Unified analysis of equal-gain diversity on Rician and Nakagami fading channels

An exact analytical expression in a simple form for computing the average symbol error rate (SER) of an arbitrary two-dimension signaling format with equal-gain diversity (EGC) receiver is not available in the literature despite its practical and theoretical importance. The principle difficulty is finding a closed-form expression for the probability density function (PDF) of a sum of L (i.e., diversity order) random fading amplitudes. We develop an alternative, direct technique to evaluate the exact performance of EGC diversity systems (expressed in terms of a single or double finite-range integrals) in Rayleigh, Rician and Nakagami fading channels. Our new approach relies on the use of Parseval´s theorem to transform the error integral into the frequency domain. Since the Fourier transform of the PDF is the characteristic function (CHF), which is available in this case, our solution is general and exact. The CHF method also circumvents the need to perform an L-fold convolution integral which is usually encountered in the calculation of the PDF of the sum of the received signal amplitudes. Interestingly, we can also get some new closed-form solutions for binary CPSK and CFSK in the Nakagami fading channel for all L⩽3. Closed-form formulas for binary DPSK and NCFSK with EGC may also be obtained for L<3