Angular Superresolution of the Antenna-Array Signals Using the Root Method of Minimum Polynomial of the Correlation Matrix

Angular Resolution of Closely Spaced Signal Sources Using a Two-Dimensional Antenna Array on the Basis of the Minimum-Polynomial Method

“…The correlation matrix M = x(l)x H (l) of the input process (here, the superscript "H" denotes Hermitian conjugation, the angle brackets denote statistical averaging, and the matrix size is MN × MN ) has a minimum polynomial, whose roots are given by the unequal eigenvalues [21]. It should be noted that the number of different eigenvalues and, therefore, the degree Q of the minimum polynomial are determined by the number of signal sources, i.e., Q = J + 1 [6,11]. The least eigenvalue λ J+1 is called the noise eigenvalue since the corresponding eigenvector subspace is orthogonal to the phasing vectors of the sources, and the remaining eigenvalues are called the signal eigenvalues [6,10].…”

“…The minimum-polynomial method provides a statistically reasonable estimate of the number of signal sources. At the same time, the probability of correct estimation, especially in the case of correlated sources or a short time sample, is higher compared with that when using the AIC and MDL criteria [10][11][12][13].…”

“…To determine the angular location of each of the closely spaced sources, the superresolution methods are used, with the help of which it is possible to significantly exceed the Rayleigh limit of the angular resolution, which is equal to the width of the main lobe of the antenna-array radiation pattern. These methods may include the Capon method, the method of the maximum-likelihood classification of signals, the multiple signal classification (MUSIC) algorithm, the estimation of signal parameters via rotational invariant techniques (ESPRIT), and the method of the minimum polynomial of the correlation matrix of signals in the antenna array [6][7][8][9][10][11].…”

“…For the MUSIC algorithm, there exists a root-MUSIC approach to direction finding, which does not require calculation of a pseudospectral function and uses the procedure for finding the roots of a polynomial constructed on the basis of this function when estimating the angular coordinate [6,7]. The root variant of the minimum-polynomial method is proposed in [11]. The experimental results of determining the angular locations of the closely spaced radiation sources are presented in [12] for the minimum-polynomial method and the MUSIC algorithm.…”

“…The experimental results of determining the angular locations of the closely spaced radiation sources are presented in [12] for the minimum-polynomial method and the MUSIC algorithm. The simulation and experimental results show that the root approach has a better resolution and accuracy of estimating the angular coordinates compared with the pseudospectral approach [7,11,12]. In addition, for sufficiently small-size antenna arrays, the root approach allows one to estimate the angles analytically, which significantly simplifies its implementation and reduces the computational complexity [12].…”