Angle of Arrival Estimation (AOA) Patrick McCormick EECS 725
Types of AOA estimation • Single or Dual-Axis Monopulse • Phase-comparison monopulse Fig 1: Dual axis monopulse model  Fig 2: ULA AOA estimation model 
Beamforming • In phased-arrays, beamforming is the concept of applying complex weightings to a waveform on transmit or receive. • A simple form of this is applying a uniform phase shift across the array to steer to a particular point in space. • This requires the use of multiple elements and knowledge of their arrangement (i.e. ULA or planar array) • The beam-pattern and spatial resolution are dependent on the number of elements and their spacing. Fig 3: ULA Rx Beamforming 
Steering Vector • Knowing the phase shift between received elements, we can compensate for the phase misalignment using a steering vector. • Typically in signal processing, the data is converting down to complex baseband (I and Q) samples for processing. Therefore, the phase shift can be represented by a complex exponential.
Coherent Integration Analogy • The array is typically comprised of elements of low gain, but when combined coherently (beamforming) they can create large gains. • For an isotropic antenna, the receive gain of an array is essentially the coherent integration within one pulse over many elements. • Can still integrate over many pulses to achieve an even higher processing gain!
Future Work • Extension into elevation and azimuth planes (planar array). • Matlab examples • Generalized steering vector including both angles