Movement accuracy is the key factor to be considered in designing precision instrument linkage and mini-linkage mechanisms. Although manufacturing errors, elastic deformation, kinematic pair clearance and friction fac...Movement accuracy is the key factor to be considered in designing precision instrument linkage and mini-linkage mechanisms. Although manufacturing errors, elastic deformation, kinematic pair clearance and friction factors all will have synthesis effect on the position accuracy of the mechanical system, the essential factor to guarantee the movement precision remains the kinematic dimensions. Combining the classical theory of mechanical synthesis with the modern error theory and the numerical method, the authors put forward a systematic and complete process and method of computer aided design for the instrument crank-coupler mechanism in which the follower takes the linear displacement approximately within a certain limited domain, with the design result of least transmission ratio error.展开更多
The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower b...The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.展开更多
The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destro...The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.展开更多
Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying ac...Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.展开更多
In luminescence and ESR dating methods,total count rate from thick source alpha counting is commonly used fox estimating annual dose with assumption of equal activities for both uranium and thorium decay chains.This i...In luminescence and ESR dating methods,total count rate from thick source alpha counting is commonly used fox estimating annual dose with assumption of equal activities for both uranium and thorium decay chains.This is equal to a Th/U weight ratio of 3.2.The systematic error in total dose rate due to uncertainty of the ratio is calculated.It is found that the error is insignificant for uniformly distributed samples such as sediment,but can be significant for some extreme circumstances.展开更多
Bit Error Probability (BEP) provides a fundamental performance measure for wireless diversity systems. This paper presents two new exact BEP expressions for Maximal Ratio Combining (MRC) diversity systems. One BEP exp...Bit Error Probability (BEP) provides a fundamental performance measure for wireless diversity systems. This paper presents two new exact BEP expressions for Maximal Ratio Combining (MRC) diversity systems. One BEP expression takes a closed form, while the other is derived by treating the squared-sum of Rayleigh random variables as an Erlang variable. Due to the fact that the extant bounds are loose and could not properly characterize the error performance of MRC diversity systems, this paper presents a very tight bound. The numerical analysis shows that the new derived BEP expressions coincide with the extant expressions, and that the new approximation tightly bounds the accurate BEP.展开更多
This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shif...This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying(BPSK), quadrature phase shift keying(QPSK), quadrature amplitude modulation(QAM)-16 and QAM-64 with four error correction codes(convolutional code(CC), Reed-Solomon code(RSC)+CC, low density parity check(LDPC)+CC, Turbo+CC) is studied under three channel models(additive white Guassian noise(AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate(BER) and the peak signal to noise ratio(PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance.展开更多
Although various estimating methods have been developed for measuring Q from near-surface seismic data, less thought has been given to the accuracy of Q obtained. The errors of Q depend on the ways of measuring Q and ...Although various estimating methods have been developed for measuring Q from near-surface seismic data, less thought has been given to the accuracy of Q obtained. The errors of Q depend on the ways of measuring Q and the computation techniques used in estimating. The main purpose of this paper is to give a compre- hensive evaluation for the accuracy of measuring near-surface Q. We discuss the possible origins from which errors may develop, and provide a statistical guide to the accuracy that can be expected. A set of real data based on the improved spectral ratio method for near-surface Q was used as an example of validation and sensitivity analysis. The Bonferroni procedure was adopted for deriving the joint confidence intervals for k and n of the power law model. The same approach with modest modification may be applied to analyze the accuracy of Q estimated by other methods.展开更多
Nowadays,distance is usually used to evaluate the error of trajectory compression.These methods can effectively indicate the level of geometric similarity between the compressed and the raw trajectory,but it ignores t...Nowadays,distance is usually used to evaluate the error of trajectory compression.These methods can effectively indicate the level of geometric similarity between the compressed and the raw trajectory,but it ignores the velocity error in the compression.To fill the gap of these methods,assuming the velocity changes linearly,a mathematical model called SVE(Time Synchronized Velocity Error)for evaluating compression error is designed,which can evaluate the velocity error effectively,conveniently and accurately.Based on this model,an innovative algorithm called SW-MSVE(Minimum Time Synchronized Velocity Error Based on Sliding Window)is proposed,which can minimize the velocity error in trajectory compression under the premise of local optimization.Two elaborate experiments are designed to demonstrate the advancements of the SVE and the SW-MSVE respectively.In the first experiment,we use the PED,the SED and the SVE to evaluate the error under four compression algorithms,one of which is the SW-MSVE algorithm.The results show that the SVE is less influenced by noise with stronger performance and more applicability.In the second experiment,by marking the raw trajectory,we compare the SW-MSVE algorithm with three others algorithms at information retention.The results show that the SW-MSVE algorithm can take into account both velocity and geometric structure constraints and retains more information of the raw trajectory at the same compression ratio.展开更多
Network Coding (NC) brings correlation between the coded signals from different sources, which makes the system more vulnerable to the decode error at relay. Conventional Cyclic Redundancy Code (CRC) has been implemen...Network Coding (NC) brings correlation between the coded signals from different sources, which makes the system more vulnerable to the decode error at relay. Conventional Cyclic Redundancy Code (CRC) has been implemented for error bit detection. However, its error correction is simply ignored. To fully exploit this feature, this paper proposes a novel joint Log-Likelihood Ratio (LLR) CRC error mitigation for NC two way relay channel. Specific thresholds are designed to estimate the error number of data block and identify those which can be recovered if the number is within the error correction scope of CRC. We examine two modes of the thresholds, one based on the average Bit Error Rate (BER) of source-relay link, while the other based on that of instantaneous one. We provide the full analysis for the Pair-wise Error Probability (PEP) performance of the scheme. A variety of numerical results are presented to reveal the superiority of the proposed scheme to conventional CRC NC under independent Rayleigh fading channels. Moreover, the efficiencies of the proposed thresholds are also validated.展开更多
To address the eccentric error of circular marks in camera calibration,a circle location method based on the invariance of collinear points and pole–polar constraint is proposed in this paper.Firstly,the centers of t...To address the eccentric error of circular marks in camera calibration,a circle location method based on the invariance of collinear points and pole–polar constraint is proposed in this paper.Firstly,the centers of the ellipses are extracted,and the real concentric circle center projection equation is established by exploiting the cross ratio invariance of the collinear points.Subsequently,since the infinite lines passing through the centers of the marks are parallel,the other center projection coordinates are expressed as the solution problem of linear equations.The problem of projection deviation caused by using the center of the ellipse as the real circle center projection is addressed,and the results are utilized as the true image points to achieve the high precision camera calibration.As demonstrated by the simulations and practical experiments,the proposed method performs a better location and calibration performance by achieving the actual center projection of circular marks.The relevant results confirm the precision and robustness of the proposed approach.展开更多
This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme,...This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.展开更多
Extending the work carried out by [1], this paper proposes six combined-type estimators of population ratio of two variables in post-stratified sampling scheme, using variable transformation. Properties of the propose...Extending the work carried out by [1], this paper proposes six combined-type estimators of population ratio of two variables in post-stratified sampling scheme, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations,(on–1), both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions were obtained. Under these conditions the proposed combined-type estimators would perform better than the associated customary combined-type estimator. Furthermore, optimum estimators among the proposed combined-type estimators were obtained both under the conditional and unconditional arguments. An empirical work confirmed the theoretical results.展开更多
The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estim...The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations, both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions, under which the proposed separate-type estimators would perform better than the associated customary separate-type estimators in terms of having smaller mean squared errors, were obtained. Furthermore, conditions under which some of the proposed separate-type estimators would perform better than other proposed separate-type estimators were also obtained. The optimum estimators among the proposed separate-type estimators were obtained and an empirical illustration confirmed the theoretical results.展开更多
Peak to Average Power Ratio (PAPR) is defined as the instantaneous power (maximum value) to the average power ratio. PAPR is considered to be a major problem in OFDM systems. This problem can cause radical unexpected ...Peak to Average Power Ratio (PAPR) is defined as the instantaneous power (maximum value) to the average power ratio. PAPR is considered to be a major problem in OFDM systems. This problem can cause radical unexpected behavior of the signal fluctuation. This fluctuation is constituted by a large number of power states. The enormous number of these states leads to an additional complexity of ADCs and DACs. This research addresses the previous problem in OFDM systems utilizing Turbo Codes. μLaCP technique is employed for the purpose of decreasing PAPR. Moreover, our OFDM system was simulated in the presence of an AWGN channel with four types of codes (without the presence of ADCs and DACs). These were constituted of PCCC (typical and new), SCCC, and Convolutional Codes. Our Turbo Coded OFDM exhibited unchanged BER performance before and after the use of μLaCP technique. This was accomplished by modifying our previous PAPR reduction technique without sacrificing greatly its attributes.展开更多
This manuscript deals with new class of almost unbiased ratio cum product estimators for the estimation of population mean of the study variable by using the known values auxiliary variable. The bias and mean squared ...This manuscript deals with new class of almost unbiased ratio cum product estimators for the estimation of population mean of the study variable by using the known values auxiliary variable. The bias and mean squared error of proposed estimators are obtained. An empirical study is carried out to assess the efficiency of proposed estimators over the existing estimators with the help of some known natural populations and it shows that the proposed estimators are almost unbiased and it perform better than the existing estimators.展开更多
Cooperative communication is going to play a vital role in the next generation wireless networks. In this paper we derive the expression for symbol error probability (SEP) of a two-user cooperative diversity system, w...Cooperative communication is going to play a vital role in the next generation wireless networks. In this paper we derive the expression for symbol error probability (SEP) of a two-user cooperative diversity system, where two users cooperate through the decode-and-forward (DF) relaying with binary phase-shift keying (BPSK) modulation in a flat Rayleigh fading environment. We compare the computational results obtained by the SEP expression with the simulation results using maximal-ratio combining (MRC), equal-gain combining (EGC) and selection combining (SC) techniques. Numerical results show the performance of a cooperative diversity system with maximal-ratio combining is giving better results compared to SC and EGC techniques.展开更多
文摘Movement accuracy is the key factor to be considered in designing precision instrument linkage and mini-linkage mechanisms. Although manufacturing errors, elastic deformation, kinematic pair clearance and friction factors all will have synthesis effect on the position accuracy of the mechanical system, the essential factor to guarantee the movement precision remains the kinematic dimensions. Combining the classical theory of mechanical synthesis with the modern error theory and the numerical method, the authors put forward a systematic and complete process and method of computer aided design for the instrument crank-coupler mechanism in which the follower takes the linear displacement approximately within a certain limited domain, with the design result of least transmission ratio error.
文摘The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.
文摘The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.
基金This work is supported by NNSF of China (10571093)
文摘Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.
文摘In luminescence and ESR dating methods,total count rate from thick source alpha counting is commonly used fox estimating annual dose with assumption of equal activities for both uranium and thorium decay chains.This is equal to a Th/U weight ratio of 3.2.The systematic error in total dose rate due to uncertainty of the ratio is calculated.It is found that the error is insignificant for uniformly distributed samples such as sediment,but can be significant for some extreme circumstances.
基金Supported by the National Natural Science Foundation of China (No.60572059)Foundation of Guangdong Province for Ph.D. (No. 5300707).
文摘Bit Error Probability (BEP) provides a fundamental performance measure for wireless diversity systems. This paper presents two new exact BEP expressions for Maximal Ratio Combining (MRC) diversity systems. One BEP expression takes a closed form, while the other is derived by treating the squared-sum of Rayleigh random variables as an Erlang variable. Due to the fact that the extant bounds are loose and could not properly characterize the error performance of MRC diversity systems, this paper presents a very tight bound. The numerical analysis shows that the new derived BEP expressions coincide with the extant expressions, and that the new approximation tightly bounds the accurate BEP.
文摘This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying(BPSK), quadrature phase shift keying(QPSK), quadrature amplitude modulation(QAM)-16 and QAM-64 with four error correction codes(convolutional code(CC), Reed-Solomon code(RSC)+CC, low density parity check(LDPC)+CC, Turbo+CC) is studied under three channel models(additive white Guassian noise(AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate(BER) and the peak signal to noise ratio(PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance.
文摘Although various estimating methods have been developed for measuring Q from near-surface seismic data, less thought has been given to the accuracy of Q obtained. The errors of Q depend on the ways of measuring Q and the computation techniques used in estimating. The main purpose of this paper is to give a compre- hensive evaluation for the accuracy of measuring near-surface Q. We discuss the possible origins from which errors may develop, and provide a statistical guide to the accuracy that can be expected. A set of real data based on the improved spectral ratio method for near-surface Q was used as an example of validation and sensitivity analysis. The Bonferroni procedure was adopted for deriving the joint confidence intervals for k and n of the power law model. The same approach with modest modification may be applied to analyze the accuracy of Q estimated by other methods.
基金the National Natural Science Foundation of China under Grants 61873160 and 61672338.
文摘Nowadays,distance is usually used to evaluate the error of trajectory compression.These methods can effectively indicate the level of geometric similarity between the compressed and the raw trajectory,but it ignores the velocity error in the compression.To fill the gap of these methods,assuming the velocity changes linearly,a mathematical model called SVE(Time Synchronized Velocity Error)for evaluating compression error is designed,which can evaluate the velocity error effectively,conveniently and accurately.Based on this model,an innovative algorithm called SW-MSVE(Minimum Time Synchronized Velocity Error Based on Sliding Window)is proposed,which can minimize the velocity error in trajectory compression under the premise of local optimization.Two elaborate experiments are designed to demonstrate the advancements of the SVE and the SW-MSVE respectively.In the first experiment,we use the PED,the SED and the SVE to evaluate the error under four compression algorithms,one of which is the SW-MSVE algorithm.The results show that the SVE is less influenced by noise with stronger performance and more applicability.In the second experiment,by marking the raw trajectory,we compare the SW-MSVE algorithm with three others algorithms at information retention.The results show that the SW-MSVE algorithm can take into account both velocity and geometric structure constraints and retains more information of the raw trajectory at the same compression ratio.
基金Supported by the National 973 Programs (2013CB329104)the National Natural Science Foundations of China (No. 61071090, No. 61171093)+3 种基金the Postgraduate Innovation Programs of Scientific Research of Jiangsu Province (CXZZ11_0388)Jiangsu Province Natural Science Foundation Key Projects (11KJA510001)National Science and Technology Key Projects (2011ZX03005-004-003)Jiangsu 973 Projects (BK2011027)
文摘Network Coding (NC) brings correlation between the coded signals from different sources, which makes the system more vulnerable to the decode error at relay. Conventional Cyclic Redundancy Code (CRC) has been implemented for error bit detection. However, its error correction is simply ignored. To fully exploit this feature, this paper proposes a novel joint Log-Likelihood Ratio (LLR) CRC error mitigation for NC two way relay channel. Specific thresholds are designed to estimate the error number of data block and identify those which can be recovered if the number is within the error correction scope of CRC. We examine two modes of the thresholds, one based on the average Bit Error Rate (BER) of source-relay link, while the other based on that of instantaneous one. We provide the full analysis for the Pair-wise Error Probability (PEP) performance of the scheme. A variety of numerical results are presented to reveal the superiority of the proposed scheme to conventional CRC NC under independent Rayleigh fading channels. Moreover, the efficiencies of the proposed thresholds are also validated.
基金supported by the Aerospace Science and Technology Joint Fund(6141B061505)the National Natural Science Foundation of China(61473100).
文摘To address the eccentric error of circular marks in camera calibration,a circle location method based on the invariance of collinear points and pole–polar constraint is proposed in this paper.Firstly,the centers of the ellipses are extracted,and the real concentric circle center projection equation is established by exploiting the cross ratio invariance of the collinear points.Subsequently,since the infinite lines passing through the centers of the marks are parallel,the other center projection coordinates are expressed as the solution problem of linear equations.The problem of projection deviation caused by using the center of the ellipse as the real circle center projection is addressed,and the results are utilized as the true image points to achieve the high precision camera calibration.As demonstrated by the simulations and practical experiments,the proposed method performs a better location and calibration performance by achieving the actual center projection of circular marks.The relevant results confirm the precision and robustness of the proposed approach.
文摘This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.
文摘Extending the work carried out by [1], this paper proposes six combined-type estimators of population ratio of two variables in post-stratified sampling scheme, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations,(on–1), both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions were obtained. Under these conditions the proposed combined-type estimators would perform better than the associated customary combined-type estimator. Furthermore, optimum estimators among the proposed combined-type estimators were obtained both under the conditional and unconditional arguments. An empirical work confirmed the theoretical results.
文摘The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations, both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions, under which the proposed separate-type estimators would perform better than the associated customary separate-type estimators in terms of having smaller mean squared errors, were obtained. Furthermore, conditions under which some of the proposed separate-type estimators would perform better than other proposed separate-type estimators were also obtained. The optimum estimators among the proposed separate-type estimators were obtained and an empirical illustration confirmed the theoretical results.
文摘Peak to Average Power Ratio (PAPR) is defined as the instantaneous power (maximum value) to the average power ratio. PAPR is considered to be a major problem in OFDM systems. This problem can cause radical unexpected behavior of the signal fluctuation. This fluctuation is constituted by a large number of power states. The enormous number of these states leads to an additional complexity of ADCs and DACs. This research addresses the previous problem in OFDM systems utilizing Turbo Codes. μLaCP technique is employed for the purpose of decreasing PAPR. Moreover, our OFDM system was simulated in the presence of an AWGN channel with four types of codes (without the presence of ADCs and DACs). These were constituted of PCCC (typical and new), SCCC, and Convolutional Codes. Our Turbo Coded OFDM exhibited unchanged BER performance before and after the use of μLaCP technique. This was accomplished by modifying our previous PAPR reduction technique without sacrificing greatly its attributes.
文摘This manuscript deals with new class of almost unbiased ratio cum product estimators for the estimation of population mean of the study variable by using the known values auxiliary variable. The bias and mean squared error of proposed estimators are obtained. An empirical study is carried out to assess the efficiency of proposed estimators over the existing estimators with the help of some known natural populations and it shows that the proposed estimators are almost unbiased and it perform better than the existing estimators.
文摘Cooperative communication is going to play a vital role in the next generation wireless networks. In this paper we derive the expression for symbol error probability (SEP) of a two-user cooperative diversity system, where two users cooperate through the decode-and-forward (DF) relaying with binary phase-shift keying (BPSK) modulation in a flat Rayleigh fading environment. We compare the computational results obtained by the SEP expression with the simulation results using maximal-ratio combining (MRC), equal-gain combining (EGC) and selection combining (SC) techniques. Numerical results show the performance of a cooperative diversity system with maximal-ratio combining is giving better results compared to SC and EGC techniques.
