  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.
