DOA Estimation Method of Short Snapshots Based on Cultural Pigeon-inspired Optimization Algorithm
Hongyuan Gao, Yuwei Ma, Wanting Xie, Harbin Engineering University, China
Location: Pavilion Ballroom West
Alternate Number 3
The short snapshots direction of arrival (DOA) estimation has always been a hot topic in array signal processing, and has been widely used in communication, radar, sonar and other systems. As classic DOA estimation methods, multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT) have high estimation performance, but these algorithms are based on eigenvalue decomposition, and not only can not directly estimate coherent sources, but also often need a large number of snapshots in order to obtain good estimation performance. This is not practical in most engineering applications which requires real-time implementation. Under the influence of multipath effect or the interference of the non-independent information sources, the estimation performance of the traditional subspace algorithms decrease sharply and even fails. In order to reduce the computational cost of DOA estimation?expand the scope of application and improve the real-time performance of the system, the short-snapshots DOA estimation method which only need to process the data of a few snapshots has been widely concerned by scholars. We designed a novel maximum likelihood (ML) function based on reconstructing pseudo-covariance (RP) matrix from the received short snapshots data which is named as RP-ML. To obtain the optimal solution of RP-ML, cultural pigeon-inspired optimization (CPIO) algorithm is designed to solve the RP-ML function with high convergent accuracy and fast convergent speed.
The pseudo-signal matrix is extended by the short snapshots data received by the Uniform linear array. The pseudo-covariance matrix is reconstructed by calculating the average of covariance of the pseudo-signal matrix. The fundamental problem is to estimate the angle of arrival with received short snapshots. After getting the pseudo-covariance of the reconstructed matrix, we may deduce the RP-ML function for estimating the angle from the received signals. DOA estimation based on RP-ML can be considered as continuous optimization problems, inspired optimization algorithms may be used to obtain an available solution of DOA. But traditional optimization algorithms are difficult to attain the global optimal solution of RP-ML in real time, and we design CPIO algorithm to resolve this problem.
The pigeon-inspired optimization (PIO) algorithm is a new swarm intelligent optimization algorithm which is inspired by the pigeons’ autonomous homing behavior in nature. Although it has some advantages for some classic continuous optimization problems with previous intelligent algorithm, it can not resolve the designed RP-ML which is special engineering problem with high efficiency. In order to overcome the disadvantages of PIO algorithm, the cultural pigeon-inspired optimization (CPIO) algorithm proposed in this paper is improved on basis of original pigeon-inspired optimization algorithm with chaotic weight, cultural mechanism, reverse-learning mechanism and new influence function. In CPIO algorithm, we divide all pigeons into three subgroups, which are basic pigeon swarm, cultural pigeon swarm and reverse pigeon swarm. The evolution process of these subgroups is carried out according to the basic operators of pigeon swarm, the cultural mechanism and the reverse mechanism respectively. We use CPIO-RP-ML to estimate the direction of arrival. In CPIO, the position of each pigeon represents a potential solution of the estimation of direction of arrival. The initial population of CPIO is created randomly. The pigeons of three subgroups evolve according to the basic operators of pigeon swarm, the cultural mechanism and the reverse mechanism respectively. The fitness function is used to evaluate each pigeon’s status. Fitness of each pigeon’s position is calculated and exchanged information of the whole pigeon swarm to determine the global optimal position and obtain updating positions. For CPIO, the target is maximizing the maximum likelihood function. We use CPIO algorithm to obtain the optimal solution of RP-ML which is the DOA estimation result.
We give four simulation comparison experiments to improve the superiority of the proposed CPIO-RP-ML in Gaussian noise background. The first simulation experiment depicts the performance comparison of CPIO-RP-ML and the MUSIC algorithm based on reconstructing pseudo-covariance (RP-MUSIC) when the snapshot is 1 under independent narrowband signal sources. We can get the conclusion that the accuracy of CPIO-RP-ML is better than RP-MUSIC. The second simulation experiment depicts the probability of success of CPIO-RP-ML under single snapshot and short snapshots. Simulation results show that whether single snapshot or short snapshots can get excellent DOA estimation results. When the number of snapshots is larger, the estimated performance is better. As the number of snapshots increases, the estimated performance is improving. The third simulation experiment depicts the probability of success of CPIO-RP-ML, alternative projection algorithm (AP) and multiple signal classification (MUSIC) under independent narrowband signal sources. We can get the conclusion that the probability of success of CPIO-RP-ML get to 1 when SNR is the lowest, and its performance is better than the other two methods. The forth simulation comparison experiment depicts the direction of arrival measured using the CPIO-RP-ML and spatial smoothing multiple signal classification (SS-MUSIC) algorithm based on reconstructing pseudo-covariance (RP-SS-MUSIC) when the snapshot is 1 under coherent narrowband signal sources. We can get the conclusion that the accuracy of CPIO-RP-ML is better than RP-SS-MUSIC.
Based on the maximum likelihood function of reconstructing pseudo-covariance matrix, we have proposed a RP-ML method to estimate the direction of arrival with short snapshots data. By using CPIO, we can reduce the computational cost of RP-ML and improve the searching accuracy. CPIO-RP-ML only uses short data snapshots to estimate the direction of arrival, and we can reduce the computational cost and improve the searching accuracy of the DOA estimation. In the near future, we will design wideband DOA estimation with the designed CPIO and RP-ML method.