Frequency Assignment for Collocated Transmitters Using the Branch-and-Bound Technique

Personnel in the Electromagnetic Compatibility (EMC) area have provided specification compliance limits, techniques, hardware, and prediction and analysis models to the engineering fields for years in order to reduce electromagnetic interference between equipments. The EMC area has been growing all through the military and civilian environment. But, as the EC area grows so does the number of Radio Frequency (RF) equipments and users. This growth of RF equipments is staggering and is creating a severe problem commonly called "Spectrum Pollution." A great majority of the RF spectrum pollution is caused by unintentional emitters (i.e., television sets, automobile engines, mix masters, etc.). But, eliminating unintentional emissions alone will not stop the problem. There is, however, another major source of RF spectrum pollution, which this paper deals with, and that is "Unnecessary Emissions." This source of pollution is created by harmonic outputs, transmitter intermodulation, poorly designed EM transmitters, etc. This paper discusses the possible reduction of unnecessary emissions through the use of Operations Research Techniques. Specifically the paper proposes a method of assigning frequencies to collocated transmitters such that the total amount of transmitter intermodulation signal power emanating from a transmitter site is at a minimum. The paper discusses a realistic problem of eleven transmitters collocated on an actual transmitter site. A criterion function for reducing spectrum pollution due to transmitter intermodulation signal power (TISP
¹¹
) is discussed. A sample problem is solved involving four transmitters, and a discussion of the results is given. A portion of this paper is devoted to the derivation of the operations research technique employed to obtain the solution of the sample problem. The technique can best be described as a two-fold procedure of the Branch-and-Bound Technique. The first procedure is to obtain a maximum value of the criterion function (TISP
¹¹
), for each frequency/antenna assignment, that is independent of all other assignments. The second phase is to determine the frequency/antenna configuration that minimizes the independent maximum values of the criterion function paper, the criterion function derived, and the approach taken are open for discussion as far as accuracy of the results obtained. But, the applications of Operations Research Techniques to the EMC area to reduce RF spectrum pollution requires further investigation because, the possibility of a large pay off to the EMC community definitely exists.