Automatic tuning of photonic beamformers: A data-driven approach

Beamforming is a signal processing technique used in highly directional antennas. An array of antenna elements transmits the same signal, but with a different time delay for each element. By providing the right time delays for each antenna element, the whole array transmits a high-powered signal in one desired direction. This technique can be used for example to provide satellite television and Internet connections on board of aircrafts. Recently, developments in the field of integrated microwave photonics have paved the way for broadband, low-loss, and low-weight beamformer systems. These photonic beamformers convert the signals to be transmitted to the optical domain, provide the correct time delays with tunable optical delay lines, and then convert the signal back to the radio frequency domain. The main challenge here lies in tuning the actuators of the tunable optical delay lines in such a way that they provide the desired time delays. Challenges like actuator crosstalk, parameter sensitivity, noise and model errors cause complications when traditional tuning algorithms are used, such as nonlinear optimization routines. All results obtained with these photonic beamformers in the literature so far have been achieved by tuning the whole system by hand, or by applying nonlinear
optimization techniques to a simplified simulation of the system rather than the actual system. In order to find a practical way of tuning a photonic beamformer in real time, this thesis takes a data-driven approach. Instead of relying on perfectly accurate physical models, a surrogate function is used that approximates the relation between the system actuators and a cost function, namely the difference between the measured and desired time delay of each antenna element. By performing nonlinear optimization techniques on this surrogate cost function and by continuously updating the approximation as new measurements are obtained, the time delays of each antenna element should converge towards the desired values. The Data-based Online Nonlinear Extremum-seeker (DONE) algorithm is used to update and optimize the surrogate function in real time. This algorithm is especially designed to optimize cost functions that are costly to evaluate (for example in terms of time), that contain noise, and for which derivatives cannot be easily computed or approximated. The DONE algorithm is applied to a simulation of a photonic beamformer and to the real system, as well as to several other applications. It is shown that the algorithm outperforms comparable methods on several fronts, especially computation time. Furthermore, the theory behind the algorithm is investigated, but practical results are also given, for example rules of thumb for choosing the hyper-parameters. Finally, variations to the DONE algorithm have been developed that are easier to use, can be implemented more efficiently, and can deal with time-varying objective functions.