Direction Finding Based On Single Channel Array Using Sparse Recovery

Direction-of-arrival (DOA) estimation is an important research field in array signal processing. Most of the DOA estimation algorithms so far are based on multi-channel array systems, where every array element is followed by a circuit, the so-called "channel", in order to sample the received signal and convert it from analog to digital. However, in micro systems and low-cost devices, this may increase hardware scales and bring difficulty in the design of ratio frequency circuits. Single channel array receiver offers an alternate against these problems at the cost of some processing ability and accuracy, where multiple antennas share a single channel receiver by combining them with a weight vector in order to present the receiver with a single signal. Moreover, this will reduce the channel mismatch in multi-channel systems.In recent years, sparse recovery and compressed sensing theory provide a new perspective for DOA estimation and achieve better performance in many circumstances. But DOA estimation algorithms based on single channel array using sparse recovery are not sufficient yet. We made further research in this field and summarized the results as follows.1. For narrow-band signals, we constructed a sparse model for the column vectors of the array covariance matrix which is compatible for single systems. Then the model error is derived in order to convert the problem of DOA estimation into one of l1.2 mixed norm minimization under a given error constrain which can be solved by convex optimization. The selection of weight vectors is also considered based on the principles of beamforming and compressed sensing theory. We designed a series of weight vectors which formed appropriate beam patterns to cover the whole angle space and achieved stable estimates. Simulations showed that the proposed method had better performance than other single channel methods, especially when SNR is low, and is applicable for both uncorrelated and correlated signals.2. When the frequency of signals are unknown, we proposed a joint DOA-FOA estimation method for slow-fading signals. Firstly, based on single weight vector, for signals coming from the main lobe of the beam pattern, we constructed an angle-frequency 2D sparse model which is a typical LASSO problem and is easy to solve. Then, for signals of arbitrary directions, a series of weight vectors are used to handle the corresponding areas. Finally, reconstruction error is calculated to pick the real signal directions.3. For wideband signals, we divide them into a series of narrow-band signals and then utilized both ISSM and CSSM method based on the algorithm proposed before. Simulation shows that CSSM method makes better use of the joint information between different bands and achieves better performance, especially when signal-to-noise ratio is low and the number of snapshots is small.