAPM is available to improve BER performance without amplifying transmit power, and MRC diversity makes the performance improvement of QAPM system even bigger by intentionally maximizing SNR. Error performances are shown for the 32-QAPM system and a 32-phase silence shift keying (PSSK) system in order to examine the effects of fading severity, for various values of the Rician parameter, K. The dependence of error rates on MRC diversity is also analyzed. The simulation results show that the BER performance of the 32-QAPM system is better than that of the 32-PSSK system under the above mentioned conditions.

Analysis of Error Rate Performance Limit of DBPSK/NCFSK Modulations for OFDM System with MRC Diversity in Correlated Nakagami-m Fading Channels

In this paper, we derive exact and asymptotic bit error rate (BER) formulas of differential binary phase shift keying (DBPSK) and non-coherent frequency shift keying (NCFSK) modulations for orthogonal frequency division multiplexing (OFDM) system employing maximal ratio combining (MRC) receive diversity technique, especially over correlated Nakagami-m fading channels. In particular, exploiting the derived asymptotic BER formulas, asymptotic modulation gain and diversity order can be subsequently achieved, which enable us to easily predict the performance limit of the considered system and channel environments. Based on our asymptotic analysis, we can also analytically demonstrate the asymptotic SNR performance gap between DBPSK and NCFSK.

Ergodic Channel Capacity for Rayleigh Fading Channels with Impairments Due to Errors in M-Branch Hybrid Diversity Combining

Novel closed-form expressions are derived for Ergodic channel capacity for fading channels with impairments due to combining errors for M-branch Rayleigh fading with Generalized Diversity Combining. Four different adaptation policies are analyzed for (1) maximal ratio combining (MRC) diversity, (2) spread spectrum (SS) diversity with MRC and Antenna diversity with selection combining (SC), and (3) SS diversity with SC and Antenna diversity with MRC diversity reception cases. Correlation is defined physically as the similarity between the channel coefficients of the pilot and the message. If the pilot and the message are highly correlated, we have a high system performance. Optimal power and rate adaptation policy yields the best spectrum efficiency, while channel inversion with fixed rate policy suffers the highest penalty in comparison to other policies.

Performance Evaluation of $$\pi /4$$ π / 4 -DQPSK OFDM over Underwater Acoustic Channels

This paper investigates the performance of orthogonal frequency division multiplexing (OFDM) with $$\pi /4$$ź/4-differential quadrature phase shift keying ($$\pi /4$$ź/4-DQPSK) modulation, over underwater acoustic (UWA) channels. The orthogonal multicarrier scheme with non-coherent detection technique results in spectrally efficient, reliable and simple receiver design. $$\pi /4$$ź/4-QPSK has less envelop fluctuation and performs better in multipath UWA channels. It is shown that with a pair of hydrophones for reception and maximum-ratio combining (MRC) technique, one can achieve considerably low bit-error-rate (BER) at practical signal-to-noise ratio (SNR) value. Further, the BER expression for such a scheme is obtained by using the probability density function and is shown to consist of a series with fast converge rate. The series solution approximation provides a reasonable match between the simulation and the analytical results with and without the MRC diversity technique.