Equal Gain Combining Research Articles

Optimal Combining for Optical Wireless Systems With Amplification: The $\chi ^{2}$ Noise Regime

We present novel analytical results on the optimal combiner (OC) for pre-amplified optical wireless receivers under chi-squared noise. The results show that the OC architecture that minimizes the average bit-error rate (BER) is determined by the level of the signal-spontaneous beating noise. Moreover, the OC provides increased gain to the diversity branches with the higher energies, up to the point where the beating noise becomes detrimental to the BER. The performance of the OC is simulated for practical receiver arrangements and it is shown that it performs better than the maximal-ratio and equal-gain combiners. The performance improvement amounts to an energy gain of less than 1 dB for implementations that utilize narrow optical filters and a modest number of diversity branches.

New Analytical Expressions for ASEP of Modulation Techniques with Diversity Over Lognormal Fading Channels with Application to Interference-Limited Environment

In this paper, the analytical expressions of the average symbol error probability (ASEP) for both coherent and non-coherent modulation formats with diversity schemes such as maximal ratio combining (MRC), equal-gain combining (EGC), and selection combining (SC) over the lognormal (LN) distribution assuming independent and identically distributed (i.i.d.) channels have been derived. The functions involving LN distribution are simplified using the Gauss–Hermit and Gaussian Quadrature integration. Furthermore, the effect of the diversity order and constellation size on the error probability has been examined extensively under various shadowing conditions such as infrequent light, average, and frequent heavy shadowing. As an application, the derived results are used to analyze the performance of the communication systems over the interference-limited environment. The impact of the number of interferers on important performance metrics such as the outage probability, the ASEP, and the channel capacity has been examined. The accuracy of the analytical results are validated by comparing them with the exact numerical results and Monte Carlo simulations. The analytical expressions are simple and easily implementable in software package such as MATLAB. The proposed analytical expressions are supposed to be a vital tool in areas such as IEEE 802.15.3a wireless communication system, indoor environment, radio channel effect by body worn devices, ultra-wideband indoor channel.

Multi-antenna Spectrum Sensing Based on Stochastic Resonance

Aiming at the problem of spectrum sensing in cognitive radio under low signal to noise ratio (SNR) and channel fading, proposed a spectrum sensing method based on Stochastic Resonance (SR) and multi-antenna. The received signal of each antenna will pass through SR, to enhance the source signal using noise energy. Then the output of multi-antenna will be combined by Equal Gain Combining (EGC), and Differential Energy Detection (DED_SR) and Periodogram Energy Detection (PED_SR) will be adopted. Simulation experiments compare the traditional Energy Detection (ED), DED_SR and PED_SR. The results show that the detection probability of PED_SR and DED_SR perform higher than ED, but the sensing time also perform higher.

FSO communication with EGC diversity receiver over double generalised gamma turbulence channel

Recently, double generalised gamma (GG) distribution has been proposed as a generic model, to describe the irradiance fluctuations in free-space optical (FSO) communication systems. In this study, first the authors derive an approximate analytical expression for the distribution of the sum of independent but not necessarily identically distributed double GG random variables (RVs), considering the effects of the turbulence and pointing errors. Using well-known Beaulieu series, the authors describe the probability density function (pdf) and the cumulative distribution function (cdf) of the sum of double GG RVs in the form of a convergent series. The authors derive novel, exact closed-form expressions for the coefficients of the series in terms of the Meijer's G-function, which makes it possible to calculate the pdf and cdf of the sum of double GG variates under different turbulence conditions. In the next step, based on the presented results, the authors derive approximate analytical expression for the outage probability of the system and investigate the outage performance of the FSO link with equal-gain combining (EGC) receivers over double GG fading channels with pointing errors. Numerical results are further demonstrated to confirm the analytical results and also to show the good accuracy of the derived expressions.

Asymptotically Tight Performance Bounds of Diversity Receptions Over $\alpha$-$\mu$ Fading Channels With Arbitrary Correlation

Exact performance analyses over correlated α-μ fading channels result in intractable multifold integrals or infinite series. In this paper, upper and lower bounds are derived for outage probabilities and error rates of maximum-ratio combining (MRC), selection combining (SC), and equal-gain combining (EGC) over the α-μ fading channels with arbitrary correlation. The derived bounds are in closed form and asymptotically tight. Our applied correlation structure uniquely determines the joint probability density function of the α-μ random variables, thus it is a generalization of the other correlation models based on branches' hyperpower or power correlation. Based on these closed-form bounds, one can easily estimate the performance of MRC, SC, and EGC in large signal-to-noise ratio region, where performing Monte Carlo simulation is time consuming. These new bounds also reveal a fact that SC can in fact outperform EGC under some certain channel conditions. More importantly, these bounds reveal which factors determine the asymptotic performance of diversity reception systems, and provide criteria for system design.

Performance of M ‐EGC receiver over TWDP fading channels

This study gives a general bit-error rate expression, using Gil-Palaez lemma-based approach, of a M branch equal gain combining (EGC) receiver over two-wave diffused power (TWDP) fading channels. The expressions obtained are evaluated numerically and the results are verified using Monte Carlo simulation. Also the impact of the fading parameters δ and K on the performance of M branch-EGC has been analysed.

Performance analysis of decode-and-forward dual-hop optical spatial modulation with diversity combiner over atmospheric turbulence

Dual-hops transmission is a growing interest technique that can be used to mitigate against atmospheric turbulence along the Free Space Optical (FSO) communication links. This paper analyzes the performance of Decode-and-Forward (DF) dual-hops FSO systems in-conjunction with spatial modulation and diversity combiners over a Gamma–Gamma atmospheric turbulence channel using heterodyne detection. Maximum Ratio Combiner (MRC), Equal Gain Combiner (EGC) and Selection Combiner (SC) are considered at the relay and destination as mitigation tools to improve the system error performance. Power series expansion of modified Bessel function is used to derive the closed form expression for the end-to-end Average Pairwise Error Probability (APEP) expressions for each of the combiners under study and a tight upper bound on the Average Bit Error Rate (ABER) per hop is given. Thus, the overall end-to-end ABER for the dual-hops FSO system is then evaluated. The numerical results depicted that dual-hops transmission systems outperformed the direct link systems. Moreover, the impact of having the same and different combiners at the relay and destination are also presented. The results also confirm that the combination of dual hops transmission with spatial modulation and diversity combiner significantly improves the systems error rate with the MRC combiner offering an optimal performance with respect to variation in atmospheric turbulence, change in links average received SNR and link range of the system.

Optical Spatial Modulation with Diversity Combiner in Dual-Hops Amplify-and-Forward Relay Systems Over Atmospheric Impairments

In this paper, we analyzed a dual-hop optical spatial modulation channel state information-assisted amplified and forward (AF) relay system with spatial diversity combiner under the influence of gamma-gamma atmospheric turbulence induced fading and pointing error impairments. Maximum ratio combiner (MRC) and equal gain combiner (EGC) with heterodyne detection are considered at the destination as mitigation tools to improve the system error performance. The statistical characteristics of AF relay in terms of moment generating function (MGF), probability density function and cumulative density function are derived for both impairments. Based on these expressions, the average pairwise error probability for each of the combiners under study is determined and the average bit error rate (ABER) for the system is given by using union bounding technique. By utilizing the derived ABER expressions, the effective capacity for the considered system is then obtained. The effect of turbulence strength ranging from weak to strong levels and pointing errors in terms of beam width and jitter displacement are studied. The numerical results obtained show that the more the turbulence strength and/or pointing error increases, the more the error rate and effective capacity of the system deteriorates. Under the same conditions, the results confirmed that MRC system offers an optimal performance compared with EGC.

Bit error rate analysis of the K channel using wavelength diversity

The presence of atmospheric turbulence in the free space causes fading and degrades the performance of a free space optical (FSO) system. To mitigate the turbulence-induced fading, multiple copies of the signal can be transmitted on a different wavelength. Each signal, in this case, will undergo different fadings. This is known as the wavelength diversity technique. Bit error rate (BER) performance of the FSO systems with wavelength diversity under strong turbulence condition is investigated. K-distribution is chosen to model a strong turbulence scenario. The source information is transmitted onto three carrier wavelengths of 1.55, 1.31, and 0.85 μm. The signals at the receiver side are combined using three different methods: optical combining (OC), equal gain combining (EGC), and selection combining (SC). Mathematical expressions are derived for the calculation of the BER for all three schemes (OC, EGC, and SC). Results are presented for the link distance of 2 and 3 km under strong turbulence conditions for all the combining methods. The performance of all three schemes is also compared. It is observed that OC provides better performance than the other two techniques. Proposed method results are also compared with the published article.

Improved Decision Fusion Model for Wireless Sensor Networks over Rayleigh Fading Channels

This paper deals with decision fusion in wireless sensor networks (WSNs) over Rayleigh fading channels. The likelihood ratio test (LRT) is considered as the optimal fusion rule when applied at the fusion center (FC). However, applying the LRT at the FC requires both the channel state information (CSI) and the local sensors’ performance indices. Acquiring such information is considered as an overhead in energy and bandwidth constrained systems such as WSNs. To avoid these drawbacks, we propose a modification to the traditional three-layer system model of a WSN where the LRT is applied as a local decision making method at the sensors level. Applying the LRT at the sensors level does not require the CSI or the local sensors’ performance indices. It only requires the signal-to-noise ratio (SNR). Moreover, a new fusion rule based on selection combining (SC) is suggested. This fusion method has the lowest complexity when compared to other diversity combining based fusion rules such as the equal gain combiner (EGC) and the maximum ratio combiner (MRC). Simulation results show that the performance of the proposed model outperforms the traditional model. In addition, applying the EGC at the FC in the proposed model provides comparable performance to the traditional model that applies the LRT at the FC.

A tight approximate analytical framework for performance analysis of equal gain combining receiver over independent Weibull fading channels

In this paper, a method for approximating the probability distribution of sum of independent and identical Weibull random variables is adopted to analyze the performance of equal gain combiner (EGC) receiver over non-identical Weibull fading channel (WFC). Our main result is to derive a generalized expression of the probability density function (PDF) of the signal-to-noise ratio (SNR) at the EGC output in the case of non-identical WFC. Based on this PDF, accurate approximation of significant performance criteria, such as outage probability (OP), the amount of fading (AoF), and average symbol/bit error probability (ASEP/ABEP), are derived. In addition, we derived the analytical expressions for channel capacities under various adaptation policies such as optimal rate adaptation (ORA), optimal simultaneous power and rate adaptation (OPRA), channel inversion with fixed rate (CIFR), and truncated channel inversion with fixed rate (TCIFR). The proposed mathematical analysis is complemented by several numerical results and validated using Monte Carlo simulation method.

Performance evaluation of spatial diversity-based free space optical communication over atmospheric turbulence channels

Free space optics is widely regarded as the next-generation high-speed wireless communication technology. It has demonstrated its capability to deliver data faster than any other state-of-the-art wireless communication technique. Moreover, it has emerged recently as an efficient solution to match the larger bandwidth and high data rates requirement of the upcoming wireless communication systems. Optical multiple-input multiple-output (MIMO) scheme was mostly inspired by its recent successes in RF communication, where the employment of multiple antennas leads to the expansion of the wireless channel capacity and/or enhancing the reliability of the wireless communication link. Here we investigate a terrestrial atmospheric FSO communication system operating under the influence of strong atmospheric turbulence-induced, which is modelled as a lognormal channel, and based on MIMO technique with equal gain combining (EGC). Through the use of NRZ line coding, an FSO highly sensitive receiver using either APD or PIN is designed and simulated for best system performance. It was found that APD receiver using Gaussian filter is suited for long-range link with APD gain of 3. Additionally, the system behaviour can be clearly enhanced through the insertion of an amplified version of 2×2 MIMO-FSO technique provided that it is supplemented by booster amplifier.

Cooperative subcarrier sensing using antenna diversity based weighted virtual sub clustering

The idea of cooperation and the clustering amongst cognitive radios (CRs) has recently been focus of attention of research community, owing to its potential to improve performance of spectrum sensing (SS) schemes. This focus has led to the paradigm of cluster based cooperative spectrum sensing (CBCSS). In perspective of high date rate 4th generation wireless systems, which are characterized by orthogonal frequency division multiplexing (OFDM) and spatial diversity, there is a need to devise effective SS strategies. A novel CBCSS scheme is proposed for OFDM subcarrier detection in order to enable the non-contiguous OFDM (NC-OFDM) at the physical layer of CRs for efficient utilization of spectrum holes. Proposed scheme is based on the energy detection in MIMO CR network, using equal gain combiner as diversity combining technique, hard combining (AND, OR and Majority) rule as data fusion technique and antenna diversity based weighted clustering as virtual sub clustering algorithm. Results of proposed CBCSS are compared with conventional CBCSS scheme for AND, OR and Majority data fusion rules. Moreover the effects of antenna diversity, cooperation and cooperating clusters are also discussed.

An Adaptive Combiner Model for Multi-Rate Relaying Transmissions in Cognitive Systems

This paper proposes an adaptive combiner model that maximizes the performance of multi-rate cooperative relaying transmission in resources aware systems. Users’ cooperation is applied to smartly profit from the network resources to reach for efficient multi-rate transmissions. The low rate terminal uses a part of his bandwidth and power to relay the high rate user data side by side with his own data. This results in small performance degradation to the low rate user performance. The combiner model at the high rate terminal is carefully investigated for an optimized system performance and an adaptive combiner is proposed. The model calculates the weights adaptively for each bit based on a dynamic-blind method. The adaptive combiner is evaluated against the maximal-ratio combiner MRC and the equal gain combiner EGC to reach for the best model for the multi-rate relaying framework. Based on half-duplex mode, the probability of error performance is studied and compared for each combiner model under different channel conditions. The results show that the proposed adaptive combiner, characterized by its reliability and simplicity, leads to the best performance compared to the other models.

Effective capacity of MIMO free-space optical systems over gamma–gamma turbulence channels

In this paper, we provide the capacity limits of multiple-input multiple-output (MIMO) free-space optical communication (FSO) system in the presence of quality of service (QoS) requirements. Closed-form expression for the effective capacity of MIMO FSO system with equal gain combining (EGC) is derived. In order to provide insights into the impact of various system parameters, asymptotic expressions are further analyzed in the high signal-to-noise ratio (SNR) regime. Special cases are provided according to the derived results at the same time. Numerical results are given to validate all the analytical results, and the influences of QoS requirements and MIMO configurations are also illustrated.

Robust Neural Network based Multiuser Detector in MC-CDMA for Multiple Access Interference Mitigation

The aim of this paper is to design a multiuser detector technique using artificial Neural Network under multiple access interference mitigation. To improve the performance of Multi Carrier Code Division Multiple Access (MC-CDMA) under multiple access interference, we have used a multilayered perceptron model of Neural Network that has three layers namely, input layer, hidden layer and output layer. The Neural Network is further trained by Levenberg-Marquardt algorithm. This algorithm uses the error function as key factor based on which the weights are adjusted to get the desired output. The Bit Error Rate (BER) performance of the system has been evaluated under Rayleigh and Stanford University Interim (SUI) channels for Binary Phase Shift Keying (BPSK) and Quadrature Amplitude Modulation (QAM) techniques. The proposed Neural Network based receiver is compared with Equal Gain Combining (EGC) and Maximal Ratio Combining (MRC) with varying number of users and Signal to Noise Ratio (SNR). Under SUI channel conditions and for a BER of 10 -3 , the Neural Network based receiver shows an improvement of 1 dB and 8 dB than EGC and MRC receivers, respectively.

Performance analysis of free space optical system with spatial modulation and diversity combiners over the Gamma Gamma atmospheric turbulence

Atmospheric turbulence is a major impairment that degrades the performance of free space optical (FSO) communication systems. Spatial modulation (SM) with receive spatial diversity is considered as a powerful technique to mitigate the fading effect induced by atmospheric turbulence. In this paper, the performance of free space optical spatial modulation (FSO-SM) system under Gamma–Gamma atmospheric turbulence is presented. We studied the Average Bit Error Rate (ABER) for the system by employing spatial diversity combiners such Maximum Ratio Combining (MRC) and Equal Gain Combining (EGC) at the receiving end. In particular, we provide a theoretical framework for the system error by deriving Average Pairwise Error Probability (APEP) expression using a generalized infinite power series expansion approach and union bounding technique is applied to obtain the ABER for each combiner. Based on this study, it was found that spatial diversity combiner significantly improved the system error rate where MRC outperforms the EGC. The performance of this system is also compared with other well established diversity combiner systems. The proposed system performance is further improved by convolutional coding technique and our analysis confirmed that the system performance of MRC coded system is enhanced by approximately 20dB while EGC falls within 17dB.

Performance analysis of fiber-based free-space optical communications with coherent detection spatial diversity

The performances of fiber-based free-space optical (FSO) communications over gamma-gamma distributed turbulence are studied for multiple aperture receiver systems. The equal gain combining (EGC) technique is considered as a practical scheme to mitigate the atmospheric turbulence. Bit error rate (BER) performances for binary-phase-shift-keying-modulated coherent detection fiber-based free-space optical communications are derived and analyzed for EGC diversity receptions through an approximation method. To show the net diversity gain of a multiple aperture receiver system, BER performances of EGC are compared with a single monolithic aperture receiver system with the same total aperture area (same average total incident optical power on the aperture surface) for fiber-based free-space optical communications. The analytical results are verified by Monte Carlo simulations. System performances are also compared for EGC diversity coherent FSO communications with or without considering fiber-coupling efficiencies.

Iterative receiver based on the EGC for massive MIMO schemes using SC‐FDE modulations

This Letter considers the use of massive multiple-input, multiple-output (MIMO) combined with single-carrier with frequency-domain equalisation (SC-FDE) modulations. A low-complexity iterative frequency-domain receiver based on the equal gain combining (EGC) approach is proposed. This receiver does not require matrix inversions and has excellent performance, which can be very close to the matched filter bound after just a few iterations, even when the number of receive antennas is not very high.

Optimal error analysis of receive diversity schemes on arbitrarily correlated Rayleigh fading channels

A simple optimal error analysis of multiple-branch equal gain combining (EGC) and selection combining (SC) in the presence of arbitrarily correlated Rayleigh fading channels is presented. It is shown that the error rates over correlated branches for diversity combining schemes can be analysed at the output of an eigenfilter splitter, which is placed at the output of the diversity combiner. Since the outputs of the splitter are uncorrelated, the error analysis of maximal ratio combining (MRC) technique is applied to EGC and SC. This analysis is possible since error performance of MRC with correlated branches is optimal and invariant to eigenfilter or eigenvector decorrelation and the decorrelated outputs can simply be analysed similar to independent branches. The authors exploit extensive simulations for average bit error probability, which show tight bounds with the proposed analytical approach. Channel correlations for different practical antenna spacing of 0.15, 0.2 and 0.5 of the signal carrier wavelength, λ are analysed.