This paper presents the vital role mathematical modeling plays in the solution to the signal processing problem. The paper will compare the traditional open loop methodology of signal processing to the modern closed loop methodology. Advantages and disadvantages will be discussed. In the past, the system discriminants have been derived from knowledge of the signal bandwidth and characteristics of the receiver while actual signal propagation has been ignored. The result of such a formulation generally leads to incorrect statistics. This traditional approach has been improved by use of a closed loop methodology (CLM) technique. The methodology employs an adaptive processor which provides correct signature statistics.