This article investigates a symbiotic ambient backscatter communication (AmBC) system, where for the primary system, a source node T1 transmits information to a destination node T2. Whereas for the backscatter system, by riding on T1’s signal, the backscatter device passively conveys its own information <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> to T1 and T2 via backscattering. For such, the coexistence outage probability (COP) and ergodic capacity (EC) of the AmBC system are characterized for three cases of coexistence constraints, i.e., 1) both T1 and T2 decode <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> (Case I); 2) only T2 decodes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> (Case II); and 3) only T1 decodes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> (Case III). It is analytically shown that for sufficiently high transmit signal-to-noise ratio (SNR), the COP obeys the scaling law of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$({1}/{\sqrt {P_{s}}})$ </tex-math></inline-formula> (with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{s}$ </tex-math></inline-formula> denoting T1’s transmit power) for Cases I and III, whereas its scaling law is determined by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$([{\mathrm {log}(P_{s})}]/{P_{s}})$ </tex-math></inline-formula> as well as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$({1}/{P_{s}})$ </tex-math></inline-formula> for Case II. In addition, it is shown that the restriction condition of decoding <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> at T1 results in a dominating term <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$({1}/{\sqrt {P_{s}}})$ </tex-math></inline-formula> for the COP at high SNR, whereas the restriction condition of decoding <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> at T2 results in an infinitesimal relative to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$({1}/{\sqrt {P_{s}}})$ </tex-math></inline-formula> . It is also shown that for different cases, the effects of the T1–T2 channel statistics on the COP are significantly different. However, unlike the metric of COP, for the EC, the impacts of decoding constraints of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> gradually disappear at high SNR and the ECs of the backscatter channels for Cases II and III approach, respectively, toward the counterpart for Case I.
Read full abstract