The region R ig r is obtained when the secondary receiver can decode the signal of primary user i.
For the proof, we consider i = 1, i.e., the secondary user is assumed to be able to decode the signal of primary user 1.
State the achievable rate region R i r, where the signal of primary transmitter i is to be fully decodable at the secondary receiver besides being decodable at the primary receiver.
For this channel, we define the set δ i r ( Z ) as the set of all achievable rate tuples (R1,R2,S,T) when the signal of primary transmitter i, i ∈ {1,2}, is decodable by the secondary receiver.
By decoding the signal of primary user 1 at the secondary receiver, the range of achievable primary rates in R g o remains the same for R 1 g r while the secondary link can achieve higher rate at a given primary rate in R 1 g r than in R g o.
Consequently, if for any Z ∈ P ∗ condition (82) is satisfied, then allowing the secondary receiver to decode the signal of primary user i at this Z enhances the range of the secondary achievable rates without reducing the range of the achievable primary sum rates.
Please refer to Appendix 5. Hence, if inequality (99) is satisfied, R ig r is obtained without rate splitting, specifically, when λ = 0. Figures 9 and 10 show the performance of rate splitting under same power setup used with Figures 6 and 7 where it is assumed that the secondary receiver can decode the signal of primary user 1.
Thus, since we showed that if (99) is satisfied, assuming that the secondary receiver can decode the signal of primary user 1, then ρ p r, ρ sp r, ρ s 2 r, and ρ 2 p r decrease with λ, whereas ρ s r does not depend on λ; hence, R 1 r ( Z ) at λ=0 coincides on R 1 g r.
Wnt pathway activation promotes neuronal differentiation and inhibits Notch signaling of primary human glioblastoma multiforme- (GBM-) derived cells [ 65].
Typically, secondary labeling is performed to boost the signal of primary labeling agents that directly bind the protein or biomolecule under investigation.
