An Application of the Theory of Games to Radar Reception Problems

Book excerpt: The problem of radar reception in the presence of jamming is treated by an application of the theory of games. The game formulation is as follows: assume the radar receiver employs a matched filter, matched to the radar echo signal, and let the choice of band-limited power spectral distributions for both the radar signal and the jamming noise constitute the respective strategy decisions for the radar designer and the jammer. Games with strategies of this type are known as function-space games. For each opponent, optimum spectral strategies are specified when the payoff function is the receiver output signal-to-noise ratio or the mean squared time error in target location. A new expression for this output signal-to-noise ratio is used which reduces to the familiar 2E/No for the case of constant density noise jamming. When the output S/N ratio is the game payoff function, the optimum spectra are shown to be constant density band-limited spectra for both the radar signal and the jamming noise. The game theoretically optimum linear receiver is a matched filter receiver. When the time error is used as a payoff function, the set of spectra from which the radar designer may choose is limited in a certain way so that the resulting game may be more easily solved. However, a special trick must be used to solve it. Optimum spectra for this game are other than simple constant density spectra.