A Multi-Band Active Array for Direction-of-Arrival Estimation

This paper introduces a new multi-band active array for direction-of-arrival (DoA) estimation. In this active array, we use both transmitted and received signals to estimate angles of targets. As the steering vector is highly nonlinear function of frequency, processing multiple frequency bands efficiently in DoA estimation is still challenging. We solve this problem by constructing a new single steering vector representing those all frequency bands. To implement it, we choose the greatest common divisor (GCD) of the multiple frequency in this single vector. We name this joint processing as GCD-based method. To estimate angles by using both transmitted and received signals, we model this single frequency band DoA estimation as the Hankel matrix recovery problem. As pointed out in the literature, nuclear norm minimisation (NNM) fails to recover the Hankel matrix when targets are closed, so we propose rank projection minimisation (RPM) formulation to recover the Hankel matrix. By the help of GCD-based method, this new multi-band active array can estimate targets accurately with only one snapshot. Our simulations demonstrate the advantages of our GCD-based joint processing and RPM formulation in a uniform linear array.