Multiple signal classification (MUSIC) algorithm by peak searching is a classical algorithm in direction finding algorithm

which has been widely used because of its good parameter estimation performance

while it needs huge amounts of calculation

which increases the complexity of the direction finding system and the development cost. In contrast

root-MUSIC algorithm that utilizes polynomial rooting to obtain the target source direction information can reduce the computational complexity of the direction finding. However

root-MUSIC algorithm involves complex-valued coefficient polynomial rooting operation

and its complexity is still high. To further effectively reduce complexity

a novel fast array direction finding algorithm based on the real-valued coefficient polynomial closed root finding was proposed. By utilizing coordinate mapping technique as well as the fact that the derivatives with respect to the extreme values of the MUSIC spectrum equal to zero

a new polynomial in the domain with the same order as root-MUSIC in the domain was constructed. Since roots of the polynomial were found symmetric about the real axis

the new polynomial could be further decomposed into several quadratic polynomials by exploiting Bairstow’s method. Consequently

the target source direction information could be estimated by finding the roots of those quadratic polynomials with closed forms. Theoretical analysis and numerical simulation results show that the calculation complexity of the proposed method was significantly reduced compared with the standard root-MUSIC

and the direction finding speed was improved as the estimate accuracy remained the same.