  Energy harvesting can enable a reconfigurable intelligent surface (RIS) to
self-sustain its operations without relying on external power sources. In this
paper, we consider the problem of energy harvesting for RISs in the absence of
coordination with the ambient RF source. We propose a series of sequential
phase-alignment algorithms that maximize the received power based on only power
measurements. We prove the convergence of the proposed algorithm to the optimal
value for the noiseless scenario. However, for the noisy scenario, we propose a
linear least squares estimator. We prove that within the class of linear
estimators, the optimal set of measurement phases are equally-spaced phases. To
evaluate the performance of the proposed method, we introduce a random phase
update algorithm as a benchmark. Our simulation results show that the proposed
algorithms outperform the random phase update method in terms of achieved power
after convergence while requiring fewer measurements per phase update. Using
simulations, we show that in a noiseless scenario with a discrete set of
possible phase shifts for the RIS elements, the proposed method is sub-optimal,
achieving a higher value than the random algorithm but not exactly the maximum
feasible value that we obtained by exhaustive search.
