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Table 1 A summary of abbreviations, notations, and symbols

From: Spectrum sharing on interference channels with a cognitive relay

SIC

Successive interference cancellation

IFC-CR

Interference channel with a cognitive relay

DPC

Dirty paper coding

AF/DF

Amplify-and-forward/decode-and-forward

PT/PR

Primary transmitter/primary receiver

ST/SR

Secondary transmitter/secondary receiver

MRC

Maximal-ratio combining

AWGN

Additive white Gaussian noise

x p

Signal transmitted from PT

x s

Signal transmitted from ST

x r

Signal transmitted from CR

y p

Signal received at PR

y s

Signal received at SR

y r

Signal received at CR

n 0

AWGN that is with unitary variance

h ij

Channel coefficient of link i→j

γ ij =|h ij |2

Channel power gain of link i→j

exp(δ)

An exponential distribution with mean δ −1

P P

Transmit power at PT

P S

Transmit power at ST

P R

Transmit power at CR

R pt

Target rate at PT

R st

Target rate at ST

\(\mathcal {E}\), \(\overline {\mathcal {E}}\)

An event and its complementary event

\(\Pr \{\mathcal {E}\}\)

Probability of event \(\mathcal {E}\)

O P

End-to-end outage probability of the primary system

O S

End-to-end outage probability of the secondary system

α

Power allocation factor at CR

θ

Ratio between P S and P P

Ï„

Ratio between \(\delta _{\textit {sr}}^{-1}\) and \(\delta _{\textit {pr}}^{-1}\)

φ

Ratio between \(\delta _{\textit {sp}}^{-1}\) and \(\delta _{\textit {pp}}^{-1}\)