A NOMA-MEC security calculation bit maximization method considering transceiver hardware impairment

Abstract

The application discloses a NOMA-MEC security computing bit maximization method considering transceiver hardware damage, and the method comprises the following steps: according to the computing bits of the legal user security transmission and the local security computing bits, an optimization problem is constructed, which takes the legal user transmitting power and the local computing frequency as constraints, and maximizes the security computing bits of the system; firstly, by introducing the maximum lemma 1 and auxiliary variables, the security rate in the legal user transmitting power optimization sub-problem is transformed into a convex problem, and then the optimal solution of the sub-problem is obtained through an alternating optimization algorithm; secondly, by introducing a Lagrange multiplier, a Lagrange function is constructed, and the KKT condition is obtained, so that the optimal solution of the sub-problem can be obtained; through the block coordinate descent method, the transmitting power of the legal user and the local computing frequency are iterated to convergence, and the maximum security computing bits of the system are obtained. The security computing bits of the application are obviously improved compared with the non-robust transmission system without considering the transceiver hardware damage.

Description

TECHNICAL FIELD

[0001] The application relates to a NOMA-MEC security computing bit maximization method considering transceiver hardware damage, and belongs to the technical field of wireless communication. BACKGROUND

[0002] With the increasing popularity of the Internet of Things, a boom in computationally intensive applications has emerged. However, due to the low computing power of Internet of Things devices, the execution of computationally intensive services is limited by resource constraints. Mobile edge computing (MEC) has become a promising technology that can solve this conflict by offloading computing tasks to the vicinity of Internet of Things devices. Therefore, the computing tasks of Internet of Things devices can be offloaded and computed at the network edge.

[0003] However, due to the broadcast nature of wireless communication, offloading computing tasks from Internet of Things devices to MEC servers will bring security problems. Physical layer security (PLS) is an effective method to achieve secure transmission, which utilizes the inherent randomness of wireless channels (such as fading, noise and interference) to ensure that eavesdroppers cannot collect useful information at the physical layer. In particular, PLS technology for MEC networks has attracted much attention in recent years. Under the constraint of the power consumption of Internet of Things devices, it is of great significance to study the trade-off between secure offloading computing bits and local secure computing bits for maximizing the performance of the system.

[0004] In addition, in terms of improving spectral efficiency, non-orthogonal multiple access (NOMA) technology has received widespread attention. With the growing demand for data transmission and access in the fifth generation (5G) and future wireless communication, NOMA has become a promising technology due to its large capacity and high spectral efficiency. Unlike traditional orthogonal multiple access (OMA), NOMA can serve multiple users simultaneously in the same time or frequency through appropriate power allocation. Generally speaking, there is a strong power imbalance between the signals of different users in a NOMA communication system. Therefore, successive interference cancellation (SIC) is considered to be a key technology for eliminating interference between users.

[0005] In addition, existing research is mainly conducted under the assumption of perfect hardware equipment. However, actual radio frequency (RF) components inevitably have hardware defects, including phase noise, quantization error, amplification noise, and nonlinearity, which will affect the performance of the communication system to some extent. Although the impact of hardware impairment on system performance can be mitigated by compensation algorithms, due to inaccurate estimation of temporal hardware characteristics and random noise, there will still be a non-negligible negative impact during wireless transmission. Therefore, it is of great significance to study the security system performance with hardware impairment. SUMMARY

[0006] The present application aims to overcome the defects and shortcomings of the prior art and provides a NOMA-MEC security calculation bit maximization method considering hardware impairment of the transceiver end. In the actual eavesdropping scenario, the hardware impairment of the transceiver end is considered, the legitimate user uses the uplink NOMA technology for secure transmission, and at the same time, the legitimate user performs local security calculation. In order to achieve the maximum security throughput of the system, the legitimate user needs to allocate its power resources, realize the compromise design of the security transmission calculation bit and the local security calculation bit, and based on this, an optimization problem of maximizing the total security calculation bit is constructed with the legitimate user transmission power and the local calculation frequency as constraints. Due to the coupling of noise and variables caused by hardware impairment, the optimization problem is non-convex. In order to effectively solve the problem, the coupled variables are decoupled and divided into two sub-problems, i.e. the legitimate user's transmission power optimization sub-problem and the legitimate user's local calculation frequency sub-problem. By introducing Lemma 1, the legitimate user's transmission power optimization sub-problem is transformed, and then the block coordinate descent method is used for solving. The legitimate user's local calculation frequency sub-problem is solved by the Lagrange multiplier method, and the optimal solution of the sub-problem is solved by the KKT condition. The optimal solutions of the above two sub-problems are alternately optimized, and the maximum security calculation bit of the system is obtained, and the robustness design of the device transceiver end is realized.

[0007] The technical scheme adopted by the present application to solve its technical problems is: a NOMA-MEC security calculation bit maximization method considering hardware impairment of the transceiver end, comprising the following steps:

[0008] Step 1: establishing a system model including a base station, U legitimate users, and K eavesdroppers, and determining the security transmission calculation bit of the legitimate user and the local security calculation bit of the legitimate user.

[0009] Step 2: according to the security transmission calculation bit and the local security calculation bit of the legitimate user, constructing a total optimization model with the legitimate user transmission power and the local calculation frequency as joint optimization variables, and maximizing the security calculation bit of the legitimate user as the optimization objective.

[0010] Step 3: The optimization model obtained in step 2, which takes the transmission power of the legitimate user and the local computing frequency as the joint optimization variable and maximizes the safe computing bits of the legitimate user as the optimization objective, is converted into sub-problem 1 which takes the transmission power of the legitimate user as the optimization variable and maximizes the safe offloading bits of the legitimate user as the optimization objective, and is solved.

[0011] Step 4: The optimization model obtained in step 2, which takes the transmission power of the legitimate user and the local computing frequency as the joint optimization variable and maximizes the safe computing bits of the legitimate user as the optimization objective, is converted into sub-problem 2 which takes the local computing frequency of the legitimate user as the optimization variable and maximizes the safe computing bits of the legitimate user as the optimization objective, and is solved.

[0012] Step 5: Based on the transmission power of the legitimate user obtained in step 3 and the local computing frequency of the legitimate user obtained in step 4, the block coordinate descent method is used to iteratively update the objective function until convergence is achieved, and the maximum safe computing bits of the system are obtained.

[0013] Further, the implementation method of the safe transmission computing bits of the legitimate user and the local safe computing bits of the legitimate user in step 1 is as follows:

[0014] Step 1.1 to determine the safe transmission computing bits of the legitimate user is as follows:

[0015] A system model including a base station, U legitimate users, and K eavesdroppers is established. The legitimate users need to perform computing tasks through local computing and offloading tasks to the base station. Considering the existence of a sending-end hardware impairment of the legitimate user, the signal sent by the legitimate user u is represented as:

[0016]

[0017] where x u represents the signal sent by the legitimate user u, P u represents the transmission power of the legitimate user u, s u represents the signal symbol sent by the legitimate user u, E t，u represents a distorted signal due to the existence of a hardware impairment of the legitimate user u, which follows a complex Gaussian distribution with a mean of 0 and a variance of δ t P u , δ t ≥ 0 represents an impact factor of the sending-end hardware impairment of the legitimate user u.

[0018] Considering the existence of a receiving-end hardware impairment of the base station, the signal received by the base station is represented as:

[0019]

[0020] where y Bdenotes the signal received at the base station, U denotes the number of legitimate users, g u denotes the channel gain between the legitimate user u and the base station, n r denotes the Gaussian white noise at the base station, ε r denotes the distorted received signal due to the hardware impairment at the base station, which follows a complex Gaussian distribution with mean 0 and variance γ;

[0021] According to the signal received at the base station, the calculation of the variance γ is denoted as:

[0022]

[0023] wherein, denotes the received signal without the hardware impairment at the receiving end;

[0024] In the process of multi-user uplink transmission, mutual interference will occur between the multi-users. In order to reduce the interference, the multi-users use uplink NOMA to perform the task of offloading, and the continuous interference cancellation (SIC) can be performed at the base station. For uplink NOMA, the users with better channel conditions are often decoded earlier, i.e., |g1I≥…≥|g U |;

[0025] According to the signal received at the base station and the NOMA theory, the signal-to-interference-and-noise ratio at the base station is denoted as:

[0026]

[0027] wherein, the first term in the denominator of the above formula denotes the interference generated when the legitimate users transmit simultaneously, when u=U, the second term denotes the hardware impairment at the transmitting end of the legitimate user, the third term denotes the hardware impairment at the receiving end of the base station, and the fourth term denotes the noise interference amplified at the receiving end of the base station due to the hardware impairment;

[0028] Due to the broadcast characteristics of wireless communication, the signal transmitted by the legitimate user u will also be received at the eavesdropper k. In order to ensure that the system can achieve secure transmission in the worst case, it is assumed that the eavesdropper k has better hardware performance, i.e., the eavesdropper k will not generate distortion noise due to hardware impairment. In addition, in order to show the upper bound of the data rate of the eavesdropper, the worst case is considered that all eavesdroppers are not affected by the inter-user interference introduced by NOMA, and thus the signal received by the eavesdropper k is denoted as:

[0029]

[0030] wherein, y Ek denotes the signal received at the eavesdropper, h u,k denotes the channel gain between the legitimate user u and the eavesdropper k, ne，k denotes the Gaussian white noise at the eavesdropper k;

[0031] Based on the signal received by the eavesdropper k, the signal-to-interference-and-noise ratio (SINR) at the eavesdropper k E，k，u is denoted as:

[0032]

[0033] where, denotes the variance of the Gaussian white noise at the eavesdropper k;

[0034] Based on the signal-to-interference-and-noise ratio at the base station and the signal-to-interference-and-noise ratio at the eavesdropper k, the secure transmission rate R sec,u is calculated as:

[0035]

[0036] where, [s] + = max(s, 0). In fact, log2(1 + SINR B,u )- max k log2(1 + SINR E，k，u ) is always non-negative, because if the above term is less than 0, we can set P u = 0. Therefore, without loss of optimality, we will omit the operator [s] + in the following analysis.

[0037] Based on Shannon theory, the secure transmission calculates bits D sec，trans as:

[0038]

[0039] where, B denotes the bandwidth of the system, and T denotes the length of time for which the legitimate user is offloaded.

[0040] Step 1.2 determines the local secure computation bits of the legitimate user, which is specifically:

[0041] The local secure computation bits D sec，loc is denoted as:

[0042]

[0043] where, f u denotes the local computation frequency size of the legitimate user u, and C u denotes the number of CPU cycles required for the legitimate user u to perform 1-bit tasks.

[0044] Further, the bits of the security transmission and the local security bits of the legitimate user are calculated in step 2, and a total optimization model is constructed, in which the joint optimization variables are the transmission power of the legitimate user and the local calculation frequency, and the optimization objective is to maximize the security bits of the legitimate user, and the total optimization model is specifically:

[0045]

[0046] s.t.C1: P u + ξf u 3 ≤ P max，u

[0047] C2: P u ≥ 0

[0048] C3: f u ≥ 0

[0049] Wherein, P max，u represents the maximum transmission power of the legitimate user u. C1 represents that the sum of the transmission power and the local calculation power of the legitimate user u cannot exceed the maximum power limit of the legitimate user u, C2 represents that the transmission power of the legitimate user u is non-negative, and C3 represents that the local calculation frequency of the legitimate user u is non-negative.

[0050] Further, in step 3, the optimization model obtained in step 2, in which the joint optimization variables are the transmission power of the legitimate user and the local calculation frequency, and the optimization objective is to maximize the security bits of the legitimate user, is converted into an optimization model in which the optimization variable is the transmission power of the legitimate user, and the optimization objective is to maximize the security offloading bits of the legitimate user, and the implementation method is specifically:

[0051] Step 3.1: based on the given local calculation frequency f u of the legitimate user u, the total optimization model is converted into a sub-problem 1 with the transmission power P u as the optimization variable, and the sub-problem 1 is specifically:

[0052]

[0053] s.t.C1-C2

[0054] Wherein, the specific expression of R sec，u is:

[0055]

[0056] Step 3.2: in order to simplify the sub-problem 1, a variable is introduced, and R sec，u is re-expressed as:

[0057]

[0058] Since log(1+SINR B，u )

[0059] l+1], log2(1+SINR B，u )For P u It is non-concave. In order to solve this non-convex problem, Lemma 1 needs to be introduced;

[0060] Lemma 1: Let function f(t) = -tx + ln(t) + 1, if and only if Yes, it satisfies

[0061]

[0062] Based on Lemma 1, we introduce the auxiliary variable t u =t, let Importing functions You can get:

[0063]

[0064] in,

[0065]

[0066] Step 3.3: Similarly, introduce auxiliary variables Log2(1+SINR E，k，u ) is reformulated as:

[0067] log2(1+SINR E，k，u )

[0068]

[0069] Since log2(1+SINR E，k，u ) The existence of -log2(1+SINR E,k，u )For P u is non-concave, and Lemma 1 is still needed to solve this non-convex problem.

[0070] Based on Lemma 1, we introduce the auxiliary variable q u，k =t, let Introducing function λ u,k (P u， q u，k ), we can get:

[0071]

[0072] in,

[0073]

[0074] Step 3.4: Based on the max-min theorem of Sion, the above problem is transformed into:

[0075]

[0076] s.t.C1-C2

[0077] C4: t u >0

[0078] C5: q u，k >0

[0079] In the objective function, the constant ln2 is omitted, but there is no loss of optimality, and it can be proved that the above problem is convex, and is solved using alternating optimization counting;

[0080] Step 3.5: Introducing auxiliary variable W u = max k λ u，k (P u， q u，k ), the above problem can be transformed into:

[0081]

[0082] s.t.C1: P u + ξf u 3 ≤ P max，u

[0083] C2: P u ≥ 0

[0084] C4: t u > 0

[0085] C5: q u，k > 0

[0086] C6: W u ≥ λ u，k (P u , q u，k )

[0087] Based on Lemma 1, when P u and W u are given, the optimal values t u and q u，k can be calculated t u * and q u，k * , where,

[0088]

[0089]

[0090] When given t u * and q u，k * , the optimal value P u * can be obtained by the following problem, which is expressed as:

[0091]

[0092] s.t.C1: P u + ξf u 3 ≤ P max，u

[0093] C2: P u ≥ 0

[0094] C6: W u ≥ λ u，k (P u , q u，k )

[0095] The problem is convex and can be effectively solved by using a convex optimization solver (such as CVX) by alternately updating P u and (t u , q u,k ) can obtain an approximate solution of subproblem 1.

[0096] Further, in step 4, the optimization model obtained in step 2, which takes the legitimate user transmission power and local computing frequency as joint optimization variables and maximizes the legitimate user safe computing bits as the optimization objective, is converted into subproblem 2 which takes the legitimate user local computing frequency as the optimization variable and maximizes the legitimate user local safe computing bits as the optimization objective, and the implementation method is specifically:

[0097] Step 4.1: Based on the given legitimate user u transmission power P u , the total optimization model is converted into subproblem 2 which takes the legitimate user u local computing frequency f u as the optimization variable, specifically:

[0098]

[0099] s.t.C1: P u + ξf u 3 ≤ P max，u

[0100] C3: f u ≥ 0

[0101] The standard form of convex optimization is that the objective function and the constraint function are both convex functions, so the optimization model can be approximated as a convex optimization problem, and solved by using the Lagrange multiplier method;

[0102] Step 4.2: Introducing Lagrange multiplier alpha u The corresponding Lagrange function can be expressed as:

[0103]

[0104] The KKT condition of the Lagrange function is:

[0105]

[0106] By solving, the optimal value of the local computing frequency of the legitimate user u can be obtained Wherein

[0107] Further, based on the transmission power of the legitimate user obtained in the above step 3 and the local computing frequency of the legitimate user obtained in the above step 4, the block coordinate descent method is used for iterative updating until the objective function converges, and the maximum safe computing bits of the system are obtained.

[0108] Beneficial effects:

[0109] 1. The NOMA-MEC safe computing bit maximization method considering the hardware damage of the transceiver end provided by the application is suitable for actual scenes under non-ideal device conditions, and the transceiver end produces hardware damage due to factors such as quantization error and phase error, thereby producing additional noise in the unloading process, compared with the safe transmission scheme without considering the hardware damage of the transceiver end.

[0110] 2. The application adopts a partial unloading mode, combines the data unloading of the legitimate user with local safe computing, realizes robust design of the maximum safe computing bits of the system, and has a significant effect on improving the system safe computing bits compared with non-robust transmission design and OMA transmission mode. In addition, the legitimate user transmits by using uplink NOMA technology, decodes the received mixed signal by using SIC technology at the base station according to the size of the channel gain, reduces the influence of interference between legitimate users on the system performance, and finally formulates an optimal resource allocation strategy with robustness by adjusting the transmission power and local computing frequency of the legitimate user, that is, under the influence of different transceiver end hardware damage factors and the limitation of limited power resources, the maximum safe computing bits of the legitimate user in the system can be effectively improved through the trade-off between the safe transmission computing bits and the local safe computing bits of the legitimate user. DETAILED DESCRIPTION

[0111] Figure 1A model diagram of the method for maximizing security computing bits of mobile edge computing.

[0112] Figure 2 A flowchart of the method for maximizing security computing bits of mobile edge computing. DETAILED DESCRIPTION

[0113] The application will be further described in detail below in combination with the accompanying drawings of the specification.

[0114] The application proposes a NOMA-MEC security computing bit maximization method considering transceiver hardware damage, which is applied to the security transmission and robustness scene of multi-user edge computing. In the system model including a base station, U legal users and K eavesdroppers: if the noise generated by the hardware damage of the transceiver is not considered, the resource allocation strategy obtained when performing local resource allocation of the user is not optimal due to the existence of hardware damage in the actual scene, which leads to that the performance of the final system is not optimal. In addition, when multiple users perform computing task offloading at the same time, mutual interference is generated. The user adopts uplink NOMA transmission, and the base station adopts SIC technology to decode the received mixed signal according to the size of the signal gain, so as to reduce the influence of the user interference on the system as much as possible. Based on the above premise, a NOMA-MEC security computing bit maximization method considering transceiver hardware damage is proposed. The optimization problem of maximizing the user security computing bits is formulated by combining the security computing offloading and local security computing of multiple users, and the optimal resource allocation strategy of the system in the actual scene with hardware damage is obtained by jointly optimizing the transmit power and local computing frequency of the legal user, so as to realize the robustness design of security transmission.

[0115] As shown in Figure 1 The system of the application is composed of a base station, U legal users and K eavesdroppers. Each legal user in the system has certain computing tasks to be processed. Due to the limitation of the computing capacity of the legal user equipment, part of the tasks are offloaded to the edge base station carrying the MEC server for processing. The transceiver of the legal user and the receiver of the base station have hardware damage related to the transmit or receive signal power. Due to the broadcast characteristics of wireless communication and the existence of multiple eavesdroppers near the base station, when the legal user transmits offloaded data, the eavesdroppers will receive part of the data. It is necessary to ensure that in the worst case, the data received by the eavesdroppers is less than the data received by the base station, that is, the perfect hardware condition is considered at the eavesdroppers, the hardware damage is not considered, and the mutual interference generated when the eavesdroppers do not consider multi-user NOMA transmission. Based on the above premise, the legal user offloads data to the base station through uplink NOMA technology while performing local computing to realize the maximum security data volume computing of the system under the condition of ensuring security.

[0116] Figure 2 A flow chart of a NOMA-MEC security calculation bit maximization method considering the hardware damage of the transceiver end is provided, and the method comprises the following steps:

[0117] Step 1: Establish a system model including a base station, U legitimate users and K eavesdroppers, and determine the security transmission calculation bits of the legitimate users and the local security calculation bits of the legitimate users.

[0118] Step 1.1 determines the security transmission calculation bits of the legitimate users, which are specifically:

[0119] A system model including a base station, U legitimate users and K eavesdroppers is established, and the legitimate users need to perform the calculation task by local calculation and task offloading to the base station. In the case of considering the existence of the sending end hardware damage of the legitimate users, the signal sent by the legitimate user u is represented as:

[0120]

[0121] Wherein, x u represents the signal sent by the legitimate user u, P u represents the transmission power of the legitimate user u, s u represents the signal symbol sent by the legitimate user u, ε t，u represents the distorted signal due to the existence of the hardware damage of the legitimate user u, which is subject to a complex Gaussian distribution with a mean of 0 and a variance of δ t P u , δ t ≥ 0 represents the influence factor of the sending end hardware damage of the legitimate user u;

[0122] In the case of considering the existence of the receiving end hardware damage of the base station, the signal received by the base station is represented as:

[0123]

[0124] Wherein, y B represents the signal received by the base station, U represents the number of legitimate users, g u represents the channel gain between the legitimate user u and the base station, n r represents the Gaussian white noise at the base station, ε r represents the distorted received signal due to the existence of the hardware damage of the base station, which is subject to a complex Gaussian distribution with a mean of 0 and a variance of γ;

[0125] According to the signal received by the base station, the calculation of the variance γ is represented as:

[0126]

[0127] wherein, represents the received signal without the hardware impairment of the receiving end;

[0128] In the process of multi-user uplink transmission, mutual interference will occur between multi-users. In order to alleviate the interference, multi-user uses uplink NOMA to perform the offloading of computing tasks, and the successive interference cancellation (SIC) can be performed at the base station. For uplink NOMA, the user with better channel condition is decoded earlier, that is, |g1|≥…≥|g U |;

[0129] According to the signal received by the base station and the NOMA theory, the signal-to-interference-and-noise ratio at the base station is represented as:

[0130]

[0131] wherein, the first term in the denominator of the above formula represents the interference generated when the legitimate users transmit simultaneously, when u=U, the second term represents the hardware impairment of the transmitting end of the legitimate user, the third term represents the hardware impairment of the receiving end of the base station, and the fourth term represents the noise interference amplified due to the hardware impairment of the receiving end of the base station;

[0132] Due to the broadcast characteristic of wireless communication, the signal transmitted by the legitimate user u will also be received at the eavesdropper k. In order to ensure that the system can achieve secure transmission in the worst case, it is assumed that the eavesdropper k has better hardware performance, that is, the eavesdropper k will not generate distortion noise due to hardware impairment. In addition, in order to show the upper bound of the data rate of the eavesdropper, the worst case is considered that all eavesdroppers are not affected by the inter-user interference introduced by NOMA, and therefore the signal received by the eavesdropper k is represented as:

[0133]

[0134] wherein, y Ek represents the signal received by the eavesdropper, h u，k represents the channel gain between the legitimate user u and the eavesdropper k, and n e，k represents the Gaussian white noise at the eavesdropper k;

[0135] According to the signal received by the eavesdropper k, the signal-to-interference-and-noise ratio (SINR) at the eavesdropper k is represented as: E,k,u

[0136]

[0137] wherein, represents the variance of the Gaussian white noise at the eavesdropper k;

[0138] ​Based on the signal-to-interference-and-noise ratio at the base station and the signal-to-interference-and-noise ratio at the eavesdropper k, the calculation of the secure transmission rate Rsec,u is represented as:

[0139]

[0140] where [s] + = max(s, 0). In fact, log2(1 + SINR B,u )- max k log2(1 + SINR E，k，u ) is always non-negative, because if the above term is less than 0, we can set P u = 0. Therefore, without loss of optimality, we will omit the operator [s] + in the following analysis.

[0141] Based on Shannon theory, the secure transmission calculation bits D sec，trans is represented as:

[0142]

[0143] where B represents the bandwidth of the system, and T represents the length of time for which the legitimate user offloads.

[0144] Step 1.2 determines the local secure calculation bits of the legitimate user, which is specifically:

[0145] The local secure calculation bits D sec，loc is represented as:

[0146]

[0147] where f u represents the local calculation frequency size of the legitimate user u, and C u represents the number of CPU cycles required for the legitimate user u to perform 1-bit tasks.

[0148] Step 2: According to the secure offloading calculation bits of the legitimate user and the local secure calculation bits of the legitimate user obtained in step 1, a total optimization model is constructed, which takes the transmission power of the legitimate user and the local calculation frequency as joint optimization variables, and maximizes the secure calculation bits of the legitimate user as the optimization objective, represented as:

[0149]

[0150] s.t. C1: P u + ξf u 3 ≤ P max，u

[0151] C2: P u ≥ 0

[0152] C3: f u ≥ 0

[0153] where P max，u denotes the maximum transmit power of the legitimate user u. C1 denotes that the sum of the transmit power of the legitimate user u and the local computation frequency cannot exceed the maximum power limit of the legitimate user u, C2 denotes that the transmit power of the legitimate user u is non-negative, and C3 denotes that the local computation frequency of the legitimate user u is non-negative.

[0154] Step 3: Transforming the optimization model obtained in step 2, which takes the joint optimization variables of the transmit power of the legitimate user and the local computation frequency and takes the optimization objective of maximizing the secure computation bits of the legitimate user, into sub-problem 1 which takes the optimization variable of the transmit power of the legitimate user and takes the optimization objective of maximizing the secure offloading bits of the legitimate user, including the following steps:

[0155] Step 3.1: Based on the given local computation frequency f u of the legitimate user u, transform the total optimization model into sub-problem 1 which takes the transmit power P u as the optimization variable, specifically:

[0156]

[0157] s.t. C1-C2

[0158] where R sec，u is expressed as:

[0159]

[0160] Step 3.2: In order to simplify sub-problem 1, introduce variable R sec，u is re-expressed as:

[0161] log(1+SINR B，u )

[0162]

[0163] Due to the existence of the second term B,u in log(1+SINR

[0164] , log2(1+SINR B，u ) is non-convex with respect to P u , and in order to solve this non-convex problem, lemma 1 needs to be introduced;

[0165] Lemma 1: Let f(t) = -tx + ln(t) + 1, it satisfies

[0166] ​

[0167] Based on Lemma 1, introduce auxiliary variable t u = t, let Introduce function It can be obtained that:

[0168]

[0169] where,

[0170]

[0171] Step 3.3: Similarly, introduce auxiliary variable Rewrite log2(1 + SINR E，k，u ) as:

[0172]

[0173] Due to the existence of the first term in log2(1 + SINR E , k, u), -log2(1 + SINR E，k，u ) is non-convex for P u , it is still necessary to use Lemma 1 to solve this non-convex problem.

[0174] Based on Lemma 1, introduce auxiliary variable q u，k = t, let Introduce function λ u，k (P u , q u，k ), it can be obtained that:

[0175]

[0176] where,

[0177]

[0178] Step 3.4: Based on the max-min theorem of Sion, the above problem is transformed into:

[0179]

[0180] s.t. Cl-C2

[0181] C4: t u > 0

[0182] C5: q u，k > 0

[0183] In the objective function, the constant ln 2 is omitted, but there is no loss of optimality, and it can be proved that the above problem is convex, and is solved using alternating optimization counting;

[0184] Step 3.5: Introduce auxiliary variable W u = max k λ u，k (P u , q u，k ), the above problem can be transformed into:

[0185]

[0186] s.t.C1: P u + ξf u 3 ≤ P max，u

[0187] C2: P u ≥ 0

[0188] C4: t u > 0

[0189] C5: q u，k > 0

[0190] C6: W u ≥ λ u，k (P u , q u，k )

[0191] Based on Lemma 1, when P u and W u are given, the optimal values t u and q u,k can be calculated t u * and q u，k * , where,

[0192]

[0193]

[0194] When t u * and q u，k * are given, the optimal value P u * can be obtained by the following problem, which is represented as:

[0195]

[0196] s.t.C1: P u + ξf u3 ≤ P max，u

[0197] C2: P u ≥ 0

[0198] C6: W u ≥ λ u，k (P u , q u，k )

[0199] The problem is convex and can be solved efficiently using a convex optimization solver (e.g., CVX) by alternatingly updating P u and (t u， q u，k ) to obtain an approximate solution to the original problem.

[0200] Step 4: Transform the optimization model obtained in Step 2, which has the legitimate user transmit power and local computation frequency as joint optimization variables and maximizes the legitimate user secure computation bits as the optimization objective, into a subproblem 2 with the legitimate user local computation frequency as the optimization variable and maximizes the legitimate user local secure computation bits as the optimization objective, including the following steps:

[0201] Step 4.1: Based on the given transmit power P u of the legitimate user u, transform the total optimization model into a subproblem 2 with the legitimate user u local computation frequency f u as the optimization variable, specifically:

[0202]

[0203] s.t.C1: P u + ξf u 3 ≤ P max，u

[0204] C3: f u ≥ 0

[0205] The standard form of convex optimization is that the objective function and the constraint function are both convex functions, so the optimization model can be approximated as a convex optimization problem, which is solved using the Lagrange multiplier method;

[0206] Step 4.2: Introduce the Lagrange multiplier α u , and the corresponding Lagrange function can be expressed as:

[0207]

[0208] The KKT conditions of the Lagrange function are:

[0209]

[0210] By solving, the optimal value of the local calculation frequency of the legitimate user u can be obtained Wherein

[0211]

[0212] Step 5: Based on the transmission power of the legitimate user obtained in the above step 3, the local calculation frequency of the legitimate user obtained in the above step 4, the maximum safe calculation bits of the system are obtained by iteratively updating to the convergence of the target function through the block coordinate descent method.

[0213] The above examples are only used to illustrate the technical solutions of the present application, but not to limit it. Although the present application has been described in detail with reference to the foregoing examples, it should be understood by those skilled in the art that the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced by equivalents, and these modifications or replacements will not cause the corresponding technical solutions to deviate from the protection scope of the present application.

Claims

1. A NOMA-MEC secure computation bits maximization method considering the hardware impairment of the transmitter and receiver, characterized in that, The method comprises the following steps: Step 1: establishing a system model comprising a base station, U legitimate users and K eavesdroppers, and determining the secure transmission calculation bits of the legitimate users and the local secure calculation bits of the legitimate users; Step 2: constructing a total optimization model with the transmission power of the legitimate users and the local calculation frequency as joint optimization variables and the maximum secure calculation bits of the legitimate users as an optimization objective according to the secure transmission calculation bits and the local secure calculation bits of the legitimate users; Step 3: converting the total optimization model with the transmission power of the legitimate users and the local calculation frequency as joint optimization variables and the maximum secure calculation bits of the legitimate users as an optimization objective obtained in step 2 into a sub-problem 1 with the transmission power of the legitimate users as an optimization variable and the maximum secure offloading bits of the legitimate users as an optimization objective and solving the sub-problem 1; Step 4: converting the total optimization model with the transmission power of the legitimate users and the local calculation frequency as joint optimization variables and the maximum secure calculation bits of the legitimate users as an optimization objective obtained in step 2 into a sub-problem 2 with the local calculation frequency of the legitimate users as an optimization variable and the maximum local secure calculation bits of the legitimate users as an optimization objective and solving the sub-problem 2; Step 5: based on the transmission power of the legitimate users obtained in step 3 and the local calculation frequency of the legitimate users obtained in step 4, the block coordinate descent method is used to iteratively update until the objective function converges, and the maximum secure calculation bits of the system are obtained.

2. The method of claim 1, wherein the method is characterized in that: The implementation method for determining the secure transmission calculation bits of the legitimate users and the local secure calculation bits of the legitimate users in step 1 is that, Step 1.1 determining the secure transmission calculation bits of the legitimate users specifically comprises: A system model comprising a base station, U legitimate users and K eavesdroppers is established, and the legitimate users need to perform a calculation task by local calculation and offloading the task to the base station, and in consideration of the existence of a sending-end hardware damage of the legitimate users, the signal transmitted by the legitimate user u is represented as: where x u represents the signal transmitted by the legitimate user u, P u represents the transmit power of the legitimate user u, s u represents the signal symbol transmitted by the legitimate user u, ε t，u represents the distorted signal due to the hardware impairment of the legitimate user u, which is subject to a complex Gaussian distribution with mean 0 and variance δ t P u , δ t ≥ 0 represents the impact factor of the hardware impairment of the transmitting end of the legitimate user u; In consideration of the existence of a receiving-end hardware damage of the base station, the signal received by the base station is represented as: where y B represents the signal received by the base station, U represents the number of legitimate users, g u represents the channel gain between the legitimate user u and the base station, n r represents the Gaussian white noise at the base station, ε r represents the distorted received signal due to the existence of hardware impairment of the base station, which obeys a complex Gaussian distribution with a mean of 0 and a variance of Y; According to the signal received by the base station, the calculation of the variance γ is represented as: wherein represents the received signal without hardware impairment at the receiving end; In the process of multi-user uplink transmission, mutual interference will be generated between multi-users. In order to reduce the interference, multi-user uses uplink NOMA to unload the computing task, and the successive interference cancellation (SIC) can be performed at the base station. For uplink NOMA, the user with better channel condition is often decoded earlier, that is, |g1|≥…≥|g U |; According to the signal received by the base station and the NOMA theory, the signal-to-interference-and-noise ratio at the base station is represented as: where the first term in the denominator of the above formula represents the interference caused by simultaneous transmission between legitimate users, when u = U, The second term represents the hardware impairment of the transmitting end of the legitimate user, the third term represents the hardware impairment of the receiving end of the base station, and the fourth term represents the noise interference amplified due to the hardware impairment of the receiving end of the base station. Due to the broadcast characteristic of wireless communication, the legitimate user u transmits a signal at the eavesdropper k, in order to ensure that the system can achieve secure transmission in the worst case, it is assumed that the eavesdropper k has better hardware performance, that is, the eavesdropper k will not produce distortion noise due to hardware damage, in addition, in order to show the upper bound of the data rate of the eavesdropper, the worst case that all eavesdroppers are not affected by the inter-user interference introduced by NOMA is considered, and therefore the signal received by the eavesdropper k is represented as: where y Ek represents the signal received by the eavesdropper, h u，k represents the channel gain between the legitimate user u and the eavesdropper k, n e，k represents the Gaussian white noise at the eavesdropper k; According to the signal received by the eavesdropper k, the signal to interference and noise ratio SINR at the eavesdropper k E，k，u Expressed as: wherein denotes the variance of the Gaussian white noise at the eavesdropper k; Based on the signal-to-interference-and-noise ratio at the base station and the signal-to-interference-and-noise ratio at the eavesdropper k, the calculation is represented as: where [s] + = max(s, 0), in fact, log2(1 + SINR B，u ) - max k log2(1 + SINR E，k，u ) is always non-negative, because if the above term is less than 0, we set P u = 0, thus, without loss of optimality, we will omit the operator [s] + in the following analysis; Based on the Shannon theory, the secure transmission calculates bits D sec，trans is expressed as: Wherein, B represents the bandwidth of the system, and T represents the time length of the legitimate user offloading; Step 1.2 determining the local secure calculation bits of the legitimate users specifically comprises: Local security computation bit D sec,loc is represented as: where f u represents the local computing frequency size of the legal user u, C u represents the number of CPU cycles required by the legal user u to perform a 1-bit task.

3. The method of claim 2, wherein the method is characterized by, According to the legitimate user security offloading calculation bits obtained in step 1 and the legitimate user local security calculation bits, a total optimization model is constructed, in which the legitimate user transmission power and the local calculation frequency are taken as joint optimization variables, and the maximum legitimate user security calculation bits are taken as an optimization objective, and is expressed as: s.t. C1: P u + ξf u 3 ≤ P max，u C2: P u ≥ 0 C3: f u ≥0 where P max,u represents the maximum transmit power of the legitimate user u, C1 represents that the sum of the transmit power of the legitimate user u and the locally calculated power cannot exceed the maximum power limit of the legitimate user u, C2 represents that the transmit power of the legitimate user u is non-negative, and C3 represents that the locally calculated frequency of the legitimate user u is non-negative.

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