Equal Gain Combining Receiver Research Articles

Performance analysis of coherent DPSK SIMO laser-based satellite-to-ground communication link over weak-to-strong turbulence channels considering Kolmogorov and non-Kolmogorov spectrum models

The performance of satellite-to-ground laser-based communication links is highly affected by atmospheric turbulence. Coherent detection with spatial diversity at the ground station receiver can mitigate the scintillation effects caused by atmospheric turbulence. Traditionally, the scintillation effects are modeled based on the Kolmogorov spectrum model. However, the experiments have indicated that scintillation effects on the laser beam propagation have non-Kolmogorov properties. Our goal in the present work is to analyze the average bit error rate (BER), outage probability (OP), and ergodic capacity of the satellite-to-ground heterodyne optical communication system with receiver spatial diversity. A differential phase-shift keying modulation technique is considered in this work. The propagated laser signal from the satellite to the ground station is assumed to be subjected to Málaga-distributed atmospheric turbulence. The atmospheric turbulence statistics are carried out based on the conventional Kolmogorov spectrum model and the three-layer altitude (TLA) non-Kolmogorov spectrum model. The performance of popular diversity combining techniques, namely, maximum ratio combining (MRC) and equal gain combining (EGC) techniques are analyzed. The statistical models of the MRC technique under the Málaga-distributed atmospheric channel model are obtained in analytical form expressions. The statistical models of the EGC technique under the Málaga-distributed atmospheric channel model are obtained via the fast Fourier transform representation of the characteristic function method. Based on these statistical models, average BER, OP, and ergodic capacity expressions for each type of diversity combining technique are derived. For the communication system under investigation, the performance of MRC and EGC multiple aperture receiver systems are compared to a single aperture receiver with the same total aperture area. These comparisons are carried out under the same conditions in terms of zenith angle and signal-to-noise ratio. The obtained results show that the performance of the optical communication system under investigation with MRC and EGC receivers can be improved by increasing the order of diversity. In addition, it is found that the difference in the performance between Kolmogorov and TLA non-Kolmogorov spectrum models is not significant at low zenith angles, while this difference increases as the zenith angle increases. All numerical results are verified by Monte-Carlo simulations.

Experimental demonstration and analysis of underwater wireless optical communication link: Design, BCH coded receiver diversity over the turbid and turbulent seawater channels

AbstractIn this article, we demonstrate an experimental underwater wireless optical communication (UWOC) system in the presence of air bubbles and weak turbulence for varying turbidity levels of the aquatic optical medium. The major limiting factors of the UWOC system are: absorption, scattering, and beam fluctuations; these effects can be mitigated by employing transmitter/receiver diversity schemes and channel codes. In this proposed system, we have employed receiver diversity (selection combining (SC), majority logic combining (MLC), and equal gain combining (EGC)) techniques augmented with Bose‐Chaudhuri‐Hocquenghem (BCH) codes to improve the performance of on‐off keying modulated UWOC system. The bit error rate (BER) expressions are derived for the proposed system and results are validated using analytic and experimental means. The results show that the proposed system, that is, the receiver employing SC, MLC, and EGC receiver combining techniques augmented with the BCH code provides a transmit power gain of 4, 6, and 8 dB respectively, when compared with the uncoded single‐input single‐output system, at a BER of 10−5.

Pre-detection dual EGC receiver over correlated η-μ channels with arbitrary fading parameters

ABSTRACT In this letter, we derive a novel expression of the correlated joint PDF of the η–µ distribution to evaluate the performance of correlated equal gain combining (EGC) receiver over η–µ fading channels. The joint PDF is derived from the correlated chi-square distribution using the method of random variable transformations and some algebraic calculations. The derived expressions which consider arbitrary channel parameters along with the correlation and non-identical fading will be closer to the practical scenario as these effects are frequently encountered in practical situations. In the analytical section, we have analyzed the effect of non-identical fading condition along with the impact of correlation and fading severity on the bit error rate (BER) and outage. The results were verified with the help of Monte Carlo simulations and found to be in close.

Bit-error rate investigation of satellite-to-ground downlink optical communication employing spatial diversity and modulation techniques

In this paper, the error performance of multiple apertures receiver system under different modulation schemes is evaluated for satellite-to-ground downlink optical communications. Gamma–Gamma channel model is used for the consideration of moderate to strong atmospheric turbulence. Error rate expression equations of maximum ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) techniques are derived for M-ary pulse position modulation (M-PPM) and M-ary differential PPM (M-DPPM) modulation schemes. Bit-error rate (BER) performances of M-PPM and M-DPPM modulated MRC, EGC, and SC direct detection receiver systems are compared with a single monolithic aperture receiver system. Performances of downlink direct detection multiple apertures receiver system are also compared among on–off keying (OOK), M-PPM, and M-DPPM modulation schemes. Numerical calculations and Monte Carlo (MC) simulations are used to exam the results of our analysis. It is found that, for M-PPM and M-DPPM, the effect of atmospheric turbulence can be reduced by MRC and EGC receiver system, and SC receiver system can show its advantages compared to a single aperture receiver system in the case of large zenith angles. The downlink BER performances of OOK, 8-PPM, and 8-DPPM multiple apertures receiver system are decreased according to the order of 8-PPM, 8-DPPM, and OOK.

BER analysis of EGC receiver over correlated Nakagami-m fading channels with phase error and asynchronous CCI

Performance analysis of an L-branch Equal Gain Combining (EGC) receiver with phase estimation error and asynchronous Co-Channel Interference (CCI) over correlated Nakagami-m fading channel is presented. Both the desired and interfering signals are assumed to be Nakagami-m distributed. The output Signal to Noise Ratio (SINR) of the EGC combiner is derived. Closed form expression for the n-th moment of the output SINR is derived. Using the n-th moment expression, Average Bit Error Probability (ABEP) for Binary Phase Shift Keying (BPSK) modulation is derived using Moment Generating Function (MGF) and Pade approximation method. Numerical and simulation results of ABEP for various desired and interfering signal parameters are obtained. ABEP results for various degrees of phase errors are also obtained. The results for special cases are verified with the available results.

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.

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.

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 satellite‐to‐ground downlink optical communications with spatial diversity over Gamma–Gamma atmospheric turbulence

The performances of satellite‐to‐ground downlink optical communications over Gamma–Gamma distributed turbulence are studied for a multiple‐aperture receiver system. Equal gain‐combining (EGC) and selection‐combining (SC) techniques are considered as practical schemes to mitigate the atmospheric turbulence under thermal‐noise‐limited conditions. Bit‐error rate (BER) performances for on‐off keying‐modulated direct detection and outage probabilities are analyzed and compared for SC diversity receptions using analytical results and for EGC diversity receptions through an approximation method. To show the net diversity gain of a multiple‐aperture receiver system, BER performances and outage probabilities of EGC and SC receiver systems are compared with a single monolithic‐aperture receiver system with the same total aperture area (same average total incident optical power) for satellite‐to‐ground downlink optical communications. All the numerical results are also verified by Monte‐Carlo simulations.

Performance Evaluation of Adaptive Indoor Matched Rake Receiver Using Multiple-Combining Techniques

This paper discusses the enhancement of the wireless rake receiver for high speed and short distance indoor ultra wideband (UWB) propagation with line-of sight (LOS) and non line-of sight (NLOS) channel models. The proposed matched rake receiver uses three main combining techniques, maximum ratio combining (MRC), equal gain combining (EGC), and selective combining (SC) to capture most of the energy of the multi-path components (MPCs). When the wireless communication systems work with high capacity and high speed in transmission and reception scenarios, there will be a serious challenge defined as inter-symbol interference (ISI) during the reception process. The ISI causes increasing in the bit error rate (BER) when the wireless communication systems work with high bit rate propagation. The matched rake receiver scheme was designed to suppress ISI by maximizing the signal to noise ratio (SNR) before constructing the desired signal in decision circuit and effectively the system enhancement is improved. After adding additive white Gaussian noise (AWGN) to the received signal, the improvement is cleared comparing with the theoretical results that has no AWGN. During the comparison of the simulation results, MRC partial rake receiver of less complexity showed better performance than the EGC and SC rake receivers.

ABEP of EGC Receiver over Composite and Non-homogenous Fading Channels with Phase Error and Co-channel Interference

Average bit error probability (ABEP) performance of a dual branch equal gain combining (EGC) receiver is analyzed in correlated composite fading channels and in independent and identically distributed (i.i.d.) non-homogenous fading channels in the presence of phase error and co-channel interference. Closed form expressions for moments of the combiner output signal to interference plus noise ratio are derived individually for correlated composite fading channels and i.i.d. non-homogenous fading channels. Using the obtained expressions, the ABEP for binary phase shift keying modulation is obtained, applying moment generating function and Padé approximation approach. Numerical and simulation results for different degrees of phase errors and different values of ρ are obtained. The results for special cases were checked with the available results.

An Outage Analysis of Multibranch Diversity Receivers with Cochannel Interference in α-μ, κ-μ, and η-μ Fading Scenarios

Wireless communications systems in a frequency reuse environment are subject to cochannel interference. In order to improve the system performance, diversity techniques are deployed. Among the practical diversity schemes used, Equal-Gain Combining (EGC) appears as a reasonably simple and effective one. Unfortunately, the exact analysis of the outage probability of EGC receivers is rather intricate for it involves the evaluation of multifold nested integrals. It becomes mathematically intractable with the increase of the number of diversity branches and/or interferers. For example, for N B diversity branches and N I arbitrary independent cochannel interferers, the exact formulation using the convolutional approach requires 2 + N B + (N B × N I ) nested integrals, which, very quickly, and for any practical system, turns out to be mathematically intractable. In this paper, we propose accurate approximate formulations for this problem, whose results are practically indistinguishable from the exact solution. In our model, the system is composed by N B branches and N I interferers so that the desired signals are coherently summed, whereas the interfering signals are incoherently summed at the EGC receiver. Three sets of fading scenarios, namely ?-μ , ?-μ, and ?-μ, are investigated. The proposed approach is indeed flexible and accommodates a variety of mixed fading scenarios for desired and interfering signals.

Differentially Amplitude- and Phase-Encoded QAM for Amplify-and-Forward Multiple-Relay Systems

This paper studies the differentially amplitude- and phase-encoded quadrature amplitude modulation (DAPE QAM) transmission for the amplify-and-forward multiple-relay system using the fixed-relay-gain mechanism over independent Rician and Nakagami- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading links. In the multiple-relay system, the destination collects signals from the source and multiple relays in distinct phases. Operating over two successively received symbols, an equal-gain combining (EGC) receiver and a weighted-gain combining (WGC) receiver are developed to noncoherently combine received signals from direct and multiple-relay links and thereby achieve cooperative diversity. The EGC receiver operates without any link-side information, whereas the knowledge of average signal-to-noise ratios (SNRs) on source-relay and relay-destination links is required for realizing the WGC receiver. Based on Beaulieu's convergent series approach, efficient computation formulas of the bit error probability (BEP) upper bounds are derived for both receivers. Numerical and simulation results on 16- and 64-point signal constellations show that the WGC receiver exhibits better BEP performance than the EGC receiver when link SNR estimates are not significantly large in error. The WGC receiver for DAPE QAM is also shown to outperform, in terms of BEP, the conventional receiver for differentially detecting the differential phase-shift keying modulation signal with the same constellation size.

On the Sum of Kappa Stochastic Variates and Applications to Equal-Gain Combining

In this paper we study the statistics of the sum of not necessarily identically distributed kappa, that is, K, random variables (RV)s. Assuming half-integer values for the shaping parameters, novel closed-form expressions for the probability density function (PDF) of the sum of independent K RVs are obtained, while for arbitrary values of the shaping parameters, a corresponding PDF expression is derived in terms of fast converging infinite series. Furthermore, an infinite series representation for the PDF of the sum of two arbitrarily correlated K RVs is derived. The proposed analysis is employed to the performance analysis of equal-gain combining (EGC) receivers operating over composite fading/shadowing channels modeled by the K distribution. More specifically, the outage and the average bit error probabilities, as well as the average channel capacity of EGC receivers operating over such composite environment are studied. Considering different channel fading/shadowing conditions and correlation effects, various numerical performance evaluation results are presented. These results are complemented by equivalent computer simulated ones that validate the accuracy of the proposed analysis.

Influence of imperfect cophasing on performance of EGC receiver of BPSK and QPSK signals transmitted over Weibull fading channel

This paper presents an analysis of maximum ratio combining (MRC) receiver of quaternary phase-shift keying (QPSK) signals transmitted over a Weibull fading channel. We determine the influence of imperfect cophasing and branches unbalance on bit error rate dependence on average signal-to-noise ratio. The performance dependence on diversity order and fading severity is also observed. Keywords — Cophasing, Diversity systems, Error probability, Fading. I. INTRODUCTION N order to reduce the influence of multipath fading on signal detection, it is possible to use spatially separated receiver antennas at the reception and to combine the signals from different branches of the receiver in a certain manner. The optimal combining technique is maximum ratio combining (MRC). This combining technique involves cophasing of the useful signal in all branches, multiplication of the received signal in each branch by the estimated envelope of that particular signal and summing of the received signals from all antennas (1). By cophasing, all the random phase fluctuations of the signal that emerged during the transmission are eliminated. For this process it is necessary to estimate the phase of the received signal. This phase estimation can be performed from the modulated or unmodulated received signal carrier. In previous papers concerning this matter the assumptions of the ideal phase estimation of the incoming signal were mainly used (2), (3). Only in (4) and (5) the influence of the imperfect phase estimation was examined and that was in the case of the equal gain combining (EGC) in the receiver. In paper (4), the influence of the phase error on the error probability in the case of digital binary (BPSK) and quaternary phase-shift keying (QPSK) signal detection was observed. This error probability was calculated applying the Gram-Charlier expansion. The analysis is performed under the assumption of the uncorrelated Rayleigh fading at receiving antennas. In paper (5) closed-form expressions for outage probability and error probability during the BPSK and QPSK signal detection over the Nakagami-m fading channel were obtained. Dual branch EGC technique was applied. In both papers the analysis of the system was done under the assumption that the branches of the receiver are balanced. However, as it is well-known (6), it is very rare to meet in practice the identical propagation paths in each branch. Also, the electrical components in different branches of the receiver are not ideal. Thus, it is also of interest to consider the influence of the branch unbalance in the receiver on system performances. In this paper an analysis of QPSK signal reception is presented. The signal is transmitted over the Weibull fading channel and MRC technique is applied in the receiver, while the receiving branches are assumed unbalanced. The phase estimation is performed from the unmodulated carrier and is not ideal. The difference between the phase of the incoming signal and the estimated phase for that signal is a statistical process and it follows the Tikhonov distribution (4), (5), (7). It is shown in which measure the imperfect phase estimation affects the bit-error rate (BER).

Deterministic Linear Combining Receivers for Random Fading Channels

In this paper, linear combining receivers with deterministic weights are considered for a communication system employing receive diversity in flat Rician fading. We propose two receiver structures: (1) a modified maximum likelihood (ML) receiver in which detection is performed by maximizing the likelihood function of the combined received signal, (2) a deterministic maximal-ratio combining (MRC) receiver which uses the same structure as that of an MRC receiver but with deterministic weights. The deterministic weight vector is chosen such that it minimizes the union bound on the symbol error probability. Methods of computing this deterministic weight vector are presented. The error performance of the receivers is numerically compared with that of the square-law combining receiver and the equal-gain combining (EGC) receiver (which requires more complex phase estimation rather than using fixed, deterministic weights). Numerical results show that in the case of phase-shift keying, the EGC receiver performs better than the modified ML receiver (which has the same performance as that of the deterministic MRC receiver), but the performance gap decreases with increase of the Rician K-factor. It is also seen that in the case of orthogonal frequency-shift keying, the modified ML and deterministic MRC receivers outperform the square-law combining receiver.

On the Effect of Imperfect Cophasing in MRC and EGC Receivers Over Correlated Weibull Fading

This paper presents a comparative analysis of dual-branch maximal-ratio combining (MRC) and equal-gain combining (EGC) receivers with coherent modulations over correlated Weibull fading channels. The numerical and simulations results show the influence of imperfect cophasing, branch unbalancing and correlation on the error performance. It is interestingly shown that EGC has lower irreducible error floor than MRC in the presence of incoherent combining, while the higher value of the correlation coefficient results to lower irreducible error floor. Furthermore, the unbalance parameter has practically no influence on the irreducible error floor.

Diversity reception over generalized-K (KG) fading channels

A detailed performance analysis for the most important diversity receivers operating over a composite fading channel modeled by the generalized-K (Kg) distribution is presented. The Kg distribution has been recently considered as a generic and versatile distribution for the accurate modeling of a great variety of short term fading in conjunction with long term fading (shadowing) channel conditions. For this relatively new composite fading model, expressions for important statistical metrics of maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC) and switch and stay combining (SSC) diversity receivers are derived. Using these expressions and by considering independent but not necessarily identical distributed fading channel conditions, performance criteria, such as average output signal-to-noise ratio, amount of fading and outage probability are obtained in closed form. Moreover, following the moments generating function (MGF) based approach for MRC and SSC receivers, and the Pade approximants method for SC and EGC receivers, the average bit error probability is studied. The proposed mathematical analysis is complemented by various performance evaluation results which demonstrate the accuracy of the theoretical approach.

Channel Quality Estimation Index (CQEI): A Long-Term Performance Metric for Fading Channels and an Application in EGC Receivers

We introduce the channel quality estimation index (CQEI) as an alternative improved long-term performance criterion for wireless communications systems operating over fading channels. CQEI is simple to evaluate, since it depends on the channel statistics which vary much more slowly than the channel state itself, and thus can be obtained at the initialization state using a long training sequence and afterwards continuously improved during the whole communication period. Considering generalized fading channels (Nakagami-m, Nakagami-n, Nakagami-q) and a variety of modulations, we show that CQEI assesses the average error performance of a communication system more efficiently, compared to other long- term performance criteria such as the average signal to noise ratio (ASNR) and the amount of fading (AoF). As an application, we utilize CQEI to present a new class of equal gain combining (EGC) receivers operating over non-identical independent fading channels, called selection-EGC (S-EGC). This kind of receivers reduces or eliminates the combining loss by rejecting the weak branches that contribute more to increasing the noise than the signal during the combining stage. S-EGC could be efficiently applied in the emerging broadband communication systems (e.g., ultra-wideband), where the number of diversity paths can be considerably large due to the strong multipath effects. Numerical results show that the new proposed selection-EGC (S-EGC) receiver outperforms the classical one, when fading with non- identically distributed diversity branches is assumed.

Performance analysis of equal-gain diversity receivers over generalized Gamma fading channels

Generalized Gamma (GG) distribution is a generic model that covers many well-known fading distributions as special cases. This paper deals with the performance analysis of L-branch equal gain combining (EGC) receivers operating over GG fading channels. For these receivers and by using convergent infinite series approach, the probability of error ( P e ) can be formulated in the form of an infinite series. The coefficients of P e series can be derived by calculating complicated integrations over the fading envelope distribution. In this paper, it is shown that the required integrations for the case of GG distribution have a complex closed-form in terms of Meijer's G function, and then, a new approximation method is developed for computation of them. The proposed method only needs mean and variance of the fading envelope; hence it has low complexity and eliminates the need for calculation of complex functions. The presented numerical examples show that the developed method can approximate the required parameters and also the individual coefficients accurately and this accuracy increases with the increase of L. The proposed method is applied to analyze the probability of error performance of the L-branch EGC receiver with both coherent phase shift keying (CPSK) and frequency shift keying (CFSK) modulation schemes under different GG channel conditions. Also the effect of gain unbalance between diversity branches on the probability of error is investigated.