  The success of Internet-of-Things (IoT) paradigm relies on, among other
things, developing energy-efficient communication techniques that can enable
information exchange among billions of battery-operated IoT devices. With its
technological capability of simultaneous information and energy transfer,
ambient backscatter is quickly emerging as an appealing solution for this
communication paradigm, especially for the links with low data rate
requirement. In this paper, we study signal detection and characterize exact
bit error rate for the ambient backscatter system. In particular, we formulate
a binary hypothesis testing problem at the receiver and analyze system
performance under three detection techniques: a) mean threshold (MT), b)
maximum likelihood threshold (MLT), and c) approximate MLT. Motivated by the
energy-constrained nature of IoT devices, we perform the above analyses for two
receiver types: i) the ones that can accurately track channel state information
(CSI), and ii) the ones that cannot. Two main features of the analysis that
distinguish this work from the prior art are the characterization of the exact
conditional density functions of the average received signal energy, and the
characterization of exact average bit error rate (BER) for this setup. The key
challenge lies in the handling of correlation between channel gains of two
hypotheses for the derivation of joint probability distribution of magnitude
squared channel gains that is needed for the BER analysis.
