Theoretical aspects of radar imaging using stochastic waveforms

In this work, we develop the theory of radar imaging using stochastic waveforms, such as random noise or chaotic signals. Specifically, we consider one-dimensional (1-D) (range profiles) and two-dimensional (2-D) (range-Doppler) radar imaging performed with a random signal radar, in which the transmit signals are assumed to be stationary random processes. We calculate the 1-D and 2-D point-spread functions as the expected value of the radar return. We show that the 2-D point-spread function is spatially invariant; however, the reduction in height and broadening of the mainlobe is small in the case of bandlimited noise. We also derive a formula that is useful in calculating the variance of the radar return under the assumption that the transmit signal is real valued and Gaussian.