Table 1 List of symbols

\(\gamma _1\), \(\gamma _3\)

HPA nonlinear distortion coefficient

\(\Delta F\)

Frequency spacing

\(T_s\)

Symbol time

B

Number of beams

K

Number of secondary users per beam

L

Number of primary users (FS)

N

Number of secondary users (FSS)

P

Number of operators

S

Number of adjacent FSS subbands in one FS subband

T

Number of FS subbands

\(H_{k}^{(j,p)}\)

Channel response between user k of beam j

for satellite p and antenna j of the same satellite

\(H_{k}^{(b,j,p)}\)

Channel response between user k of beam b

for satellite p and antenna j of the same satellite

\(H_{k}^{(b,q,j,p)}\)

Channel response between user k of beam b

for satellite q and antenna j of the satellite p

\(I_{th}^{(\ell )}(m)\)

Interference-temperature at FS \(\ell\) on band interval m

\(F_k^{(j,p,\ell )}\)

Channel gain between user k belonging to beam j

of satellite p to FS receiver \(\ell\)