Auxiliary covert communication method and system based on movable antenna

Abstract

The invention provides an auxiliary covert communication method and system based on a movable antenna, and belongs to the technical field of covert communication, and the system comprises a transmitting end equipped with a linear movable antenna array, a receiving end and a monitor. The positions of array elements in the linear movable antenna array can be independently adjusted in a one-dimensional feasible region with a certain length; constructing a receiving signal model and a signal-to-noise ratio expression of a receiving end as system performance indexes; the method comprises the following steps: deducing an optimal detection threshold value and a corresponding minimum detection error probability based on a strategy that a monitor adopts radiometer detection under bounded noise uncertainty, and taking the minimum detection error probability as a concealment constraint; constructing a joint optimization problem aiming at maximizing the signal-to-noise ratio of a legal receiving end; solving the joint optimization problem to obtain an optimal system parameter meeting the concealment constraint and the physical constraint; and carrying out covert communication according to the solved optimal parameter. According to the invention, better transmission performance can be obtained under hidden constraints.

Description

Technical Field

[0001] This invention belongs to the field of covert communication technology, and in particular relates to an auxiliary covert communication method and system based on a movable antenna. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Covert communication differs from traditional point-to-point communication in that it involves a monitor attempting to detect the communication activity. Covert communication requires not only improving the communication performance of the legitimate receiver but also strictly adhering to covertness constraints, ensuring that the monitor's error probability is not lower than a given threshold. Movable antennas can be locally moved within a feasible area, thereby reshaping the wireless channel. By adjusting the antenna position, the transmitter can more effectively align with the desired channel direction, thus improving beamforming gain, mitigating multipath fading, and improving channel conditions.

[0004] However, in covert communication scenarios, since the detector's performance is also affected by the spatial characteristics of the transmitted signal, expanding the movable area, while enhancing the receiver's channel quality, may inadvertently improve the detector's capabilities. Specifically, as the movable area increases, the distribution range of the transmitting antenna in space widens, and the statistical characteristics observed by the detector also change. Under the noise uncertainty model, the minimum detection error probability of the detector exhibits a non-monotonic relationship with the size of the movable area, meaning that a larger movable area is not necessarily beneficial for satisfying the covertness constraint. To maintain covert communication conditions, the transmitter may have to reduce its transmission power, thereby weakening the receiver's performance. Due to this trade-off between legitimate link gain and detection risk, the conclusion that "the larger the area, the better" in traditional point-to-point communication no longer applies in covert communication scenarios. Furthermore, most existing research methods use AO iteration to solve the movable antenna location problem, often getting stuck in local extrema, making it even more difficult to explain whether a larger feasible area is always advantageous. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention proposes an auxiliary covert communication method and system based on a movable antenna. This addresses the technical problem that the traditional approach of simply expanding the movable range of a fixed-position antenna / array in covert communication may fail, and that there is a lack of systematic characterization of the coupling relationship between the "feasible domain size of the movable antenna (MA), the detection performance of the monitor, and the legal link rate".

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: In a first aspect, the present invention discloses an auxiliary covert communication method based on a movable antenna, the method being applied to a covert communication system comprising a transmitter, a receiver, and a monitor equipped with a linear movable antenna array; wherein each element in the linear movable antenna array can independently adjust its position within a one-dimensional feasible domain of a certain length; Construct the received signal model and signal-to-noise ratio expression at the receiver end as a system performance indicator; Based on the strategy of using radiometer detection by the monitor under bounded noise uncertainty, the optimal detection threshold and the corresponding minimum detection error probability are derived, and the minimum detection error probability is used as a concealment constraint. A joint optimization problem is constructed with the objective of maximizing the signal-to-noise ratio of the legitimate receiver. The optimization variables include the transmit power of the transmitter, the beamforming vector, the position of each movable antenna, and the length of the feasible antenna region. The joint optimization problem is solved to obtain the optimal system parameters under the constraints of concealment and physical constraints. Covert communication is then performed based on the obtained optimal parameters.

[0007] A further technical solution is that the linear movable antenna array has the following array response vector for each propagation path:

[0008] in, The wavelength of the communication signal; ,…, Equip Alice The location of the antenna; For the first transmission node from the sender to the propagation node The propagation direction angle of the path; This is a transpose.

[0009] A further technical solution is to formulate the joint optimization problem as follows:

[0010]

[0011]

[0012]

[0013]

[0014] in, This refers to the location of the movable antenna; For beamforming vectors; This refers to the transmission power of the transmitting end; The feasible range for a movable antenna; This is the channel vector from the transmitter to the receiver; This represents the noise power at the receiving end. This represents the minimum distance between adjacent antennas. , This refers to the location of the movable antenna; This refers to the number of movable antennas; This represents the minimum probability of a listener making a detection error. This is the threshold for tolerable performance loss.

[0015] A further technical solution is that the minimum detection error probability of the eavesdropper is a monotonically decreasing function of the eavesdropper's total detection error rate, and the concealment constraint is expressed as:

[0016] Among them, let:

[0017] in, The complex gain of the l-th path from the transmitter to the monitor; For the sending end to the monitor The propagation direction angle of the path; express The conjugate; The number of paths from the sender to the monitor; The wavelength of the communication signal.

[0018] A further technical solution employs the differential evolution method to solve the joint optimization problem, specifically: Step S4-2-1: Randomly generate Potential antenna location vectors ,in ,and Each element represents a movable antenna position; Step S4-2-2: For each movable antenna location, from Randomly select three more position vectors from the given vectors to obtain the updated vector; Step S4-2-3: For each updated vector, first randomly select an index, and then further update each element of the position vector to generate a new position vector; Step S4-2-4: If the above two steps result in the new position vector not satisfying the constraints of avoiding coupling effects and the movable antenna position being within the feasible region, then the elements of the new position vector can be updated according to the following equation:

[0019] in, For the new position vector; The feasible range for a movable antenna; This represents the minimum distance between adjacent antennas. Step S4-2-5: Continue updating until all updates are complete. After identifying the position vectors, find the position vector that yields the maximum objective function value; repeat steps S4-2-2 to S4-2-4 until the maximum number of iterations is reached. Or, the termination condition is met.

[0020] A further technical solution is that the signal-to-noise ratio of the receiving end is:

[0021] in, This refers to the transmit power of the transmitting end; This is the channel vector from the transmitter to the receiver; For beamforming vectors; This represents the noise power at the receiving end.

[0022] A further technical solution is proposed, where the minimum detection error probability for the monitor is:

[0023] in, for The mean, The transmit power of the transmitting end. The channel vector from the transmitter to the monitor. For beamforming vectors; This represents the lower bound of the noise distribution. This represents the upper bound of the noise distribution.

[0024] Secondly, the present invention discloses an auxiliary covert communication system based on a movable antenna, comprising a transmitter, a receiver, and a monitor equipped with a linear movable antenna array; each element in the linear movable antenna array can independently adjust its position within a one-dimensional feasible domain of a certain length; The indicator construction module is used to construct the received signal model and signal-to-noise ratio expression at the receiver end, which serve as system performance indicators. The constraint calculation module is used to derive the optimal detection threshold and the corresponding minimum detection error probability based on the monitor's strategy of using radiometer detection under bounded noise uncertainty, and to use the minimum detection error probability as a concealment constraint. The joint optimization module is used to construct a joint optimization problem with the goal of maximizing the signal-to-noise ratio of the legitimate receiver. The optimization variables include the transmit power of the transmitter, the beamforming vector, the position of each movable antenna, and the length of the feasible antenna region. The module solves the joint optimization problem to obtain the optimal system parameters under the constraints of concealment and physical constraints. Covert communication is then performed based on the obtained optimal parameters.

[0025] Thirdly, the present invention discloses an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, complete the steps of the above-described auxiliary covert communication method based on a movable antenna.

[0026] Fourthly, the present invention discloses a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the above-described assisted covert communication method based on a movable antenna.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention proposes a method for narrowing the search space of the optimal feasible region based on non-monotonicity: firstly, utilizing... The strategy filters out invalid intervals by identifying local minima and then forms the final candidate set. This strategy significantly reduces the complexity of the outer search without sacrificing optimality, making the joint optimization of "feasible region-power-location" more computationally feasible and efficient.

[0028] In terms of power control, this invention utilizes an explicit monotonic relationship: the legitimate receiver target follows... Monotonically increasing, while the hidden constraints Follow The solution is monotonically decreasing, therefore the optimal solution must satisfy the boundary conditions. This allows the optimal transmit power to be determined directly by solving this equation, thus avoiding blind traversal along the power dimension, further improving solution efficiency and ensuring that the hidden constraints are strictly satisfied.

[0029] This invention demonstrates that the minimum detection error probability of a listener is independent of the transmitted beam vector, thus the beam can be focused on enhancing the quality of legitimate reception. Based on this, the maximum ratio transmission can improve the signal-to-noise ratio at the receiver without weakening the stealth. This "decoupling of stealth constraints and beam design" structure makes the system design clearer and the implementation simpler.

[0030] To address the non-convex and strongly coupled characteristics of array element position optimization, this invention employs a differential evolution algorithm for solution, along with repair and projection to force candidate solutions back to the feasible region, ensuring that each iteration satisfies boundary and minimum spacing constraints, thereby obtaining stable and achievable array element layout results.

[0031] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0032] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0033] Figure 1 This is a schematic diagram of the covert communication model described in Embodiment 1 of the present invention.

[0034] Figure 2 This is a graph showing the performance comparison results of the algorithm described in Embodiment 1 of the present invention.

[0035] Figure 3 This is a process diagram of the optimal feasible region described in Embodiment 1 of the present invention.

[0036] Figure 4 This is a performance comparison chart of optimizing other system parameters given a feasible region of MA, as described in Embodiment 1 of the present invention. Detailed Implementation

[0037] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0038] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0039] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0040] Terminology Explanation: Covert communication: By embedding secret signals into ambient noise or legitimate traffic, making them statistically indistinguishable from noise. Unlike traditional methods that only protect the message content, it hides the existence of the transmission itself, thus providing greater security.

[0041] Movable antenna: The antenna is no longer fixed in a single location, but can be moved within a small, controllable range (such as sliding along a straight line or a two-dimensional plane) within a preset feasible area. By adjusting the antenna position, the system can actively change the geometric relationship between the receiver / transmitter and the environmental scattering objects, thereby "reshaping" the instantaneous wireless channel and achieving better signal enhancement, interference suppression, or security performance improvement.

[0042] The key advantage of movable antennas lies in their ability to be locally moved within a feasible region, thereby reshaping the wireless channel. From a spatial degree of freedom perspective, an expanded movable region means an increased set of possible antenna locations, allowing the system to search for optimal antenna position combinations over a larger spatial area. By adjusting the antenna position, the transmitter can more effectively align with the desired channel direction, thereby improving beamforming gain, mitigating multipath fading, and improving channel conditions. Therefore, in point-to-point communication scenarios that focus solely on legitimate communication links (such as the Alice–Bob link), a larger movable region typically does not result in performance loss but rather provides a higher performance ceiling for the system.

[0043] Secondly, in traditional point-to-point communication, the system optimization objective is usually to maximize the signal-to-noise ratio, throughput, or capacity at the receiver, without any constraints from third-party eavesdropping or detection. In this case, expanding the movable region only increases the feasible solution space and does not introduce additional performance penalties. Therefore, the conclusion that "the larger the movable region, the better" has been repeatedly verified and widely adopted in existing literature.

[0044] However, the above conclusions do not necessarily hold true in covert communication scenarios. Unlike traditional point-to-point communication, covert communication systems also involve a monitor, Willie, attempting to detect the communication activity. Therefore, in light of the technical problems described in the background, the question of "whether a larger feasible area is always advantageous" needs to be investigated, which leads to the direct motivation for this invention.

[0045] Example 1 In one or more embodiments, an assisted covert communication method based on a movable antenna is disclosed. This method is applied to a covert communication system comprising a transmitter, a receiver, and a monitor equipped with a linear movable antenna array; wherein each element in the linear movable antenna array can independently adjust its position within a certain length of a one-dimensional feasible domain, including: Step S1, as follows Figure 1 As shown, a covert communication model is constructed.

[0046] This embodiment considers a covert communication scenario where the transmitter (Alice) wishes to transmit confidential information to the receiver (Bob) in the presence of the monitor (Willie). Both the receiver and the monitor are equipped with a single antenna, while the transmitter is equipped with a linear movable antenna (MA) array containing N elements.

[0047] In this embodiment, it is assumed that the positions of each antenna can be within a length of The adjustments can be made flexibly and independently on a one-dimensional line segment. This embodiment uses a two-dimensional coordinate system and arranges the linear array along the x-axis. Therefore, the positions of these movable antennas are represented as... The system employs a far-field propagation model; therefore, for each propagation path, the angles from all N mobile antennas to Bob and Willie are considered the same. Specifically, consider the angle from Alice to the node... exist There are several transmission paths, among which and Let represent the number of paths in the Alice-Bob link and the Alice-Willie link, respectively. For the first The effective angles of the path, among which , . No. The array response vector for each path is: (1) in, The wavelength of the communication signal; ,…, Equip Alice The location of the antenna; For Alice to propagate to the node The propagation direction angle of the path; This is the transpose. Correspondingly, the channel vector from Alice to node t can be expressed as: (2) in, The propagation nodes represent Bob and Willie, respectively. This indicates the number of paths from Alice to the propagation node. Indicates the number of nodes from the sender to the node. Complex path gain of a propagation path.

[0048] Step S2: Construct the received signal model and signal-to-noise ratio expression for the receiver as a system performance indicator.

[0049] When the sending end sends a signal, the receiving end receives the following signal: (3) in, The symbols selected from the complex signal constellation satisfy the average power constraint. Use an index for the channel. This represents the total number of channel uses. Additionally, The beamforming vector for the concealed information signal satisfies , Let be the transmit power of the transmitting end. For ease of representation, it is defined as: (4) in, and These represent beamforming vectors respectively. The amplitude and phase; The additive white Gaussian noise (AWGN) at the receiver follows the... ,in Let be the noise power at the receiver. The signal-to-noise ratio (SNR) at the receiver is: (5) in, This refers to the transmission power of the transmitting end; This is the channel vector from Alice to Bob.

[0050] Step S3: Based on the monitor's strategy of using a radiometer for detection under bounded noise uncertainty, derive its optimal detection threshold and the corresponding minimum detection error probability, and use the minimum detection error probability as a concealment constraint.

[0051] In covert communication, monitors attempt to rely on observation sequences To determine whether the sending end has sent a signal to the receiving end, This is the signal received by the monitor during the first use of the channel. and Let each represent one of the two assumptions: whether the transmitter sends a signal or not. Then we have... (6) in, For the AWGN at the monitor's location, obey In real-world environments, wireless transceivers may be affected by varying noise (such as random interference), leading to noise uncertainty. This paper employs a bounded noise uncertainty model, assuming the noise power of the monitor... In the interval [ , It is uniformly distributed on [the surface]. Specifically, its probability density function is: (7) in, This represents the lower bound of the noise distribution. This represents the upper bound of the noise distribution.

[0052] This embodiment assumes that the monitor uses a radiometer as a detector. The channel is used a sufficiently large number of times ( The average received signal power at the monitor is: (8) in, Let be the channel vector from Alice to Willie; then the decision rule for the monitor Willie is: (9) in, To detect threshold, and These represent Willie's judgment on whether Alice has sent a signal. Formula (9) is the likelihood ratio decision rule for the monitor Willie: compare the probability density when there is a secret signal with that when there is only noise, and if the ratio exceeds the threshold, it is determined that there is a transmission.

[0053] In covert communication, Willie's total detection error rate Used to measure the stealth of a system. Generally speaking, ,in This represents the probability of a false alarm. This represents the probability of a missed detection. Willie will optimize to minimize the detection error rate. .exist and Under the assumption of equal prior probabilities, the concealment constraint is: ,in A small positive number indicates the system's concealment level.

[0054] Channel vectors from Alice to Bob and from Alice to Willie and Highly dependent on the specific location of the movable antenna In this embodiment, it is assumed that Willie knows that, except for Beyond the channel All parameters, therefore For Willie, this is a random variable. Furthermore, it is assumed that Willie is unaware of the beamforming vector. ,and May depend on .therefore, For Willie, it is a random variable, and its detection performance limit is given in the following formula: (10) in, This represents the lower bound of the noise distribution. This represents the upper bound of the noise distribution; for The mean, given as: (11) in, express The conjugate; Let L be the complex gain of the l-th path from Alice to Willie; For Alice to Willie The propagation direction angle of the path; This represents the number of paths from Alice to Willie.

[0055] Step S4: Construct a joint optimization problem with the objective of maximizing the signal-to-noise ratio of the legitimate receiver. The optimization variables include the transmit power of the transmitter, the beamforming vector, the position of each movable antenna, and the length of the feasible antenna region. Solve the joint optimization problem to obtain the optimal system parameters under the constraints of concealment and physical constraints. Perform covert communication based on the obtained optimal parameters.

[0056] Step S4-1: Construct a joint optimization problem with the goal of maximizing the signal-to-noise ratio of the legitimate receiver.

[0057] The objective of this embodiment is to optimize the MA position jointly under conditions of concealment and other inherent constraints. Beamforming vector Alice's transmission power and the feasible range of MA To maximize the SNR from Alice to Bob, the optimization problem can be formulated as follows: (12) (13) (14) (15) (16) (17) Among them, constraint (13) restricts the minimum distance between adjacent antennas. To avoid coupling effects, , The location of the movable antenna. For the number of movable antennas, (14) ensure that the MA location is within the feasible area, and (15) define the maximum feasible range of the MA. The constraints are as follows: (16) represents Alice's beamforming constraint, and (17) represents the concealment constraint. This is the threshold for tolerable performance loss.

[0058] By controlling To satisfy the implicit constraint, the optimization problem (P1) is always feasible. Furthermore, This does not affect any constraints in (P1), therefore the optimal value can be obtained. for Alice's optimal strategy is to use maximum ratio transmission (MRT) for Bob. The optimal values ​​for other system parameters will be determined later.

[0059] As mentioned earlier, for a given , optimal for The objective function varies with Monotonically increasing; while Follow Monotonically decreasing. Therefore, in the solution of the original optimization problem (P1), constraint (17) must be equal. Therefore, (P1) can be rewritten as: (18) (19) (20) (twenty one) (twenty two) According to formula (10), the minimum detection error probability yes It is a monotonically decreasing function. Therefore, constraint (22) can be written as Among them, let: (twenty three) and, Is to make When it was established Therefore, in the solution to the optimization problem (P2), we have... The objective function is about It is a monotonically increasing function, thus yielding two conclusions about the solution (P2).

[0060] Conclusion 1: For a fixed ,because , A smaller value will result in a higher value for the objective function.

[0061] Conclusion 2: For a given Take a larger value Typically, (P2) will result in a higher objective function value.

[0062] Furthermore, the two conclusions above are used to determine a significantly smaller optimal feasible region.

[0063] Step 1: First, identify all The minimum value is less than The values ​​of and the corresponding values ​​of these minimum values Recorded as Because according to conclusions 1 and 2, for all satisfying The minimum value, It can achieve a higher (or at least no lower) objective function value.

[0064] Step 2: What we got from Step 1 Determine its minimum value, and assign the value corresponding to that minimum value. Recorded as Then, exclude all that satisfy the condition. of Take values, because all of these All of these will lead to .

[0065] Step 3: In the remaining area Inside, identify again The minimum value, and the value corresponding to that minimum value Recorded as At this time, there are And it is possible to find a satisfactory one. and At the same time, it is closest in numerical value. of Record it as Ultimately, we can conclude that: This constitutes the surrounding of The feasible region, because according to conclusion 1, compared to satisfying of Values, It is a better candidate point.

[0066] Step 4: Replace with And repeat step three until the condition is met. The largest Recorded as This step can identify multiple [items / entities]. and The pairings yield multiple feasible regions. Finally, an additional feasible region is obtained, namely... .

[0067] Following the four steps outlined above, the final significantly reduced size can be determined. Feasible area, denoted as Furthermore, constraint (22) can be equivalently rewritten as Therefore, substituting this expression into the objective function, problem (P2) can be reformulated as: (twenty four) (25) (26) (27) Through Perform a numerical search within the range, for each fixed range. The corresponding optimization problem (P3) is solved through the following technical solution, and the overall optimal solution is finally obtained.

[0068] Step S4-2: Solve the joint optimization problem to obtain the optimal system parameters under the constraints of concealment and physical constraints.

[0069] This embodiment employs the Differential Evolution (DE) method to solve the optimization problem (P3), which is a non-convex optimization problem with highly coupled variables. Specifically, the DE method iteratively searches for and identifies solutions by performing mutation, crossover, and selection operations based on the differences between solutions between consecutive iterations. The main steps for solving (P3) using the DE method are as follows.

[0070] Step S4-2-1: Initialization.

[0071] First, generate randomly. Potential antenna location vectors ,in ,and Each element represents a MA position, i.e. Indicates the first The location of each antenna satisfies .

[0072] Step S4-2-2: Mutation.

[0073] For each From this Randomly select three other position vectors from the vectors (denoted as , ... , and ), to obtain the updated vector.

[0074] (28) in, This is a scaling factor used to control the magnitude of variation.

[0075] Step S4-2-3: Cross operation.

[0076] For each First, randomly select an index. Then, each element of the position vector is further updated, i.e. To generate a new position vector: (29) in, For each Randomly generated, obey Distributed random variables This is a preset threshold. Preferably, It is randomly selected before this step, therefore there is at least one. satisfy This ensures that for each All .

[0077] Step S4-2-4: Feasibility check.

[0078] If the above two steps lead to If constraints (25) and (26) are not satisfied, then the equations can be applied as follows: Update the elements: (30) Step S4-2-5: Iteration and Termination.

[0079] After updating all steps S4-2-2 to S4-2-4 as described above. After identifying the position vectors, the position vector that yields the maximum objective function value is determined (denoted as ). ), and record the corresponding objective function value as ,in , This is the maximum number of iterations. Then, steps S4-2-2 to S4-2-4 are repeated to update the new... and until the maximum number of iterations is reached. Or, the termination condition is met.

[0080] Step S4-3: Perform covert communication based on the optimal parameters obtained from the solution.

[0081] The above technical solution provides a joint optimization method for covert communication assisted by a movable antenna: introducing a linear MA array at the transmitting end, so that each array element can be positioned with a length of [missing information]. Within the one-dimensional feasible region, the position is independently adjusted to reshape the spatial channel and improve the link quality of legitimate receivers. Simultaneously, under the condition of noise uncertainty for the eavesdropper, an energy detection (radiometer) strategy is employed, deriving its optimal detection threshold and corresponding minimum detection error probability, which are then embedded as a concealment constraint into the system design, thus forming a joint optimization framework for transmit power, MA position, and feasible region. Analysis results show that the eavesdropper's minimum detection error probability is not only related to transmit power but also to the feasible region. The presence of non-monotonic dependency means that a larger feasible region for MA does not necessarily lead to better covert communication performance; the reason is that On the one hand, this expands the spatial degrees of freedom for the transmitter to shape legitimate channels; on the other hand, it may simultaneously enhance the detectability of eavesdroppers. Based on this finding, this paper further significantly narrows the optimal... By determining the search range and combining methods such as differential evolution to solve for the optimal array element positions, the SNR / rate of the legitimate receiver is improved while satisfying the concealment constraint.

[0082] The results show that, compared with the traditional design of "fixed feasible region or blindly taking the maximum feasible region", the proposed scheme can achieve better transmission performance under covert constraints, and provides a more refined, feasible and engineering-guiding design idea for MA-assisted covert communication systems.

[0083] This technical solution presents a key conclusion: expanding the feasible domain in covert communication. This does not necessarily improve system performance. The reason lies in the minimum probability of a listener making a detection error. Depends on ,and Based on transmission power Feasible domain Jointly decided; among them Follow Monotonically increasing, but with The relationship changes with relative position, thus leading to right It exhibits non-monotonicity. This discovery challenges the conventional intuition that "a larger range of motion is always better" and provides direct guidance for engineering design: It needs to be precisely selected rather than blindly taking the maximum value.

[0084] like Figure 2The figure illustrates the performance gap between the DE and AO algorithms, and also compares their performance with that of a fixed-position antenna (FPA). Firstly, the figure shows that the optimal gain achievable by FPA is far less than that of a movable antenna, thanks to the movable antenna's ability to reconstruct the channel. The figure also shows that the AO algorithm is prone to getting trapped in local optima, optimizing antenna positions at extreme points. However, in the movable antenna problem, due to coupling and range limitations, the optimal antenna position is not necessarily at an extreme point. As shown in the figure, the antenna position optimized by the DE algorithm is not at an extreme point, yet its performance far surpasses that obtained by the AO algorithm.

[0085] like Figure 3 As shown, the optimal feasible region is obtained by combining conclusions 1 and 2. The process diagrams correspond to... The first four steps of the acquisition process significantly reduce the amount of searching required. The size of the algorithm is reduced, thus decreasing the algorithm complexity. Figure 4 The shaded area is You can see the optimal It is in Among them.

[0086] Furthermore, numerical results are presented through experiments to verify the feasible region. The impact on the performance of the proposed covert communication system. This embodiment takes... , , , dBm and dBm. The minimum distance between two adjacent antennas is set to... And set the upper bound of the feasible region of the movable antenna array as Complex channel gain and All obey Specifically, such as Figure 4 The diagram shows the feasible region for a given MA. In this case, by optimizing other system parameters (e.g.) The maximum SNR achieved by Bob (denoted as ) ).like Figure 4 As shown, it can be seen that with the concealment parameter The reduction (i.e., the hidden constraints become more stringent). A significant reduction. This confirms that system performance is fundamentally limited by the concealment constraint, which directly restricts the allowable transmit power. This limits the rate that can be achieved at Bob.

[0087] In addition, Figure 4It was also observed that, Not following Monotonically increasing, which means overall optimal It may not be its maximum value. This verifies the correctness of the analysis in this invention. It should be noted that this conclusion differs from conclusions in general point-to-point wireless communication, where the latter has a greater... This typically results in higher communication rates. Intuitively, this is because, in the context of covert communication, It will also affect Willie's detection performance.

[0088] Example 2 In one or more embodiments, an auxiliary covert communication system based on a movable antenna is disclosed, including a transmitter, a receiver, and a monitor equipped with a linear movable antenna array; each element in the linear movable antenna array can independently adjust its position within a one-dimensional feasible domain of a certain length; The indicator construction module is used to construct the received signal model and signal-to-noise ratio expression at the receiver end, which serve as system performance indicators. The constraint calculation module is used to derive the optimal detection threshold and the corresponding minimum detection error probability based on the monitor's strategy of using radiometer detection under bounded noise uncertainty, and to use the minimum detection error probability as a concealment constraint. The joint optimization module is used to construct a joint optimization problem with the goal of maximizing the signal-to-noise ratio of the legitimate receiver. The optimization variables include the transmit power of the transmitter, the beamforming vector, the position of each movable antenna, and the length of the feasible antenna region. The module solves the joint optimization problem to obtain the optimal system parameters under the constraints of concealment and physical constraints. Covert communication is then performed based on the obtained optimal parameters.

[0089] Example 3 This embodiment provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, they complete the steps of the above-described assisted covert communication method based on a movable antenna.

[0090] Example 4 This embodiment provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the aforementioned assisted covert communication method based on a movable antenna.

[0091] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0092] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0093] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0094] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0095] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for assisted covert communication based on a movable antenna, characterized in that, include: The method is applied to covert communication systems comprising a transmitter, a receiver, and a monitor equipped with a linear movable antenna array; Each element in the linear movable antenna array can independently adjust its position within a certain length of a one-dimensional feasible domain. Construct the received signal model and signal-to-noise ratio expression at the receiver end as a system performance indicator; Based on the strategy of using radiometer detection by the monitor under bounded noise uncertainty, the optimal detection threshold and the corresponding minimum detection error probability are derived, and the minimum detection error probability is used as a concealment constraint. A joint optimization problem is constructed with the objective of maximizing the signal-to-noise ratio of the legitimate receiver. The optimization variables include the transmit power of the transmitter, the beamforming vector, the position of each movable antenna, and the length of the feasible antenna region. The joint optimization problem is solved to obtain the optimal system parameters under the constraints of concealment and physical constraints. Covert communication is then performed based on the obtained optimal parameters.

2. The assisted covert communication method based on a movable antenna as described in claim 1, characterized in that, The linear movable antenna array has the following array response vector for each propagation path: in, The wavelength of the communication signal; ,…, Equip Alice The location of the antenna; For the first transmission node from the sender to the propagation node The propagation direction angle of the path; This is a transpose.

3. The assisted covert communication method based on a movable antenna as described in claim 1, characterized in that, The joint optimization problem is expressed as follows: in, This refers to the location of the movable antenna; For beamforming vectors; This refers to the transmission power of the transmitting end; The feasible range for a movable antenna; This is the channel vector from the transmitter to the receiver; This represents the noise power at the receiving end. This represents the minimum distance between adjacent antennas. , This refers to the location of the movable antenna; This refers to the number of movable antennas; This represents the minimum probability of a listener making a detection error. This is the threshold for tolerable performance loss.

4. The assisted covert communication method based on a movable antenna as described in claim 3, characterized in that, The minimum detection error probability of the eavesdropper is a monotonically decreasing function of the eavesdropper's total detection error rate, and the concealment constraint is expressed as: Among them, let: in, The complex gain of the l-th path from the transmitter to the monitor; For the sending end to the monitor The propagation direction angle of the path; express The conjugate; The number of paths from the sender to the monitor; The wavelength of the communication signal.

5. The assisted covert communication method based on a movable antenna as described in claim 1, characterized in that, The joint optimization problem is solved using the differential evolution method, specifically: Step S4-2-1: Randomly generate Potential antenna location vectors ,in ,and Each element represents a movable antenna position; Step S4-2-2: For each movable antenna location, from Randomly select three more position vectors from the given vectors to obtain the updated vector; Step S4-2-3: For each updated vector, first randomly select an index, and then further update each element of the position vector to generate a new position vector; Step S4-2-4: If the above two steps result in the new position vector not satisfying the constraints of avoiding coupling effects and the movable antenna position being within the feasible region, then the elements of the new position vector can be updated according to the following equation: in, For the new position vector; The feasible range for a movable antenna; This represents the minimum distance between adjacent antennas. Step S4-2-5: Continue updating until all updates are complete. After identifying the position vectors, find the position vector that yields the maximum objective function value; repeat steps S4-2-2 to S4-2-4 until the maximum number of iterations is reached. Or, the termination condition is met.

6. The assisted covert communication method based on a movable antenna as described in claim 1, characterized in that, The signal-to-noise ratio of the receiving end is: in, This refers to the transmit power of the transmitting end; This is the channel vector from the transmitter to the receiver; For beamforming vectors; This represents the noise power at the receiving end.

7. The assisted covert communication method based on a movable antenna as described in claim 1, characterized in that, The minimum detection error probability of the monitor is: in, for The mean, The transmit power of the transmitting end. The channel vector from the transmitter to the monitor. For beamforming vectors; This represents the lower bound of the noise distribution. This represents the upper bound of the noise distribution.

8. An auxiliary covert communication system based on a movable antenna, characterized in that, It includes a transmitter, a receiver, and a monitor equipped with a linear movable antenna array; each element in the linear movable antenna array can independently adjust its position within a one-dimensional feasible domain of a certain length; The indicator construction module is used to construct the received signal model and signal-to-noise ratio expression at the receiver end, which serve as system performance indicators. The constraint calculation module is used to derive the optimal detection threshold and the corresponding minimum detection error probability based on the monitor's strategy of using radiometer detection under bounded noise uncertainty, and to use the minimum detection error probability as a concealment constraint. The joint optimization module is used to construct a joint optimization problem with the goal of maximizing the signal-to-noise ratio of the legitimate receiver. The optimization variables include the transmit power of the transmitter, the beamforming vector, the position of each movable antenna, and the length of the feasible antenna region. The module solves the joint optimization problem to obtain the optimal system parameters under the constraints of concealment and physical constraints. Covert communication is then performed based on the obtained optimal parameters.

9. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the assisted covert communication method based on a movable antenna as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the assisted covert communication method based on a movable antenna as described in any one of claims 1-7.

Images