Distributed estimation of the average value over a Wireless Sensor Network has recently received a lot of attention. Most papers consider single variable sensors and communications with feedback (e.g. peer-to-peer communications). However, in order to use efficiently the broadcast nature of the wireless channel, communications without feedback are advocated. To ensure the convergence in this feedback-free case, the recently introduced Sum-Weight-like algorithms which rely on two variables at each sensor are a promising solution. In this paper, the convergence towards the consensus over the average of the initial values is analyzed in depth.