The ambiguity function of a linear signal space and its application to maximum-likelihood range/Doppler estimation

The concept of the ambiguity function (AF) is extended to linear signal spaces. Some properties of the AF of a linear signal space, its relations with other space representations, and the results obtained for some specific signal spaces are discussed. It is shown that the AF of a signal space describes the performance of the maximum likelihood (ML) range/Doppler estimator for a slowly fluctuating point target when a series of orthogonal signal pulses are transmitted. This multipulse estimator is more accurate than a conventional signal-pulse estimator since the AF of a linear signal space may have arbitrarily good thumbtack shape.<>