  In this paper, we solve the optimal target detection problem employing the
thoughts and methodologies of Shannon's information theory. Introducing a
target state variable into a general radar system model, an equivalent
detection channel is derived, and the a posteriori probability distribution is
given accordingly. Detection information (DI) is proposed for measuring system
performance, which holds for any specific detection method. Moreover, we
provide an analytic expression for the false alarm probability concerning the a
priori probability. In particular, for a sufficiently large observation
interval, the false alarm probability equals the a priori probability of the
existing state. A stochastic detection method, the sampling a posteriori
probability, is also proposed. The target detection theorem is proved
mathematically, which indicates that DI is an achievable theoretical limit of
target detection. Specifically, when empirical DI is gained from the sampling a
posteriori detection method approaches the DI, the probability of failed
decisions tends to be zero. Conversely, there is no detector whose empirical DI
is more than DI. Numerical simulations are performed to verify the correctness
of the theorems. The results demonstrate that the maximum a posteriori and the
Neyman-Pearson detection methods are upper bounded by the theoretical limit.
