Improving the performance of the Bartlett method for single-snapshot direction-of-arrival (DOA) estimation using signal processing on graphs (SPG)

Single-snapshot direction-of-arrival (DOA) estimation has long been studied under the framework of conventional signal processing. The most well-studied method estimates DOA from the power spectrum of data that is assumed to lie on a fixed grid in which samples are uniformly spaced, an algorithm known as the conventional Bartlett method. By using a fixed grid, the linear weights used to calculate power are fixed and the method's estimation performance, which can be measured by RMSE versus SNR, is fixed as well. Is it possible improve the Bartlett method's performance by appropriately adjusting these linear weights? In this presentation we show that we can if we apply principles and tools from Signal Processing on Graphs (SPG) so that data now lies on a variable grid known as a graph. We first replicate the system used for the conventional Bartlett method using SPG and then extend the system so it can work on other grids (or graphs). From this SPG-based system, we then show there exist graph structures that will produce linear weights in which RMSE, for certain SNRs, are lower than the conventional Bartlett method. Finally, we validate these results further through simulations.