DOA Estimation in the Presence of Doppler Shifts Using Quantum-Inspired Swarm Intelligence Algorithms

Direction of arrival (DOA) estimation is an important problem of wireless sensor network (WSN) where the objective is to calculate the angle of incidence of the source signal at the sensor array. The estimation performance degrades due to the presence of Doppler shifts, which are caused by the mobility of sources. To determine the effective solution, here new models based on quantum-inspired swarm intelligence algorithms are proposed for DOA estimation: quantum-inspired sailfish optimization (QSFO), quantum-inspired gray wolf optimization (QGWO), quantum-inspired whale optimization (QWoA), and quantum-inspired particle swarm optimization (QPSO). The beauty of these algorithms is that they provide high-speed convergence on large-scale optimization problems. The quantum entanglement principle is embodied in the swarm intelligence algorithms to improve the exploration capability of the population in the hunting phase. The DOA estimation is carried out using a maximum likelihood estimator (MLE) with quantum-inspired swarm intelligence algorithms in these scenarios: (1) variation of Doppler frequencies, (2) variation of a number of sources, (3) different noise conditions (SNR variation), (4) different noise environments (stationary and non-stationary), and (5) different types of sources (uncorrelated and correlated). Superior DOA estimation results are reported for the proposed algorithm for different Doppler frequencies. The performance of the proposed quantum-inspired algorithms is also compared with two state-of-the-art classical algorithms: MUSIC and ESPIRIT. Proposed QSFO offers better results for 4 CEC, 12 uni-modal, and 12 multi-modal benchmark functions. A practical application of the proposed approach is demonstrated to solve DOA estimation with Doppler shift in automotive radar.