Symbiotic Ambient Backscatter Systems: Outage Behavior and Ergodic Capacity

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> <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> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> (Case I); 2) only T2 decodes <inline-formula> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> (Case II); and 3) only T1 decodes <inline-formula> <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> <tex-math notation="LaTeX">$({1}/{\sqrt {P_{s}}})$ </tex-math></inline-formula> (with <inline-formula> <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> <tex-math notation="LaTeX">$([{\mathrm {log}(P_{s})}]/{P_{s}})$ </tex-math></inline-formula> as well as <inline-formula> <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> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> at T1 results in a dominating term <inline-formula> <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> <tex-math notation="LaTeX">$c(n)$ </tex-math></inline-formula> at T2 results in an infinitesimal relative to <inline-formula> <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> <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.