Ambient backscatter is an intriguing wireless communication paradigm that allows small devices to compute and communicate by using only the power they harvest from radio-frequency (RF) signals in the air. Ambient backscattering devices reflect existing RF signals emitted by legacy communications systems, such as digital TV broadcasting, cellular or Wi-Fi ones, which would be otherwise treated as harmful sources of interference. This paper deals with the ultimate performance limits of ambient backscatter systems in broadband fading environments, by considering different amounts of network state information at the receivers. After introducing a detailed signal model of the relevant communication links, we study the influence of physical parameters on the capacity of both legacy and backscatter systems. We find that, under reasonable operative conditions, a legacy system employing multicarrier modulation can turn the RF interference arising from the backscatter process into a form of multipath diversity that can be suitably exploited to noticeably increase its performance. Moreover, we show that, even when employing simple single-carrier modulation techniques, the backscatter system can achieve significant data rates over relatively short distances, especially when the intended recipient of the backscatter signal is co-located with the legacy transmitter, i.e., they are on the same machine.