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Optimum combining (OC) is a powerful means for combating co-channel interference. The characteristic function (CHF) of output signal to interference-plus-noise ratio (SINR) is an important tool for the performance analysis with optimum combining of faded signals in the presence of both co-channel interferers and noise. However, so far there has not existed an exact closed-form expression available for the output SINR CHF except for some special cases. The difficulty arises from the quadratic form of interference term. Based on the theory of complex matrix variate distributions, this paper considers the correlated Rayleigh/Rayleigh scenarios, and derives an exact closed-form expression for the output SINR CHF in the presence of unequal-power interference and noise.