Finite rate of innovation method for DOA estimation of multiple sinusoidal signals with unknown frequency components

We consider multiple sinusoidal signals with unknown frequency components that are transmitted from unknown directions. The unknown frequency components may reside in a very high frequency range such that sampling at the Nyquist rate is undesirable. Our goal is to recover the frequency components and the direction of arrivals (DOAs) of the transmitted signals in time domain without any prior knowledge about the signals except that they are sinusoids. We show that multiple sinusoidal signals can be categorized as signals with finite rate of innovation (FRI signals) whose finite number of parameters can be recovered by using the annihilating filter method. We also show that we can sample the signals at a much lower rate than the Nyquist rate. The proposed method is proven to be robust against noise. The performance is compared with the theoretical limit of Cramér-Rao lower bound.