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In this letter, we derive an average symbol error rate (ASER) expression of rectangular quadrature amplitude modulation (RQAM) scheme for unmanned aerial vehicle-enabled communication systems operating over double-shadowing and double-scattering composite fading channel. A moment generating function for the receiver output signal-to-noise ratio is obtained to analyze the ASER expression of non-coherent modulation schemes. An asymptotic expression of ASER for RQAM scheme is also derived to examine diversity order of the considered system. Further, the impact of composite fading parameters and path loss on ASER performance is highlighted. Finally, we validate all the theoretical results through Monte Carlo simulations.