Hidden information age optimization method based on time modulation array

Abstract

This paper discloses a method for optimizing the age of concealed information based on a time-modulated array (TMA). The method aims to minimize the average age of concealed information (CAoI) by optimizing beamforming parameters and block length, thereby improving the concealment of covert communications and the timeliness of information. The present invention uses a time-modulated array (TMA) scheme and radio frequency switches to implement beamforming. By introducing the Kullback-Leibler (KL) divergence as a measure of concealment, the method further derives the average age of concealed information (CAoI) to comprehensively illustrate the communication concealment and timeliness performance. Based on this, an optimization scheme is proposed, which uses a cuckoo search algorithm to solve the problem of minimizing the average CAoI under concealment constraints. Experimental results show that the TMA scheme significantly outperforms the traditional phased array (PA) scheme in terms of convergence speed and average CAoI, reduces hardware complexity, and improves beamforming flexibility. These findings provide new perspectives and methods for optimizing covert communication systems.

Description

Technical Field

[0001] The present 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 core issues in IoT communications. 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 arrays (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] Furthermore, the timeliness issue of existing covert communications has not been effectively addressed. The age of information (AoI) reflects the timeliness of information, and existing technologies struggle to provide optimal timeliness while maintaining covertness. Therefore, a technical solution is needed that can simultaneously improve the covertness and timeliness of information transmission while reducing system complexity and power consumption. Summary of the Invention

[0004] The present invention aims to address the aforementioned problems in the prior art by providing a method for optimizing the age of concealed information based on a time-modulated array. This method minimizes the average concealed age of information (CAoI) by optimizing beamforming parameters and packet length, thereby improving the concealment of covert communications and the timeliness of information. A closed-form expression for the Kullback-Leibler (KL) divergence is derived as a concealment constraint, and the average CAoI is derived based on this. Based on this, an optimization scheme is proposed, using the Cuckoo Search (CS) algorithm 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: Build a covert communication system architecture based on a time-modulated array as a transmitter. This covert communication system architecture includes a transmitter (Alice), a receiver (Bob), and an eavesdropper (Willie). The transmitter transmits a covert signal via the time-modulated array, and each antenna element of the transmitter is controlled by a radio frequency switch. The radio frequency switch implements beamforming by modulating the signal in a time series.

[0007] Step 2: Using KL divergence as a measure of communication concealment, a performance optimization function of the covert communication system is established 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 controlled by the signal processor, and the transmission signal is generated by the digital-to-analog converter; then, the generated transmission signal is combined with the local oscillator signal, and modulated by the time modulator after passing through the 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 one 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] Where 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 i-th 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, where m = 1, 2, ..., M, and 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, where 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, i.e. Alice does not send a signal; For the alternative hypothesis, Alice sends a signal, represents the complex additive Gaussian noise at Willie on the i-th 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 Expressed as:

[0026]

[0027] And the following constraints must be met:

[0028]

[0029] Among them, the false alarm probability Probability of missed detection 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, ρ1 represents the prior probability that Alice transmits, represents the minimum total detection error probability, ε is the preset concealment tolerance level, and Represented in and Willie's decision. and and are respectively expressed in and The probability distribution of Willie's observation value under , 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] Where, 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; 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 switching 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. S represents the total number of RF switch state types.

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

[0045]

[0046] Where μ aw and μ ab Respectively |h aw | 2 and h ab | 2 The average value of .

[0047] Furthermore, 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:

[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: Uses Levy flight strategy to randomly search and find the optimal beamforming parameter combination;

[0051] Select the optimal solution: After multiple iterations, the optimal beamforming parameter combination that minimizes the age of the hidden information is selected. 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) This invention improves the Age of Information (AoI) performance of covert communications by reducing hardware complexity. The TMA scheme uses RF switches instead of phase shifters to implement beamforming, reducing hardware complexity and increasing beamforming flexibility. This invention controls the radiation pattern by designing the switching state of the TMA to obtain an equivalent synthetic beamforming vector.

[0054] (2) This paper uses the Kullback-Leibler (KL) divergence to quantitatively describe the stealth of communications and derives closed-form expressions for the KL divergence under TMA and PA schemes. The KL divergence-based stealth detection model can effectively prevent communications from being detected by eavesdroppers.

[0055] (3) This paper proposes and solves the problem of minimizing the average CAoI by adjusting the communication packet length and beamforming parameters. A cuckoo search algorithm is used for optimization. By optimizing the CAoI metric, the transmitted data packets are ensured to be the latest data, improving the timeliness of information transmission.

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

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

[0058] FIG2( a ) is a diagram of a system architecture based on TMA according to an embodiment of the present invention.

[0059] FIG2( b ) is a diagram of a conventional TMA-based system architecture in one embodiment.

[0060] Figure 3 FIG. 1 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 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 calculate the amplitude |αm | and phase β m Optimization result diagram.

[0064] Figure 7 FIG. 4 is a schematic diagram of the switching sequence after the TMA solution of the present invention is optimized in one embodiment.

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

[0066] Figure 9 In this embodiment, the minimum average CAoI and Alice's transmission power P a Schematic diagram of the relationship.

[0067] Figure 10 FIG. 1 is a schematic diagram showing 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 solutions and advantages of this application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this 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 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 such 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 this 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. 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, a TMA-based transmitter, Alice, modulates a carrier signal and transmits it to the legitimate receiver, Bob, while an eavesdropper, Willie, wants to determine whether Alice is transmitting. Assume that Alice is equipped with M antennas, while Bob and Willie are each equipped with one antenna. It is also assumed that channel state information for the detection channel is available. Furthermore, it is assumed that the wireless signal is in a quasi-static channel, meaning that the fading gain remains constant when using N channels and varies independently across 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, a performance optimization function of the covert communication system is established 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] Furthermore, in one embodiment, in combination with Figure 2(a), the covert communication system architecture described in step 1 is specifically as follows: the transmitting end generates a transmission signal by a digital-to-analog converter (DAC) under the control of a signal processor; then, the generated transmission signal is combined with a local oscillator (LO) 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 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 one RF signal output.

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

[0079]

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

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

[0082]

[0083] Where 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, which is 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 i-th 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, where m = 1, 2, ..., M, and 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, where 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 phased array (PA)-based system architecture, shown in Figure 2(b), 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 aforementioned 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 represented as:

[0091]

[0092] in, is the signal received by Willie on the i-th channel, is the null hypothesis, i.e. Alice does not send a signal; For the alternative hypothesis, Alice sends a signal, represents the complex additive Gaussian noise at Willie on the i-th 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 Expressed as:

[0097]

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

[0099]

[0100] Among them, the false alarm probability Probability of missed detection 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, ρ1 represents the prior probability that Alice transmits, represents the minimum total detection error probability, ε is the preset concealment tolerance level, and Represented in and Willie's decision. and and are respectively expressed in and The probability distribution of Willie's observation value under , Pr represents the received signal power.

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

[0108] Furthermore, in one embodiment, 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] Where, 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 switching function states in the I / Q path can generate symbols with different phases. At the same time, a modulation period T p The vector synthesis effect of all states in the θ 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 differs only 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 Where, 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 depend only on the symbol states and their respective occurrence counts, not on the arrangement of these states. Based on this, a method is proposed to randomly rearrange the switching states within each modulation cycle according to a pseudo-random distribution, thereby enhancing the randomness of the spectrum during information transmission and suppressing undesirable harmonics.

[0117] At the same time, beamforming is performed using the amplitude and phase states synthesized from all symbols within 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] Where, S m,e is a modulation period T p The e-th symbol of , after Fourier transform, as follows:

[0123]

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

[0125]

[0126] Where 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 a 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 cycle is related to the number of sub-cycles, E. Theoretically, a larger value of E results in greater randomness. Therefore, if fewer harmonics are desired, the number of sub-cycles can be increased, and the switching sequence can be optimized specifically for efficiency. However, more sub-cycles place greater demands on hardware processing performance. Therefore, parameter selection requires a comprehensive consideration of both practical needs 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 primarily utilize a single RF channel, while the PA solution consists of M RF channels. Implementing CAoI optimization in the TMA requires changing the traditional design used in conventional TMAs so that the CAoI metric can be used to analyze and evaluate the TMA.

[0129] Furthermore, in one embodiment, 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; 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 switching 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. S represents 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] Where, for:

[0139]

[0140] Alice faces challenges in obtaining the 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 transmitting data packets. Alice selectively transmits 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 data 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] Let ΔT be the interval 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, since 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 deduction, we can get

[0170] Furthermore, in one embodiment, step 3 of solving the performance optimization function of the covert communication system using a cuckoo search algorithm to obtain a beamforming parameter combination corresponding to minimizing CAoI specifically includes:

[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: Uses Levy flight strategy to randomly search and find the optimal beamforming parameter combination;

[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 into account the influence of these factors, the optimization problem of minimizing the average CAoI of TMA and PA schemes can be expressed as:

[0177]

[0178] Where, Ω v These are the alternative amplitude and phase shift values ​​for conventional solutions. In the PA solution, the attenuator's performance affects the amplitude weighting, while the phase shifter's performance affects the phase weighting. Due to practical limitations of the equipment, beamforming accuracy can deviate significantly 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 exists 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 CAoI performance. Therefore, assuming P a , and then uses an optimization algorithm to solve it. An optimization method based on the Cuckoo Search (CS) algorithm is proposed. The Lévy flight strategy employed in the CS algorithm can achieve the optimal goal in a shorter time than other algorithms. Therefore, it reduces complexity, especially in the field of beamforming.

[0184] Optimization variables of TMA scheme Need to start from N max ,N min , initialized in E. The PA solution requires initialization In addition, the initial packet length N needs to be considered i . Then the fitness function The calculation 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 the age of concealed information based on a time modulation array is provided, the system comprising:

[0187] The first module is used to build a covert communication system architecture based on a time-modulated array as a transmitter. This covert communication system architecture includes a transmitter Alice, a receiver Bob, and an eavesdropper Willie. The transmitter transmits a covert signal via the time-modulated array, and each antenna element of the transmitter is controlled by a radio frequency switch, which implements beamforming by modulating the signal in a time series.

[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 using a cuckoo search algorithm to obtain a beamforming parameter combination corresponding to minimizing CAoI.

[0190] The specific limitations of the time-modulation array-based covert information age optimization system can be found in the limitations of the time-modulation array-based covert information age optimization method described above and will not be further elaborated here. Each module within the time-modulation array-based covert information age optimization system can be implemented in whole or in part via software, hardware, or a combination thereof. Each of these modules can be embedded in or independent of a processor within a computer device in hardware form, or stored in a computer device memory in software form, allowing the processor to call and execute the corresponding operations of each module.

[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, and the path attenuation is set to α = 2.2. The distance between Alice and Bob, and Alice and Willie is d ab =25m,d aw = 20 m. 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 TMA scheme include and N. For the PA scheme, |α is optimized m |, β m 、N.

[0194] Figure 5 The iterative process for CS optimization for the TMA and PA schemes shows that, as the number of iterations increases, the TMA scheme proposed in this paper converges faster to the minimum average CAoI than the PA scheme. Furthermore, the TMA scheme achieves a smaller CAoI compared to the PA scheme. This is due to the TMA scheme's higher amplitude and phase control accuracy, resulting in a smaller CAoI under the same conditions and requiring fewer optimization iterations.

[0195] Figure 6 The equivalent weights after optimization for the PA scheme. The blue portion on the coordinate axis represents the equivalent amplitude, and the yellow portion 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 selectable states. Figure 7 The illustrations in Figure 1 show different phases that are synthesized from the eight states considered previously in the switching time design. In practice, the number of sub-cycles and the number of states are determined by hardware performance, so it is important to consider the scenario and usage overhead.

[0197] Figure 8 Demonstrates the optimal TMA solution and PA solution optimal|α m |, β m The following plots the relationship between average CAoI and packet length N. First, the TMA scheme's average CAoI outperforms the PA scheme at different transmit powers from Alice. This is because the TMA scheme provides better accuracy in amplitude and phase control, ensuring higher gain in Bob's direction, resulting in better average CAoI. It can be seen 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. Furthermore, it can be observed that the average CAoI performance decreases with increasing ρ1, as a larger ρ1 introduces a higher transmission probability.

[0198] Figure 9 Describes different P a When P is , the relationship between Alice’s minimum average CAoI and transmit power under TMA and PA schemes is shown. It can be seen that no matter the prior transmission probability ρ1 = 0.5, 0.6 or 0.7, as P a As the value of 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] Figure 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 improves. This can be explained by the fact that the increase in M ​​enhances the power of the reflected signal. Figure 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 solution of the present invention outperforms the PA solution in terms of average CAoI and has a faster optimization convergence speed. By utilizing radio frequency switches to implement beamforming through the TMA solution, the present invention reduces hardware complexity and improves beamforming flexibility compared to traditional phased arrays (PAs). This enhances security beyond covert communications and facilitates efficient data transmission, sensing, and monitoring in critical 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 to the above embodiments. The above embodiments and descriptions are only illustrative of the principles of the present invention. Without departing from the spirit and scope of the present invention, any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the age of hidden information based on a time modulation array, characterized in that: The method comprises the following steps: Step 1: Build a covert communication system architecture based on a time-modulated array as a transmitter. This covert communication system architecture includes a transmitter (Alice), a receiver (Bob), and an eavesdropper (Willie). The transmitter transmits a covert signal via the time-modulated array, and each antenna element of the transmitter is controlled by a radio frequency switch. The radio frequency switch implements beamforming by modulating the signal in a time series. Step 2: Using KL divergence as a measure of communication concealment, a performance optimization function of the covert communication system is established to minimize the average age of concealed information (CAoI). Step 3: Using a cuckoo search algorithm to solve the performance optimization function of the covert communication system, obtain a beamforming parameter combination corresponding to minimizing CAoI; 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: the I path and the Q path. Each branch has a variable gain amplifier (VGA), and the Q path 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 a single RF signal output. 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 Where, 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.

2. The method for optimizing hidden information age based on a time modulation array according to claim 1, characterized in that: The architecture of the covert communication system described in step 1 is as follows: the transmitting end generates a transmission signal by a digital-to-analog converter under the control of a signal processor; then, the generated transmission signal is combined with a local oscillator signal, passed through a power amplifier, and modulated by a time modulator.

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

4. The method for optimizing hidden information age based on a time modulation array according to claim 3, characterized in that: The received signal at the receiving end Bob is expressed as: Where 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 i-th 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, where m = 1, 2, ..., M, and 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, where 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 method for optimizing hidden information age based on a time modulation array according to claim 4, 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, i.e. Alice does not send a signal; For the alternative hypothesis, Alice sends a signal, represents the complex additive Gaussian noise at Willie on the i-th 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 a time modulation array according to claim 5, characterized in that: The total detection error probability at the eavesdropper Willie Expressed as: And the following constraints must be met: Among them, the false alarm probability Probability of missed detection 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, ρ1 represents the prior probability that Alice transmits, represents the minimum total detection error probability, ε is the preset concealment tolerance level, and Represented in and Willie's decision. and and are respectively expressed in and The probability distribution of Willie's observation value under , Pr represents the received signal power.

7. The method for optimizing hidden information age based on a time modulation array according to claim 1, 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; 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 switching 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. S represents the total number of RF switch state types.

8. The method for optimizing hidden information age based on time modulation array according to claim 7, characterized in that: The probability of covert communication interruption The upper bound of is: Where μ aw and μ ab Respectively |h aw | 2 and h ab | 2 The average value of .

9. The method for optimizing hidden information age based on a time modulation array according to claim 8, 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: Uses Levy flight strategy to randomly search and find the optimal beamforming parameter combination; 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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