There is always a scope on a particular topic if the field is identified properly. Antenna array is very important. Please work on it. To know the effect of central element of the working principle of a circular array, please consult these books:
1. Antenna Theory & Design Book by Robert S. Elliott
It increases the gain and the directivity. They are less if it isn't there, and the sidelobes are higher.
The radiation pattern in the far-field is the Fourier transform of the aperture excitation. The transform is linear, so the transforms of every element can be added together (remembering to take account of the effect of position on the phase of the transform result). The central element has zero added phase, so the effect of removing it can be seen by subtracting its (complex number) radiation pattern from the complex number) radiation pattern of the whole array. Because it has a wider radiation pattern than the whole array, it will have a wide main lobe that subtracts from the main lobe of the array to reduce its gain (and the second and fourth sidelobes), but adds to the first sidelobe(and third and fifth etc probably) to increase its level.
It will also affect the impedance match of the elements around it. Usually the edge elements of an array behave differently in impedance to elements within the array (which are the ones more easily predicted, because they behave as if they were in an infinite array). Removing the centre element will affect the ones around it. If you are really fussy it is the outside two rows that are different.