Moment Generating Function Approach in Diversity Combiner with M-PSK over Hoyt Fading Channel


  • Ajadi, A.S. Department of Electronic and Electrical Engineering, Ladoke Akintola University of Technology, Ogbomoso, Oyo State, Nigeria.
  • Semire F.A Department of Electronic and Electrical Engineering, Ladoke Akintola University of Technology, Ogbomoso, Oyo State, Nigeria.
  • Ojo, S.I. Department of Electronic and Electrical Engineering, Ladoke Akintola University of Technology, Ogbomoso, Oyo State, Nigeria.



, Radio Frequency (RF), Moment Generating Function (MGF), Maximum Ratio Combiner (MRC), M-PSK, Match Filter (MF)


Wireless communication system is the processing, transmitting and receiving signals over an open space. This system suffers from time varying environment disturbance due to propagation of signals through different paths which prompt the signals to have different statistical distributions. The existing modified diversity combiners diversity such as Maximal Ratio Combiner (MRC), Equal Gain Combiner (EGC) with one Match Filter (MF) and one Radio Frequency (RF) chain, lack closed form expression. Therefore, in this paper, Moment Generating Function (MGF) approach is used to analyse the performance of the modified MRC over Hoyt fading distribution through the closed form expression. A closed formed expression is developed using the existing modified MRC with one Radio Frequency (RF) chain and one Matched Filter (MF) at the RF stage. Binary data of ten thousand bits are generated randomly as source data and modulated with M-ary Phase Shift Keying (M-PSK). The modulated signal is passed through the Hoyt fading channel which is then modeled using Moment Generating Function (MGF) approach in order to generate the resultant signals. The resultant signals at varying paths ‘L’ (2, 3 and 4) and Hoyt fading factors’q’ (0.2, 0.4 and 0.6) are combined using the modified MRC. The output signal is passed through a comparator which compares the output signal with 9.5 dB set as threshold value. The outage probability of the modified MRC using M-PSK (2-PSK and 4-PSK) at varying ‘L’ and ‘q’ is evaluated, while processing time is used to compare the performance of the conventional MRC with the modified MRC. The results obtained with the modified MRC using closed form expression give lower Outage Probability (OP) and processing time. The research can be used by satellite communication system designers to improve the quality of service.

Author Biography





(1) Abramovitz, M., and Stegun, I.A, “Hand book of Mathematical functions with formulas, graphs, and mathematical tables” Dover, New York, USA. (1992),

(2) Adeyemo, Z. K. and Raji T. I, “Effects of Diversity combining in mobile Terrestrial Environment” Continental Journal of Engineering Sciences 5:27-37. (2010)

(3) Adeyemo, Z. K. and Ojedokun Isaac A., “EGC Receiver using single Radio Frequency chain and single matched filter over combined Rayleigh and Rician Fading channels” ARPN Journal of Engineering and Applied Science, (2014). 9(7): 1819-6608.

(4) Anamllyas, Ejaz Ansari and Saleem Akhtar “Accurate BERSER Analysis and performance of different modulation schemes over wireless fading channel,” Science Inernation, (2013). 25(2):367-374.

(5) Adeyemo Z.K, Rabiu E.O and Abolade R.O. Offset Phase Shift Keying modulation in Multiple-Input Multiple-Output Spatial Multiplexing; Transaction on Networks and Communications, (2015): 3(20): 117-127.

(6) Amindavar H., and Ritcey J. A., “Pade approximation of probability density functions”, IEEE Transaction Aerospace. Electron System, (1994). 30(1):416-424

(7) Annamalai A., and Tellambura C., “Performance evaluation of generalized selection Diversity systems over Nakagami–m fading channels”, Wireless Communications and Mobile Computing, (2003). 3(1):99 – 116.

(8) Blaunstein, N., and Christodoulou, C. G., “Radio Propagation and Adaptive Antennas for Wireless Communication Links”, John Wiley and Sons, Inc., Hoboken, New Jersey. (2007),

(9) Brennan, D.G, “Linear Diversity Combining Techniques,” Proceeding of the IEEE, (2003), 91 (2):1075-1102

(10) Dighe, P. A., Mallik, R. K., and Jamuar, S. S., “Analysis of transmit-receive diversity

in Rayleigh Fading”,IEEE Transactions on communication, (2003). 51(1):694 – 703.

(11) Dimitris A. Zogas “Equal Gain Combining over Nakagami-n (Rice) and Nakagamiq(Hoyt) Generalized fading channels” IEEE Transactions on wireless communications, (2005). 4(2): 374-379

(12) Goldsmith, A., “Wireless Communications,” Standford University Press, California. (2005),

(13) Helstrom C.W., “Probability and Stochastic processes for engineers”, Second edition Macmillan, New York, USA. (1991),

(14) Hoyt, R., “Probability functions for the modulus and angle of the normal complex variate,” Belly Syst. Tech. J., (1947). 26(1):318-359.

(15) Jahn, A., “Propagation Considerations and fading counter measures for Mobile Multimedia Services”, Int. Journal of Satellite Communication, (2001). 19(3), pp 223-250

(16) Jochen S., Mobile Communications, 2nd Ed. Pearson Education Ltd., India. (2006).

(17) Jyoteesh Malhotra, Ajay Sharma, K., and Kaler R.S., “On the performance analysis of wireless receiver using generalized- gamma fading model”, Annals of Telecommunications. (2009). 46(1) :147-157.

(18) Karagiannidis G. K., Sagias N. C., and Zogas D. A. “Error analysis of M-QAM with equal Gain Combining diversity over generalized fading channels”, IEEE Transactions on wireless communications, (2005). 152(1):69-74.

(19) Kim S.W. and Wang Z. “Maximum Ratio Diversity Combining Receiver using single Radio Frequency chain and single Matched Filter”, IEEE Globecom proceedings, (2007). 2(1):269-274.

(20) Lee T., and Lee Z “A Beam Space Diversity Combiner for sector Division Multiple Access Communications”, IEEE Antennas and Propagation Society Symposium Digest, Atlanta, (1998) 1(1):372 – 375.

(21) Malhotra J. “Investigation of M-QAM and MPSK with EGC in Generalized Flat Fading channels”, Journal of Advances in information Technology, (2011). 2(4):250-256.

(22) Malhotra J., Sharma A. K., and Kaler R. S. “On the performance Analysis of wireless receiver using generalized-gamma fading Model”, Annals of Telecom, (2009), Vol. 64, No. 1, pp147-153.

(23) Mohammed J., Leszek S., and Mustapha B., “Outage probability of Diversity combining Receivers in Arbitrarily Fading channels, (2011)

(24) Nakagami M., “The m-distribution- A General Formula of intensity Distribution of Rapid Fading” Statistical Methods of Radio Wave Propagation, pergamon (1960). 1(1):3-36.

(25) Patzoid, M., “Mobile Fading Channels” John Wiley and Sons, Ltd, Baffins Lane, Chichester, West Sussex, po191 IUD, England. (2002).

(26) Pornchai, S., Wanaree, W. and Sawasd, T. “Performance of M-PSK in Mobile Satellite Communication Over Combined Ionosphere Scintillation and Flat Fading Channels with MRC Diversity”, IEEE Transactions on Wireless Communications, (2009), Vol. 8, No. 7.

(27) Proakis, J. G, “Digital Communications”, McGraw-Hill companies, incorporation. International Edition, 2001.

(28) Rappaport, T.S., “Wireless Communication Principles and Practice” 2nd edition Prentice Hall of India Private limited view Delhi, (2002), pp1-526.

(29) Simeon M.K.and Alouini, M. S, “Digital Communications Over Fading Channels”,2nd edition, John Wiley and Sons, Incorporation, Hoboken, New Jersey, (2005), Pp1 – 523.

(30) Stewart, K.A., Labedz, and sohrabi K., “Wideband channel measurements at 900MHZ” in Proc. IEEE Vehicular Technology Conf. (VTC’95), Chicago IL, (1995) pp 236-240.

(31) Tang L. and Hongbo Z., “Analysis of Nakagami Fading channel with MATLAB” Asifat Pacific Conference on Environmental Electromagnetic CEEM Hang zhou, China. (2003), Pp490 – 494.

(32) Tse, D., and Viswanath, P., “Fundamentals of Wireless Communication” 1st Edition; Cambridge University Press, New York. (2005).

(33) Ye, Z. and Satorius “Channel modeling and simulation for mobile user objective system (MUOS) – part 1: flat scintillation and fading”, in proceeding IEEE ICC, (2003), 5(1):3508-3510.




How to Cite

Z.K, A., A.S., A., F.A, S., & S.I., O. (2019). Moment Generating Function Approach in Diversity Combiner with M-PSK over Hoyt Fading Channel. Transactions on Networks and Communications, 7(1), 51.