  We study a novel communication mechanism, ambient backscatter, that utilizes
radio frequency (RF) signals transmitted from an ambient source as both energy
supply and information carrier to enable communications between low-power
devices. Different from existing non-coherent schemes, we here design the
semi-coherent detection, where channel parameters can be obtained from unknown
data symbols and a few pilot symbols. We first derive the optimal detector for
the complex Gaussian ambient RF signal from likelihood ratio test and compute
the corresponding closed-form bit error rate (BER). To release the requirement
for prior knowledge of the ambient RF signal, we next design a suboptimal
energy detector with ambient RF signals being either the complex Gaussian or
the phase shift keying (PSK). The corresponding detection thresholds, the
analytical BER, and the outage probability are also obtained in closed-form.
Interestingly, the complex Gaussian source would cause an error floor while the
PSK source does not, which brings nontrivial indication of constellation design
as opposed to the popular Gaussian-embedded literatures. Simulations are
provided to corroborate the theoretical studies.
