Page 97 - 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

Fig. 1 –Massive distributed IRS aided communication Fig. 2 –System model

reflector R with 1-bit control of reflect (ON) or ℎ = ℎ = + (4)
ℎ
penetrate (OFF). One way to implement this binary Here, and are the real parts and and
control is to incorporate PIN diodes into the metal
parts of the IRS reflector and switch it with an are the imaginary parts. j is an imaginary unit.
external bias [4]. Also, the IRS reflector with few When selecting distributed IRS reflectors, the
elements turns all the elements ON and OFF at the propagation channel of interfered receiver P can be
same time, like with or without a metal reflector. expressed as the sum of the propagation channels
This assumption can greatly simplify the via the selected IRS reflectors. The same can be said
operational complexity of optimizing the states of to hold for receiver D. Accordingly, interfered
the IRS reflective elements, making it an IRS signal at interfered receiver P and received

combinatorial selection problem. Sender S signal at receiver D can be written as follows:

transmits signal x toward receiver D so as not to
give interference to interfered receiver P. The signal [ ] = [ ] + [ ] , (5)

of sender S has the potential of becoming harmful
interference to interfered receiver P. To solve this = [ℎ 1 ⋯ ℎ ⋯ ℎ ], (6)
problem, combination M of IRS reflectors must = [ℎ ⋯ ℎ ⋯ ℎ (7)

be determined so as to suppress the interference on 1 ],

interfered receiver P and maximize the channel = [ℎ 1 ⋯ ℎ ⋯ ℎ ] , (8)
capacity of sender S and receiver D. Combination where and represent the additive white
matrix M can be written as follows:
Gaussian noise.
0 ⋯ ⋯ 0
1
0 ⋱ ⋱ ⋱ ⋮ 2.2 Formulation of optimization problem

= ⋮ ⋱ ⋱ ⋮ , (1) The purpose of this subsection is to determine the
⋮ ⋱ ⋱ ⋱ 0 IRS reflector combination that can maximize the
[ 0 ⋯ ⋯ 0 ] channel capacity of sender S and receiver D while

1
= { (2) maintaining the interference level of interfered
0 , receiver P below a certain value.
where is a binary variable that specifies
The signal x in Eq. (5) varies depending on the sum
whether the IRS reflector is selected (ON) or not of the selected IRS channels. If we substitute the

(OFF). coefficient of signal x with ℎ and ℎ , we get:

The propagation channel from sender S to ℎ
interfered receiver P via IRS reflectors can be [ ] = [ ℎ ] + [ ] , (9)

expressed as the product of propagation channels
ℎ between sender S and IRS reflectors and

propagation channels ℎ between IRS reflectors ℎ = (∑ ) + (∑ ) , (10)

and interfered receiver P as follows: = =

ℎ
ℎ = ℎ = + (3)

ℎ = (∑ ) + (∑ ) , (11)
Similarly, the propagation channel from sender S to
receiver D via IRS reflectors can be expressed as = =

follows:

© International Telecommunication Union, 2021 85