Information bounds for random signals in time-frequency plane

Renyi entropy has been proposed as one of the methods for measuring signal information content and complexity on the time-frequency plane by several authors [1, 2]. It provides a quantitative measure for the uncertainty of the signal. All of the previous work concerning Renyi entropy in the time-frequency plane has focused on determining the number of signal components in a given deterministic signal. In this paper, we are going to discuss the behaviour of Renyi entropy when the signal is random, more specifically white complex Gaussian noise. We are going to present the bounds on the expected value of Renyi entropy and discuss ways to minimize the uncertainty by deriving conditions on the time-frequency kernel. The performance of minimum entropy kernels in determining the number of signal elements will be demonstrated. Finally, some possible applications of Renyi entropy for signal detection will be discussed.