Estimating the power spectrum of a wide-sense stationary stochastic process is a core component of several signal processing tasks. Distributed spectrum sensing problems naturally emerge in cases where measurements of different realizations of a stochastic process are collected at multiple spatial locations. This paper describes a distributed power spectrum sensing scheme for stochastic processes which are well represented by an autoregressive (AR) process. The sensing model comprises a network of scattered low-end sensors which transmit randomly filtered, one bit quantized power measurements to a fusion center. The problem of AR power spectrum estimation from such binary power measurements is cast as a non-convex optimization problem, and an alternating minimization algorithm is proposed to obtain a stationary point. Simulations showcase the effectiveness of this scheme when the AR parametrization is valid.