Performance analysis of equal gain combining in Nakagami-m fading channels using approximate moment generating function

A moment generating function (MGF) based performance analysis is presented for N-branch equal gain combining (EGC) in independent Nakagami-m fading channels as well as dual-branch EGC in correlated Nakagami-m fading channels. Since exact MGFs of received SNRs are in general difficult to acquire, Gauss quadrature rule is employed to efficiently and accurately approximate relevant MGFs. As such, symbol error rates (SERs) of various binary and M-ary modulation formats can be readily calculated. We further investigate the performance of EGC in terms of diversity order. Assuming average SNR tends to infinity, we derive exact MGFs for EGC in both independent and correlated Nakagami-m fading channels. Then we prove that the diversity order achieved by EGC is equal to the sum of Nakagami-m fading indexes of all diversity branches.

[1]  Vijay K. Bhargava,et al.  Equal-gain diversity receiver performance in wireless channels , 2000, IEEE Trans. Commun..

[2]  Mohamed-Slim Alouini,et al.  Closed-form analysis of dual-diversity equal-gain combining over Rayleigh fading channels , 2003, IEEE Trans. Wirel. Commun..

[3]  Georgios B. Giannakis,et al.  A simple and general parameterization quantifying performance in fading channels , 2003, IEEE Trans. Commun..

[4]  George K. Karagiannidis,et al.  BER performance of dual predetection EGC in correlative Nakagami-m fading , 2004, IEEE Transactions on Communications.

[5]  P. Takis Mathiopoulos,et al.  Exact Performance Analysis of Dual-Branch Coherent Equal-Gain Combining in Nakagami- $m$, Rician, and Hoyt Fading , 2008, IEEE Transactions on Vehicular Technology.

[6]  E. M. N. Ekanayake,et al.  Equal-gain combining diversity reception of M-ary cpsk signals in nakagami fading , 2010, IEEE Communications Letters.

[7]  Keith Q. T. Zhang.  Probability of error for equal-gain combiners over Rayleigh channels: some closed-form solutions , 1997, IEEE Trans. Commun..

[8]  Moe Z. Win,et al.  MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels , 2000, IEEE Communications Letters.

[9]  George K. Karagiannidis,et al.  Moments-based approach to the performance analysis of equal gain diversity in Nakagami-m fading , 2004, IEEE Transactions on Communications.

[10]  Khairi Ashour Hamdi,et al.  Some Notes on the Fourier Transform Methods for Error-Rate Analysis of Equal-Gain Combining , 2010, IEEE Transactions on Communications.

[11]  M. Nakagami.  The m-Distribution—A General Formula of Intensity Distribution of Rapid Fading , 1960 .

[12]  P. R. Sahu,et al.  Performance analysis of predetection EGC in exponentially correlated Nakagami-m fading channel , 2005, IEEE Transactions on Communications.

[13]  Mohamed-Slim Alouini,et al.  Performance analysis of coherent equal gain combining over Nakagami-m fading channels , 2001, IEEE Trans. Veh. Technol..

[14]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[15]  P. R. Sahu,et al.  ABER of Dual Predetection EGC in Correlated Nakagami-m Fading Channels with Arbitrary m , 2008, IEEE Communications Letters.

[16]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[17]  Ranjan K. Mallik,et al.  Performance of dual-diversity predetection EGC in correlated Rayleigh fading with unequal branch SNRs , 2002, IEEE Trans. Commun..

[18]  Robert F. Pawula.  Generic error probabilities , 1999, IEEE Trans. Commun..

[19]  George K. Karagiannidis,et al.  Error analysis of M-QAM with equal-gain diversity over generalised fading channels , 2005 .

[20]  Mohamed-Slim Alouini,et al.  Digital Communication Over Fading Channels: A Unified Approach to Performance Analysis , 2000 .

[21]  J. Craig.  A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations , 1991, MILCOM 91 - Conference record.

[22]  E. M. Gelbard,et al.  Gaussian quadratures for the integrals ₀^{∞}(-²)() and ₀^{}(-²)() , 1969 .

[23]  G. D. Byrne,et al.  Gaussian Quadratures for the Integrals , 2010 .

[24]  Norman C. Beaulieu,et al.  Analysis of equal gain diversity on Nakagami fading channels , 1991, IEEE Trans. Commun..

[25]  Lorenzo Rubio,et al.  Generation of bivariate Nakagami-m fading envelopes with arbitrary not necessary identical fading parameters , 2007, Wirel. Commun. Mob. Comput..

[26]  Q. T. Zhang.  A simple approach to probability of error for equal gain combiners over Rayleigh channels , 1999 .