Abstract
An algorithm based on back propagation neural network and particle swarm optimization is proposed to solve the direction of arrival (DOA) estimation of coherent signals received by the sensor array in colored noise environment. First, a spatial differential smoothing algorithm is adopted to eliminate colored noise and the independent signals to obtain a covariance matrix only containing the coherent sources. Then, the first line of the covariance matrix is extracted as an input characteristic parameter vector, meanwhile, the DOA of the coherent signals are taken as output. Finally, the trained back propagation neural network optimized by particle swarm algorithm is exploited to reckon the directions of coherent signals. The algorithm put forward in this paper does not require eigen-decomposition and spectral peak searching, so the computational burden is low. Theoretical analysis and simulations demonstrate that the proposed algorithm has high angular resolution and direction finding accuracy in colored noise environment.
Highlights
In nowadays, the theoretical research for direction of arrival(DOA) estimation has gradually matured, but the actual environment is not as ideal as the theory, signal propagation paths are complex and variable
Instead of precise mathematical expression, back propagation neural network (BPNN) constructs neural network with training samples in the process of modeling, this paper has three contributions at least: first, a spatial differential smoothing algorithm is adopted eliminate colored noise and the independent signals to obtain a covariance matrix only containing the information of coherent signals
The BPNN algorithm based on gradient descent has the insurmountable defects that it is easy to fall into local extremum, or convergence very slowly, so it is necessary to use particle swarm optimization (PSO) to optimize BPNN, and there is no need to introduce any extra parameters in the learning process, its essence is to adjust the initial weight and threshold according to the training samples [40]
Summary
The theoretical research for direction of arrival(DOA) estimation has gradually matured, but the actual environment is not as ideal as the theory, signal propagation paths are complex and variable. The information of the signal subspace extends into noise subspace, the covariance matrix of array received data will miss the rank under the influence of correlation, the corresponding matrix dimensions of traditional subspace algorithms are asymmetric, the spatial spectrum functions can not be established reasonably. The spatial difference smoothing (SDS) algorithm [11] combines SDS and MUSIC to estimate the DOA in colored noise environment. It needs eigen-decomposition and spectral peak searching. Instead of precise mathematical expression, BPNN constructs neural network with training samples in the process of modeling, this paper has three contributions at least: first, a spatial differential smoothing algorithm is adopted eliminate colored noise and the independent signals to obtain a covariance matrix only containing the information of coherent signals. It can be seen from (10) that Rn is a Toeplitz matrix with noise correlation between each array element, and the eigenvalue of Rn is completely determined by the noise power σn and the correlation coefficient ρ
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