Imaging with an optical incoherent synthetic aperture (SA) means that the incoherent light from observed objects is processed over time from various points of view to obtain a resolution equivalent to single-shot imaging by the SA larger than the actual physical aperture. The operation of such systems has always been based on two-wave interference where the beams propagate through two separate channels. This limitation of two channels at a time is removed in the present study with the proposed SA where the two beams pass through the same single channel at any given time. The system is based on a newly developed self-interference technique named coded aperture correlation holography. At any given time, the recorded intensity is obtained from interference between two waves co-propagating through the same physical channel. One wave oriented in a particular polarization is modulated by a pseudorandom coded phase mask and the other one oriented orthogonally passes through an open subaperture. Both subapertures are multiplexed at the same physical window. The system is calibrated by a point spread hologram synthesized from the responses of a guide star. All the measurements are digitally processed to achieve a final image with a resolution higher than that obtained by the limited physical aperture. This unique configuration can offer alternatives for the current cumbersome systems composed of far apart optical channels in the large optical astronomical interferometers. Furthermore, the proposed concept paves the way to an SA system with a single less-expensive compact light collector in an incoherent optical regime that may be utilized for future ground-based or space telescopes.