Aperture averaging in multiple-input single-output free-space optical systems using partially coherent radial array beams. 
Multiple-input single-output (MISO) techniques are employed in free-space optical (FSO) links to mitigate the degrading effects of atmospheric turbulence.  In this paper, for the MISO FSO system, a partially coherent radial array and a finite-sized receiver aperture are used at the transmitter and the receiver, respectively.  Using the extended Huygens-Fresnel principle, we formulate the average power and the power correlation at the finite-sized slow detector in weak atmospheric turbulence.  System performance indicators such as the power scintillation index and the aperture averaging factor are determined.  Effects of the source size, ring radius, receiver aperture radius, link distance, and structure constant and the degree of source coherence are analyzed on the performance of the MISO FSO system.  In the limiting cases, the numerical results are found to be the same when compared to the existing coherent and partially coherent Gaussian beam scintillation indices.