The implementation of a null-steering antenna array using dual polarised patch antennas is considered. Several optimality criterion for adjusting the array weights are discussed. The most effective criteria minimises the output power of the array subject to maintaining a right hand circular polarisation (RHCP) response on the reference antenna. An unconstrained form of this criteria is derived, in which the reference channel is the RHCP output of the reference antenna and the LHCP output of the reference antenna is included as one of the auxiliary channels. An FPGA implementation of the LMS algorithm is then described. To prevent weight vector drift a variant of the circular leakage LMS algorithm was used. The implementation details of a simplified circular leakage algorithm more suited to an FPGA implementation are presented. This simplified leakage algorithm was shown to have a similar steady state weight vector as the full algorithm.