Page 89 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 6 – Wireless communication systems in beyond 5G era

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 6

APPENDIX A Υ Ω , ( , , )
,
∈ℐ ∈ ∈{ℰ∪ℳ∪ℛ}
′
We give a detailed expression for the terms in (P1 ) as fol‑ = ( , , )
lows: ∈ℐ ∈ ∈ℰ ′′
′′
ℰ ={ ∈(ℰ ∪ℳ )|Υ , Ω , =1}
Υ Ω , ( , , )
,
+ ( , , )
∈ℐ ∈ ∈{ℰ∪ℳ∪ℛ}
∈ℐ ∈ ∈ ℱ ′′
∈ℰ
= ( , , ) ℰ ′′ ={ ∈(ℰ ∪ℳ )|Υ , Ω , =1}
∈ℐ ∈ ′
∈ℰ
′
ℰ ={ ∈(ℰ ∪ℳ ∪ℛ )|Υ , Ω , =1}
(52)
+ ( , , )
where the irst term on the RHS in (52) represents the net
∈ℐ ∈ℱ ′
∈ℰ
utility of slice users located within a picocell and asso‑

′
ℰ ={ ∈(ℰ ∪ℳ )|Υ , Ω , =1}
ciated with the same picocell . The second term denotes

the additive utility of slice users associated with the pico‑
+ ( , , ) cell , but located within a clustered femtocell .
∈ℐ ∈ ′ ′
∈ℰ Lastly, from (P1 ), we give a detailed expression of the
′
ℰ ={ ∈(ℰ ∪ℳ )|Υ , Ω , =1} fourth term as:
+ ( , , )
Υ Ω , ( , , )
,
∈ℐ ∈ ∈ ℱ ′
∈ℰ
∈ℐ ∈ ∈ ℱ ∈{ℰ∪ℳ∪ℛ}
ℰ ′ ={ ∈(ℰ ∪ℳ )|Υ , Ω , =1}
= ( )
(50) , ,
∈ℐ ∈ ∈ ℱ ∈ℰ ′′

ℰ ′′ ={ ∈(ℰ ∪ℳ )|Υ , Ω , =1}
where the irst term on the RHS in (50) represents the
additive utility of slice users within the macro‑tier of (53)
an InP ∈ ℐ. The second term indicates the sum utility
of slice users located within a femtocell but associated where the RHS of (53) denotes the net utility of slice users
with the macro‑tier . The third term represents the net located within a clustered femtocell and associated

with same.
utility of slice users located within the picocell but asso‑
ciated with the macro‑cell of an InP . Lastly, the fourth
term denotes the net utility of slice users associated with
REFERENCES
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Similarly, from (P1 ), we have (51):
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, ,
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′′
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