Abstract
In this paper, we analyze the achievable rate for ambient backscatter communications under three different channels: the binary input and binary output (BIBO) channel, the binary input and signal output (BISO) channel, and the binary input and energy output (BIEO) channel. Instead of assuming Gaussian input distribution, the proposed study matches the practical ambient backscatter scenarios, where the input of the tag can only be binary. We derive the closed-form capacity expression as well as the capacity-achieving input distribution for the BIBO channel. To show the influence of the signal-to-noise ratio (SNR) on the capacity, a closed-form tight ceiling is also derived when SNR turns relatively large. For BISO and BIEO channel, we obtain the closed-form mutual information, while the semi-closed-form capacity value can be obtained via one dimensional searching. Simulations are provided to corroborate the theoretical studies. Interestingly, the simulations show that: (i) the detection threshold maximizing the capacity of BIBO channel is the same as the one from the maximum likelihood signal detection; (ii) the maximal of the mutual information of all channels is achieved almost by a uniform input distribution; and (iii) the mutual information of the BIEO channel is larger than that of the BIBO channel, but is smaller than that of the BISO channel.
Highlights
T HE Internet of Things (IoT) that could connect millions or even billions of physical objects to the Internet has drawn increasing attentions from both academia and industry recently [1]
We show the mutual information between the binary input D and binary output Dversus the input distribution p for various specific channel realizations in Fig. 7, where signal-tonoise ratio (SNR) = 10 dB, N = 50, and the detection threshold is set as TML
We investigate three kinds of channels, i.e., the binary input and binary output (BIBO), binary input and signal output (BISO) and binary input and energy output (BIEO) channels, for the ambient backscatter system from information theoretic viewpoint
Summary
T HE Internet of Things (IoT) that could connect millions or even billions of physical objects (including typical ones such as computers and smartphones) to the Internet has drawn increasing attentions from both academia and industry recently [1]. In term of achievable date rate analysis, the existing works assume Gaussian input and directly apply the Shannon theorem [13] to evaluate typical information-theoretic figures of merit for both the ambient source and backscatter systems. Such assumption is far from the practical binary signalling in the ambient backscatter system. We consider three different types of channels for ambient backscatter communications and analyze their corresponding achievable rate as well as the capacity. N (μ, σ2) and CN (μ, σ2) represent the Gaussian distribution and complex Gaussian distribution with mean μ and variance σ2, respectively; in particular, a complex Gaussian RV X ∼ CN (0, σ2) with independent and identically distributed zero-mean Gaussian real and imaginary components is circularly symmetric, i.e., R{X}, I{X} ∼ N (0, σ2/2)
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