Low Complexity Algorithms Of Direction-of -Arrival Estimation For Array Signals

The direction of arrival(DOA) estimation for array signals has been an important research field in the array signal processing. In recent years, low complexity algorithms of DOA estimation for array signals has attracted a wide spread attention. With multiple sensors are set in different positions to make up the sensor array, the DOAs of signal sources are acquired by the signal processing of multi-channel receiver’s output data. In the development of DOA estimation, some classical algorithms have solved a lot of practical problems and provide new thoughts for this field. The importance of DOA estimation makes it still an flourishing and evolving problem, and it still faces some new challenge. Low complexity DOA estimation algorithms for array signals are studied in this paper, the author’s major contributions are outlined as follows:1. Subspace estimation is needed in the traditional subspace based DOA estimation algorithms. Aiming at the problem of heavy computation in the subspace estimation, low computational DOA estimation algorithms without covariance matrix eigenvalue decomposition have been studied. Firstly, the subspace projection(SP) algorithm is introduced into the DOA estimation field, which is combined with MUSIC algorithm and the formation algorithm is called subspace projection based MUSIC algorithm. Secondly, the simplified SP-MUSIC algorithm is developed, in which the large matrix multiplication operations in the SP algorithm are converted into a series of small matrix multiplication operations. Thirdly, another low complexity algorithm called efficient SP-MUSIC is developed by decomposition of the covariance matrix to simplify the procedure of SP algorithm.2. Aiming at the problem of heavy computation in the two-dimensional spectral peak searching required in the traditional two-dimensional MUSIC algorithm, low computational two-dimensional DOA estimation algorithms have been studied, which only need one dimensional spectral peak searching and without angle pairing. Firstly, the reduced dimensional MUSIC(RD-MUSIC) algorithm is introduced into the twodimensional DOA estimation field, extracting the roots in the RD-MUSIC algorithm forms the root RD-MUSIC algorithm, which lead to lower computation. Secondly, the modulus constraint RD-MUSIC is proposed, which maintains the low computation and improves the estimation performance by using the modulus constraint to construct the constraint condition of the quadratic optimization function, and strongly constraints the steering vectors. Thirdly, the strong-constraint optimization RD-MUSIC algorithm is proposed, which also maintains the low computation and further improves the estimation performance by the direct derivation of the quadratic optimization function, and the steering vectors are strongly constrained in the solving process.3. DOA estimation can be achieved by jointly finding the sparsest coefficients of the arrays output data in an overcomplete basis. Two DOA estimation algorithms using a sparse representation of array covariance matrix and recovering a sparse vector of only a single measurement vector have been studied. They all have high estimation performance and low computation as well, and without giving the source number. In order to make the algorithms get the capability of estimating coherent signals on an uniform array, one algorithm performs spatial smoothing on the covariance matrix, another algorithm reconstructs a vector using the covariance matrix’s elements.4. In order to make the sparse representation DOA estimation algorithms get good performance with less samples, two Bayesian sparse representation algorithms have been studied, named as multiple measurement vectors sparse Bayesian learning(MSBL) and fast sparse Bayesian learning(FSBL). A series of DOA estimation sparse presentation models are combined with different Bayesian sparse representation algorithms to do simulation experiments, and the characteristics and properties of these algorithms are summarized.