Random wireless network covert communication rate optimization method based on STAR-RIS assistance

Abstract

The invention discloses a random wireless network covert communication rate optimization method based on STAR-RIS assistance, which is suitable for an indoor and outdoor communication network system in a random wireless network assisted by STAR-RIS, wherein the indoor and outdoor communication network system comprises an outdoor covert signal transmitter, an indoor covert signal receiver, a prison leader, a plurality of interferers and a plurality of STAR-RIS. All devices are provided with single antennas; due to the influence of a random wireless environment, a hidden signal sender can send a hidden signal to a receiver through a direct line-of-sight link or an indirect line-of-sight link with the STAR-RIS; under the condition of exact transmitting power and transmitting position, the maximum covert communication rate is obtained by optimizing a plurality of STAR-RIS passive beam forming matrixes, and the communication performance of the covert communication system is improved. According to the invention, the throughput of the system is improved, and the method has great application value.

Description

Technical Field

[0001] The invention relates to the technical field of wireless communications, and in particular to a method for optimizing concealed communication rate of a random wireless network based on STAR-RIS assistance. Background Art

[0002] Reconfigurable smart surface (RIS) is an artificial metasurface composed of many low-cost, sub-wavelength and independently controllable reflective elements, which can be equivalently characterized as a radio link control circuit. As the core, each element of RIS can control the reflection phase and amplitude of the incident signal through software programming. It is essentially the adjustment of capacitance, resistance and inductance, so as to intelligently adjust the wireless environment and achieve precise control of electromagnetic wave propagation. This improves the signal quality of the intended receiver. Current research on RIS involves many aspects, such as cellular networks, drone networks, Internet of Things networks, edge network enhancement, etc. However, most existing research works assume that RIS can only reflect the incident signal, which requires that the transmitter and receiver are on the same side of RIS. This situation greatly limits the flexibility of RIS deployment.

[0003] To overcome this challenge, simultaneous transmission and reflection RIS (hereinafter referred to as STAR-RIS) came into being. It has three modes and can simultaneously transmit and reflect the incident signal, perfectly solving the problem of RIS single-sided coverage. STAR-RIS quickly attracted people's interest by providing the benefits of RIS while achieving full spatial coverage.

[0004] However, considering the large-scale deployment scenario of STAR-RIS in the future, there is a large gap in the performance research of STAR-RIS-assisted covert communication systems in wireless environments with randomly distributed obstructions. Summary of the invention

[0005] The present invention aims to provide a method for optimizing the concealed communication rate of a random wireless network based on STAR-RIS assistance.

[0006] The technical solution adopted by the present invention is:

[0007] The invention discloses a method for optimizing the covert communication rate of random wireless network assisted by STAR-RIS, comprising an indoor and outdoor covert communication system composed of an outdoor covert signal sender Alice, an indoor covert signal receiver Bob, a warden Willie and at least one STAR-RIS, wherein the indoor and outdoor covert communication system is arranged in a random wireless network with random distribution blocking assisted by STAR-RIS, and the wireless network is randomly distributed with a density of 10 -4 ~10 -2 pcs / m 2 Friendly interference;

[0008] The optimization method comprises the following steps:

[0009] S1, obtain the scenario layout parameters, including the number of STAR-RIS elements, positions and distribution of blockages, construct a STAR-RIS-assisted random distribution scenario, and deploy STAR-RIS on one side of the partial blockage in the wireless network;

[0010] S2, confirming the optimization problem according to the connection status of the covert communication user; the covert communication user connection status includes a direct line-of-sight link or other indirect line-of-sight link assisted by STAR-RIS;

[0011] S3, adopt the corresponding optimization scheme for the optimization problem to obtain the maximum concealed throughput of the optimized system.

[0012] Furthermore, the specific steps of S1 are as follows: obtain the number of STAR-RIS deployments in the scene and the number of STAR-RIS elements in the region through surveys, and then obtain the size and location information of buildings and obstructions in the basic geographical environment through topographic maps or base station planning data, artificially process the environment to obtain the STAR-RIS deployment ratio, obstruction size and density statistics, and use random geometry theory to build a virtual model.

[0013] Further, the specific steps of S2 are: the transmitting source adjusts the reflection formation matrix of the target STAR-RIS through the controller of the STAR-RIS, and after receiving the reflection signal of the target STAR-RIS, the transmitting source determines the existence of the LOS link between the transmitting source and the target STAR-RIS based on the distance, direction and received signal strength information, and then determines the connection status of the communication system;

[0014] S21, constructing a communication model when the covert communication user connection is a direct line-of-sight link, the specific steps include:

[0015] The link goes through nodes from the outdoor covert signal sender Alice to STAR-RIS to the indoor covert signal receiver Bob. At this time, the received signal of the indoor covert signal receiver Bob can be expressed as:

[0016]

[0017] Where P a represents the transmission power of Alice, the outdoor covert signal sender, s a is the unit power information of Alice, the outdoor covert signal sender, is the additive Gaussian white noise received by the indoor covert signal receiver Bob, H asb =H as Θs H sb represents the channel matrix from the covert signal sender Alice to STAR-RIS to Bob, H as represents the channel matrix between the outdoor covert signal sender Alice and STAR-RIS, represents the beamforming matrix of STAR-RIS, the subscript n∈[1,N] represents the nth element of STAR-RIS, and all STAR-RIS in the network have N elements; I b The noise in the outdoor random wireless network received by the indoor covert signal receiver Bob via STAR-RIS is expressed as follows:

[0018]

[0019] Where P I is the transmit power of the interfering node TXs, denote the set of TXs with direct LoS links to STAR-RIS and the set of TXs with indirect LoS links to STAR-RIS respectively; s i represents the interference signal transmitted by the i-th TX, and When i≠j Indicates whether TX exists or not i -STAR-RIS-Bob link or TX i -STAR-RIS j -STAR-RIS-Bob link;

[0020] S22, constructing a communication model when the covert communication user connection is an indirect line-of-sight link, the specific steps include:

[0021] The link goes through nodes from the outdoor covert signal sender Alice to the nearest RIS0, then from RIS0 to STAR-RIS, and finally to the indoor covert signal receiver Bob. At this time, the received signal of the indoor covert signal receiver Bob can be expressed as:

[0022]

[0023] In the formula, represents the channel matrix of the indirect line-of-sight link from Alice, the outdoor covert signal sender, to Bob, the indoor covert signal receiver, is the reflection matrix of RIS0;

[0024] The optimization problem in this case is constructed as follows:

[0025]

[0026] sqF b >R w (4b)

[0027] R b ≥R min (4c)

[0028]

[0029] Furthermore, the specific steps of S3 are:

[0030] S31, the optimization steps for S21 are: with the goal of maximizing the covert communication rate, under the constraints of ensuring the communication rate requirement and concealment requirement of the indoor covert signal receiver Bob, construct an optimization problem; the formula is as follows:

[0031]

[0032] sqF b >R w (5b)

[0033] R b ≥R min (5c)

[0034]

[0035] In the formula, and are the STAR-RIS amplitude and phase constraints;

[0036] The rate expression of indoor hidden signal receiver Bob is:

[0037]

[0038] Similarly, the rate expression of Warden Willie can be obtained as:

[0039]

[0040] SINR b The numerator and denominator of are processed as follows:

[0041]

[0042] and

[0043]

[0044] Therefore, the rate expression can be rewritten as:

[0045]

[0046] In the formula, Meet V s ≥0, and its rank is 1, that is, Rank(V s )=1,v s is the beamforming vector of STAR-RIS, Indicates v s The conjugate transpose of .

[0047] S32, due to R b and R w is a logarithmic function, and the numerator and denominator of the internal signal-to-interference-noise ratio also contain the variable V s The objective function (5a) and the two constraints (5b) and (5c) are all non-convex functions, so the following two slack variables are introduced:

[0048]

[0049] Based on the above slack variables, when the constraint x b ≥1 / P a Tr(Z ab V s )and When R b ≤log2(1+1 / x b y b ); Similarly, for R w Introduce two slack variables x w and w , the optimization problem can be rewritten as:

[0050]

[0051] V s ≥0 (12e)

[0052] R b ≥R min (12f)

[0053] Rank(V s )=1 (12g)

[0054] R b >R w (12h)

[0055] R b >R min (12i)

[0056]

[0057]

[0058] However, the problem is still non-convex due to constraints (12b), (12g) and (12h); when x>0, y>0, log2(1+1 / xy) is a convex function with respect to x and y. The first-order Taylor expansion at obtains the linearized lower bound of the above non-convex constraints:

[0059]

[0060] Based on formula (13), the objective function, (12b) and (12h) are replaced, and the constraint (12g) is removed and solved using the Matlab CVX toolbox.

[0061] S33, since the constraint condition (12g) is discarded, the result can be solved using the Gaussian randomization solution:

[0062] S331, expansion points using first-order Taylor expansion in S32 process The following initial point search algorithm is used to solve the problem; by introducing a new variable δ, the following search problem is constructed:

[0063]

[0064] st(10b) * -(10f) * ,(10h) * -(10k) * (14b)

[0065] Where, (10b) * -(10f) * ,(10h) * -(10k) * It is obtained by transforming the constraints (10b)-(10f), (10h)-(10k) into the form of f(x)≤0, and then replacing 0 with δ; thus, the initial feasible point required for problem (12) can be solved through this problem;

[0066] S332, for the rank-one constraint (12g) in problem (12), a sequential rank-one constraint relaxation scheme is adopted, that is, the constraint condition (12g) is replaced by the following formula:

[0067] max(eig(V s ))≥ε i Tr(V s ) (15)

[0068] Where, max(eig(V s )) indicates taking V s The maximum eigenvalue of i∈[0,1] represents the tightness parameter obtained after the i-th iteration; when ε i = 0, it is the common solution that ignores the non-convex rank-one constraint; when ε i =1, it is equivalent to a strict rank-one constraint.

[0069] S34, due to the existence of variables and V s The present invention adopts an alternating optimization method to solve this problem. The optimization steps for S22 are:

[0070] Let V s As a constant, optimize the phase shift matrix of RIS0 In this case, the channel gain can be expressed as:

[0071]

[0072] Similarly, for a given V s In the case of , the interference can be treated in the same way; at this time, since the only variable left is Therefore, the original optimization problem is directly expressed as an optimization problem about the signal-to-interference-noise ratio:

[0073]

[0074] This problem can be solved directly using the Matlab CVX toolbox, which can be solved

[0075] S35, Assuming it as a constant, substitute it into problem (4) and construct a new s Optimization problem;

[0076] The new optimization problem is as follows:

[0077]

[0078] sqF b >R w (18b)

[0079] R b ≥R min (18c)

[0080]

[0081] Referring to step S31, the rewrite rate expression is:

[0082]

[0083] In the formula, Meet V s≥0, and its rank is 1, that is, Rank(V s )=1,v s is the beamforming vector of STAR-RIS, Indicates v s The conjugate transpose of .

[0084] For R b and R w Introduce slack variables x b ,y b and x w ,y w ,Right now

[0085]

[0086]

[0087] When the constraint x b ≥1 / P a Tr(Z ab V s )and When R b ≤log2(1+1 / x b y b ).

[0088] Similarly, we can get R w The upper limit of and the constraints on its slack variables are used to reconstruct the optimization problem:

[0089]

[0090] V s ≥0 (24e)

[0091] R b ≥R min (24f)

[0092] Rank(V s )=1 (24g)

[0093] R b >R w (24h)

[0094] R b >R min (24i)

[0095]

[0096] For the logarithmic functions in the non-convex constraints (24b) and (24h), the first-order Taylor expansion method is used, that is, when x>0, y>0, log2(1+1 / xy) is a convex function with respect to x and y, which is The first-order Taylor expansion at can obtain the linearized lower bound of the above non-convex constraints:

[0097]

[0098] Based on this formula, replace (24b) and (24h) in the problem. Here, the first-order Taylor expansion point is obtained using the following initial point search algorithm. By introducing a new variable δ, the following search problem is constructed:

[0099]

[0100] st(10b) * -(10f) * ,(10h) * -(10k) * (26b)

[0101] Where, (10b) * -(10f) * ,(10h) * -(10k) * It is obtained by transforming the constraints (10b)-(10f), (10h)-(10k) into the form of f(x)≤0 and then replacing 0 with δ; thus, the initial feasible point required for problem (24) can be solved through this problem.

[0102] In addition, there is a non-convex constraint (24g) in the problem. Here, the sequential rank-one constraint relaxation solution in S332 is used to solve it, that is, the constraint (24g) is replaced by the following formula:

[0103] max(eig(V s ))≥ε i Tr(V s ) (27)

[0104] Where, max(eig(V s )) indicates taking V s The maximum eigenvalue of i ∈[0,1] represents the tightness parameter obtained after the i-th iteration; when ε i = 0, it is the common solution that ignores the non-convex rank-one constraint; when ε i =1, it is equivalent to a strict rank-one constraint.

[0105] S36, V obtained in S35 s Return to step S34 and re-optimize the variables This cycle continues until the target R is finally optimized. b The number of stable or alternating optimizations has reached the limit.

[0106] The beneficial effects of the present invention are as follows: the present invention can obtain a maximized covert communication rate by optimizing the passive beamforming matrices of multiple STAR-RIS under the condition of exact transmission power and transmission position, thereby improving the communication performance of the covert communication system and the throughput of the system, and has a high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 A system model diagram for the implementation of the present invention;

[0108] Figure 2 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0109] In order to more clearly illustrate the technical method used in the examples of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0110] The present invention is a random wireless network concealed communication rate optimization method based on STAR-RIS assistance, such as Figure 2 As shown, the present invention comprises the following steps:

[0111] S1, obtain the scene layout parameters through investigation, including the number of STAR-RIS elements, location and distribution of obstructions, and then obtain the size and location information of buildings and obstructions in the basic geographical environment through topographic maps or base station planning data, artificially process the environment to obtain the STAR-RIS deployment ratio, obstruction size and density statistics, and use the random geometry theory to construct the STAR-RIS-assisted random distribution scene to deploy STAR-RIS on one side of the partial obstruction in the wireless network.

[0112] like Figure 1 As shown, in a random wireless network there are 10 -4 ~10 -3 pcs / m 2 Density blocking and 10 -4 ~10 -2 pcs / m 2The density of interference nodes TXs, the length and width of the blockage obey uniform distribution; STAR-RIS are deployed on the surface of these blocks with probability 0 to 1, and are expressed as blocking coverage ratios on a large scale. In this wireless network, there is a covert communication system, including Alice, an outdoor covert signal sender, Bob, an indoor covert signal receiver, and Willie, the warden. Willie's main responsibility is to detect whether there is covert communication between Alice, an outdoor covert signal sender, and Bob, an indoor covert signal receiver. Assume that indoor and outdoor communications are blocked, and STAR-RIS needs to be deployed to provide links. Assume that all nodes in the network are single-antenna devices, and STAR-RIS has N reflective elements, and the channels between nodes are Rice fading channels.

[0113] Considering that in a covert communication system, the transmission power and deployment location of the outdoor covert signal sender Alice will significantly affect Willie's average detection error probability. In the random wireless network assisted by STAR-RIS set in the present invention, assuming that Willie does not know the setting parameters of STAR-RISs, from the perspective of Willie's average detection error probability, the outdoor covert signal sender Alice should choose an optimal location to send a covert signal with an appropriate optimal power to achieve covert communication or meet the concealment requirements of the system. Subsequently, the present invention considers that the STAR-RIS that assists in covert communication will fully adjust the amplitude and phase parameters of its own reflection or transmission to support and optimize the performance of the covert communication system. The optimization problem mentioned in the present invention is mainly for STAR-RISs serving covert communication, rather than all STAR-RISs in the wireless environment. The present invention optimizes the amplitude and phase parameters of STAR-RISs serving covert communication to maximize the concealment rate within a given effective transmission rate constraint.

[0114] For the sake of easy identification, the present invention records the STAR-RIS that connects indoor and outdoor communications in the covert communication system as STAR-RIS, and records other STAR-RIS as RIS. This is because from the perspective of the covert communication system, the outdoor signals from other STAR-RIS received by the receiving node are all reflected signals. As a distinction, the present invention records the RIS that is closest to the outdoor covert signal sender Alice and can provide STAR-RIS as RIS0, and it is only used by the outdoor covert signal sender Alice.

[0115] In the present invention, the channel parameter between any two nodes is recorded as H s , which includes path loss and channel fading, and x∈{ir j ,is,r j s,ar j ,as,sw,sb} represent TXi -RIS j TX i -STAR-RIS, RIS j -STAR-RIS, Alice-RIS j , Alice-STAR-RIS, STAR-RIS-Willie and STAR-RIS-Bob channels. represents the beamforming matrix of STAR-RIS, and Represents RIS i In the case of random distribution of blocking, the covert signal will be transmitted only when there is a link between the outdoor covert signal sender Alice and STAR-RIS. Here, it is divided into two main cases for discussion, namely, the case of direct line-of-sight link between the outdoor covert signal sender Alice and STAR-RIS or the case of indirect line-of-sight link between the outdoor covert signal sender Alice and STAR-RIS assisted by other RIS.

[0116] S2, confirm the optimization problem according to the connection status of the covert communication user; the transmitting source can adjust the reflection formation matrix of the target STAR-RIS through the controller of STAR-RIS, and after receiving the reflection signal of the target STAR-RIS, the transmitting source determines the existence of the LOS link between the transmitting source and the target STAR-RIS based on information such as distance, direction and received signal strength, and then determines the connection status of the communication system. Since there is a certain density of random blocking in the random wireless network in the present invention, this may cause two situations in the communication link between the outdoor covert signal sender Alice and STAR-RIS, namely, a direct line-of-sight link and an indirect line-of-sight link assisted by other STAR-RIS.

[0117] S21, constructing a communication model when the covert communication user connection is a direct line-of-sight link, the specific steps include:

[0118] In the case of a direct line-of-sight link between the outdoor covert signal sender Alice and STAR-RIS, since the gain of the indirect line-of-sight link is obviously smaller than that of the direct line-of-sight link, the indirect line-of-sight link is directly ignored here. The link passes through the nodes from the outdoor covert signal sender Alice to STAR-RIS to the indoor covert signal receiver Bob; in this case, the received signal of the indoor covert signal receiver Bob can be expressed as:

[0119]

[0120] Where P a represents the transmission power of Alice, the outdoor covert signal sender, s ais the unit power information of Alice, the outdoor covert signal sender, is the additive Gaussian white noise received by the indoor covert signal receiver Bob, H asb =H as Θ s H sb H represents the channel matrix from the outdoor covert signal sender Alice to STAR-RIS to Bob. as represents the channel matrix between the outdoor covert signal sender Alice and STAR-RIS, represents the beamforming matrix of STAR-RIS, the subscript n∈[1,N] represents the nth element of STAR-RIS, and all STAR-RIS in the network have N elements; and I b Then it represents the noise in the outdoor random wireless network received by the indoor covert signal receiver Bob through STAR-RIS, which is expressed as follows:

[0121]

[0122] Where P I is the transmit power of the interfering node TXs, denote the set of TXs with direct LoS links to STAR-RIS and the set of TXs with indirect LoS links to STAR-RIS respectively; s i represents the interference signal transmitted by the i-th TX, and When i≠j, Indicates whether TX exists or not i -STAR-RIS-Bob link or TX i -STAR-RIS j -STAR-RIS-Bob link.

[0123] S22, constructing a communication model when the covert communication user connection is an indirect line-of-sight link, the specific steps include:

[0124] The link goes through nodes from the outdoor covert signal sender Alice to the nearest RIS0, then from RIS0 to STAR-RIS, and finally to the indoor covert signal receiver Bob. In this case, the received signal of the indoor covert signal receiver Bob can be expressed as:

[0125]

[0126] In the formula, represents the channel matrix of the indirect line-of-sight link from Alice, the outdoor covert signal sender, to Bob, the indoor covert signal receiver, is the reflection matrix of RIS0;

[0127] This allows us to formulate the optimization problem in this case:

[0128]

[0129] sqF b >R w (4b)

[0130] R b ≥R min (4c)

[0131]

[0132] S3, adopting the corresponding optimization scheme for the optimization problem to obtain the optimized maximum concealed throughput of the system; the specific steps include:

[0133] S31, the optimization steps for S21 are: with the goal of maximizing the concealed communication rate, under the constraints of guaranteeing Bob's communication rate requirements and concealment requirements, the component optimization problem is solved; the formula is as follows:

[0134]

[0135] sqF b >R w (5b)

[0136] R b ≥R min (5c)

[0137]

[0138] In the formula, and are the STAR-RIS amplitude and phase constraints;

[0139] The indoor covert signal receiving rate expression of Bob is:

[0140]

[0141] Similarly, we can also get the rate expression of Warden Willie:

[0142]

[0143] SINR b The numerator and denominator of are processed as follows:

[0144]

[0145] and

[0146]

[0147] Therefore, the rate expression can be rewritten as:

[0148]

[0149] In the formula, Meet V s ≥0, and its rank is 1, that is, Rank(V s )=1,v s is the beamforming vector of STAR-RIS, Indicates v s The conjugate transpose of .

[0150] S32, due to R b and R w is a logarithmic function, and the numerator and denominator of the internal signal-to-interference-noise ratio also contain the variable Vs s The objective function (5a) and the two constraints (5b) and (5c) are all non-convex functions, so the following two slack variables are introduced:

[0151]

[0152] Based on the above slack variables, when the constraint x b ≥1 / P a Tr(Z ab V s )and When R b ≤log2(1+1 / x b y b ); Similarly, for R w Introduce two slack variables x w and w , the optimization problem can be rewritten as:

[0153]

[0154] V s ≥0 (12e)

[0155] R b ≥R min (12f)

[0156] Rank(V s )=1 (12g)

[0157] R b >R w (12h)

[0158] R b >R min (12i)

[0159]

[0160] However, the problem is still non-convex due to constraints (12b), (12g) and (12h); when x>0, y>0, log2(1+1 / xy) is a convex function with respect to x and y. The first-order Taylor expansion at obtains the linearized lower bound of the above non-convex constraints:

[0161]

[0162] Based on formula (13), the objective function, (12b) and (12h) are replaced, and the constraint (12g) is removed and solved using the Matlab CVX toolbox.

[0163] S33, since the constraint condition (12g) is discarded, the result can be solved using the Gaussian randomization solution:

[0164] S331, expansion points using first-order Taylor expansion in S32 process The following initial point search algorithm is used to solve the problem; by introducing a new variable δ, the following search problem is constructed:

[0165]

[0166] st(10b) * -(10f) * ,(10h) * -(10k) * (14b)

[0167] Where, (10b) * -(10f) * ,(10h) * -(10k) * It is obtained by transforming the constraints (10b)-(10f), (10h)-(10k) into the form of f(x)≤0, and then replacing 0 with δ; thus, the initial feasible point required for problem (12) can be solved through this problem;

[0168] S332, for the rank-one constraint (12g) in problem (12), a sequential rank-one constraint relaxation scheme is adopted, that is, the constraint condition (12g) is replaced by the following formula:

[0169] max(eig(V s ))≥ε i Tr(V s) (15)

[0170] Where, max(eig(V s )) indicates taking V s The maximum eigenvalue of i ∈[0,1] represents the tightness parameter obtained after the i-th iteration; when ε i = 0, it is the common solution that ignores the non-convex rank-one constraint; when ε i =1, it is equivalent to a strict rank-one constraint.

[0171] S34, due to the existence of variables and V s The present invention adopts an alternating optimization method to solve this problem. The optimization steps for S22 are:

[0172] Let V s is a constant, optimizing the phase shift matrix of RIS0 In this case, the channel gain can be expressed as:

[0173]

[0174] Similarly, for a given V s In the case of , the interference can be treated in the same way; at this time, since the only variable left is Therefore, the original optimization problem is directly expressed as an optimization problem about the signal-to-interference-noise ratio:

[0175]

[0176] This problem can be solved directly using the Matlab CVX toolbox, which can be solved And apply it to subsequent operations.

[0177] S35, Assuming it as a constant, substitute it into problem (4) and construct a new s Optimization problem;

[0178] The new optimization problem is as follows:

[0179]

[0180] sqF b >R w (18b)

[0181] R b ≥R min (18c)

[0182]

[0183] Referring to step S31, the rewrite rate expression is:

[0184]

[0185] In the formula, Meet V s ≥0, and its rank is 1, that is, Rank(V s )=1,v s is the beamforming vector of STAR-RIS, Indicates v s The conjugate transpose of .

[0186] For R b and R w Introduce slack variables x b ,y b and x w ,y w ,Right now

[0187]

[0188]

[0189] When the constraint x b ≥1 / P a Tr(Z ab V s )and When R b ≤log2(1+1 / x b y b ); Similarly, we can get R w The upper limit of and the constraints on its slack variables are used to reconstruct the optimization problem:

[0190]

[0191] V s ≥0 (24e)

[0192] R b ≥R min (24f)

[0193] Rank(V s )=1 (24g)

[0194] R b >R w (24h)

[0195] R b >R min (24i)

[0196]

[0197] For the logarithmic functions in the non-convex constraints (24b) and (24h), the first-order Taylor expansion method is used, that is, when x>0, y>0, log2(1+1 / xy) is a convex function with respect to x and y, which is The first-order Taylor expansion at can obtain the linearized lower bound of the above non-convex constraints:

[0198]

[0199] Based on this formula, replace (24b) and (24h) in the problem. Here, the first-order Taylor expansion point is obtained using the following initial point search algorithm. By introducing a new variable δ, the following search problem is constructed:

[0200]

[0201] st(10b) * -(10f) * ,(10h) * -(10k) * (26b)

[0202] Where, (10b) * -(10f) * ,(10h) * -(10k) * It is obtained by transforming the constraints (10b)-(10f), (10h)-(10k) into the form of f(x)≤0 and then replacing 0 with δ; thus, the initial feasible point required for problem (24) can be solved through this problem.

[0203] In addition, there is a non-convex constraint (24g) in the problem. Here, the sequential rank-one constraint relaxation solution in S332 is used to solve it, that is, the constraint (24g) is replaced by the following formula:

[0204] max(eig(V s ))≥ε i Tr(V s ) (27)

[0205] In the formula, max(eig(V s )) indicates taking V s The maximum eigenvalue of i ∈[0,1] represents the tightness parameter obtained after the i-th iteration; when ε i = 0, it is the common solution that ignores the non-convex rank-one constraint; when ε i =1, it is equivalent to a strict rank-one constraint.

[0206] S36, V obtained in S35s Return to step S34 and re-optimize the variables This cycle continues until the target R is finally optimized. b The number of stable or alternating optimizations has reached the limit.

Claims

1. A random wireless network covert communication rate optimization method based on STAR-RIS assistance, characterized by: The invention comprises an indoor and outdoor covert communication system composed of an outdoor covert signal sender Alice, an indoor covert signal receiver Bob, a warden Willie and at least one STAR-RIS. The indoor and outdoor covert communication system is set in a random wireless network with random distribution blocking assisted by STAR-RIS, and the wireless network is randomly distributed with a density of 10 -4 ~10 -2 pcs / m 2 Friendly interference; The optimization method The following steps are involved: S1, obtain the scenario layout parameters, including the number of STAR-RIS elements, positions and distribution of blockages, construct a STAR-RIS-assisted random distribution scenario, and deploy STAR-RIS on one side of the partial blockage in the wireless network; S2, confirming the optimization problem according to the connection status of the covert communication user; the covert communication user connection status includes a direct line-of-sight link or other indirect line-of-sight link assisted by STAR-RIS; S3, adopt the corresponding optimization scheme for the optimization problem to obtain the maximum concealed throughput of the optimized system.

2. The method for optimizing the concealed communication rate of a random wireless network based on STAR-RIS assistance according to claim 1, characterized in that: The specific steps of S1 are: Through investigation, the number of STAR-RIS deployed in the scene and the number of STAR-RIS elements in the area are obtained, and then the size and location information of buildings and obstructions in the basic geographical environment are obtained through topographic maps or base station planning data. The environment is artificially processed to obtain the STAR-RIS deployment ratio, obstruction size and density statistics, and the virtual model is constructed using random geometry theory.

3. The method for optimizing the concealed communication rate of a random wireless network based on STAR-RIS assistance according to claim 1, characterized in that: The specific steps of S2 are: The transmitter adjusts the reflection matrix of the target STAR-RIS through the controller of the STAR-RIS. After receiving the reflection signal of the target STAR-RIS, the transmitter determines the existence of the LOS link between the transmitter and the target STAR-RIS based on the distance, direction and received signal strength information, and then determines the connection status of the communication system; S21, constructing a communication model when the covert communication user connection is a direct line-of-sight link, the specific steps include: The link goes through nodes from the outdoor covert signal sender Alice to STAR-RIS to the indoor covert signal receiver Bob. At this time, the received signal of the indoor covert signal receiver Bob is expressed as: Where P a represents the transmission power of Alice, the outdoor covert signal sender, s a is the unit power information of Alice, the outdoor covert signal sender, is the additive Gaussian white noise received by the indoor covert signal receiver Bob, H asb =H as Θ s H sb represents the channel matrix from the covert signal sender Alice to STAR-RIS to Bob, H as represents the channel matrix between the outdoor covert signal sender Alice and STAR-RIS, represents the beamforming matrix of STAR-RIS, the subscript n∈[1,N] represents the nth element of STAR-RIS, and all STAR-RIS in the network have N elements; I b The noise in the outdoor random wireless network received by the indoor covert signal receiver Bob via STAR-RIS is expressed as follows: Where P I is the transmit power of the interfering node TXs, denote the set of TXs with direct LoS links to STAR-RIS and the set of TXs with indirect LoS links to STAR-RIS respectively; s i represents the interference signal transmitted by the i-th TX, and When i≠j Indicates whether TX exists i -STAR-RIS-Bob link or TX i -STAR-RIS j -STAR-RIS-Bob link; S22, constructing a communication model when the covert communication user connection is an indirect line-of-sight link, the specific steps include: The link goes through nodes from the outdoor covert signal sender Alice to the nearest RIS0, then from RIS0 to STAR-RIS, and finally to the indoor covert signal receiver Bob. At this time, the received signal of the indoor covert signal receiver Bob is expressed as: In the formula, represents the channel matrix of the indirect line-of-sight link from Alice, the outdoor covert signal sender, to Bob, the indoor covert signal receiver, is the reflection matrix of RIS0; The optimization problem in this case is constructed as follows: s.t.R b >R w (4b) R b ≥R min (4c) 4. The method for optimizing the concealed communication rate of a random wireless network based on STAR-RIS assistance according to claim 1, characterized in that: The specific steps of S3 are: S31, the optimization steps for S21 are: with the goal of maximizing the covert communication rate, under the constraints of ensuring the communication rate requirement and concealment requirement of the indoor covert signal receiver Bob, construct an optimization problem; the formula is as follows: s.t.R b >R w (5b) R b ≥R min (5c) In the formula, and are the STAR-RIS amplitude and phase constraints; The rate expression of indoor hidden signal receiver Bob is: Similarly, you can get Warden Willi e The rate expression is: SINR b The numerator and denominator of are processed as follows: and Thus, the rate expression can be rewritten as: In the formula, Meet V s ≥0, and its rank is 1, that is, Rank(V s )=1,v s is the beamforming vector of STAR-RIS, Indicates v s The conjugate transpose of ; S32, due to R b and R w is a logarithmic function, and the numerator and denominator of the internal signal-to-interference-noise ratio also contain the variable V s The objective function (5a) and the two constraints (5b) and (5c) are all non-convex functions, so the following two slack variables are introduced: Based on the above slack variables, when the constraint x b ≥1 / P a Tr(Z ab V s )and When R b ≤log2(1+1 / x b y b ); Similarly, for R w Introduce two slack variables x w and w , the optimization problem can be rewritten as: V s ≥0 (12e) R b ≥R min (12f) Rank(V s )=1 (12g) R b >R w (12h) R b >R min (12i) However, due to constraints (12b), (12g) and (12h), the problem is still non-convex; when x>0, y>0, log2(1+1 / xy) is a convex function with respect to x and y. The first-order Taylor expansion at obtains the linearized lower bound of the above non-convex constraints: Based on formula (13), the objective function, (12b) and (12h) are replaced, and the constraint (12g) is removed and solved using the Matlab CVX toolbox; S33, since the constraint condition (12g) is discarded, the result is solved using the Gaussian randomization solution: S34, due to the existence of variables and V s The present invention adopts an alternating optimization method to solve this problem. The optimization steps for S22 are: Let V s is a constant, optimizing the phase shift matrix of RIS0 In this case, the channel gain is expressed as: Similarly, for a given V s In the case of , the interference is treated in the same way; At this time, since the variable is only Therefore, the original optimization problem is directly expressed as an optimization problem about the signal-to-interference-noise ratio: This problem can be solved directly using the Matlab CVX toolbox, which can be solved S35, Assuming it as a constant, substitute it into problem (4) and construct a new s Optimization problem; The new optimization problem is as follows: s.t. R b >R w (18b) R b ≥R min (18c) Referring to step S31, the rewrite rate expression is: In the formula, Meet V s ≥0, and its rank is 1, that is, Rank(V s )=1,v s is the beamforming vector of STAR-RIS, Indicates v s The conjugate transpose of ; For R b and R w Introduce slack variables x b ,y b and x w ,y w ,Right now When the constraint x b ≥1 / P a Tr(Z ab V s )and When R b ≤log2(1+1 / x b y b ); Similarly, we can get R w The upper limit of and the constraints on its slack variables are used to reconstruct the optimization problem: V s ≥0 (24e) R b ≥R min (24f) Rank(V s )=1 (24g) R b >R w (24h) R b >R min (24i) For the logarithmic functions in the non-convex constraints (24b) and (24h), the first-order Taylor expansion method is used, that is, when x>0, y>0, log2(1+1 / xy) is a convex function with respect to x and y, which is The first-order Taylor expansion at can obtain the linearized lower bound of the above non-convex constraints: Based on this formula, replace (24b) and (24h) in the problem; the first-order Taylor expansion point here is obtained using the following initial point search algorithm; by introducing a new variable δ, the following search problem is constructed: s.t.(10b) * -(10f) * ,(10h) * -(10k) * (26b) In the formula, (10b) * -(10f) * , (10h) * -(10k) * It is obtained by transforming the constraints (10b)-(10f), (10h)-(10k) into the form of f(x)≤0, and then replacing 0 with δ; thus, the initial feasible point required for problem (24) can be solved through this problem; In addition, there is a non-convex constraint (24g) in the problem. Here, the sequential rank-one constraint relaxation solution in S332 is used to solve it, that is, the constraint (24g) is replaced by the following formula: max(eig(V s ))≥ε i Tr(V s ) (27) In the formula, max(eig(V s )) indicates taking V s The maximum eigenvalue of i ∈[0,1] represents the tightness parameter obtained after the i-th iteration; when ε i = 0, it is the common solution that ignores the non-convex rank-one constraint; when ε i =1, it is equivalent to a strict rank-one constraint; S36, V obtained in S35 s Return to step S34 and re-optimize the variables This cycle continues until the target R is finally optimized. b The number of stable or alternating optimizations has reached the limit.

5. The method for optimizing the concealed communication rate of a random wireless network based on STAR-RIS assistance according to claim 4 is characterized in that: The specific steps of S33 include: S331, expansion points using first-order Taylor expansion in S32 process The following initial point search algorithm is used to solve the problem; by introducing a new variable δ, the following search problem is constructed: s.t.(10b) * -(10f) * ,(10h) * -(10k) * (14b) Where, (10b) * -(10f) * , (10h) * -(10k) * It is obtained by transforming the constraints (10b)-(10f), (10h)-(10k) into the form of f(x)≤0, and then replacing 0 with δ; thus, the initial feasible point required for problem (12) can be solved through this problem; S332, for the rank-one constraint (12g) in problem (12), a sequential rank-one constraint relaxation scheme is adopted, that is, the constraint condition (12g) is replaced by the following formula: max(eig(V s ))≥ε i Tr(V s ) (15) In the formula, max(eig(V s )) indicates taking V s The maximum eigenvalue of i ∈[0,1] represents the tightness parameter obtained after the i-th iteration; when ε i = 0, it is the common solution that ignores the non-convex rank-one constraint; when ε i =1, it is equivalent to a strict rank-one constraint.

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