Joint Wideband Spectrum Sensing and Direction-of-arrival Estimation for Sub-Nyquist Sampled Sparse Linear Arrays

We investigate the problem of joint wideband spectrum sensing and direction-of-arrival (DOA) estimation for sub-Nyquist sampled sparse linear arrays. A number of uncorrelated narrow-band signals spread over a wide frequency band are considered and sampled at a frequency below Nyquist sampling frequency. Our goal is to estimate the carrier frequencies and the DOAs associated with the narrow-band sources using sparse linear arrays with arbitrary geometry. Time-delayed array framework is employed where the received signal at each antenna is delayed by a flexible amount of time. Candecomp-Parafac (CP) decomposition is usually performed on the delayed array signals for unambiguous frequency estimation. However, at least three consecutive antennas are needed for CP decomposition to guarantee the umambiguity of both frequency and DOA estimation, thus the framework is not applicable to arbitrary geometry of sparse linear arrays. In this work, we propose a novel joint spectrum sensing and DOA estimation method for arbitrary sparse linear arrays, where an augmented virtual uniform array is formulated from the sub-Nyquist samples. A neural network (NN) based matrix completion-based method is employed to recover the correlation matrix of the virtual uniform array, where both spatial and time domain sparse structures are taken advantage of to form the correlation matrix efficiently. The CP decomposition can then be performed on the virtual correlation matrix without the constraint of array geometry. With the aid of augmented virtual array response, the estimation performance is further boosted using weighted average algorithm. Simulation results demonstrate the proposed method is not only applicable to arbitrary geometry of sparse linear arrays but also achieves outstanding performance gain compared to the state-of-the-art method.