In this paper, we introduce a direction of arrival (DoA) estimation method based on a technique named phase spectrometry (PS) that is mainly suitable for mm-Wave and Tera-hertz applications as an alternative for DoA estimation using antenna arrays. PS is a conventional technique in optics to measure phase difference between two waves at different frequencies of the spectrum. Here we adapt PS for the same purpose in the radio frequency band. We show that we can emulate a large array exploiting only two antennas. To this end, we measure phase difference between the two antennas for different frequencies using PS. Consequently, we demonstrate that we can radically reduce the complexity of the receiver required for DoA estimation employing PS. We consider two different schemes for implementation of PS: via a long wave-guide and frequency code-book. We show that using a frequency code-book, higher processing gain can be achieved. Moreover, we introduce three PS architectures: for device to device DoA estimation, for base-station in uplink scenario and an ultra-fast DoA estimation technique mainly for radar and aerial and satellite communications. Simulation and analytical results show that, PS is capable of detecting and discriminating between multiple incoming signals with different DoAs. Moreover, our results also show that, the angular resolution of PS depends on the distance between the two antennas and the band-width of the frequency code-book. Finally, the performance of PS is compared with a uniform linear array (ULA) and it is shown that PS can perform the same, with a much less complex receiver, and without the prerequisite of spatial search for DoA estimation.
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