Page 325 - Kaleidoscope Academic Conference Proceedings 2024

Innovation and Digital Transformation for a Sustainable World

Correspondingly, the CPU energy consumed per second of user should be lower than the maximum available power
3
by user is modeled as , where is corresponding . The constraint (7)d states the received SNR at AP to

coefficient related to the chip architecture [18]. Then, the detect successfully should be no less than the target SNR.
energy consumption for local computing at user is expressed The constraint (7)e shows the receive beamforming matrix
3
as = . restriction of user . In addition, the range of CPU frequency

and IRS phase shifts is characterized by constraint (7)f and
2.2.2 Task Offloading (7)g, respectively.
Besides, in the stage of task offloading, users need to 3. ALTERNATING OPTIMIZATION SOLUTION
transmit a portion of their computation tasks to AP by
applying NOMA strategy. Also, simliar to [19], we set the Because of coupling variables with regard to receiver
time consumption of task offloading as . Then, we can beamforming matrix, phase matrix and transmission power
obtain the computational bits of task offloading at user as in (7)a and (7)d, the optimization problem (7) is not

= . Accordingly, the energy consumption for task jointly convex and challenging to solve. To make the

problem tractable, an AO-based algorithm is adopted to
offloading is expressed as = .
efficiently tackle it. Specifically, we split the problem (7)

into receiver beamforming optimization, CPU frequency
2.2.3 Edge Computing and Result Downloading
optimization, transmission power optimization and IRS phase
In the stage of edge computing and result downloading, the shift optimization subproblems, and then handle these four
MEC server calculate computational task and subsequently subproblems alternately. In particular, we first derive the
return results to users. Due to the abundant computation closed form expression of receiver beamforming matrix and
resources of MEC servers and the typically very small size CPU frequency, then exploit SCA-based iterative algorithm
of computing result, the energy and time consumption can be to optimize transmission power, and finally adopt SDR-based
ignored [20]. iterative algorithm to optimize phase matrix.
Based on the above analysis, we can get that the total
computational bits completed by user as 3.1 Optimize receiver beamforming
For given p, { }, and Θ, it is easy to verify that

= + . (6)
maximizing the total computational bits of users is
equivalent to maximizing the sum rate of users in the
Correspondingly, the total energy consumed by user to
system. Furthermore, the maximum achievable sum rate of
complete its computational bits can be represented as =
users is given by [21, 22]:
3
+ = + .

!
2
∑︁
|w h ( )|

2.3 Problem Formulation log 2 1 + Í
2 2
=1 = +1 |w h ( )| + (8)

As introduced above, we aim to maximize the total ∑︁ h ( )h ( ) !
computation bits of users through appropriate receiver = log det I + 2 .
2
beamforming matrix, transmission power, CPU frequency, =1
and IRS phase shifts control. To proceed, the considered
According to [23], the SIC receiver with minimum MSE can
problem is formulated as:
achieve the maximum sum rate, then we obtain

∑︁
! −1

max + (7)a ∑︁
W,{ },p,Θ ¯ w = 0 I + h ( )h ( ) h ( ). (9)
=1
= +1
3
s.t. + ≤ , ∀ ∈ K (7)b
¯ w
By standardizing ¯ w , w can be given by w = .
| ¯ w |
0 ≤ ≤ , ∀ ∈ K, (7)c
Correspondingly, we can obtain the rate of user as

≥ , ∀ ∈ K, (7)d !

h ( )h ( )
∑︁
2
|w | = 1, ∀ ∈ K (7)e = log det I + 2
2

=
(10)
0 ≤ ≤ , ∀ ∈ K, (7)f !

h ( )h ( )
∑︁
0 ≤ ≤ 2 , ∀ ∈ N, (7)g − log det I + 2 .
2

= +1
where W = [w 1 , · · · , w ] denotes the receiver beamforming
matrix of AP, p = [ 1 , · · · , ] denotes the transmission 3.2 Optimize CPU Frequency
power vector. The objective function represents the total
computation bits of users. The constraints (7)b and (7)c Secondly, we optimize the CPU frequency { } for local
indicates that the power consumption and transmission power computing. Given W, p, and Θ, the CPU frequency
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