Results for Infinite Integrals Involving Higher-Order Powers of the Gaussian Q-Function with Application to Average SEP Analysis of DE-QPSK

Exact results are presented for infinite integrals that consist of higher-order powers of the one dimensional Gaussian
Q
-function averaged over Rayleigh fading envelopes in multi-branch diversity reception with maximal ratio combining (MRC). Some known results for the average of the 1st and 2nd powers are shown as special cases. The results obtained in this paper are utilized to study the average symbol error probability (SEP) performance of differentially encoded quadri-phase shift-keying (DE-QPSK) in Rayleigh fading channels employing MRC, and new exact expressions are presented for different fading scenarios. The derived mathematical expressions are verified using Monte Carlo simulations.