Composite matched filter output partitioning

A common pattern recognition problem is finding a library element closest, in some sense, to a given reception. In many scenarios, optimal detection requires N matched filters for N library elements. Since N can often be quite large, there is a need for suboptimal techniques that base their decisions on a reduced number of filters. The use of composite matched filters (CMFs) (also called synthetic discriminant functions or linear combination filters) is one technique to achieve this reduction. For two level CMF outputs, the reduction is from N to log(2)N matched filters. Previously, the coefficients of the CMF output were restricted to positive values-often 0 and 1. We refer to such filters as binary CMFs. An alternative approach is to use -1 and +1 for filter coefficients. This alternative filter will be called a bipolar CMF. This paper demonstrates how the extension from a binary to a bipolar CMF greatly improves the detection performance while still maintaining the reduced computational requirements of the binary CMF. Furthermore, the bipolar CMF is invariant to scale: multiplying the input by a positive constant gives the same processor output. This desirable behavior does not exist for the binary CMF.