Parameter estimation of hybrid pulse streams based on sub-Nyquist sampling and Shift-invariant subspace projection

Finite Rate of Innovation (FRI) sampling theory offers an efficient approach for the sub-Nyquist measurement of the short pulse stream signal, but it can only address parameter measurement problems under waveform consistency. To overcome the measurement challenge of the hybrid pulse streams, this paper proposes a sub-space projection-based FRI parameter estimation method under sub-Nyquist sampling conditions. Our method is based on the concept of subspace decomposition, which involves finely dividing different pulse signals within their respective Shift-invariant (SI) subspaces. We use the generating function of the corresponding space as a decoupling object to achieve parameter estimation through FRI measurement methods. The sampling process is efficient and simple, requiring only single-channel sampling to measure the characteristic parameters of all hybrid pulses. We not only provide theoretical guarantees for the implementation of this approach but also conduct numerous numerical simulations and hardware verification experiments. Our experimental results demonstrate that our method achieves higher parameter measurement accuracy compared to classical methods in a simpler manner.