Systems and methods for detecting targets using pulse-compressed radar signals are disclosed. In one application, relatively small targets that are masked by the time-sidelobes of a larger target's return signal can be detected. The methods include a signal expansion type algorithm that is used to process the pulse-compressed return signal. Specifically, a generalized Fourier expansion expression having a summation of PSF terms is used to expand the pulse-compressed signal. Each term represents a respective target and includes a point spread function and a complex coefficient. The signal expansion procedure can be used to determine a set of optimum complex coefficients, with one coefficient for each range bin. Doppler frequency can be used together with range to optimize the complex coefficients. Next, targets are detected by analyzing each range bin to determine whether the corresponding complex coefficient has an absolute magnitude greater than a pre-determined threshold.