Direction of arrival

In signal processing, direction of arrival (DOA) denotes the direction from which usually a propagating wave arrives at a point, where usually a set of sensors are located. These set of sensors forms what is called a sensor array. Often there is the associated technique of beamforming which is estimating the signal from a given direction.^[1]^[2] Various engineering problems addressed in the associated literature are:

Find the direction relative to the array where the sound source is located
Direction of different sound sources around you are also located by you using a process similar to those used by the algorithms in the literature
Radio telescopes use these techniques to look at a certain location in the sky
Recently^[when?] beamforming has also been used in radio frequency (RF) applications such as wireless communication. Compared with the spatial diversity techniques, beamforming is preferred in terms of complexity. On the other hand, beamforming in general has much lower data rates. In multiple access channels (code-division multiple access (CDMA), frequency-division multiple access (FDMA), time-division multiple access (TDMA)), beamforming is necessary and sufficient
Various techniques for calculating the direction of arrival, such as angle of arrival (AoA), time difference of arrival (TDOA), frequency difference of arrival (FDOA), or other similar associated techniques.
Limitations on the accuracy of estimation of direction of arrival signals in digital antenna arrays are associated with jitter ADC and DAC.^[3]

Advanced sophisticated techniques perform joint direction of arrival and time of arrival (ToA) estimation to allow a more accurate localization of a node. This also has the merit of localizing more targets with less antenna resources. Indeed, it is well-known in the array processing community that, generally speaking, one can resolve $P$ targets via $N>P$ antennas. When JADE ^[4]^[5] (joint angle and delay) estimation is employed, one can go beyond this limit.

Typical DOA estimation methods

References

^ Zhang, Qilin; Abeida, Habti; Xue, Ming; Rowe, William; Li, Jian (2012). "Fast implementation of sparse iterative covariance-based estimation for source localization". The Journal of the Acoustical Society of America. 131 (2): 1249–1259. Bibcode:2012ASAJ..131.1249Z. doi:10.1121/1.3672656. PMID 22352499.
^ Abeida, Habti; Zhang, Qilin; Li, Jian; Merabtine, Nadjim (2013). "Iterative Sparse Asymptotic Minimum Variance Based Approaches for Array Processing". IEEE Transactions on Signal Processing. 61 (4). Institute of Electrical and Electronics Engineers (IEEE): 933–944. arXiv:1802.03070. Bibcode:2013ITSP...61..933A. doi:10.1109/tsp.2012.2231676. ISSN 1053-587X. S2CID 16276001.
^ M. Bondarenko and V.I. Slyusar. "Influence of jitter in ADC on precision of direction-finding by digital antenna arrays. // Radioelectronics and Communications Systems. - Volume 54, Number 8, 2011.- Pp. 436 - 445.-" (PDF). doi:10.3103/S0735272711080061.
^ Vanderveen, Michaela C., Constantinos B. Papadias, and Arogyaswami Paulraj. "Joint angle and delay estimation (JADE) for multipath signals arriving at an antenna array." IEEE Communications letters 1.1 (1997): 12-14.
^ Ahmad Bazzi and Dirk Slock. "Joint Angle and Delay Estimation (JADE) by Partial Relaxation." 2019 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2019.
^ Barabell, Arthur. "Improving the resolution performance of eigenstructure-based direction-finding algorithms." ICASSP'83. IEEE International Conference on Acoustics, Speech, and Signal Processing. Vol. 8. IEEE, 1983.