Performance Bounds for Two-Channel Delay-Doppler Estimation Using Unknown Waveforms

In this paper, we derive Cramer-Rao Lower Bound (CRLB) expressions for two-channel radar target delay-Doppler estimation with unknown transmit waveforms. We have access to these unknown waveforms only via the noisy reference measurements. Further, we assume that the waveform source transmits periodic pulses as is common for most pulsed radar illuminators. Recent CRLB literature for radar has focussed on specific types of illuminators and derived the CRLB assuming these specific transmitted waveforms are known and incorporating them directly into the measurement model. Further, some papers while assuming the waveform itself to be unknown, make simplifying statistical assumptions on the waveforms or the waveform structure. Contrary to this, we compute a more general result that is not restricted to any specific waveform and we also include the noisy reference channel measurements in our derivation of the CRLB to obtain a more accurate performance analysis. The only assumption we make is on the periodicity of the transmit signal, which is true in practice. We demonstrate the CRLB using extensive numerical simulations both in the presence and absence of phase synchronization between the transmitter and receiver.