Optimal Receiving Polarization Obtained Through Solving Unitary Quadratic Equation

This letter provides a simple method for optimal polarization filtering, which can be viewed as an optimization problem with a nonlinear constraint. The optimization is then turned into an unconstraint one through variable substitution. Based on the extremum necessary condition, the optimization is further changed into a problem of solving a unitary quadratic equation. It is found that the maximal signal-to-interference-plus-noise ratio (SINR) is the greater root of the unitary quadratic equation, and thus the optimal receiving polarization can be obtained analytically in a succinct form. This method can give the global optimum without numerical iteration and suits both completely and partially polarized situations.