Page 324 - Kaleidoscope Academic Conference Proceedings 2024

2024 ITU Kaleidoscope Academic Conference

control link IRS denoted by h ∈ C ×1 , Θ ∈ C × and G ∈
controller ×
IRS C . Wherein, the reflection-coefficient matrix is Θ =

1
diag 1 , · · · , , in which ∈ [0, 2 ], ∀ ∈
G
k h N represent the phase shift, and the amplitude reflection
User 1 coefficient is fixed as = 1, ∀ ∈ N. Thus, the effective
MEC server
channel between user and AP can be represented as
User k
h , a k
User K h ( ) = GΘh + h , , (1)
AP
in which represents nonzero elements of matrix Θ.
Figure 1 – MISO-based MEC system with IRS. Accordingly, the received signal of AP is given by
most direct performance metric to evaluate MEC systems
√
∑︁
[15, 16]. To our best knowledge, extremely few studies y = h ( ) + n, (2)
have considered the introduction of MISO technology and =1
optimization analysis of computational rate performance in
NOMA-based IRS-aided MEC systems. in which n ∼ CN (0, 0 I ) denotes zero-mean additive
white Gaussian noise at AP. denotes transmission power
In this paper, we consider a IRS-aided MEC system, where
of user , subjecting to ≤ , in which denotes
AP is equipped with multiple antennas and NOMA strategy
maximum available transmission power. represents the
is adopt. Also, the receiver beamforming matrix at the AP 2
transmitted signal of user , satisfying E | | = 1, ∈ K.
is optimized. A computation rate maximization problem
Since the received antenna at the AP is multi-antenna ,
is established, which optimizes receiver beamforming,
multiplying y by w , we can obtain
CPU frequency, transmission power, as well as IRS
phase shifts, subject to constraints on energy, transmit
√ ∑︁ √
power, signal-to-noise ratio (SNR), IRS phase shifts, and w y =w h ( ) +w h ( ) +w n, (3)

receiver beamforming matrix. To handle this multi-variable
≠
coupled non-convex problem, we decouple the problem into
×1
four subproblems and adopt alternating optimization (AO) where w ∈ C is the normalized beamforming vector,
2
approach. In particular, closed-form optimal solutions are satisfying |w | =1. Note that uplink NOMA strategy is adopt.
proposed to optimize the receiving beamforming matrix Similar to [17], we assume that the channel gain of users
and CPU frequency, respectively. And then successive can be sorted as
convex approximation (SCA)-based iterative algorithm and
semi-definite relaxation (SDR) algorithm based on Gaussian ∥GΘh 1 + h ,1 ∥ 2 ≥ · · · ≥ ∥GΘh + h , ∥ 2 . (4)
randomization are exploited to optimize transmit power and
Thus, the SNR of user is given by
IRS phase shifts, respectively. Numerical results demonstrate
that our MISO-based MEC system with IRS can achieve 2
|w h ( )|
superior performance gains. , (5)
= Í
2
|w h ( )| + 2

= +1
2. SYSTEM MODEL AND PROBLEM 2 2
where = |w n| . Then, the achievable rate of user is

FORMULATION
= log (1 + ), where denotes the signal bandwidth.
2
Consider a MISO-based MEC system with IRS in Fig.1, in
2.2 Partial Computational Offloading Model
which an IRS comprised of reflecting elements is installed
near edge users to assist computation offloading from users In this subsection, partial computational offloading model
to AP equipped with antennas. Let K = {1, 2, · · · , } is considered, which indicate that a portion of computation
and N = {1, 2, · · · , } denote the set of all users and tasks are offloaded to the AP for remote execution, while the
reflecting elements of IRS, respectively. Each user partially or
remaining portion is computed locally [4]. Then, we denote
completely offloads tasks to AP for edge computing via direct
as the maximum tolerated computation latency. Next,
link and reflected link, while the remain portion can be locally
we will introduce the four parts of completing each user’s
computed. Also, we adopt NOMA strategy for information
computing task, including local computing, task offloading,
transmission. We assume that channel state information of
edge computing and result downloading.
all involved channels is fully available at AP.
2.2.1 Local Computing
2.1 Communication Model
In the stage of local computing, the time required for
×1
Let h , ∈ C denote the direct channel from user processing task is . Then, we denote as the CPU
to AP. The cascade channel of IRS divides into tripartite: frequency of user , and as CPU cycles per bit
the channel from user to IRS, the reflection-coefficient required for local computing. Then, the computational bits
matrix of IRS and from IRS to AP, are respectively locally computed at user can be given by = .

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