Page 98 - 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

Now, denoting the Signal-to-Noise Ratio (SNR) as γ, reflectors (approximately 1,040,000 combinations),
the channel capacity of sender S and receiver D the exhaustive search required 9.5 seconds on

can be written as: average while SCIP was able to find a solution in 1
second on average. These results indicate that the
= log (1 + γℎ 2 ), (12) computational time can be speeded up by
2

In addition, the Interference-power-to-Noise Ratio approximately 10 times when using SCIP.
(INR) of interfered receiver P can be written as: The SCIP solver can solve the nonlinear 0-1 integer

2
INR = 2 log 2 (1+ℎ ) − 1 = γℎ , (13) programming problem that we would like to solve

in this paper, but there is still the problem that the
From the above, the optimization problem to be computational time increases exponentially as the
solved in this paper can be written as follows: number of IRS reflectors to be selected increases.
2 2
max (∑ ) + (∑ ) (14) 3. IRS REFLECTOR CLUSTERING

= = In this paper, we additionally propose a method for
2 2 keeping computational complexity down while
INR maintaining interference suppression performance
s. t. (∑ ) + (∑ ) ≤ (15)
γ
by efficiently thinning out IRS reflectors as
= = candidates in a combinatorial search using radio
∈ {0, 1} (16) characteristics. Specifically, this method partitions
a total of N IRS reflectors into K clusters according
Eq. (14) indicates the objective function by
maximizing the channel capacity of sender S and to a certain rule and selects from each cluster the
receiver D, Eq. (15) specifies to maintain the IRS reflector closest to the center of gravity of that
interference level of interfered receiver P below the cluster as a candidate for the combinatorial search.
In the following, we explain in detail the random
threshold ( INR ) and Eq. (16) is a binary variable
γ method [17], k-means method [18], and proposed
constraint and specifies whether the IRS reflector method for the sake of comparing different
has been selected or not. techniques.

Here, variable is an integer that takes on the 3.1 Random method

value of 0 or 1 while the objective function and This method selects K IRS reflectors randomly from
limiting conditions are quadratic functions, so this a total of N IRS reflectors without clustering as
problem constitutes a nonlinear binary integer candidates for a combinatorial search. This is an
programming problem. This type of problem is NP- extremely simple and high-speed method, but as the
hard and is known to be a problem in which the value of K increases, the probability of selecting
computational time increases exponentially [15]. duplicate IRS reflectors having similar

One example of a technique for solving a formulated characteristics likewise increases, which may result
optimization problem is a method that uses a in a drop in interference suppression performance.
dedicated program called a solver. In this paper, we 3.2 k-means method
use Solving Constraint Integer Programs (SCIP),
which is relatively fast among general-purpose This method clusters together IRS reflectors having
solvers and available for non-commercial similar propagation channel characteristics on an I-
applications [16]. Given the optimization problem, a Q complex plane and selects one representative IRS
general-purpose solver can output optimal values reflector from that cluster as a combinatorial search
and an optimal solution at high speed based on that candidate. In this regard, the propagation channel
formula although the specific calculation method is from the sender to the receiver and interfered
a black box. receiver via IRS reflectors can be expressed in the
form of complex numbers as in Eq. (3) and Eq. (4).
We compared the computational time between a Here, we consider mapping the channel
method that performs a simple exhaustive search characteristics to the interfered receiver (Eq. (3))
and a method that searches for a solution using the onto an I-Q complex plane and forming clusters of
SCIP solver. The CPU of the computer used in this
evaluation was an Intel Xeon W-2125 @ 4GHz. For IRS reflectors having close characteristics.
the case of searching the combinations of 20 IRS

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