Ambient Backscatter Systems: Exact Average Bit Error Rate under Fading Channels

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.