3.1 UAV-assisted MEC System Model and Problem Analysis
A technical algorithm of computing migration and resource allocation for the end-to-side
computing network is proposed, and a multi-UAV cooperative edge computing (MEC) system
model is constructed to reduce the energy consumption of the end-to-side computing
network of UAV (Unmanned Aerial Vehicle) terminal equipment under the field level
Artificial Intelligence (AI) reasoning. As a communication terminal, the high-speed
mobility of UAVs makes the wireless communication between UAVs and ground terminal
equipment unpredictable. In the process of UAV route planning, UAVs can assist in
effective energy distribution in MEC networks owing to the rapid development of field-level
AI [16]. In actual work, the MEC network is usually composed of multiple UAVs and users.
Fig. 1 presents a schematic diagram.
From Fig. 1, the MEC network assisted by multiple UAVs includes multiple UAV communication terminals
and ground terminal equipment. Among them, the UAV communication terminal has many
edge ECS and computing resources. It has a flight mission from the initial point to
the target point, while the ground terminal equipment monitors the surrounding environment.
Based on limited computing and storage resources, the sensor data collected by the
terminal can be transmitted to the UAV through the wireless uplink. Therefore, according
to the European theorem, the distance between the UAV communication terminal and the
ground terminal equipment in the time slot is expressed in Eq. (1).
In Eq. (1), $D$ represents the distance between the UAV communication terminal and ground terminal
equipment; $n$ represents time slot; $h$ represents UAV flight altitude; $\omega $
represents the coordinates projected on the horizontal plane during UAV flight; $U$
represents a horizontal coordinate of ground terminal equipment; $i$ represents ground
terminal equipment; $j$ indicates UAV communication terminal. Generally, the wireless
transmission line between the UAV communication terminal and ground terminal equipment
can be considered a typical line of sight (LoS) transmission [17]. Therefore, the gain expression of the wireless signal channel is expressed as Eq.
(2).
In Eq. (2), $\beta _{0}$ represents the power gain of the wireless signal channel at a distance
of one meter. For conventional ground terminal equipment, the calculation task when
using field-level AI estimation can be performed at the local and UAV communication
ends. When computing at the local end, the number of computing tasks that can be performed
by the terminal device and the energy consumption generated by executing tasks can
be calculated using Eq. (3).
In Eq. (3), $R_{i}^{l}\left(n\right)$ represents the number of executable computing tasks of
the terminal device; $\zeta _{i}\left(n\right)$ is the calculation rate; $\rho $ is
the number of CPU calculation cycles; $E_{i}^{l}\left(n\right)$ is the energy loss;
$\kappa $ is the energy coefficient; $\tau $ indicates the length of the sub timeslot.
When the terminal device migrates the computing task to the edge cloud for execution,
it needs to transfer the input data of the computing task to the UAV. The computing
task amount and energy consumption are expressed as Eq. (4).
In Eq. (4), $R_{i,j}^{c}\left(n\right)$ is the task amount calculated at the UAV end; $\gamma
$ is the proportion of spectrum resources; $W$ is the total spectrum bandwidth; $\lambda
$ is transmission power; $N_{0}$ is the density of background noise power spectrum;
$E_{i,j}^{c}\left(n\right)$ indicates the energy consumption of the UAV terminal for
task execution. Therefore, the expression of total computing tasks and total energy
consumption of the MEC network assisted by multiple UAVs is expressed as Eq. (5).
In Eq. (5), $N$ is the number of sub timeslots; $M$ is the number of ground terminal equipment;
$F$ is the number of UAVs; $P_{c}$ is the static power consumption constant; $T$ is
the total time for UAV to execute tasks. Therefore, the energy efficiency expression
of the system is expressed as Eq. (6).
In Eq. (6),$\eta _{CE}$ represents the calculated energy efficiency of the system. Aiming to
maximize system energy efficiency, this study examines the model construction based
on the partial task migration model, combined with the rate-constrained transmission
power value calculated locally and the planning of spectrum resource allocation UAV
aircraft. Fig. 2 presents the modeling of the computing energy efficiency maximization in the MEC
network assisted by multiple UAVs.
This study evaluates question $Q$ when building the problem model (Fig. 2), wherein $\varphi _{i,j}\left(n\right)$ represents an integer variable; $l$ is a
UAV communication terminal that is not equal to $j$; $C1$ is the actual speed efficiency
of local calculation of terminal equipment; $C2$ is the upper limit of the maximum
transmission power of the terminal equipment; $C3$ is that each terminal device can
connect at most one UAV in the same time slot for task migration, $C4$ is the spectrum
resource constraints for all terminal devices associated with the same UAV; $C5$ is
the total amount of computing tasks completed by each terminal device in the total
time of UAV task execution cannot be less than the minimum amount of computing tasks;
$C6$ means that the flight speed of the UAV cannot exceed the maximum speed upper
limit; $C7$ is the shortest safe distance between multiple UAVs; $C8$ is the shortest
safe distance between UAV and obstacle; $\omega _{I,j}$ in $C9$ represents the initial
point of a UAV; $\omega _{F,j}$ represents the target point of UAV. In addition, the
problem becomes a mixed integer programming problem that is difficult to solve because
of the integer of $\varphi _{i,j}\left(n\right)$.
Fig. 1. MEC network assisted by multiple UAVs.
Fig. 2. Modeling of the computational energy efficiency maximization in MEC networks assisted by multiple unmanned aerial vehicles.
3.2 Research on Computational Energy Efficiency Maximization Algorithm based on Two-level
Iteration
The research adopts the Dinkelbach method to eliminate fractional structure, which
makes the problem easy to solve because the problem is nonlinear as a mixed integer
programming problem [18]. The research decomposes the problem into multiple sub-problems considering that
the actual UAV communication terminal and ground terminal equipment makes the problem
associate with the users, resource allocation of communication computing, and UAV
route planning, under the reasoning of field-level AI. Based on the two-level iteration,
a computational energy efficiency maximization algorithm is proposed to solve each
independent sub-problem. Dinkelbach is used to transform the problem into a parameter-planning
problem. At this time, the reconstruction expression of the system computing energy
efficiency can be expressed as Eq. (7).
In Eq. (7), $\eta $ is the calculated energy efficiency after reconstruction; $X\left(n\right)$
is the set of variables such as local calculation rate and transmission power. Fig. 3 shows the flow of the computational energy efficiency maximization (ICEM) algorithm
using the Dinkelbach method.
In Fig. 3, $k$ represents the number of iterations, and $\sigma $ is the threshold parameter.
The Dinkelbach method establishes a set of increasing energy efficiency coefficients
$\eta $ and tries to close the value of the $\zeta \left(\eta \right)$ function to
0 to obtain the best energy efficiency $\eta ^{*}$. Under the given conditions of
$\eta $, the optimal solution of a group of $X\left(n\right)$ can be obtained using
question $Q1$. According to Eq. (7), the value of $\eta $ can be updated according to the available solution $X\left(n\right)$.
The best energy efficiency value $\eta ^{*}$ can be obtained after one iteration,
and $\zeta \left(\eta ^{*}\right)=0$. Although the converted problem $Q1$ makes the
objective function solution easier, the coupling relationship between UAV and other
variables in the actual route planning makes the problem non-convex. Therefore, the
solution to a non-convex problem $Q1$ is divided into user association, resource allocation,
UAV route planning, and other sub-problems. In the user association optimization,
$Q1$ can be converted to a user association problem if the local calculation rate,
the transmission power of the terminal device, and other conditions are known. The
expression is written as Eq. (8).
In Eq. (8), in question $SQ1$, the continuous variable is completely separated from the original
question $Q1$, leaving only the integer variable of 0-1. At this point, the problem
can be identified as a standardized linear programming problem about integers, and
current optimization algorithms can solve problem $Q1$. In the process of a reasonable
allocation of resources, any designated user is associated with the route planning
of UAVs. The resource optimization configuration problem in question $Q1$ is expressed
as Eq. (9).
In Eq. (9), the objective function in question $SQ2$ is convex, and the conditions of each constraint
are convex sets. Therefore, the standard convex optimization algorithm can be selected
to solve problem $SQ2$. Finally, in the UAV route planning problem, the optimized
problem expression is expressed as Eq. (10).
In Eq. (10), problem $SQ3$ is still a non-convex problem because of the association of users,
reasonable allocation of resources, and decoupling of route delineation. For the UAV
flight path, the left equation of the cost function and constraint condition $C5$
is not convex or concave. Therefore, $SQ3$ is a non-convex problem, which is difficult
to solve. The problem of $SQ3$ is solved by selecting the continuous convex approximation
method to transform its non-convex functions. The uplink achievable spectrum efficiency
of the ground terminal equipment is expressed as Eq. (11).
In Eq. (11), $g_{0}$ represents the signal-to-noise ratio. $R_{i,j}\left(n\right)$ is a convex
function associated with $\left\| \omega _{j}\left(n\right)-U_{i}\right\| ^{2}.$ Therefore,
any point of $R_{i,j}\left(n\right)$ on $\left\| q_{j}\left(n\right)-u_{i}\right\|
^{2}$can be expanded by the corresponding first-order Taylor expansion to obtain the
global lower bound. The low bound expression is expressed as Eq. (12).
In Eq. (12), $\hat{R}_{i,j}\left(n\right)$ is the global lower bound of $R_{i,j}\left(n\right)$;
$\omega _{j}^{k}\left(n\right)$ is the UAV flight path obtained after the $k$ iteration;
$R_{i,j}^{k}\left(n\right)$ is the spectral efficiency obtained after the $k$ iteration;
$\nabla {R^{k}}_{i,j}\left(n\right)$ is the first order partial derivative associated
with $\omega _{j}^{k}\left(n\right)-u_{i}\,.$ $R_{i,j}^{k}\left(n\right)$ and $\nabla
{R^{k}}_{i,j}\left(n\right)$ are expressed as Eq. (13).
In Eq. (13), the constraint conditions $C7$ and $C8$, the continuous convex approximation method
is selected to relax it. The inequality obtained after the first order Taylor expansion
of $\omega _{j}^{k}\left(n\right)$ and $\omega _{l}^{k}\left(n\right)$ can be written
as Eq. (14).
In Eq. (14), $b_{m}$ represents the offset, and $T$ is the transposition. According to Eqs. (13) and (14), problem $SQ3$ can be transformed into an approximate convex problem, which is expressed
as Eq. (15).
In Eq. (15), it is an approximate convex problem because the cost function and restraint condition
are both approximate convex functions. Hence, a standard convex optimization tool
can be selected to solve it. Combining Dinkelbach with the optimization of the three
subproblems, the two-layer iterative algorithm is used to maximize the computational
efficiency, which is also called the iterative optimization algorithm of the two-layer
loop structure. Among them, its external circular structure uses the relevant Dinkelbach
methods to plan the parameters for calculating the efficiency, and the inner loop
structure is mainly a joint optimization problem of the three subproblems. Theoretically,
the internal loop structure of the algorithm achieves local optimization. The actual
requirements for the convergence speed of the algorithm is greatly reduced under the
actual terminal equipment field-level AI reasoning.
In terms of computational complexity, when the actual end-to-side computing force
network is expanded, the computational complexity of the ICEM algorithm increases
significantly, which poses a huge challenge to the computing power of field-level
AI reasoning of terminal equipment. Hence, the threshold parameters can be adjusted
to alleviate the problem in practical situations, i.e., increasing the threshold of
the algorithm proposed in the study can reduce the number of iterations and computational
energy efficiency. Therefore, under the field-level AI reasoning oriented to UAV communication
terminals and ground terminal equipment, an average point can be selected in terms
of the algorithm complexity and accuracy.
Fig. 3. Flow chart of the energy efficiency maximization algorithm using the Dinkelbach method.