  In mutualistic cooperative ambient backscatter communications (AmBC),
Internet-of-Things (IoT) device sends its information to a desired receiver by
modulating and backscattering the primary signal, while providing beneficial
multipath diversity to the primary receiver in return, thus forming a mutualism
relationship between the AmBC and primary links. We note that the hardware
impairments (HIs), which are unavoidable in practical systems and may
significantly affect the transmission rates of the primary and AmBC links and
their mutualism relationships, have been largely ignored in the study of
mutualistic cooperative AmBC networks. In this paper, we consider a mutualistic
cooperative AmBC network under HIs, and study the impacts of HIs on the
achievable rates of the primary link and the AmBC link. In particular, we
theoretically prove that although HIs degrades the rate of each link, the
mutualism relationship between the AmBC and primary links is maintained, i.e.,
the rate of the primary link in the mutualistic cooperative AmBC network is
still higher than that without the AmBC link. The closed-form rate expressions
of both the AmBC and primary links are derived. Computer simulations are
provided to validate our theoretical analysis.
