With the drive towards better and faster communication systems, wireless communications has assumed a new significance in today''s world. In this context, it becomes all the more important to increase the efficiency of the antennas involved with these systems. Patch antennas are used because of their popularity arising from their adaptability and unobtrusive nature. Here we have tried to look at an optimum design for a patch antenna and also the best possible feed network for the same which would enhance its radiation properties as has been shown through the results obtained here. Furthermore, the mutual coupling between antennae in a 2 x 2 array when the antennae are linearly, non-linearly and circularly polarized is studied and compared. During this process, the frequency variation produced is also noted. The data from the variation of the mutual coupling between adjacent antennae and the resonant frequency of the antennae themselves, its dependence on polarization, feed direction and distance can be used in designing an array.