This paper presents a study on the worsening caused by a random perturbation of the weighting window (modeling, in this way, the uncertainty on the channel sensitivity), or by an alteration of the shape of the transmitted pulse, for a wideband array. In the stability evaluation, main-lobe width and signal to noise ratio evaluated at different dB levels of the beam pattern play the role of quality parameters. Two different profiles of the weighting window have been used for this analysis: a typical raised cosine, and a window optimized by a Simulated Annealing procedure. Also for the pulse envelope, two distinct shapes have been chosen: perfectly Gaussian and experimentally measured. The analysis of the obtained results provides useful hints about the amount and the kind of the beam pattern worsening, when realistic fluctuations occur. Moreover, the results show that the weighting windows provided by the simulated annealing procedure are particularly robust to such fluctuations.