Esprit for Time-Delay Estimation for Radar Employing Stretch Processing with a Linear FM Chirp

For radar employing a linear FM chirp as the transmit wave-form, stretch processing is a means by which the DAC behind each receive antenna can operate at a significantly lower sampling rate than the Nyquist Sampling rate for the transmit chirp itself. Stretch processing converts the received signal to a sum of sinewaves, each having a common length equal to the length of the chirp, with a frequency that is linearly proportional to its respective time-delay through the chirp rate. Algorithms such as MUSIC and ESPRIT were originally developed for estimating spatial frequencies associated with planar wavefronts incident upon a uniform linear array of antennas. They are premised on the Narrowband Assumption that at an instant in time, the phase progression across the array is a discrete sinewave. A critical aspect of this problem is that each superimposed discrete sinewave is “turned on” across the entire array. In the stretch processing problem, each sinewave is only turned on for a fraction of the listening period, and is turned-on at a different time-delay. In this work, we effectively pre-process the sampled data with an inverse stretch processing step, which enables the use of ESPRIT in the frequency domain. Simulations are presented demonstrating the efficacy of the method.