# Sequential Learning and Decision Making in Networks

Millimeter-wave (mmWave) with phase array systems are utilized to increase the data rate in wireless communication systems. In order to perform beamforming, however, one must find the Angle of Arrival (AoA). To estimate the AoA for the mmWave systems, one must also consider the cost of the receiver hardware structure. Currently, analog array structure is the most common receiver structure in practice. Compared to traditional digital array structure, which have access to the signal for all antenna elements, receivers with analog array structure can only access the signal after the analog-to-digital-converter (ADC). This will increase the difficulty for the AoA estimation, especially for the low SNR scenario.

In prior work, Tara Javidi’s team developed new active learning algorithms to estimate the best beamforming directions by using the magnitude information of the received signal. However, since the observation after the ADC at the receiver end is a complex number, the phase information should also be utilized to help find the AoA. Therefore, a three-stage adaptive alignment algorithm based on the posterior probability, called Adaptive Phase Matching, is proposed.

Figure 1 shows designed constellations with noisy observations for the proposed Adaptive Phase Matching algorithm. On the left, all the candidate angles are mapped on the unit circle, so the equivalent noise ball is large. In contrast (right), if only a portion of the candidate angles are mapped on the unit circle, the equivalent noise ball will be smaller.

Once the constellation is designed, we can see that this is equivalent to an encoding problem for a Gaussian channel, as shown:

In our proposed Adaptive Phase Matching algorithm, all the candidate angles will be separated by random mapping them to the constellation. By making more and more observations, one can keep the candidate angles with high probability on the unit circle and map the rest on the zero point. With this operation it is possible to keep reducing the equivalent noise ball and achieve a higher channel capacity.

Finally, we compare the benefit of using the phase information with prior work that used only the magnitude information of the received signal. Figure 2 shows the performance improvement by utilizing the phase information for the AoA estimation problem.

We formulate the AoA searching problem as a coding problem for a sequence of Gaussian channels. With the phase information and our proposed algorithm we can improve the AoA estimation performance significantly.

## Team Members

Tara Javidi^{1}

### Collaborators

Per Johansson^{2}

1. UC San Diego

2. Maxentric