  Massive arrays deployed in millimeter-wave systems enable high angular
resolution performance, which in turn facilitates sub-meter localization
services. Albeit suboptimal, up to now the most popular localization approach
has been based on a so-called two-step procedure, where triangulation is
applied upon aggregation of the angle-of-arrival (AoA) measurements from the
collaborative base stations. This is mainly due to the prohibitive
computational cost of the existing direct localization approaches in
large-scale systems. To address this issue, we propose a deep unfolding based
fast direct localization solver. First, the direct localization is formulated
as a joint $l_1$-$l_{2,1}$ norm sparse recovery problem, which is then solved
by using alternating direction method of multipliers (ADMM). Next, we develop a
deep ADMM unfolding network (DAUN) to learn the ADMM parameter settings from
the training data and a position refinement algorithm is proposed for DAUN.
Finally, simulation results showcase the superiority of the proposed DAUN over
the baseline solvers in terms of better localization accuracy, faster
convergence and significantly lower computational complexity.
