Equal Gain Combining Research Articles

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.

Coherent Wireless Optical Communications With Predetection and Postdetection EGC Over Gamma–Gamma Atmospheric Turbulence Channels

Wireless optical communication systems with coherent detection are analyzed for Gamma–Gamma distributed turbulence channels. In addition to the shot noise, we consider the impacts of both turbulence amplitude fluctuations and phase fluctuations on the error performance. Error rate analyses of predetection and postdetection equal gain combining (EGC) are carried out. We derive the exact error rate expressions for predetection and postdetection EGC using a characteristic function method. In the case of predetection EGC, we also study the impact of phase noise compensation error on the error rate performance. It is shown that the error rate performance of predetection EGC is sensitive to phase noise compensation errors for both weak and strong turbulence conditions. In order to alleviate the impact of phase noise, postdetection EGC with differential phase-shift keying is introduced and analyzed. In addition, postdetection EGC is compared with predetection EGC in the presence of phase noise compensation errors, and it is found to be an effective alternative to predetection EGC with low complexity implementation.

New Representations for the Gaussian Class Multivariate Weibull Distribution with Constant Correlation and Applications

Novel single-integral representations for the multivariate probability density functions (PDFs) and cumulative distribution functions (CDFs) of the Gaussian class Weibull distribution are derived. The solutions are expressed in terms of familiar mathematical functions which are available in common mathematical software. The well known equal (constant) correlation model is considered. A special linear transformation of independent Gaussian random variables is used to generate correlated Weibull random variables. The advantage of the new representation is that only a single integral computation is needed to compute a N-dimensional distribution. The new representation of the CDF is used for the performance evaluation of a selection diversity combiner operating in equally correlated Weibull fading channels. The new PDF representation is also used for an analysis of the moments of the output signal-to-noise ratio of an equal-gain diversity combiner operating in equally correlated Weibull fading channels.

The κ-μ Extreme Distribution

A number of realistic wireless applications can be found for which the propagated signal may experience extreme fading conditions. In particular, a recent work has reported on an experiment conducted within an enclosed environment where it has been shown that the fading conditions are indeed harsh, drastically departing from those predicted by traditional fading models. This paper investigates the κ-μ Extreme fading distribution, a member of the κ-μ fading model and obtained from it when its parameters reach their extreme values (κ → ∞ and μ → 0) for a fixed amount of fading. Field data reported elsewhere and collected in enclosed environment, along with other fading data collected by the authors' team, are used to compare the curve fit performance of the κ-μ Extreme model and the recently proposed Two-Ray distribution. The results show that the κ-μ Extreme distribution is flexible and suitable to model these scenarios. The performance of this new model is then explored in the three basic combining techniques, namely selection, maximum ratio, and equal gain, and a number of exact, closed-form formulas are obtained. Interestingly, it is shown that in extreme fading conditions, the selection combiner may outperform the equal gain combiner.

The impact of spatial correlation on the statistical properties of the capacity of nakagami-m channels with MRC and EGC

In this article, we have studied the statistical properties of the instantaneous channel capacitya of spatially correlated Nakagami-m channels for two different diversity combining methods, namely maximal ratio combining (MRC) and equal gain combining (EGC). Specifically, using the statistical properties of the instantaneous signal-to-noise ratio, we have derived the analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the instantaneous channel capacity. The obtained results are studied for different values of the number of diversity branches and for different values of the receiver antennas separation controlling the spatial correlation in the diversity branches. It is observed that an increase in the spatial correlation in the diversity branches of an MRC system increases the variance as well as the LCR of the instantaneous channel capacity, while the ADF of the channel capacity decreases. On the other hand, when EGC is employed, an increase in the spatial correlation decreases the mean channel capacity, while the ADF of the instantaneous channel capacity increases. The presented results are very helpful to optimize the design of the receiver of wireless communication systems that employ spatial diversity combining techniques. Moreover, provided that the feedback channel is available, the transmitter can make use of the information regarding the statistics of the instantaneous channel capacity by choosing the right modulation, coding, transmission rate, and power to achieve the capacity of the wireless channelb.

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.

Energy Detection of Unknown Signals in Fading and Diversity Reception

A comprehensive performance analysis of the energy detector over fading channels with single antenna reception or with antenna diversity reception is developed. For the no-diversity case and for the maximal ratio combining (MRC) diversity case, with either Nakagami-m or Rician fading, expressions for the probability of detection are derived by using the moment generating function (MGF) method and probability density function (PDF) method. The former, which avoids some difficulties of the latter, uses a contour integral representation of the Marcum-Q function. For the equal gain combining (EGC) diversity case, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2,3,4 and L >; 4, where L is the number of diversity branches. For the selection combining (SC) diversity, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2 and L >; 2. A discussion on the comparison between MGF and PDF methods is presented. We also derive several series truncation error bounds that allow series termination with a finite number of terms for a given figure of accuracy. These results help quantify and understand the achievable improvement in the energy detector's performance with diversity reception. Numerical and simulation results are also provided.

Turbo-Coded MC-CDMA Communication Link over Strong Turbulence Fading Limited FSO Channel with Receiver Space Diversity

This paper demonstrates an analytical approach on the bit error rate (BER) performance evaluation of a multi- carrier code division multiple access (MC-CDMA) communication link operating over terrestrial free space optical (FSO) channel considering effect of atmospheric turbulence The turbulence induced intensity fading is statistically modeled by Gamma-Gamma PDF (probability density function). Bit error rate performance improvement is proposed using photo detector spatial diversity with Equal Gain Combining (EGC) and Turbo Coding. Analysis is carried out with different bandwidth efficient phase shift keying (PSK) based sub-carrier intensity modulation (SIM) with direct detection. Numerical simulation results of proposed analytical model indicate that, sub-carrier intensity modulation scheme; number of receiver photo detectors, turbo coding parameter and link length should be optimally engineered for ensuring system reliability. It can be inferred from the simulation that, a reliable communication link ( BER) can be established over a link length of 4 Km in strong turbulence fading condition using an array of 4 PIN photo detectors, 8-ary PSK based sub-carrier intensity modulation scheme and appropriate turbo coding parameter with an average 10.2 dB CINR (Carrier to Interference and Noise Ratio) requirement per photo detector. Besides, more than 130 dB average CINR gain is also confirmed from BPSK modulated, un-coded SISO (single input-single output) system for maintaining targeted BER () in presence of strong turbulence fading.

New Results on the Statistics and the Capacity of Dual-Branch MRC and EGC Diversity in Correlated Lognormal Channels

This letter addresses the performance analysis of dual diversity reception systems in correlated lognormal fading channels with not-necessarily-identical parameters. More specifically, novel results on the probability density function (PDF) and the ergodic capacity of dual-branch maximal ratio combining (MRC) and equal gain combining (EGC) diversity receivers are presented. The proposed expressions find application in cost-sensitive diversity receiver implementations and handover designs.

Diversity Gains for Different Cooperative Schemes on Fast Fading Channels

The use of single-antenna terminals for coherent cooperative wireless communications has received more attention in literature than for non-coherent communications. But acquiring knowledge of the fading coefficients in a cooperative scheme is very challenging in a fast fading case. In this paper, we develop several cooperative schemes suited for systems which do not require channel state information at either relays or destination. We analyze the performance of these schemes in terms of diversity gain and error probability. The diversity gained with an equal gain combiner at the destination is investigated too. The proposed cooperative schemes are compared to the literature and are shown to achieve significant performance gain depending on the type of relaying protocol.

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).

수신 다이버시티를 이용한 음향 통신 시스템의 성능 향상 분석

Acoustic communication system is a transmission technology sending sound and data simultaneously. However, data signal can be audible in this system when data is transmitted with high transmission power. The more transmission power is reduced, the more distance that can transmit data is shortened. Therefore, the study that increase the transmission distance is needed. In this paper, we would like to increase transmission distance by adapting receive diversity in acoustic communication system. We measure received performance of both proposed system and Single Input Sing Output (SISO) system according to distance with same transmission power. When SISO satisfies Bit Error Rate (BER) of at about 2m, Selection Combining (SC) technique satisfies 2 meters, and Equal Gain Combining (EGC) technique satisfies 4 meters.

Performance Analysis of Smart Relaying with Equal Gain Combining

Relaying communications has been proposed as a way to provide spatial diversity. In general, one is interested in a relaying system that can achieve the maximal diversity order with a low system complexity. One enabling technique is equal gain combining (EGC) and its application in relaying systems is the main focus of this paper. In particular, the techniques of EGC and smart relaying are combined in the decode-and-forward (DF) processing method. It is shown that for a system with one relay and M-ary phase-shift-keying (M-PSK) modulation, maximal diversity orders of 2m and 2 are achieved over Nakagami-m and Hoyt fading environments, respectively. With K relays, simulation results suggest that the corresponding diversity orders are m(K + 1) and (K + 1).

Pre‐filtering technique for MAI cancellation in MC‐CDMA systems

ABSTRACTMulticarrier code division multiple access (MC‐CDMA), is a promising multiplexing technique for future communication systems. In this study, we employ the well‐known Walsh‐Hadamard spreading codes for synchronous downlink transmission of MC‐CDMA systems. The spreading codes allow that the frequency diversity to be efficiently exploited. However, multipath propagation may cause orthogonality among users is distorted, and this distortion produces multiple access interference (MAI). To eliminate this effect, we propose a pre‐filtering‐based MC‐CDMA system which uses a pre‐filtering technique at the transmitter and an equal gain combining (EGC) scheme at the receivers, respectively. Our proposed pre‐filtering technique transforms the transmitted signals so that the MAI can be eliminated, and the EGC scheme weights the signals received from all subcarriers so that channel distortions can be compensated. Furthermore, the proposed technique can calculate the transmitted power over all subcarriers to satisfy the required quality of service of each user and archive MAI‐free. In this paper, performance in terms of bit error rate is analyzed; in comparison with the EGC, orthogonal restoring combining, and maximal ratio combining schemes at receiver, respectively. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Some Notes on the Fourier Transform Methods for Error-Rate Analysis of Equal-Gain Combining

Transform techniques based on moment generating functions (MGFs) and characteristic functions (CHFs) have recently provided efficient analytical tools for the performance evaluation of digital communication systems over fading channels. More recently, the convolution theorem of the Fourier transform has been employed to obtain unified expressions for the average error probabilities of equal gain combining (EGC) diversity reception in terms of the CHFs of the branches' amplitude gains. In this paper, we prove that these expressions include redundant terms. Furthermore, simpler analytical expressions for the average error rates of EGC diversity reception can be obtained when the convolutional theorem of the sine and cosine transforms are used instead of the conventional Fourier transform.

Bit Error Rate Approximation of MIMO-OFDM Systems with Carrier Frequency Offset and Channel Estimation Errors

The bit error rate (BER) of multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with carrier frequency offset and channel estimation errors is analyzed in this paper. Intercarrier interference (ICI) and interantenna interference (IAI) due to the residual frequency offsets are analyzed, and the average signal-to-interference-and-noise ratio (SINR) is derived. The BER of equal gain combining (EGC) and maximal ratio combining (MRC) with MIMO-OFDM is also derived. The simulation results demonstrate the accuracy of the theoretical analysis.

A CMOS imaging diversity receiver for gigabit free-space optical MIMO

A 7-channel imaging diversity receiver based on current-summing is implemented in a 180 nm CMOS technology for broadband free-space optical (FSO) multi-input/multi-output (MIMO) communication. Each channel employs a low input-impedance current mirror (CM) as the input stage, which allows the implementation of direct current-summing for equal-gain combining (EGC). The summed current signal drives a second stage transimpedance amplifier (TIA) to generate the output voltage. Electrical characterization was performed using a photodiode emulation circuit and chip-on-board FR-4 assembly, demonstrating a total transimpedance gain of 62 dB?, ?3 dB bandwidth of 1.2 GHz, and eye diagrams up to 2 Gb/s for 0.25 pF photodiode capacitance. The theoretical sensitivity of the imaging receiver is ?16.8 dBm for a bit error rate (BER) of 10?9 at a photodetector responsivity of 0.4 A/W. The simulated power consumption for a single front-end amplifier circuit is 4.2 mW, and for the second stage TIA is 10.3 mW from a single 1.8 V supply. The diversity receiver is flip-chip compatible to enable hybrid integration to a custom InGaAs photodetector array.

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.

Optimal antenna configuration for non-cophase equal gain combining diversity using genetic algorithm

The equal gain combining (EGC) diversity technique is generally known to have a performance close to an optimal maximal ratio combining technique while being less complex for realization.Therefore, the implementation of EGC in practice is of interest. However, the implementation of EGC diversity is cumbersome due to additional circuitry required for making a cophase signal in each branch. As a result, it is interesting to investigate whether non-cophase EGC diversity is able to provide an acceptable performance while keeping much greater simplicity with only marginally inferior when compared with cophase method. As there is dimension constraint on wireless terminal, the problem of how to configure multiple antennas on such a limited area is of interest. This article studies the performance of non-cophase EGC diversity through the problem antenna configuration. The genetic algorithm (GA) technique is applied to achieve an optimal solution using the average signal-to-noise ratio as a fitness function. The proof of proposed method has been confirmed through simulation as well as measurement results. The investigations reveal that the antenna configuration by using optimization technique provides the best performance on limited space for non-cophase EGC diversity. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52:2462–2467, 2010; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25502

Hybrid ARQ with Partial Retransmissions and LDPC codes and its Impact on TCP

The design of a novel HARQ scheme using LDPC codes, partial retransmissions, and diversity combining is presented. The theoretical throughput of the proposed scheme is estimated by means of EXIT charts. It is shown that the proposed method outperforms the classical equal gain combining (EGC) method while requiring few more overall decoding iterations. The transmission control protocol (TCP) performance when the proposed method is used in the physical layer is also investigated. Simulation results show that the gains with respect to the classical EGC scheme can be as large as 3.5 dB.