24-10-2016, 03:08 PM
1460876008-BERanalysiswithMRCspacediversityinRayleighfadingchannel.docx (Size: 329.01 KB / Downloads: 6)
ABSTRACT :- This paper analyzes the bit error rate @ER) for quadrature amplitude modulation (QAM) with L-fold maximal ratio combining (MRC) space diversity in Rayleigh fading channel. The formula is obtained by averaging the bit error probability of M-ary QAM in an additive white
Gaussian noise channel over a chi-square distribution with 2L degrees of freedom. This formula overcomes the limitations of the earlier work, which has been limited only to deriving a
BER for QAM with two branch MRC space diversity. The BER performance of quadrature phase shift keying with MRC diversity is obtained from the derived formula by setting M=4.
1. INTRODUCTIO
Digital cellular systems have been widely developed to provide mobile communication service. With the increasing demands of the service, an important topic is to use a spectrally efficient modulation technique to raise the spectrum efficiency in the limited frequency bandwidth. Quadrature amplitude modulation (QAM) is an effective technique to achieve high spectral efficiency in additive white
Gaussian noise (AWGN) channel. Also it is a good candidate for high spectral efficiency in a Rayleigh fading channel with channel state information (CSI). In order to achieve high spectral efficiency in the land mobile communication system, Sampei et al. have introduced M-ary QAM with two branch maximal ratio combining W C ) space diversity and they have employed a pilot symbol assisted method (PSAM) to obtain the CSI. Space diversity is a well-known technique to combat multipath fading in mobile radio communications. As a result of computer simulation and laboratory
experiments, they obtained a desirable bit error rate @ER) performance based on the PSAM channel sounding technique. However, to obtain the theoretical results, they employed numerical integration or simplified approximation. In the second term on the right side of has been ignored. This approximation causes the error of the theoretical BER to be more than 7 % even though EdNo=IO dB. Furthermore, their analyses are limited only to two branch space diversity. It is also important to extend the order of diversity to the general case.
2. Probability of Error
Let us consider only the rectangular signal sets. For such signal structure, the ~ = si@ ~ points result in a symmetrical form of QAM when k is even. In this case, QAM can be viewed as two separate pulse amplitude modulation signals impressed on phase quadrature carriers.
Results and Discussion
In this Section, the BER performance of QAM with MRC space diversity is obtained from , where the 3rd term in the bracket is represented with the infinite summation. But we can obtain sufficient accuracy by truncating the summation when the absolute value of the last term added is less than 10"'. compares the calculated BER obtained in this paper to the approximate BER in for 16QAM with two branch MRC space diversity in Rayleigh fading environments. Under two branch MRC space diversity, the approximate BER is 10.1 % higher than the obtained BER in this paper when the average bit energy-to-noise density ratio (EJN0) is 5 dB, and is more than 7 % even though Ed/No=10 dB. The difference between the BER obtained in this paper and the approximate BER decreases with increasing average bit energy-to-noise density ratio. shows the BER performance of 16QAM with MRC space diversity in Rayleigh fading environments for L=1-10. BER performance of 64QAM with MRC space diversity in Rayleigh fading environments for L=1-10. From and 3, we can see that the probability of error decreases with the order of diversity. The results illustrate the advantage of diversity as a means for combating the fading phenomena.
4. Conclusions
In this paper, we analyze the bit error probability for QAM with general maximal ratio space diversity in Rayleigh fading channel. The derived equation includes an infinite summation, but we can obtain Micient accuracy by truncating the summation when the last term added is very
small value. By choosing the order of diversity, and the number of signal points from the derived formula, we can obtain the BER performance of the QAM with MRC diversity. We can also obtain the BER performance of quadrature phase shift keying with h4RC diversity fkom the derived formula by setting M=4.