There is a problem that complex operation which leads to a heavy calculation burden is required when the direction of arrival (DOA) of a sparse signal is estimated by using the array covariance matrix. The solution of the multiple measurement vectors (MMV) model is difficult. In this paper, a real-valued sparse DOA estimation algorithm based on the Khatri-Rao (KR) product called the L1-RVSKR is proposed. The proposed algorithm is based on the sparse representation of the array covariance matrix. The array covariance matrix is transformed to a real-valued matrix via a unitary transformation so that a real-valued sparse model is achieved. The real-valued sparse model is vectorized for transforming to a single measurement vector (SMV) model, and a new virtual overcomplete dictionary is constructed according to the KR product’s property. Finally, the sparse DOA estimation is solved by utilizing the idea of a sparse representation of array covariance vectors (SRACV). The simulation results demonstrate the superior performance and the low computational complexity of the proposed algorithm.
In this paper we address the problem of off-grid direction of arrival (DOA) estimation based on sparse representations in the situation of multiple measurement vectors (MMV). A novel sparse DOA estimation method which changes MMV problem to SMV is proposed. This method uses sparse representations based on weighted eigenvectors (SRBWEV) to deal with the MMV problem. MMV problem can be changed to single measurement vector (SMV) problem by using the linear combination of eigenvectors of array covariance matrix in signal subspace as a new SMV for sparse solution calculation. So the complexity of this proposed algorithm is smaller than other DOA estimation algorithms of MMV. Meanwhile, it can overcome the limitation of the conventional sparsity-based DOA estimation approaches that the unknown directions belong to a predefined discrete angular grid, so it can further improve the DOA estimation accuracy. The modified Rife algorithm for DOA estimation (MRife-DOA) is simulated based on SRBWEV algorithm. In this proposed algorithm, the largest and sub-largest inner products between the measurement vector or its residual and the atoms in the dictionary are utilized to further modify DOA estimation according to the principle of Rife algorithm and the basic idea of coarse-to-fine estimation. Finally, simulation experiments show that the proposed algorithm is effective and can reduce the DOA estimation error caused by grid effect with lower complexity.
We address the problem of a new joint Doppler frequency shift (DFS) and direction of arrival (DOA) estimation for colocated TDM-MIMO radar that is a novel technology applied to autocruise and safety driving system in recent years. The signal model of colocated TDM-MIMO radar with few transmitter or receiver channels is depicted and “time varying steering vector” model is proved. Inspired by sparse representations theory, we present a new processing scheme for joint DFS and DOA estimation based on the new input signal model of colocated TDM-MIMO radar. An ultracomplete redundancy dictionary for angle-frequency space is founded in order to complete sparse representations of the input signal. The SVD-SR algorithm which stands for joint estimation based on sparse representations using SVD decomposition with OMP algorithm and the improved M-FOCUSS algorithm which combines the classical M-FOCUSS with joint sparse recovery spectrum are applied to the new signal model’s calculation to solve the multiple measurement vectors (MMV) problem. The improved M-FOCUSS algorithm can work more robust than SVD-SR and JS-SR algorithms in the aspects of coherent signals resolution and estimation accuracy. Finally, simulation experiments have shown that the proposed algorithms and schemes are feasible and can be further applied to practical application.
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