Theory of adaptive focusing of transmitting antenna

Abstract

Known adaptive focusing (AF) of transmitting antenna methods can be non-effective in complicated situations. The author proposes a theory for an optimum synthesis procedure of AF. The problem is treated by an optimum control theory approach, as a problem of the multistage control process using energy or information criteria. AF theory is based on results of R.L. Stratonovich who created the theory of controllable Markov’s processes. The author uses the nor-mal-law approximation to derive solvable basic equations for AF procedures. Both the second-moment equations, describing the system state, and the optimum criterion depend on the choice of space-time signals radiated previously. Either Bellman’s equation or Pontryagin’s maximum principle are used for the optimization.

Using the theory has enabled the author to synthesize some new control procedures for multi-modular system with random phase errors. These procedures are more efficient than the known methods by various criteria such as maximum speed, maximum power, etc.

The theory can be used to solve various tasks of radiating systems control. For example, the minimization of a target detection time by a large-aperture multi-modular radar antenna with phase errors is considered. The developed optimum procedure is the one of succeeding detection combined with a multistage AF procedure for transmitting antenna.