CN112333702A

CN112333702A - Optimization method for delay minimization based on safe NOMA moving edge calculation

Info

Publication number: CN112333702A
Application number: CN202011200311.4A
Authority: CN
Inventors: 朱敏; 林笑盈; 李创; 柴秋子; 汪抑非; 付立; 吕巧玲; 王绪康; 沈新荣; 杨春节
Original assignee: Hangzhou Zeta Technology Co ltd
Current assignee: Hangzhou Zeta Technology Co ltd
Priority date: 2020-10-30
Filing date: 2020-10-30
Publication date: 2021-02-05

Abstract

The invention relates to the technical field of communication, and aims to provide a delay minimization optimization method based on safe NOMA moving edge calculation. The invention is realized by an uplink NOMA-based MEC network, which consists of an access point AP integrated with an MEC server, a plurality of end users and an external malicious eavesdropper. Under the NOMA and partial unloading settings, a user can simultaneously unload partial computing tasks to the AP through the same resource block; and the BSS algorithm is provided to find the optimal solution of the transformation problem, and the performance of the provided algorithm is evaluated by carrying out numerical simulation. The invention can minimize the maximum task delay of the uplink NOMA user under the constraint of the security rate, the transmission power and the security interruption probability under the worst condition. The invention unloads the task completion to the server through safe complete unloading, has no task leakage loss, and meets the requirement of ideal conditions.

Description

Optimization method for delay minimization based on safe NOMA moving edge calculation

Technical Field

The invention relates to a delay minimization optimization method based on safe NOMA mobile edge calculation, and belongs to the technical field of communication.

Background

In recent years, the demand for mobile data traffic has proliferated in the internet of things (IoT) where large-scale wireless devices are deployed. Internet of things devices suffer from energy limitations due to strict device size limitations and production cost considerations. In addition, low computing power cannot support an increasing number of applications requiring sustainable and high-performance juicing, such as virtual/augmented reality (VR/AR), telesurgery, and autopilot.

To overcome these challenges, Mobile Edge Computing (MEC) and non-orthogonal multiple access (NOMA) are considered two promising technologies in internet of things networks. The basic idea of MEC is to utilize energy calculation facilities in the radio access network. Ding et al studied that the use of NOMA in combination with MEC can reduce energy consumption for delays and unloading. There are two modes of operation in MEC networks, referred to as partial computation offload (i.e., computation tasks are split into two parts, one of which is computed locally and the other is offloaded to an MEC server for computation) and binary computation offload (i.e., computation tasks are either executed locally or offloaded to an MEC server).

On the other hand, NOMA allows multiple users to operate simultaneously in the same frequency band at different power levels to improve spectral efficiency due to superposition coding at the transmitter and Successive Interference Cancellation (SIC) at the receiver. Wang et al first studied NOMA-based MEC networks with the goal of minimizing the weighted sum of the energy consumption of all mobile users, depending on the computational latency of the partial computation offload and binary computation offload modes. Ding et al studied the time and energy minimization problem based on NOMA-MEC networks, where different users require different computation times. Although extensive research has been conducted on MECs and NOMA in recent years, little work has been done to study the minimized completion time of NOMA MEC networks. In existing work, energy minimization is mainly focused on NOMA MEC networks. For example, to minimize the task delay of one NOMA user, the Dinkelbach method and Newton method of a hybrid NOMA MEC network are compared. In the aspects of power distribution, time distribution and task distribution for energy saving, the energy consumption of the NOMA MEC network is reduced to the maximum extent. Wu et al first studied the security offload problem in an upstream NOMA-MEC system with a malicious eavesdropper, where the privacy performance of computational offload was measured using privacy interruption probability by considering the actual passive eavesdropping scenario.

Due to the broadcast nature of wireless communication, the task of offloading from a terminal device to an access point over a wireless channel is vulnerable to eavesdroppers, leading to information leakage, and it is therefore of particular importance to investigate whether an MEC can successfully offload information and secure transmissions. The current research is based on the fact that under the condition that the channel state information of the eavesdropper is known, the indexes of the measurement are highly related to the instant or statistical channel state information of the eavesdropper. Based on this, a user unloads a computing task to an access point in a server through resource blocks in the network, and the unloaded task is attacked to cause information leakage due to interference of an eavesdropper in the unloading process.

Therefore, in the case of assuming the existence of an eavesdropper, it is important to study how to perform secure transmission of the uninstall information based on the existence of the eavesdropper. At present, no research result of related work is reported in the literature.

Disclosure of Invention

The technical problem to be solved by the invention is to overcome the defects in the prior art and provide a delay minimization optimization method based on safe NOMA moving edge calculation.

In order to solve the technical problem, the solution of the invention is as follows:

the delay minimization optimization method based on the safe NOMA moving edge calculation comprises the following steps:

(1) in an Internet of things system with wireless equipment deployed in a large scale, establishing a mobile edge computing MEC network based on uplink non-orthogonal multiple access (NOMA), wherein the network comprises an Access Point (AP) integrated with an MEC server and a plurality of users; all access point nodes AP are provided with single antennas, a wireless channel adopts a frequency non-selective quasi-static block fading model, and a partial unloading model is adopted for information transmission of a user; assuming that at least one external malicious eavesdropper accesses the MEC network through the access point AP;

the kth user is represented by an index K, where K ∈ {1, …, K }; user k obeys the initial assumptions of the model; in order to reduce the complexity of the system, only two users are supposed to be served in the same resource block, namely a user m and a user n, k belongs to { m, n }; in the same resource block, a user n is allowed to enter a time slot T; the time slot will be occupied by user n alone, but will not cause any performance interference to user m; (since NOMA systems are subject to strict interference constraints, it is also of practical interest to have two users dispatched to perform NOMA; in addition, it is more appropriate to group two users together than to perform NOMA with user pairing and implement LTE-A.)

(2) Obtaining the signal-to-noise ratio of a user receiving signals at an eavesdropper at an Access Point (AP) end according to a transmission model of an uplink NOMA;

(3) it is assumed that the eavesdropper eliminates the uplink interference before decoding the uplink user information, resulting in a message s at the eavesdropping end_kThe received signal-to-noise ratio is processed, and the safety of the conservative task unloading is ensured under the worst-case assumption;

(4) the method comprises the steps of protecting transmission of messages by adopting wiener safety coding, and inserting redundant information into secret information to realize anti-monitoring; to ensure offloading security under any possible eavesdropping channel, the rate of confidential information per user must be no less than the offloading rate in the worst case;

(5) transferring a part of tasks of the user to an MEC server for remote execution, and calculating the task unloading time from the user to the MEC server;

(6) unloading a part of tasks of a user to an MEC server for remote calculation, and calculating the rest of tasks locally; introducing a privacy interruption probability to measure the privacy performance of task unloading, and calculating the optimization problem (P1) of the maximum task completion time of the uplink NOMA user under the condition of meeting the constraints of safety, transmission power and the privacy interruption probability;

(7) considering that the problem (P1) is non-convex, the optimization problem to be computed (P1) is further simplified by transformation, and the optimal solution of the optimization problem is found by using a bisection search algorithm.

In the present invention, in the step (1), the wireless channel is kept unchanged for a selected transmission period and has a limited duration; a task model that considers partial offloading of data partitions, where the input bits of each task are treated as independent subtasks; focusing on a particular time block having a duration T during which each user k needs to perform L_kThe calculation task of more than 0 input bit;

in OMA-MEC, each user is typically allocated dedicated time or frequency resources in order to offload its tasks to the MEC server; by utilizing the NOMA principle, all users can unload own tasks on unified time or frequency resources at the same time; task model considering partial offloading of data, where the input bits of each task can be treated as independent subtasks, user k divides the respective task with/_kAnd L_k-l_kTwo parts of input bits are respectively calculated locally at a user and safely shunted to an AP for remote execution; the channel coefficients from user k to AP and eavesdropper are h_AP，kAnd h_e，kIs represented by the formula (I) in which d_AP，kAnd d_e，kRespectively representing the distances from user k to the AP and the eavesdropper; alpha is alphaThe path loss index is specified, and the normalized Rayleigh fading channel state is g_AP，k，g_e，kE.g. CN (0, 1); suppose that the AP knows exactly the instantaneous channel gain, i.e. | h, of each user_AP，k|²But only the average channel gain of the eavesdropper over different fading realizations, i.e.

In the present invention, in the step (2), the signals received at the AP and the eavesdropper are respectively:

wherein s is_kIs the task bearing signal E [ | s for user k to unload_k|²]＝1，p_k> 0 is the transmit power associated therewith, n_APIs at variance of

Zero-mean Additive White Gaussian Noise (AWGN), n at the AP of (1)_eIs a variance of

Zero mean gaussian white noise (AWGN) at the eavesdropper;

the uplink adopts NOMA transmission, and the AP can successfully decode the received arbitrary sequence information; on the MEC server side, the message for user n is decoded before user m; s1NR received at the AP for decoding the user n message and the user m message is:

SINR_4P，m＝γ_AP，mp_m

SINR_AP，n＝γ_AP，np_n/1+γ_AP，mp_m

wherein the content of the first and second substances,

and

in the formula, h_AP，mAnd h_AP，nRespectively representing the channel coefficients from user m to the AP and the channel coefficients from user n to the AP,

represents the variance, p, of zero-mean Additive White Gaussian Noise (AWGN) at the AP_mRepresenting the transmission power, y, of user m_AP，mRepresents the path loss, γ, from user m to the AP_AP，nRepresenting the path loss from user n to the AP.

(according to the uplink NOMA mechanism, the AP allows user n to enter user m's dedicated time slot without any performance degradation to user m; user n is decoded before user m at the MEC server

In the present invention, in the step (3), assuming that the eavesdropper can eliminate the uplink interference before decoding the information of the uplink user, the eavesdropper will decode the information of the uplink user in the message s_kWhere the received signal-to-noise ratio is:

SINR_e，k＝γ_e，kp_k，k∈{m，n}

in the formula, gamma_e，kRepresenting the loss of k users at the eavesdropping end, k representing user m and user n.

In the present invention, in the step (4), redundant information is inserted into the secret information, and each user uses the code word transmission rate R_t，kAnd a secret information rate R_s，kThe rate of the whole code word is R_t，k＝R_s，k+R_e，k，k∈{m，n}。

In the present invention, in the step (5), in the unloading time phase, part of the tasks are unloaded to the MEC server for each user, and the task unloading time and the unloading energy consumption from the user k to the MEC server are respectively:

in the present invention, in the step (6), in the moving execution time phase, for the user k, a part of the task L is executed_k-l_kOff-load to MEC server for remote juice calculation, and remaining tasks l_kThen the calculation is performed locally; indicates that the CPU frequency of user k is

A period per second; c_kRepresenting the number of CPU cycles required to compute a task;

the local juicing time and energy consumption of the user k are respectively as follows:

in the formula, L_kThe input bit of the computing task which represents the user to execute is divided into two parts L_k-l_kAnd l_k，ξ_kRepresenting the effective capacitance coefficient of each CPU of a local user k;

defining a secret interruption probability to measure the secret performance of task offloading, using C_AP，k＝log₂(1+SINR_AP，kAnd C_e，k＝log₂(1+SINR_e，k) Representing APs and eavesdroppersThe channel capacity of (a); message s_kIs denoted as P_so，k＝P{R_t，k-R_s，k＜C_e，k}，

For user k, if C_e，kOver R_t，k-R_s，kConfidential offload data may be decoded by an eavesdropper and a privacy disruption event may occur; therefore, an optimization problem that minimizes the maximum task completion time of upstream NOMA users is defined as a problem subject to computational task execution offload security, transmit power, and privacy outage probability constraints (P1):

(P1)：

s.t.

R_t，k≤C_AP，k，k∈{m，n} (f)

R_s，k≤R_t，k，k∈{m，n} (g)

P_so，k≤ε，k∈{m，n} (h)

wherein l ═ l_m，l_n]，p＝[p_m，p_n]，R_t＝[R_t，m，R_t，n]And R_s＝[R_s，m，R_s，n]；

Wherein B represents the system bandwidth, 0 < epsilon < 1 represents the maximum tolerable privacy interruption probability,

represents the maximum allowed number of bits to be computed locally,

indicates that the CPU frequency of user k is

Is the user k to MEC server task offload time,

local computation time of user k, C_AP，kRepresenting the channel capacity of the AP, user k-code transmission rate R_t，kAnd a secret information rate R_s，k(ii) a The constraint (d) ensures that the energy consumed by each mobile user is limited to a maximum consumption E_max(ii) a In constraint (e), the worst-case privacy rate for each user k must not be less than the offload rate to ensure offload under any possible eavesdropper corridor; constraint (f) ensures that the AP can correctly decode the message S_k(ii) a The privacy constraint (h) represents the maximum allowed privacy disruption probability epsilon for each message.

In the present invention, in the step (7), the optimization problem (P1) is simplified by using lemma and theorem, and specifically includes:

introduction 1: introducing decision variables l, p, R_tAnd R_sTo meet the optimal solution requirements of the optimization problem (P1);

R_t，n＝log₂(1+γ_AP，np_n/(1+γ_AP，mp_m))

R_t，m＝log₂(1+γ_AP，mp_m)

2, leading: to minimize the maximum task completion time for different users, if and only if the offload time for each user is equal to each other

And the unloading time is equal to the local juice calculating time

Then, an optimal solution can be obtained

Namely, it is

Theorem 1: based on the theorem 1, the probability constraint of the privacy interruption is defined as follows:

wherein the content of the first and second substances,

theorem 2: when the objective function is optimal, at least one equation is taken for the simplified inequality formula in the optimization problem (P1), the formula being:

when in use

Is provided with

When in use

Is provided with

In the formula, C_mRepresenting the number of CPU cycles required by the user m to calculate a task; maximum energy consumption of the user E_maxUser n privacy interrupt probability xi_n(ii) a User n calculates time locally

The transmission rate of the code word of the user m, n is R_t，m，R_t，n(ii) a Secret information rate R_s，m，R_s，n. The

And

the optimal solution is the final result of the optimization method of delay minimization. The minimization of the delay refers to obtaining the optimal solution for the decision variables of the constraint conditions. Due to p_nAnd p_mHas constraint, solves the problem by BBS algorithm, and finds the optimum by binary search method

And

obtaining decision variables

And

the optimal solution of (1).

Description of the inventive principles:

the invention studies how to perform secure transmission of offload information based on the presence of an eavesdropper, assuming the presence of the eavesdropper. In a scene with an eavesdropper, the maximum task completion time in a minimized NOMA uplink user in the NOMA mobile edge computing network is researched, the task delay of the NOMA user is optimized, and the energy consumption of the NOMA-MEC network is reduced to the maximum extent through efficient power distribution and task distribution.

The invention is realized by an MEC network based on uplink NOMA. The network consists of an Access Point (AP) integrated with the MEC server, a plurality of end users and an external malicious eavesdropper. Under NOMA and partial offload settings, a user may offload portions of the computational tasks to the AP simultaneously over the same resource block. The problem of minimizing the task completion time on the premise of ensuring security is studied, and the aim of the invention is to minimize the maximum task delay of the uplink NOMA user under the constraints of the security rate, transmission power and security interruption probability under the worst condition. Since the formulation problem is a non-convex problem, it is difficult to solve, but after gaining important insight into the above-described technique, the original formulation problem has been changed to a simplified form. Therefore, the invention provides a BSS algorithm to find the optimal solution of the transformation problem, and numerical simulation is carried out to evaluate the performance of the proposed algorithm.

Uplink non-orthogonal multiple access (NOMA) -based Mobile Edge Computing (MEC) networks in the presence of malicious eavesdroppers are contemplated herein. The optimal solution means that the task completion time minimization problem is researched on the premise of ensuring safety. The problem is determined by the worst-case secret rate, transmit power and secret interruption probability constraint variables, and the problem under study is optimized by solving the constraint variables optimally, with the aim of minimizing the maximum task latency of the upstream NOMA users. Because the non-convexity of the problem can not be directly solved, the invention provides an algorithm based on a Binary Search System (BSS), and because the transmitting power p of n users and m users_nAnd p_mHas constraint between them to solve the problem by BBS algorithm, and uses binary search method to find out optimum

And

obtaining the probability of a privacy break for decision variables n and m users

And

the optimal solution of (2) minimizes the maximum task completion delay through the optimal solution, and then the optimization problem of minimizing the maximum task completion time can be solved. Since in NOMA-based MEC networks there is little research effort in minimizing the maximum task completion time of the network, this algorithm is used to optimize the minimization of NOMA user task delays.

Compared with the prior art, the invention has the beneficial effects that:

1. according to the invention, under the condition that a malicious eavesdropper exists, the maximum task time problem is minimally completed by the MEC network which enables the uplink NOMA, wherein a plurality of users simultaneously unload part of computing tasks to the AP through the same resource block. The problem of minimizing the task completion time on the premise of ensuring safety is researched, and the maximum task delay of the uplink NOMA user is minimized under the constraints of the confidentiality rate, the transmission power and the confidentiality interruption probability under the worst condition.

2. Due to the non-salient problem of the proposed problem, the present invention reformulates the problem and proposes a BSS algorithm to achieve the minimum task completion time for the optimal solution. The correctness of theoretical analysis is verified by using a numerical result, the relationship between the task delay and the maximum power consumption of each user under different schemes is evaluated, and in fig. 3, the relationship between the task delay and the maximum power consumption of each user under different schemes is evaluated. As the maximum power increases, the task completion time of the proposed scheme decreases accordingly, because a larger power range can help provide a higher offload rate, so that the offload information task time decreases. The NOMA-based offload scheme may provide a higher offload data rate than the OFDM scheme, so performance is better than the OFMA scheme. Fig. 4 evaluates the relationship between the task delay and the number of calculation input bits, and the task completion time increases with the increase of the calculation input bits, and the proposed scheme can achieve a shorter task completion time and thus a better unloading rate than the OFMA scheme. And proves the advantages of the proposed algorithm over the existing OFMA secure ofdma offload scheme.

3. Compared with the two reference schemes of safe complete unloading and OFMA safe OFDMA unloading in the prior art, the invention unloads the task completion to the server through the safe complete unloading, has no task leakage loss, and meets the requirement of ideal conditions. In the case of eavesdropper-based, by comparing with the OFMA secure ofdma prior art, it can be analyzed through the graph that the task completion time obtains a higher offload rate than the OFDM offload scheme, and is lower than the secure full offload rate. It can be shown that a shorter task completion time is obtained than in the prior art OFMA secure ofdma offload.

Drawings

FIG. 1 is a block diagram of a secure NOMA mobile edge computing system model with anti-eavesdropping capability according to the present invention.

Fig. 2 shows the convergence performance and optimality of the BSS algorithm in the present invention, compared with the optimal analytic expression obtained by the lagrangian method.

Fig. 3 is a relationship between task delay and maximum power of each user in the BSS algorithm based on two reference schemes of safe complete offloading and safe ofdma.

FIG. 4 shows the task delay and calculation input bit L under the BSS algorithm and the two reference schemes of safe complete unloading and safe OFDMA_kA quantitative relationship.

Detailed Description

The invention provides a delay minimization optimization method based on secure NOMA mobile edge calculation, which is used for researching the minimized maximum task completion time problem of an MEC network which enables uplink NOMA under the condition that a malicious eavesdropper exists, wherein a plurality of users simultaneously unload part of calculation tasks to an AP through one resource block. Due to the non-convexity of the problem, an optimal solution is sought to accomplish the minimum task completion time.

A delay minimization optimization method based on safe NOMA moving edge calculation comprises the following steps:

the kth user is represented by an index K, where K ∈ {1, …, K }; user k obeys the initial assumptions of the model; in order to reduce the complexity of the system, only two users are supposed to be served in the same resource block, namely a user m and a user n, k belongs to { m, n }; in the same resource block, a user n is allowed to enter a time slot T; the time slot will be occupied by user n alone, but will not cause any performance interference to user m; since NOMA systems are subject to strict interference limitations, it is also of practical interest to dispatch two users to perform NOMA. In addition, two users are grouped together, and NOMA is carried out on the user pair, so that LTE-A is more suitable.

The wireless channel remains unchanged for a selected transmission period and is limited in duration; a task model that considers partial offloading of data partitions, where the input bits of each task are treated as independent subtasks; focusing on a particular time block having a duration T during which each user k needs to perform L_kThe calculation task of more than 0 input bit;

in OMA-MEC, each user is typically allocated dedicated time or frequency resources in order to offload its tasks to the MEC server; by using the NOMA principle, allThe user unloads own tasks on unified time or frequency resources at the same time; task model considering partial offloading of data, where the input bits of each task can be treated as independent subtasks, user k divides the respective task with/_kAnd L_k-l_kTwo parts of input bits are respectively calculated locally at a user and safely shunted to an AP for remote execution; the channel coefficients from user k to AP and eavesdropper are h_AP，kAnd h_e，kIs represented by the formula (I) in which d_AP，kAnd d_e，kRespectively representing the distances from user k to the AP and the eavesdropper; alpha is the path loss exponent and the normalized Rayleigh fading channel state is g_AP，k，g_e，kE.g. CN (0, 1); suppose that the AP knows exactly the instantaneous channel gain, i.e. | h, of each user_AP，k|²But only the average channel gain of the eavesdropper over different fading realizations, i.e.

the signals received at the AP and the eavesdropper are:

Of AP, n_eIs a variance of

Zero mean gaussian white noise at the eavesdropper;

the uplink adopts NOMA transmission, and the AP can successfully decode the received arbitrary sequence information; on the MEC server side, the message for user n is decoded before user m; the SINRs received at the AP to decode the user n message and the user m message are respectively:

SINR_AP，m＝γ_AP，mp_m

SINR_AP，n＝γ_AP，np_n/1+γ_AP，mP_m

wherein the content of the first and second substances,

and

According to the uplink NOMA mechanism, the AP allows the user n to enter the dedicated timeslot of the user m without causing any performance degradation to the user m; the message for user n on the MEC server is decoded before user m. Therefore, the SINR of the messages received at the AP for decoding user n and user m, respectively, is given by the above equation.

assuming that the eavesdropper can eliminate the uplink interference before decoding the information of the uplink user, the eavesdropper performs the decoding on the message s_kWhere the received signal-to-noise ratio is:

SINR_e，k＝γ_e，kp_k，k∈{m，n}

The assumption here overestimates the eavesdropper's capability, which is a so-called worst-case assumption from the perspective of the legitimate receiver (i.e., the AP) to ensure security of conservative task offloading, since the AP is neither aware of the eavesdropper's capability nor the instantaneous CSI.

inserting redundant information in secret information, each user using code word transmission rate R_t，kAnd a secret information rate R_s，kThe rate of the whole code word is R_t，k＝R_s，k+R_e，k，k∈{m，n}。

(5) Transferring a part of tasks of the user to the MEC server for remote execution, and calculating the task unloading time from the user to the MEC server:

in the unloading time stage, partial tasks are unloaded to the MEC server for each user, and the task unloading time and the unloading energy consumption from the user k to the MEC server are respectively as follows:

in the mobile execution time phase, for a user k, part of a task L_k-l_kOff-load to MEC server for remote computation, and remaining tasks l_kThen the calculation is performed locally; indicates that the CPU frequency of user k is

the local computation time and energy consumption of user k are respectively:

defining a secret interruption probability to measure the secret performance of task offloading, using C_AP，k＝log₂(1+SINR_AP，kAnd C_e，k＝log₂(1+SINR_e，k) Representing the channel capacity of the AP and the eavesdropper; the secret interruption probability of the message sk is expressed as

For user k andin other words, if C_e，kOver R_t，k-R_s，kConfidential offload data may be decoded by an eavesdropper and a privacy disruption event may occur; therefore, an optimization problem that minimizes the maximum task completion time of upstream NOMA users is defined as a problem subject to computational task execution offload security, transmit power, and privacy outage probability constraints (P1):

(P1)：

s.t.

R_t，k≤C_AP，k，k∈{m，n} (f)

R_s，k≤R_t，k，k∈{m，n} (g)

P_so，k≤ε，k∈{m，n} (h)

wherein 1 ═ l_m，l_n]，p＝[p_m，p_n]，R_t＝[R_t，m，R_t，n]And R_s＝[R_s，m，R_s，n]；

representing the most locally computed bitsThe number of the large allowable number,

indicates that the CPU frequency of user k is

Is the user k to MEC server task offload time,

(7) Considering that the problem (P1) is non-convex, the optimization problem to be calculated (P1) is further simplified through transformation, the optimization problem is simplified by lemma and theorem, and a halving search algorithm is used for finding the optimal solution of the optimization problem.

Simplifying the optimization problem by using lemmas and theorems (P1), specifically including:

R_t，n＝log₂(1+γ_AP，np_n/(1+γ_AP，mp_m))

R_t，m＝log₂(1+γ_AP，mp_m)

2, leading: to minimize the maximum task completion time of different usersIf and only if the offload time of each user equals each other

And the offload time is equal to the local computation time

Then, an optimal solution can be obtained

Namely, it is

wherein the content of the first and second substances,

when in use

Is provided with

When in use

Is provided with

The transmission rate of the code word of the user m, n is R_t，m，R_t，n(ii) a Secret information rate R_s，m，R_s，n。

For a clearer explanation, the process of simplifying the optimization problem by using lemmas and theorems in the derivation of the optimization problem in steps (6) and (7) is further described below.

Step 1: the maximum task completion time of the uplink NOMA user is reduced to the maximum extent under the constraint of the unloading safety, the transmitting power and the secret interruption probability of the calculation task execution.

Mathematically, this optimization problem can be expressed as:

problem (P1):

s.t.

R_t，k≤C_AP，k，k∈{m，n} (1f)

R_s，k≤R_t，k，k∈{m，n} (1g)

wherein l ═ l_m，l_n]，p＝[p_m，p_n]，R_t＝[R_t，m，R_t，n]And R_s＝[R_s，m，R_s，n]. B represents the system bandwidth, 0 < epsilon < 1 represents the maximum allowed probability of a privacy interruption, and

representing the maximum allowed number of bits to be computed locally. The constraint (1d) ensures that the energy consumed by each mobile user is limited to a maximum consumption E_max. Note that in constraint (1e), the worst-case privacy rate for each user k must not be less than the offload rate to ensure offload in any possible eavesdropper path. Constraint (1f) ensures that the AP can correctly decode the message s_k. The privacy constraint (1h) represents the maximum allowed privacy disruption probability epsilon for each message.

Some lemmas and theorems are proposed to simplify the optimization problem before solving it (P1). Then, a BSS algorithm is proposed to find the best solution to the problem (P1).

Introduction 1: decision variables l, p, R_tAnd R_sThe optimal solution to the problem (P1) should satisfy:

R_t，n＝log₂(1+γ_AP，np_n/(1+γ_AP，mP_m)) (2)

R_t，m＝log₂(1+γ_AP，mp_m) (3)

2, leading: for any two users in a NOMA MEC network, in order to minimize the maximum task completion time of the different users, i.e. to minimize the number of different users

If and only if the offload time of each user equals each other

And the offload time is equal to the local computation time

Then, an optimal solution can be obtained

And (3) proving that: first, it proves

Suppose in

The optimal solution is obtained, and the minimum time delay is T^*And the optimal solution

Since user n decodes its signal first, if so

Is increased to

Then

Will be reduced.

Is fixed, and

it will increase. Therefore, must exist

Satisfy the requirement of

Therefore, the temperature of the molten metal is controlled,

should be an optimum time consumption, this is in contrast to

The assumption of being the best solution to the problem (P1) contradicts.

Secondly, prove that

Suppose in

Please note that when l_mWhen the number of the carbon atoms is increased,

will increase and

will be reduced. Thus, the optimal solution can be written to satisfy both the energy constraint and the power constraint

Therefore, there must be a solution to

Is/are as follows

Therefore, the temperature of the molten metal is controlled,

should be the optimum time consumption, this is in conjunction with T^*Is a minimum latency of

The assumption of being the best solution to the problem (P1) contradicts.

Step 2: theorem 1: based on the lemma 1, the following restatement is performed on the privacy interruption probability constraint (1h), and the formula is as follows:

wherein

And (3) proving that: first of all, attention is paid to the probability of a privacy break P_so，n. By substituting (2) and (3)

P_so，nCan be re-represented as

Wherein

|h_e，n|²Is a Probability Density Function (PDF)

Then, P_so，nThe following can be calculated:

thus, substituting (9) for (1h) yields

The inequality in (16) can be obtained immediately after some basic mathematical transformation. Next, the privacy disruption probability P will be rewritten_so，m. Also, please note | h_e，m|²PDF of

Is provided with

Wherein

Then, based on the inequality in (1h) in combination with the results given in (10), the inequality in (7) can be directly derived. The proof of theorem 1 is completed.

Then, the problem (P1) can be equivalently reconstructed as the problem (P2):

(P2)：

s.t.

(L_m-l_m)/R_s，m＝(L_n-l_n)/R_s，n. (11g)

from (11 h):

from (11g) and (12):

then, the problem (P2) is reduced to

(P3)：

(L_m-l_m)/R_s，m＝(L_n-l_n)/R_s，n. (14g)

And step 3: theorem 2: when the objective function is optimal, at least one of (14c) and (14d) is an equation.

And (3) proving that: suppose when and

obtaining an optimal solution in time

And

in this case, there must be a small positive value

Δp_mAnd Δ l_mOrder to

And (4) meeting the requirement.

Should be the best time consuming because of its low value. This is falseThe settings contradict, so the proof of theorem 2 is complete.

Case 1: when (14c) is taken as an equation, i.e.

To obtain

By substituting (13) and (15) into (14d), (14e) and (14f), the compounds are obtained

Wherein

When R is_s，mWhen increasing, the objective function will decrease, and when p is increased_mWhen increased, R_s，nWill be increased. P is to be_nAnd p_mThe constraint between is expressed as:

thus, a binary search method can be used to find

And

the details are presented in algorithm 1. New lower bound r₁And an upper bound r₂Can be obtained by the inequality (17). Therefore, the temperature of the molten metal is controlled,

can be obtained by (15), then

The optimal solution of (2) can be obtained by (13).

Algorithm 1: BSS-based problem algorithm (P3)

1. Initialization

And precision

2.while

When the temperature of the water is higher than the set temperature,

3. is provided with

4. Finding

5.if

Then

6. Updating

7. Otherwise

8. Updating

9. End if cycle

10. End of cycle

11. Output of：

Case 2: when (14d) is taken as equation

When there is

Similarly, (13) and (20) are substituted into (14c), (14e) and (14f) at p_nAnd p_mWith constraints in between, and then solve the problem by algorithm 1 (P3) to obtain the optimum

And

that obtains

And

the optimal solution of (1).

And 4, step 4: compared to the following two reference schemes of the prior art, numerical results will be provided to evaluate the performance of the proposed algorithm.

(1) Safe complete unloading: all users choose to offload all task input bits to the AP, calculated in the considered secure NOMA-MEC system. The scheme corresponds to passing the settings

The problem is solved (P1).

(2) Secure Orthogonal Frequency Division Multiple Access (OFDMA): two users adopt OFDMA protocol to calculate and distribute, and each user occupies a frequency band to share the task.

Setting simulation parameters, and calculating the unloaded system bandwidth as B1 MHzThe path loss exponent α is 4, the secret break probability ∈ is 0.1, and the noise variance is

CPU cycle of C_m＝C_n＝10³Period/bit, effective capacitance coefficient xi_m＝ξ_n＝10^-28Calculating the input digit as L_k＝1.6×10⁶Bit sum

Fig. 2 illustrates the convergence behavior and optimality of algorithm 1. As can be seen from fig. 2, the BSS algorithm converges to the same constant value in 8 iterations, thereby verifying the validity of the algorithm. The convergence point is completely matched with the optimal analytic solution obtained by the Lagrangian method.

The relationship between the task delay and the maximum power per user under different schemes is evaluated in fig. 3. As the maximum power increases, the task completion time of the proposed solution decreases accordingly. This is because a larger maximum power range can help provide a higher unload rate, thereby reducing unload time. Furthermore, the BSS algorithm has better performance than the OFDMA scheme since the NOMA-based offload scheme can provide a higher offload data rate than the OFDMA scheme.

FIG. 4 illustrates task delay and computation of input bit L_kThe relationship of the quantities is shown. Task completion time dependent computation input bit L_kIs increased. Also, the BSS algorithm scheme can achieve a shorter task completion time than the OFDMA scheme, thereby obtaining a better data transmission rate.

The above description is only for the preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution of the present invention and the inventive concept within the scope of the present invention, which is disclosed by the present invention, and the equivalent or change thereof belongs to the protection scope of the present invention.

Claims

1. A delay minimization optimization method based on safe NOMA moving edge calculation is characterized by comprising the following steps:

the kth user is represented by an index K, where K ∈ {1, …, K }; user k obeys the initial assumptions of the model; in order to reduce the complexity of the system, only two users are supposed to be served in the same resource block, namely a user m and a user n, k belongs to { m, n }; in the same resource block, a user n is allowed to enter a time slot T; the time slot will be occupied by user n alone, but will not cause any performance interference to user m;

2. The method of claim 1, wherein in step (1), the wireless channel remains unchanged for a selected transmission period and has a limited duration; a task model that considers partial offloading of data partitions, where the input bits of each task are treated as independent subtasks; focusing on a particular time block having a duration T during which each user k needs to perform L_kThe calculation task of more than 0 input bit;

in OMA-MEC, each user is typically allocated dedicated time or frequency resources in order to offload its tasks to the MEC server; by utilizing the NOMA principle, all users can unload own tasks on unified time or frequency resources at the same time; task model considering partial offloading of data, where the input bits of each task can be treated as independent subtasks, user k divides the respective task with/_kAnd L_k-l_kTwo parts of input bits are respectively calculated locally at a user and safely shunted to an AP for remote execution; the channel coefficients from user k to AP and eavesdropper are h_AP，kAnd h_e，kIs represented by the formula (I) in which d_AP，kAnd d_e，kRespectively representing the distances from user k to the AP and the eavesdropper; alpha is the path loss exponent and the normalized Rayleigh fading channel state is g_AP，k，g_e，kE.g. CN (0, 1); suppose that the AP knows exactly the instantaneous channel gain, i.e. | h, of each user_AP，k|²But only the average channel gain of the eavesdropper over different fading realizations, i.e.

3. The method according to claim 1, wherein in the step (2), the signals received at the AP and the bug are respectively:

Of AP, n_eIs a variance of

Zero mean gaussian white noise at the eavesdropper;

SINR_AP，m＝γ_AP，mp_m

SINR_AP，n＝γ_AP，np_n/1+γ_AP，mp_m

wherein the content of the first and second substances,

and

in the formula，h_AP，mAnd h_AP，nRespectively representing the channel coefficients from user m to the AP and the channel coefficients from user n to the AP,

4. The method according to claim 1, wherein in the step (3), assuming that the eavesdropper can eliminate the uplink interference before decoding the information of the uplink user, the eavesdropper performs the step of decoding the uplink user information by using the message s_kWhere the received signal-to-noise ratio is:

SINR_e，k＝γ_e，kp_k，k∈{m，n}

5. The method of claim 1, wherein in step (4), redundant information is inserted into the secret information, and the transmission rate R of the code word is used by each user_t，kAnd a secret information rate R_s，kThe rate of the whole code word is R_t，k＝R_s，k+R_e，k，k∈{m，n}。

6. The method according to claim 1, wherein in the step (5), in the unloading time phase, partial tasks are unloaded to the MEC server for each user, and the task unloading time and the unloading energy consumption from user k to the MEC server are respectively:

7. method according to claim 1, characterized in that in step (6), during the mobile execution time phase, for user k, part of task L is processed_k-l_kOff-load to MEC server for remote computation, and remaining tasks l_kThen the calculation is performed locally; indicates that the CPU frequency of user k is

the local computation time and energy consumption of user k are respectively:

defining a secret interruption probability to measure the secret performance of task offloading, using C_AP，k＝log₂(1+SINR_AP，kAnd C_e，k＝log₂(1+SINR_e，k) Representing the channel capacity of the AP and the eavesdropper; message s_kIs denoted as P_so，k＝P{R_t，k-R_s，k＜C_e，k}，

(P1)：

R_t，k≤C_AP，k，k∈{m，n} (f)

R_s，k≤R_t，k，k∈{m，n} (g)

P_so，k≤ε，k∈{m，n} (h)

wherein l ═ l_m，l_n]，p＝[p_m，p_n]，R_t＝[R_t，m，R_t，n]And R_s＝[R_s，n，R_s，n]；

Wherein B represents a system beltWide, 0 < epsilon < 1 represents the maximum tolerable privacy interruption probability,

represents the maximum allowed number of bits to be computed locally,

indicates that the CPU frequency of user k is

Is the user k to MEC server task offload time,

8. The method according to claim 1, wherein in the step (7), the optimization problem (P1) is simplified by using lemmas and theorems, and specifically comprises:

R_t，n＝log₂(1+γ_AP，np_n/(1+γ_AP，mp_m))

R_t，m＝log₂(1+γ_AP，m，p_m)