Performance of a dual channel matched filter system

We analyze the signal-to-interference plus noise ratio (SINR) performance of a dual channel matched filter system under the assumption that the input interference plus noise signal for one channel is uncorrelated with the input signal for the other channel. We develop an exact expression for the normalized SINR as a function of random variables with known distributions and then, using a Taylor series expansion, we derive approximate expressions for the mean and variance of the normalized SINR. One can easily show that under the assumption of uncorrelated inputs and known correlation matrices that the dual channel matched filter system is equivalent to a single channel matched filter designed to process both input signals. We also show that when estimated correlation matrices are used in place of the true correlation matrices the dual channel matched filter system achieves nearly the same normalized SINR performance as the single channel matched filter system with half the secondary data. The results suggest that, with the proper preprocessing to decorrelate the input signal, a single channel matched filter system can be replaced by a dual channel matched filter system of smaller size, leading to a reduction in the secondary data requirements and potentially, to a reduction in the computational cost.