Anti-interference covert communication and perception integrated robust beam forming method

Abstract

The invention discloses an anti-interference covert communication and perception integrated robust beam forming method, which comprises the following steps of: S1, establishing a system model, in a system, transmitting communication and perception signals by a base station BS, transmitting interference signals by a jammer, and having K communication users and a perception target; setting the sensing target as an eavesdropper, and trying to detect whether a communication behavior exists between the base station and the communication user; s2, depicting a channel model, a sensing detection probability index, a hidden transmission index and a transmission hidden rate in an imperfect transmission environment, and jointly optimizing base station communication, sensing beam forming and RIS beam forming under the condition of meeting transmission robustness, hidden communication safety, sensing precision and RIS phase shift constraint conditions, so as to maximize the total transmission hidden rate of the system; and S3, on the basis of fractional programming and a quadratic transformation technology, combining with an alternating direction multiplier method, and proposing the method provided by the invention. According to the invention, the concealment, the robustness and the transmission capability of the communication and inductance integrated system are obviously improved.

Description

Technical Field

[0001] This invention relates to the field of wireless communication security and sensing technology, specifically a robust beamforming method integrating anti-interference and covert communication sensing. This invention achieves covert and robust information transmission by jointly optimizing communication beamforming, sensing beamforming, and RIS beamforming. Background Technology

[0002] Reconfigurable Smart Surfaces (RIS) are a technology that can control the direction of signal propagation by designing their beamforming, and have significant potential in next-generation mobile communications (6G); Sensor-Sensing Integration is a new architecture that integrates traditional communication and sensing, and has significant efficiency improvements in both hardware and software. It has already been applied in 5G-A and is an important evolution direction for 6G; Covert Communication is a wireless security transmission technology that can ensure that the communication behavior of the two parties is not eavesdropped on by a third party; Beamforming technology is a technology that maximizes performance by controlling the phase of different antenna elements at the transmitter to focus the transmission power in a specific direction. Summary of the Invention

[0003] The purpose of this invention is to provide a robust beamforming method integrating anti-interference covert communication and sensing. By characterizing the imperfect channel, determining the upper limit of channel transmission, analyzing the form of covert transmission signals, establishing a mathematical model of detection probability, and jointly optimizing communication beamforming, sensing beamforming, and RIS beamforming, the overall system transmission covert rate is maximized.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] A robust beamforming method integrating anti-interference and covert communication sensing, comprising the following steps:

[0006] S1. Establish a system model. In the system, the base station BS transmits communication and sensing signals, and the jammer transmits jamming signals. There are K communication users and one sensing target. Assume that the sensing target is an eavesdropper, attempting to detect whether there is communication behavior between the base station and the communication users.

[0007] S2. Characterize the channel model, sensing and detection probability index, covert transmission index and transmission covert rate under imperfect transmission environment. Under the conditions of transmission robustness, covert communication security, sensing accuracy and RIS phase shift constraints, jointly optimize base station communication and sensing beamforming and RIS beamforming to maximize the total transmission covert rate of the system.

[0008] S3: Based on fractional programming and quadratic transformation techniques, combined with the alternating direction multiplier method, a robust beamforming method is proposed.

[0009] As an improvement to the above technical solution, in step S1, the signal transmitted by the base station BS is represented as follows:

[0010]

[0011] Among the optimization variables For the communication beamforming vector of the k-th user, Shape vectors for sensing beams;

[0012] To represent the imperfect channel model, we denote the channels between different parts of the system as:

[0013]

[0014] in, Given channels, all follow a Rice distribution. The uncertainty lies in the various channel components;

[0015] In addition to considering channel imperfections, we also consider the imperfections of the RIS phase shift. The phase imperfection error of the RIS is distributed as follows: Therefore, the RIS phase shift with phase shift error is expressed as:

[0016]

[0017] in For the phase of RIS, For phase error; thus, we obtain:

[0018] ;

[0019] ;

[0020] ;

[0021] .

[0022] As an improvement to the above technical solution, the signal received by the k-th user is in the following form:

[0023]

[0024] Its signal-to-interference-plus-noise ratio is:

[0025] ;

[0026] The sensing signal echo received at the base station is:

[0027]

[0028] in This refers to the channel from the base station to the sensing target. This is the channel from the jammer to the base station. This refers to the noise received at the base station.

[0029] Based on the generalized likelihood ratio test and the Neyman-Pearson criterion, the detection probability of the base station for the sensed target is...

[0030]

[0031] in This represents the probability of a false alarm. Let be the noncentral chi-square cumulative distribution function with 2 degrees of freedom (DoFs), defined as follows: The key parameters in the detection probability are expressed as follows:

[0032]

[0033] in , ;

[0034] For the target of perception, that is, the signal received by the eavesdropper, it is represented as:

[0035] The perceived target, i.e., the signal received by the eavesdropper, is represented as:

[0036]

[0037] As an improvement to the above technical solution, shielded communication ensures that eavesdroppers cannot perceive the communication activity between the base station and the communication user, and can be improved by reducing the false alarm probability. and the probability of missed alarms To maximize the probabilities of both, the false alarm probability is defined as the sum of the false alarm probability and the missed alarm probability; thus, the false alarm probability and the missed alarm probability are expressed as follows:

[0038]

[0039] The optimal decision threshold is expressed as:

[0040]

[0041] in

[0042] The corresponding detection probability is:

[0043]

[0044] Then its average detection error probability is expressed as:

[0045]

[0046] Observable It is monotonically increasing; therefore, it is expressed as:

[0047] .

[0048] As an improvement to the above technical solution, in order to derive the worst-case imperfect channel expression, these uncertainties are assumed to be unknown factors with deterministic and finite numerical values:

[0049]

[0050] in This refers to the channel error range.

[0051] Furthermore, to characterize these channel uncertainties, we define... To control for these uncertainties, they are defined as follows:

[0052]

[0053] The channel representation is then updated as follows:

[0054]

[0055] The optimization problem of maximizing the minimum transmission rate under constraints of base station transmit power, sensing, concealment, and imperfect RIS phase shift is expressed as follows:

[0056]

[0057] As an improvement to the above technical solution, the focus is on the imperfect RIS beamforming matrix, whose mean and variance are expressed as follows:

[0058]

[0059] Compared with the prior art, the advantages and positive effects of this invention are:

[0060] This invention presents a robust beamforming method for integrated sensing and communication, designed to mitigate interference. By characterizing the total transmission concealment rate of the system under imperfect transmission conditions, and by defining concealment transmission constraints and sensing constraints, the method utilizes fractional programming and quadratic transformation techniques, combined with the Alternating Direction Multiplier Method (ADMM), to design a solution algorithm that maximizes the total transmission concealment rate of the system. This method effectively handles the non-convexity of optimization problems. This invention significantly improves the concealment, robustness, and transmission capability of integrated sensing and communication systems. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0063] Figure 2 This is a model diagram of the system implementing the present invention;

[0064] Figure 3 This is a graph showing the relationship between the base station's transmit power and the total covert transmission rate in the implementation of this invention;

[0065] Figure 4 This is a graph showing the relationship between jammer power and total transmission concealment rate provided by the present invention.

[0066] Figure 5 This is a graph showing the relationship between the number of RIS reflection units and the total transmission concealment rate provided by this invention.

[0067] Figure 6 This is a graph showing the relationship between the concealment constraint and the total concealment rate of transmission provided by the present invention.

[0068] Figure 7 This is a graph showing the relationship between the perception constraint and the total transmission concealment rate provided by the present invention. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0070] Specifically, step S1 includes:

[0071] The method described in this embodiment is applicable to, for example... Figure 2 The system model shown includes the following system parameters: a base station (BS) equipped with multiple antennas, a jammer with one single antenna, K communication users, one sensing target, and a reference frame (RIS) equipped with L reflector units. The BS's transmitted signal can be represented as:

[0072] (4)

[0073] Among the optimization variables For the communication beamforming vector of the k-th user, Shape vectors for sensing beams;

[0074] The channels between them can be represented as:

[0075] (5)

[0076] in Given a known channel, This is due to channel uncertainty. Simultaneously, this invention also considers the phase error in the beamforming of the RIS (Radio Router System), with the phase error distribution of the RIS distributed as follows: Therefore, the phase error of RIS can be expressed as:

[0077] (6)

[0078] in For the phase of RIS, This is the phase error. Therefore, we can obtain... , , , .

[0079] The signal received by the k-th user is in the following form:

[0080] (7)

[0081] Therefore, its signal-to-interference-plus-noise ratio is:

[0082] (8)

[0083] The sensing signal echo received at the base station is:

[0084] (9)

[0085] Based on the generalized likelihood ratio test and the Neyman-Pearson criterion, the detection probability of a base station for a sensed target can be expressed as:

[0086] (10)

[0087] definition The key parameter in the detection probability can be expressed as:

[0088] (11)

[0089] The perceived target, i.e., the signal received by the eavesdropper, can be represented as:

[0090] (12)

[0091] Covert communication, meaning communication between a base station and a user is undetectable to eavesdroppers, can be achieved by maximizing the probabilities of false alarms and missed alarms. Therefore, the error probability is defined as the sum of the false alarm probability and the missed alarm probability. The false alarm probability and the missed alarm probability are then expressed as follows:

[0092] (13)

[0093] The optimal decision threshold can be expressed as:

[0094] (14)

[0095] in (15)

[0096] The corresponding detection probability is:

[0097] (16)

[0098] Then its average detection error probability can be expressed as:

[0099] (17)

[0100] Observable It is monotonically increasing. Therefore, it can also be expressed as:

[0101] (18)

[0102] To derive the worst-case imperfect channel expression, these uncertainties are assumed to be unknown factors that are deterministic and numerically finite:

[0103] (19)

[0104] in Let be the channel error range. To characterize these channel uncertainties, define . To control these uncertainties in the money, we can then obtain:

[0105] (20)

[0106] Therefore, we can conclude that:

[0107] (twenty one)

[0108] Therefore, the optimization problem can be transformed into:

[0109] (twenty two)

[0110] Next, we focus on the imperfect RIS beamforming matrix, whose mean and variance can be expressed as:

[0111] (twenty three)

[0112] Transforming imperfect RIS beamforming into a focus on beamforming optimization, defining... , The problem can be transformed into:

[0113] (twenty four)

[0114] in These are auxiliary variables introduced for the Lagrange duality method. Therefore, the problem can be further transformed into:

[0115] (25)

[0116] Next, we will process the constraints, starting with the perceived constraints, which can be derived as follows:

[0117]

[0118] Introduce auxiliary variables The objective function can be transformed into:

[0119] (26)

[0120] in ,definition The optimization problem can be refactored as follows:

[0121] (27)

[0122] This problem can be solved using the positive semidefinite relaxation method. Next, we will solve for the RIS phase. First, its channel expression needs to be optimized:

[0123] (28)

[0124] in , ;

[0125] and then:

[0126] (29)

[0127] in .

[0128] Similar:

[0129] (30)

[0130] in .

[0131] Furthermore, perceptual constraints can be transformed into:

[0132] (31)

[0133] in .definition We can obtain:

[0134] (32)

[0135] Substituting, we can obtain

[0136] (33)

[0137] Further simplification The constraints can be refactored as follows:

[0138]

[0139] (35)

[0140] in , .

[0141] Based on fractional programming techniques, the optimization problem can be expressed as:

[0142] (37)

[0143] in .

[0144] Introduction , , ,

[0145] The problem can be refactored as:

[0146] (38)

[0147] However, the problem described above is still non-convex and needs to be further transformed into:

[0148] (39)

[0149] (40)

[0150] in .

[0151] Further introduce auxiliary variables It can be simplified to:

[0152] (41)

[0153] in , .

[0154] To address this problem, the ADMM technique is employed for solution. First, its augmented Lagrange expression is determined as follows:

[0155] (42)

[0156] The derivative expression with respect to the optimization variable is:

[0157] (43)

[0158] Further simplification yields:

[0159] (44)

[0160] about The optimization problem can be expressed as

[0161] for: (45)

[0162] optimal The expression is:

[0163] (46)

[0164] The final for:

[0165] (47)

[0166] The system configuration parameters for this implementation are shown in the table below:

[0167] Number of users K 6 Number of IRS reflector units N 30 Base station transmit power 30dBm jammer power 10dBm Channel Rice Channel Detection probability success threshold 99.9% Hidden constraint threshold 0.01 Channel error 0.01

[0168] Figure 3 The influence of base station transmit power on the overall transmission rate of the system is illustrated. It can be seen that the higher the transmit power, the greater the performance improvement of the system. The performance upper limit scheme in the figure is also the transmission scheme of the perfect channel. The robust scheme is the beamforming scheme proposed in this invention based on imperfect channels and imperfect phases. It can be seen that although there is a certain imperfect transmission environment, its performance difference is small compared with the performance upper limit, and it can achieve safe and reliable robust transmission.

[0169] Figure 4The study revealed the impact of jammer power on performance. Jammer power has a significant impact on covert rate transmission; the higher the jamming power, the higher the achievable covert rate of reading.

[0170] Figure 5 The study depicted a positive correlation between the size of the RIS reflection units and the overall concealment rate of the system. Performance improved with every 10-unit increase in the number of units, validating the core value of RIS in breaking through traditional performance boundaries by expanding spatial degrees of freedom.

[0171] Figure 6 The impact of concealment constraint strength on communication performance was analyzed. The stricter the concealment constraint, the lower the system's transmission concealment rate. This is because the power requirement to meet the concealment constraint reduces the power demand for communication.

[0172] Figure 7 This illustrates the trade-off between the required sensing accuracy and the communication stealth rate. The more stringent the system's sensing requirements, the lower the system's transmission stealth rate, also due to power allocation considerations.

[0173] Based on the embodiments of the present invention, any modifications, equivalent substitutions, improvements, etc., made by all other embodiments obtained by those skilled in the art without creative effort should be included within the protection scope of the present invention.

Claims

1. A robust beamforming method integrating anti-interference covert communication and sensing, characterized in that: The steps of the method are: S1, a system model is established, in the system, the base station BS transmits communication and sensing signals, the jammer transmits interference signals, there are K communication users and one sensing target; let the sensing target be an eavesdropper, trying to detect whether there is communication behavior between the base station and the communication user; S2, the channel model under the imperfect transmission environment, the sensing detection probability index, the covert transmission index and the transmission covert rate are described, under the constraint conditions of satisfying the transmission robustness, the covert communication security, the sensing accuracy and the RIS phase shift, the base station communication and sensing beamforming and RIS beamforming are jointly optimized, and the total transmission covert rate of the system is maximized; S3: based on fractional programming and quadratic transformation technology, combined with the alternating direction multiplier method, a robust beamforming method is proposed.

2. The robust beamforming method for integrated anti-interference covert communication and sensing as described in claim 1, characterized in that: In the step S1, the base station BS sends signals, which are expressed as: where the optimization variables is a communication beamforming vector for the kth user, is a sensing beamforming vector; In order to express the imperfect channel model, the channels between each system are expressed as: wherein are known channels, both subject to a Rice distribution, are the uncertainties of the respective channel parts; In addition to considering channel imperfections, the case of imperfect RIS phase shifts is considered, with the phase imperfection error distribution of the RIS being Therefore, the RIS phase shift with phase shift error is represented as: wherein is the phase of the RIS, is the phase error; such that: ； ； ； 。 3. The method of claim 2, wherein the method further comprises: The signal received by the kth user is in the form of: wherein Hkis the channel from the kth user to the base station, Hris the channel from the RIS to the kth user, S is the communication signal, S is the sensing signal, Hmis the jammer-to-user interference channel, Hmis the jammer-to-RIS interference channel, then the signal-to-interference-plus-noise ratio for the kth user can be expressed as: ； The received sensing signal echo at the base station is: wherein is a channel from the base station to the sensing target, is a channel from the jammer to the base station, is noise received at the base station; According to the generalized likelihood ratio test and the Neyman-Pearson criterion, the base station has a detection probability for the sensing target : wherein is the false alarm probability, is denoted as a non-central chi-squared cumulative distribution function with 2 degrees of freedom, defined as The key parameter in the detection probability is denoted as: wherein , ; For the sensing sensing target, that is, the signal received by the eavesdropper is expressed as: The perception target, i.e. the signal received by the eavesdropper, is denoted as:

4. The method of claim 3, wherein the method further comprises: To conceal the communication means to make the eavesdropper perceive that there is no communication behavior between the base station and the communication user, from the false alarm probability and the missed alarm probability Departing from the fact that the probability of both is the largest, the false alarm probability and the missed alarm probability are defined as follows: The optimal decision threshold is expressed as: wherein The corresponding detection probability is: The average detection error probability is expressed as: observable is monotonically increasing; thus it is expressed as: 。 5. The method of claim 4, wherein the method further comprises: The deterministic expression of the imperfect channel and the deterministic expression of the imperfect RIS phase shift are established; first, the uncertainty of the channel can be expressed as: wherein is the channel error range; Further, to characterize these channel uncertainties, define To control these uncertainty factors, define The channel expression is updated as: The optimization problem of maximizing the minimum transmission rate under the constraints of the base station transmission power, sensing, concealment, imperfect RIS phase shift is established, which is expressed as: 。 6. The method of claim 5, wherein the method further comprises: Focus on the mean and variance of the imperfect RIS beamforming matrix, which are expressed as:

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