Imagine a group of eight or more vertical masts. On each mast is a Yagi antenna pointed upward toward the sky. The elements are inverted with the idea being that the incoherent RF coming down is given constructive interference to become useable coherent current. How to successfully connect multiple feeds together to support this desired outcome?
Using several antennas to improve HF reception is an old and very effective idea. The trick is combining them correctly. Simply connecting them to a splitter will generate fixed-position lobes of high gain in the sky, and regions of lower gain. For amateurs who are looking for contacts in a wide area, not a single place, this is quite advantageous already.
The udeal is to have the feeds connected to separate receivers, and then to a computer that combines them in the appropriate phase for best SNR.
The computer would first do some direction-finding to find the angle of arrival of the signal, then synthesize a beam in that direction.
The RF from the sky is not incoherent - it is very much coherent and to your "radio eyes" would appear to be coming from a fairly small spot in the sky. This is the basis of Single Site Location, where a single DF system can find the position of a transmitter, using only the angles of arrival and a model of the ionosphere.
Once you have several elements, the advantage (in receiving) of using yagis is reduced. The synthesised beam is fairly small anyway. Commercially available HF DF arrays use a pattern of crossed loops and dipoles laid out on the ground.