Hidden information age optimization method based on time modulation array

Abstract

The invention discloses a hidden information age optimization method based on a time modulation array, and aims to minimize average hidden information age CAoI by optimizing beam forming parameters and block length so as to improve the concealment of hidden communication and the timeliness of information. According to the method, beam forming is achieved through a time modulation array scheme and a radio frequency switch, Kullback-Leibler (KL) divergence is introduced to serve as concealment measurement, meanwhile, the average concealed information age (CAoI) is further deduced, and communication concealment and timeliness performance are comprehensively explained. On the basis, an optimization scheme is provided, and the problem of average CAoI minimization under the concealment constraint is solved by using a cuckoo search algorithm. Experimental results show that the TMA scheme is obviously superior to a traditional phased array (PA) scheme in the aspects of convergence rate and average CAoI, the hardware complexity is reduced, the flexibility of beam forming is improved, and the discovery provides a new view angle and method for optimization of a covert communication system.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communication, and in particular to a concealed information age optimization method based on a time modulation array. Background Art

[0002] With the widespread application of IoT devices, network information security and the timeliness of information transmission have become the core issues of IoT communication. Covert communication, as a technology to ensure the secure transmission of information, aims to transmit information without being detected. However, existing covert communication systems usually rely on multi-antenna arrays such as phased array (PA) technology. Although they can achieve high concealment, their hardware complexity and energy consumption are high, making it difficult to adapt to the low power consumption and low complexity requirements of IoT devices. Time-modulated array (TMA) can achieve low-complexity and efficient beamforming by periodically modulating RF switches. This technology can significantly reduce hardware costs while maintaining high concealment and communication performance.

[0003] In addition, the timeliness problem of existing covert communications has not been effectively solved. The age of information (AoI) reflects the timeliness of information, and existing technologies are difficult to provide better timeliness while ensuring concealment. Therefore, a technical solution is needed that can improve the concealment and timeliness of information transmission while reducing system complexity and power consumption. Summary of the invention

[0004] The purpose of the present invention is to provide a concealed information age optimization method based on a time modulation array to address the problems existing in the above-mentioned prior art. The method minimizes the average concealed age of information (CAoI) by optimizing beamforming parameters and packet length, thereby improving the concealment of covert communication and the timeliness of information. A closed expression of the Kullback-Leibler (KL) divergence is derived as a concealment constraint, and the average CAoI is obtained on this basis. Based on this, an optimization scheme is proposed, and the cuckoo search (CS) algorithm is used to solve the problem of minimizing the average CAoI under the concealment constraint.

[0005] The technical solution to achieve the purpose of the present invention is: a hidden information age optimization method based on a time modulation array, the method comprising the following steps:

[0006] Step 1, construct a covert communication system architecture based on a time modulation array as a transmitter; the covert communication system architecture includes a transmitter Alice, a receiver Bob, and an eavesdropper Willie, the transmitter transmits a covert signal through a time modulation array, and each antenna element of the transmitter is controlled by a radio frequency switch, and the radio frequency switch realizes beamforming through a time series modulation signal;

[0007] Step 2, using KL divergence as a measure of communication concealment, establish a performance optimization function for the covert communication system to minimize the average age of concealed information CAoI;

[0008] Step 3: Use the cuckoo search algorithm to solve the performance optimization function of the covert communication system and obtain the beamforming parameter combination corresponding to the minimized CAoI.

[0009] Furthermore, the architecture of the covert communication system described in step 1 is specifically as follows: the transmitting end is under the control of the signal processor, and the transmission signal is generated by a digital-to-analog converter; then, the generated transmission signal is combined with the local oscillator signal, and modulated by a time modulator after passing through a power amplifier; each antenna is connected to a time modulator, and all time modulators are supervised by a signal processor; in each time modulator, the RF signal is divided into two branches: I and Q, each branch has a variable gain amplifier VGA, and the Q path has a π / 2 phase shifter, and the signal processor controls the timing and amplitude of the VGA; finally, the signals on the I and Q paths are combined into an RF signal output.

[0010] Furthermore, the communication channel of the covert communication system in step 1 is modeled as a quasi-static Rician channel.

[0011] Furthermore, the received signal at the receiving end Bob is expressed as:

[0012]

[0013] In the formula, y ab [i] is the signal received by Bob on the i-th channel, x[i] is the transmitted signal of Alice on the i-th channel, using Gaussian codebook, d ab is the distance between Alice and Bob, κ is the coefficient; represents Bob’s steering vector, k represents the wave number, d represents the space of array elements, and θ represents the angle of Bob relative to Alice; represents the complex Gaussian noise at Bob on the ith channel; α represents the path attenuation; σ 2 represents the noise power, Φ TM represents the beamforming vector; represents the equivalent fading coefficient from Alice to Bob, where represents the Rician channel scattering component from Alice's mth antenna to Bob, m = 1, 2, ..., M, M is the total number of Alice's antennas; P a is Alice’s transmit power, I is the channel number, I = 1, 2, ..., N, N is the total number of channels;

[0014] The total gain of the Rician channel is expressed as H ab :

[0015]

[0016] The signal-to-noise ratio (SNR) at the receiving end Bob is

[0017]

[0018] in, and represents the amplitude weight of the mth antenna; u=TM, represents the time modulation array.

[0019] Furthermore, the signal received by the eavesdropper Willie is expressed as:

[0020]

[0021] in, is the signal received by Willie on the i-th channel, is the null hypothesis, that is, Alice does not send a signal; For the alternative hypothesis, Alice sends a signal, represents the complex Gaussian noise at Willie on the ith channel, d aw is the distance between Alice and Willie, represents the fading coefficient from Alice to Willie, represents the Rician channel scattering component from Alice’s mth antenna to Willie;

[0022] Willie's signal-to-noise ratio is

[0023]

[0024] in Represents the amplitude weight of the mth antenna.

[0025] Furthermore, the total detection error probability at the eavesdropper Willie is It is expressed as:

[0026]

[0027] And the following constraints must be met:

[0028]

[0029] Among them, the false alarm probability Missed detection probability They are:

[0030]

[0031] in The likelihood ratio test value corresponding to the optimal threshold μ = ρ0 / ρ1 is the LRT value, which is expressed as:

[0032]

[0033] in,

[0034]

[0035] Where ρ0 represents the prior probability that Alice does not transmit, and ρ1 represents the prior probability that Alice transmits. represents the minimum total detection error probability, ε is the preset concealment tolerance level, and Respectively represent and Willie's decision. and and are respectively expressed in and The probability distribution of Willie's observation value is shown in Figure 1, where Pr represents the received signal power.

[0036] Furthermore, the process of implementing beamforming in step 1 includes:

[0037] Establish the switching function of the mth antenna at the time modulation array at time t

[0038]

[0039] In the formula, and are the gain control time series of I and Q paths of each time modulator at time t respectively;

[0040] By design and The switching time and amplitude are adjusted to achieve beamforming of covert signals.

[0041] Furthermore, the performance optimization function of the covert communication system in step 2 is:

[0042]

[0043] Where constraint c1 is the covert communication constraint obtained using KL divergence, and Respectively expressed in and The probability distribution of Willie's observations under for and The KL divergence between Indicates taking the mean value; represents the probability of covert communication interruption; represents the average packet error probability; ρ0 represents the prior probability that Alice does not transmit, ρ1 represents the prior probability that Alice transmits; N represents the communication packet length, N min 、N max They represent the minimum packet length and the maximum packet length respectively; ε is the preset concealment tolerance level; E is the total number of switch time states; is the probability of covert communication interruption; W represents the system bandwidth; Indicates the sth state of the RF switch corresponding to the mth antenna, and S indicates the total number of RF switch state types.

[0044] Furthermore, the covert communication interruption probability The upper bound of is:

[0045]

[0046] In the formula, μ aw and μ ab Respectively |h aw | 2 and |h ab | 2 The average value of .

[0047] Furthermore, in step 3, the performance optimization function of the covert communication system is solved by using the cuckoo search algorithm to obtain a beamforming parameter combination corresponding to minimizing CAoI, which specifically includes:

[0048] Initialize the search space: define all possible beamforming parameter combinations, including the sth state of the RF switch corresponding to the antenna and the communication packet length N;

[0049] Initializing the fitness function: setting the performance optimization function of the covert communication system to be the fitness function;

[0050] CS algorithm search: Find the optimal beamforming parameter combination through random search using the Levy flight strategy;

[0051] Select the optimal solution: After multiple iterations, select the optimal beamforming parameter combination that minimizes the age of the hidden information and N, thereby pseudo-randomly generating the switching sequence of the time modulation array.

[0052] Compared with the prior art, the present invention has the following significant advantages:

[0053] (1) The present invention improves the age of information (AoI) performance of covert communication by reducing hardware complexity. The TMA scheme uses RF switches instead of phase shifters to achieve beamforming, which reduces hardware complexity and improves the flexibility of beamforming. The present invention designs the switch state of TMA to obtain an equivalent synthetic beamforming vector to control the radiation pattern.

[0054] (2) The present invention uses Kullback-Leibler (KL) divergence to quantitatively describe the concealment of communication, and derives the closed expression of KL divergence under TMA and PA schemes. The concealment detection model based on KL divergence can effectively prevent the communication from being detected by eavesdroppers.

[0055] (3) The present invention proposes and solves a problem of minimizing the average CAoI by adjusting the communication packet length and beamforming parameters. The cuckoo search algorithm is used for optimization and solution. By optimizing the CAoI index, it is ensured that the transmitted data packet is the latest data, thereby improving the timeliness of information transmission.

[0056] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the covert communication system architecture in one embodiment.

[0058] FIG. 2( a ) is a system architecture diagram based on TMA in an embodiment of the present invention.

[0059] FIG. 2( b ) is a diagram of a conventional TMA-based system architecture in an embodiment.

[0060] Figure 3 FIG. 4 is a schematic diagram of a switching sequence of a TMA and a result vector in an embodiment.

[0061] Figure 4 FIG. 4 is a schematic diagram of information age in an embodiment.

[0062] Figure 5 The figure is a schematic diagram of the relationship between the minimum average CAoI and the number of iterations when ρ1=0.5 in an embodiment.

[0063] Figure 6 In one embodiment, the conventional PA scheme is used to adjust the amplitude |αm | and phase β m Optimization result diagram.

[0064] Figure 7 The figure is a schematic diagram of the switching sequence after the TMA scheme of the present invention is optimized in one embodiment.

[0065] Figure 8 FIG. 4 is a schematic diagram of the relationship between the average CAoI and the block length N optimized by the TMA solution of the present invention in an embodiment.

[0066] Fig. 9 is the minimum average CAoI and Alice's transmission power P in an embodiment. a Schematic diagram of the relationship.

[0067] Fig.10 The diagram is a schematic diagram of the relationship between the minimum average CAoI and the total number of antennas M in an embodiment. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0069] It should be noted that if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0070] In one embodiment, the present invention provides a method for optimizing the age of hidden information based on a time modulation array, the method comprising the following steps:

[0071] Step 1: Build a covert communication system architecture based on a time modulation array (TMA) as a transmitter; Figure 1 , the covert communication system architecture includes a transmitter Alice, a receiver Bob and an eavesdropper Willie, the transmitter transmits a covert signal through a time modulation array, and each antenna element of the transmitter is controlled by a radio frequency switch, and the radio frequency switch realizes beamforming through a time series modulation signal;

[0072] Here, the communication channel of the covert communication system is modeled as a quasi-static Rician channel, and the signal transmission process is affected by fading and noise.

[0073] Here, the TMA-based transmitter Alice modulates the carrier signal and sends it to the legitimate receiver Bob, while the eavesdropper Willie wants to determine whether Alice sends. Assume that Alice is equipped with M antennas, while Bob and Willie are each equipped with one antenna. Assume that the channel state information of the detection channel is available. In addition, it is assumed that the wireless signal is in a quasi-static channel, that is, when a channel uses N channels, the fading gain remains constant and varies independently in different channels.

[0074] Here, the RF signal is modulated through time modulation, and beamforming technology is used to enhance the signal strength in a specific direction, thereby ensuring that the information can be delivered to the legitimate receiver Bob without being detected, while reducing the signal strength towards the eavesdropper Willie.

[0075] Step 2, using KL divergence as a measure of communication concealment, establish a performance optimization function for the covert communication system to minimize the average age of concealed information CAoI;

[0076] Step 3: Use the cuckoo search algorithm to solve the performance optimization function of the covert communication system and obtain the beamforming parameter combination corresponding to the minimized CAoI.

[0077] Further, in one of the embodiments, in combination with Figure 2(a), the covert communication system architecture described in step 1 is specifically as follows: the transmitting end is under the control of the signal processor, and the transmission signal is generated by a digital-to-analog converter (DAC); then, the generated transmission signal is combined with the local oscillator (LO) signal, and modulated by a time modulator after passing through a power amplifier; each antenna is connected to a time modulator, and all time modulators are supervised by the signal processor; in each time modulator, the RF signal is divided into two branches: I and Q, each branch has a variable gain amplifier VGA, and the Q path has a π / 2 phase shifter, and the signal processor controls the timing and amplitude of the VGA; finally, the signals on the I and Q paths are combined into an RF signal output.

[0078] Here, in some embodiments, it is assumed that is the beamforming vector of TMA, expressed as:

[0079]

[0080] in, and denote the equivalent amplitude and phase of the mth antenna, respectively, controlled by a time modulator. Compared to PA, TMA requires only one channel. It is also different from conventional phase / amplitude control because it uses a time modulator.

[0081] Then the received signal of the receiving end Bob in the present invention is expressed as:

[0082]

[0083] In the formula, y ab [i] is the signal received by Bob on the i-th channel, x[i] is the transmitted signal of Alice on the i-th channel, using Gaussian codebook, d ab is the distance between Alice and Bob, κ is the coefficient; represents Bob’s steering vector, k represents the wave number, d represents the spacing of the array elements, assumed to be half the wavelength, and θ represents the angle of Bob relative to Alice; represents the complex Gaussian noise at Bob on the ith channel; α represents the path attenuation; σ 2 represents the noise power, Φ TM represents the beamforming vector, represents the equivalent fading coefficient from Alice to Bob, where represents the Rician channel scattering component from Alice's mth antenna to Bob, m = 1, 2, ..., M, M is the total number of Alice's antennas; P a is Alice’s transmit power, i is the channel number, i=1,2,...,N, N is the total number of channels;

[0084] The total gain of the Rician channel is expressed as H ab :

[0085]

[0086] The signal-to-noise ratio (SNR) at the receiving end Bob is

[0087]

[0088] in, and represents the amplitude weight of the mth antenna; u=TM, represents the time modulation array scheme, and u=PA, represents the phased array scheme.

[0089] The conventional system structure based on phased array (PA) is shown in Figure 2(b), which uses a digital beamforming architecture and consists of multiple power amplifiers, attenuators, local oscillators (LOs), phase shifters, filters, and DACs. The RF channel behind each antenna includes the above components. The DAC is used to generate the transmission signal, while the filter is used to remove the image frequency. The amplifier increases the transmission power, and the local oscillator LO provides the carrier frequency for the transmission signal. In addition, the phase shifter and attenuator are used for antenna weight control to achieve beamforming. The baseband processor controls signal transmission and is connected to the DAC. The TMA solution requires a time modulator for each antenna before the signal enters the channel, while the PA solution requires more components behind each antenna for filtering, frequency conversion, and sampling.

[0090] Here, in some embodiments, the signal received by the eavesdropper Willie is expressed as:

[0091]

[0092] in, is the signal received by Willie on the i-th channel, is the null hypothesis, that is, Alice does not send a signal; For the alternative hypothesis, Alice sends a signal, represents the complex Gaussian noise at Willie on the ith channel, d aw is the distance between Alice and Willie, represents the fading coefficient from Alice to Willie, represents the Rician channel scattering component from Alice’s mth antenna to Willie;

[0093] Willie's signal-to-noise ratio is

[0094]

[0095] in Represents the amplitude weight of the mth antenna.

[0096] Here, in some embodiments, the total detection error probability at the eavesdropper Willie is It is expressed as:

[0097]

[0098] In order to achieve covert communication, the following constraints must be met:

[0099]

[0100] Among them, the false alarm probability Missed detection probability They are:

[0101]

[0102] in The likelihood ratio test value corresponding to the optimal threshold μ = ρ0 / ρ1 is the LRT value, which is expressed as:

[0103]

[0104] in,

[0105]

[0106] Where ρ0 represents the prior probability that Alice does not transmit, and ρ1 represents the prior probability that Alice transmits. represents the minimum total detection error probability, ε is the preset concealment tolerance level, and Respectively represent and Willie's decision. and and are respectively expressed in and The probability distribution of Willie's observation value is shown in Figure 1, where Pr represents the received signal power.

[0107] It should be noted that in the present invention, it is assumed that Willie fully knows the transmission power Pa, the communication packet length N and the prior probability of transmission ρ1. This extensive level of information enables Willie to use the optimal statistical hypothesis test, such as the likelihood ratio test (LRT).

[0108] Further, in one of the embodiments, the process of implementing beamforming in step 1 includes:

[0109] (1) Establish the switching function of the mth antenna at the time modulation array at time t

[0110]

[0111] In the formula, and are the gain control time series of I and Q paths of each time modulator at time t respectively; Figure 3 The basic principle of TMA vector synthesis is demonstrated, where different combinations of the switch function states in the I / Q path can generate symbols with different phases. p The vector synthesis effect of all states within can form equivalent beamforming weights.

[0112] (2) By design and The switching time and amplitude are adjusted to achieve beamforming of covert signals.

[0113] The specific analysis is as follows:

[0114] With 8 phases S m ∈Ω s ,Ω s ={(i-1)π / 4,i=1,2,…,8} as an example, and The switching functions and equivalent bits corresponding to the different states of , each state only differs in phase, so the sum of the moduli of the designed switching functions is 1. One advantage of this approach is that the TMA switch remains active, thus preventing energy leakage in the feed network. Assume that the sth symbol is represented by the imaginary coordinates on the I / Q path The period of each symbol is defined as T b , in a modulation period T p =ET b , then the vector sum of the mth antenna can be written as In the formula, is the number of times the sth symbol appears in one modulation cycle, Then the equivalent phase and equivalent amplitude for:

[0115]

[0116] The equivalent phase and amplitude generated by TMA only depend on the symbol states and their respective occurrence times, but not on the arrangement of these states. On this basis, it is proposed to randomly rearrange the switching states in each modulation cycle according to a pseudo-random distribution, which enhances the randomness of the spectrum during information transmission and suppresses undesirable harmonics.

[0117] At the same time, beamforming is performed using the amplitude and phase states synthesized by all symbols in each modulation cycle. Considering a transmitter with M antennas, the instantaneous radiation signal S(t) can be expressed as:

[0118]

[0119] Where f0 is the main frequency and θ is the receiver direction. and By adjusting the switching time and amplitude, the covert signal beamforming can be achieved. is Φ TM The time domain function of X(t) is the transmission of hidden information. is the time domain expression of beamforming.

[0120] Beamforming function can be written as:

[0121]

[0122] In the formula, S m,e is a modulation period T p The e-th symbol of , after Fourier transformation, as follows:

[0123]

[0124] where f b =1 / T b , is the hth harmonic in the eth period T b The Fourier series coefficients of can be expressed as:

[0125]

[0126] In the formula, S m,e express and The equivalent state produced. When h=0, is only related to E, and when h≠0, h and S m,e is also relevant. According to the Fourier transform, when the signal is completely random, there are almost no harmonics in the spectrum. In practice, the degree of randomization of the switching sequence within each modulation period is related to the number of sub-periods E. In theory, the larger the value of E, the stronger the randomness. Therefore, if fewer harmonics are needed, the number of sub-periods can be increased, and the switching sequence can also be optimized specifically for efficiency. However, the more sub-periods, the higher the requirements for hardware processing performance. Therefore, the selection of parameters needs to be comprehensively considered based on actual conditions and performance requirements.

[0127] In addition, in order to achieve beamforming, after selecting E, it is also necessary to determine S m,e choice. and The amplitude and switching times of the signal are controlled by the processor and can be designed into a more complex or simpler symbol set as needed. Once the symbol set is determined, the beamforming design requirements can be determined.

[0128] The hardware components of the TMA solution mainly use one RF channel, while the PA solution consists of M RF channels. Implementing CAoI optimization in TMA requires changing the traditional design adopted in traditional TMA so that the TMA can be analyzed and evaluated using the CAoI indicator.

[0129] Furthermore, in one of the embodiments, the performance optimization function of the covert communication system in step 2 is:

[0130]

[0131] Where constraint c1 is the covert communication constraint obtained using KL divergence, and Respectively expressed in and The probability distribution of Willie's observations under for and The KL divergence between Indicates taking the mean value; represents the probability of covert communication interruption; represents the average packet error probability; ρ0 represents the prior probability that Alice does not transmit, ρ1 represents the prior probability that Alice transmits; N represents the communication packet length, N min 、N max They represent the minimum packet length and the maximum packet length respectively; ε is the preset concealment tolerance level; E is the total number of switch time states; is the probability of covert communication interruption; W represents the system bandwidth; Indicates the sth state of the RF switch corresponding to the mth antenna, and S indicates the total number of RF switch state types.

[0132] The specific derivation process of average CAoI is as follows:

[0133] The lower bound of the minimum total detection error probability is expressed as:

[0134]

[0135] in, for and The total change distance between them. Then by constraining To ensure coverage.

[0136] In order to ensure stricter concealment, stricter concealment constraints are required:

[0137]

[0138] In the formula, for:

[0139]

[0140] Alice faces challenges in obtaining instantaneous channel state information of the detection channel. Assume that Alice can only obtain h from historical observations. awTherefore, this work adopts KL divergence to achieve the expression of covert communication constraints, which can be written as:

[0141]

[0142] Then the hidden constraint can be derived as:

[0143]

[0144] CAoI represents the timeliness of concealed information when data packets are transmitted. Alice will selectively spread data packets to ensure the concealment of her wireless transmission behavior. Therefore, there is a possibility that the data packets are not correctly decoded. Figure 4 As shown, assuming that the i-th valid data packet is generated at time point The departure time of the i-th data packet is recorded as The AoI of the i-th valid data packet can be expressed as Define the time interval between the i-th and (i+1)-th packets as And, the residence time of the i-th data packet is It is fixed and equal to the original age of the valid packet at Bob (i.e. ), let N(τ) denote the number of valid packets in the interval (0, τ). To determine the average arrival rate of valid packets, we can take the limit when τ approaches infinity. In this context, a valid packet is one that has been secretly transmitted and successfully decoded.

[0145] The average CAoI is defined as the average duration since Alice generated the latest valid packet, which can be expressed as:

[0146]

[0147] in express The area between the departure time of the i-th and (i+1)-th valid data packets is as follows: Figure 4 shown.

[0148] Therefore, the CAoI of the two system models analyzed can be written as:

[0149]

[0150] Where W≤2fp represents the system bandwidth, It represents the probability of covert communication interruption in TMA or PA scheme, which is defined as the probability of not satisfying the covert constraint.

[0151] The specific proof is as follows:

[0152] Since there are Q time slots between the i-th and (i+1)-th valid data packets, The first moment of is calculated as follows:

[0153]

[0154] The average arrival rate of valid data packets is:

[0155]

[0156] Assume ΔT is the interval time between the i-th data packet and the (i+1)-th data packet, then the first-order moment of ΔT can be derived as:

[0157]

[0158] The second-order moment of the interval time ΔT can be deduced as:

[0159]

[0160] Using the law of total probability, we can deduce The second moment of Figure 4 middle, represents the area of ​​the rectangular trapezoid. Then we get It can be expressed as:

[0161]

[0162] where δ u is the error probability. However, due to δ u The expression is complex and difficult to find The value of .

[0163] therefore, The linear approximation of is as follows:

[0164]

[0165] Where γ0 = 2 R -1, R = D / N is the channel coding rate, and D is the amount of information. When x≥0 The probability distribution function (PDF) of can be expressed as:

[0166]

[0167] in, When x≥0 The cumulative distribution function (CDF) can be expressed as:

[0168]

[0169] Through the above derivation, we can get

[0170] Further, in one of the embodiments, the step 3 uses the cuckoo search algorithm to solve the performance optimization function of the covert communication system to obtain a beamforming parameter combination corresponding to the minimized CAoI, specifically including:

[0171] Initialize the search space: define all possible beamforming parameter combinations, including the sth state of the RF switch corresponding to the antenna and the communication packet length N;

[0172] Initializing the fitness function: setting the performance optimization function of the covert communication system to be the fitness function;

[0173] CS algorithm search: Find the optimal beamforming parameter combination through random search using the Levy flight strategy;

[0174] Select the optimal solution: After multiple iterations, select the beamforming parameter combination that minimizes the age of the hidden information and N, thereby pseudo-randomly generating the switching sequence of the time modulation array.

[0175] The specific analysis is as follows:

[0176] For the TMA solution, the main factors affecting the average CAoI include the communication packet length N and the radiation pattern formed by TMA. For the PA solution, the optimization variables should include |α m | and β m Taking these factors into consideration, the optimization problem of minimizing the average CAoI of TMA and PA schemes can be expressed as:

[0177]

[0178] In the formula, Ω v are the alternative amplitudes and phase shifts for the conventional scheme. Under the PA scheme, the performance of the attenuator affects the amplitude weighting, and the performance of the phase shifter affects the phase weighting. Due to the practical limitations of the equipment, the accuracy of beamforming may deviate greatly from the theoretical value.

[0179] Substituting into c1, we get the following expression:

[0180]

[0181] Furthermore, it can be determined that when N is given, there is an optimal transmission power that minimizes CAoI It can be expressed as:

[0182]

[0183] It can be seen that the beamforming factor has an impact on the CAoI performance. Therefore, assuming that P a , and then use the optimization algorithm to solve it. An optimization method based on the CS (Cuckoo Search) algorithm is proposed. The Lévy flight strategy used in the CS algorithm can achieve the optimal goal in a shorter time than other algorithms. Therefore, it reduces the complexity, especially in the field of beamforming.

[0184] Optimization variables of TMA scheme Need to start from N max ,N min , E is initialized. The PA scheme requires initialization In addition, the initial packet length N needs to be considered i Then the fitness function is The calculation of is to evaluate the i-th host nest in the optimized CAoI of step c of the TMA or PA scheme. When the number of iterations is lower than the specified value K, the best nest is selected by Lévy flight.

[0185] Finally, the optimal value is output, and the output under the TMA scheme is and N, output under PA scheme and N i Subsequently, based on and E can pseudo-randomly generate the switching sequence of TMA.

[0186] In one embodiment, a system for optimizing age of concealed information based on a time modulation array is provided, the system comprising:

[0187] The first module is used to construct a covert communication system architecture based on a time modulation array as a transmitter; the covert communication system architecture includes a transmitter Alice, a receiver Bob and an eavesdropper Willie, the transmitter transmits a covert signal through a time modulation array, and each antenna element of the transmitter is controlled by a radio frequency switch, and the radio frequency switch realizes beamforming through a time series modulation signal;

[0188] The second module is used to use KL divergence as a measure of communication concealment to establish a performance optimization function of the covert communication system to minimize the average age of concealed information CAoI;

[0189] The third module is used to solve the performance optimization function of the covert communication system by using the cuckoo search algorithm to obtain the beamforming parameter combination corresponding to the minimized CAoI.

[0190] For the specific definition of the hidden information age optimization system based on the time modulation array, please refer to the definition of the hidden information age optimization method based on the time modulation array mentioned above, which will not be repeated here. Each module in the above-mentioned hidden information age optimization system based on the time modulation array can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0191] As a specific example, in one of the embodiments, a simulation experiment is conducted to evaluate the effectiveness of the proposed method.

[0192] Assume that the number of nests Z is 25, the probability of establishing a new nest P is 0.25, the number of antennas M is 10, the total number of switch time states E is 100, and there are S = 8 switch states. The minimum packet length is set to N min =25, the maximum packet length is set to N max =200. The transmission power at Alice is set to The amount of information is set to D = 10 bits. The directions of Bob and Willie are set to θ b = -40° and θ w =50°. The noise power is set to σ 2 = -80dBm, the path attenuation is set to α = 2.2. The distance between Alice and Bob, Alice and Willie is d ab =25m,d aw =20m. The concealment tolerance is set to ε=0.1.

[0193] First, the average CAoI performance of TMA and PA schemes was studied. The optimization parameters considered for the TMA scheme include and N. For the PA scheme, |α is optimized m |,β m , N.

[0194] Figure 5 Iterative process of CS optimization for TMA and PA schemes. The results show that with the increase of the number of iterations, the TMA scheme proposed in the present invention converges faster to the minimum average CAoI than the PA scheme. And compared with the PA scheme, the TMA scheme can obtain a smaller CAoI. This is because the amplitude and phase control accuracy of the TMA scheme is higher, resulting in a smaller CAoI under the same conditions and requiring fewer iterative optimization times.

[0195] Figure 6 The equivalent weight after optimization of the PA solution. The blue part on the coordinate axis represents the equivalent amplitude, and the yellow part represents the equivalent phase, with the phase variation range from -π to π.

[0196] Figure 7 The switching sequence after the optimization of the TMA scheme of the present invention is shown. It can be observed that a time modulation cycle consists of 100 sub-cycles, and each sub-cycle has 8 optional states. Figure 7 The illustration in shows different phases, which are synthesized from the 8 states considered previously in the switching time design. In practice, the number of sub-cycles and the number of states are determined by the hardware performance, so it is important to consider the scenario and usage overhead.

[0197] Figure 8 Demonstrated the best TMA solution and PA solution optimal |α m |,β m Figure 2 shows the relationship between the average CAoI and the packet length N. First, the average CAoI of the TMA scheme is better than that of the PA scheme under different transmit powers of Alice. This is because the TMA scheme provides better accuracy in amplitude and phase control, ensuring higher gain in the direction of Bob, thereby achieving better average CAoI. Then, it can be found that the average CAoI first decreases and then increases with N, indicating that there is an optimal value of N that minimizes the average CAoI. In addition, it can be observed that the average CAoI performance decreases with the increase of ρ1, because a larger ρ1 introduces a higher transmission probability.

[0198] Fig. 9 Describes different P a When P is , the relationship between Alice’s minimum average CAoI and transmit power under TMA and PA schemes. It can be seen that no matter the prior transmission probability ρ1 = 0.5, 0.6 or 0.7, as P a As P increases, the minimum average CAoI decreases. This is because a The larger it is, the smaller the average packet error probability is. At the same time, as ρ1 increases, the chance of transmitting new data packets increases, resulting in a decrease in the minimum average CAoI.

[0199] Fig.10 The relationship between the average CAoI performance of the TMA and PA schemes and the number of antennas M is described. It can be seen that as the number of antennas M increases, the minimum average CAoI gradually increases. This can be explained by the fact that the increase in M ​​enhances the power of the reflected signal. Fig. 9 It can be seen that the larger ρ1 is, the smaller the minimum average CAoI is, because there are more opportunities to transmit new data packets.

[0200] In summary, transmitters utilizing TMA reduce system cost without compromising performance while providing improved CAoI and beamforming capabilities.

[0201] In summary, the TMA scheme of the present invention is superior to the PA scheme in terms of average CAoI and has a faster optimization convergence speed. The present invention uses the TMA scheme to implement beamforming using RF switches. Compared with the traditional phased array (PA), it reduces the hardware complexity and improves the flexibility of beamforming, enhances security beyond covert communication, and promotes effective data transmission, sensing and monitoring of key applications.

[0202] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A hidden information age optimization method based on a time modulation array, characterized in that: The method comprises the following steps: Step 1, construct a covert communication system architecture based on a time modulation array as a transmitter; the covert communication system architecture includes a transmitter Alice, a receiver Bob, and an eavesdropper Willie, the transmitter transmits a covert signal through a time modulation array, and each antenna element of the transmitter is controlled by a radio frequency switch, and the radio frequency switch realizes beamforming through a time series modulation signal; Step 2, using KL divergence as a measure of communication concealment, establish a performance optimization function for the covert communication system to minimize the average age of concealed information CAoI; Step 3: Use the cuckoo search algorithm to solve the performance optimization function of the covert communication system and obtain the beamforming parameter combination corresponding to the minimized CAoI.

2. The method for optimizing hidden information age based on time modulation array according to claim 1, characterized in that: The covert communication system architecture described in step 1 is specifically as follows: the transmitting end is under the control of the signal processor, and the transmission signal is generated by the digital-to-analog converter; Subsequently, the generated transmission signal is combined with the local oscillator signal, modulated by a time modulator after passing through a power amplifier; each antenna is connected to a time modulator, and all time modulators are supervised by a signal processor; In each time modulator, the RF signal is divided into two branches: I and Q. Each branch has a variable gain amplifier VGA, and the Q branch has a π / 2 phase shifter. The signal processor controls the timing and amplitude of the VGA. Finally, the signals on the I and Q paths are combined into an RF signal output.

3. The hidden information age optimization method based on time modulation array according to claim 1 is characterized in that: In step 1, the communication channel of the covert communication system is modeled as a quasi-static Rician channel.

4. The hidden information age optimization method based on time modulation array according to claim 3 is characterized in that: The received signal of the receiving end Bob is expressed as: In the formula, y ab [i] is the signal received by Bob on the i-th channel, x[i] is the transmitted signal of Alice on the i-th channel, using Gaussian codebook, d ab is the distance between Alice and Bob, κ is the coefficient; represents Bob’s steering vector, k represents the wave number, d represents the space of array elements, and θ represents the angle of Bob relative to Alice; represents the complex Gaussian noise at Bob on the ith channel; α represents the path attenuation; σ 2 represents the noise power, φ TM represents the beamforming vector; represents the equivalent fading coefficient from Alice to Bob, where represents the Rician channel scattering component from Alice's mth antenna to Bob, m = 1, 2, ..., M, M is the total number of Alice's antennas; P a is Alice’s transmit power, i is the channel number, i=1,2,...,N, N is the total number of channels; The total gain of the Rician channel is expressed as H ab : The signal-to-noise ratio (SNR) at the receiving end Bob is in, and represents the amplitude weight of the mth antenna; u=TM, represents the time modulation array.

5. The hidden information age optimization method based on time modulation array according to claim 4 is characterized in that: The signal received by the eavesdropper Willie is expressed as: in, is the signal received by Willie on the i-th channel, is the null hypothesis, that is, Alice does not send a signal; For the alternative hypothesis, Alice sends a signal, represents the complex Gaussian noise at Willie on the ith channel, d aw is the distance between Alice and Willie, represents the fading coefficient from Alice to Willie, represents the Rician channel scattering component from Alice’s mth antenna to Willie; Willie's signal-to-noise ratio is in Represents the amplitude weight of the mth antenna.

6. The method for optimizing hidden information age based on time modulation array according to claim 5, characterized in that: The total detection error probability at the eavesdropper Willie It is expressed as: And the following constraints must be met: Among them, the false alarm probability Missed detection probability They are: in The likelihood ratio test value corresponding to the optimal threshold μ = ρ0 / ρ1 is the LRT value, which is expressed as: in, Where ρ0 represents the prior probability that Alice does not transmit, and ρ1 represents the prior probability that Alice transmits. represents the minimum total detection error probability, ε is the preset concealment tolerance level, and Respectively represent and Willie's decision. and and are respectively expressed in and The probability distribution of Willie's observation value is shown in Figure 1, where Pr represents the received signal power.

7. The method for optimizing hidden information age based on time modulation array according to claim 6, characterized in that: The process of implementing beamforming in step 1 includes: Establish the switching function of the mth antenna at the time modulation array at time t In the formula, and are the gain control time series of I and Q paths of each time modulator at time t respectively; By design and The switching time and amplitude are adjusted to achieve beamforming of covert signals.

8. The hidden information age optimization method based on time modulation array according to claim 7 is characterized in that: The performance optimization function of the covert communication system in step 2 is: Where constraint c1 is the covert communication constraint obtained using KL divergence, and Respectively expressed in and The probability distribution of Willie's observations under for and The KL divergence between Indicates taking the mean value; represents the probability of covert communication interruption; represents the average packet error probability; ρ0 represents the prior probability that Alice does not transmit, ρ1 represents the prior probability that Alice transmits; N represents the communication packet length, N min 、N max They represent the minimum packet length and the maximum packet length respectively; ε is the preset concealment tolerance level; E is the total number of switch time states; is the probability of covert communication interruption; W represents the system bandwidth; Indicates the sth state of the RF switch corresponding to the mth antenna, and S indicates the total number of RF switch state types.

9. The method for optimizing hidden information age based on time modulation array according to claim 8, characterized in that: The probability of covert communication interruption The upper bound of is: In the formula, μ aw and μ ab Respectively |h aw | 2 and |h ab | 2 The average value of .

10. The hidden information age optimization method based on time modulation array according to claim 9 is characterized in that: Step 3 uses the cuckoo search algorithm to solve the performance optimization function of the covert communication system to obtain the beamforming parameter combination corresponding to the minimized CAoI, specifically including: Initialize the search space: define all possible beamforming parameter combinations, including the sth state of the RF switch corresponding to the antenna and the communication packet length N; Initializing the fitness function: setting the performance optimization function of the covert communication system to be the fitness function; CS algorithm search: Find the optimal beamforming parameter combination through random search using the Levy flight strategy; Select the optimal solution: After multiple iterations, select the beamforming parameter combination that minimizes the age of the hidden information and N, thereby pseudo-randomly generating the switching sequence of the time modulation array.

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