Capacity of Ambient Backscatter Communications with Binary Input and Binary Output Channel

In this paper, we derive the closed-form capacity expression as well as the capacity-achieving input distribution for an ambient backscatter system with memoryless binary input and binary output (BIBO) channel. The discrete inputs are restricted to two mass points and the outputs are binary results obtained from energy detection with certain threshold. To show the influence of the signal to noise ratio (SNR) on the capacity, a closed-form tight capacity ceiling is also derived when SNR turns relatively large. Simulations are provided to corroborate the theoretical studies. Interestingly, simulations show: (i) the detection threshold maximizing the capacity is the same to the one from the maximum likelihood detector; (ii) the capacity is achieved by a uniform distribution for the inputs.