A Skywave Massive MIMO Secure Communication System and Communication Method Based on Multi-station Collaboration

Abstract

A multi-station collaborative skywave massive MIMO secure communication system and method includes a description module, a setup module, a precoding module, a base station selection module, and a data acquisition module. The description module describes the roles and relationships of the various elements in the multi-station collaborative skywave secure communication method. The setup module establishes a mathematical model for user location-based precoding schemes, base station selection, and achievable rate distribution. The precoding module solves the precoding problem for each base station. The base station selection module selects the appropriate base station based on the user's location. This method effectively improves the poor security issues inherent in traditional shortwave communications, which suffer from low user rates and wide coverage.

Description

Technical Field

[0001] The present invention relates to the field of anti-eavesdropping communication technology, and in particular to a skywave massive MIMO secure communication system and a communication method based on multi-station collaboration. Background Art

[0002] The open nature of wireless channels makes communications potentially eavesdroppers, potentially posing a risk to communication security. With the rapid development of wireless communications, users have placed higher demands on the security of communication services. Consequently, physical layer security technologies, aimed at ensuring secure information transmission, have been extensively researched.

[0003] Most existing work is based on passive and active eavesdropping schemes. Countermeasures against passive eavesdropping typically utilize artificial noise, which allows legitimate users to identify and filter out the noise while preventing the eavesdropper from identifying it, significantly reducing the eavesdropper's signal-to-noise ratio (SINR). In active eavesdropping scenarios, the eavesdropper sends the same pilot signal as the legitimate user to the base station, causing the base station to direct its beam toward the eavesdropper instead of the legitimate user, thereby ensuring better signal reception quality. Furthermore, technologies such as Coordinated Multipoint (CoMP) and Multiple-Input Multiple-Output (MIMO) can provide secure transmission for communication systems. Cooperative Multipoint (CoMP) is being applied in areas such as secure heterogeneous network coverage, secure drone communications, and multi-beam satellite communications.

[0004] The above work does not take into account the further combination of the cooperative characteristics of multi-point coordinated communication and the sparse characteristics of the channel in the angular domain in MIMO technology. They are often carried out separately, which shows that there are other aspects to improve the security of the communication system. Summary of the Invention

[0005] To address the above issues, the present invention proposes a skywave massive MIMO secure communication system and method based on multi-station collaboration. This system effectively leverages the advantages of both MIMO and CoMP to address anti-eavesdropping issues, proposes a coordinated beamforming method within the angular domain, and further leverages the spatial distribution characteristics of capacity in MIMO systems to enhance security. The details are as follows:

[0006] A skywave massive MIMO secure communication method based on multi-station collaboration includes the following steps:

[0007] Step 1: Describe the roles of various elements in the multi-station collaborative skywave secure communication method and the relationships between them;

[0008] Step 2: Build a mathematical model for the distribution of precoding schemes, base station selection, and achievable rates based on user location.

[0009] Step 3: Solve the precoding problem for each base station;

[0010] Step 4: Select the appropriate base station based on the user's location;

[0011] Step 5: Perform power optimization of the selected base station.

[0012] Preferably, the functions of the various elements in the multi-station collaborative skywave secure communication method and the relationships therebetween are described in step 1 of the present invention, and the content of the description includes:

[0013] Establish a communication system consisting of a signal source, a core network, M base stations, and a user. The signal source sends the original message to the core network. The core network splits the original message into M sub-messages and sends them to M base stations via optical cables. Each base station sends the sub-message to the user via a skywave channel. Finally, the user combines the corresponding sub-messages to restore the original message. Meanwhile, an eavesdropper can eavesdrop on the communication content by receiving the signal.

[0014] Skywave channels transmit information through reflections from the ionosphere. The ionosphere is divided into three layers: the D layer, the E layer, and the F layer. The E and F layers are the ones that can reflect signals.

[0015] The D layer is 50 to 90 kilometers above the ground and only exists during the day. It disappears at night. The free electron density in the D layer is low. The D layer absorbs signal energy, causing channel attenuation, but does not reflect signals.

[0016] The E layer is 90 to 130 kilometers above the ground. The free electron density of the E layer is higher than that of the D layer. It is the lowest layer that can reflect sky wave signals. The E layer does not completely disappear at night.

[0017] The F layer is more than 130 kilometers above the ground. It is divided into F1 and F2 layers during the day and merges into a single layer at night. The F layer has the highest degree of ionization, and most sky-wave communications are achieved through reflections from the F layer. The transmitted signal usually reaches the receiver from different angles and with different signal strengths after a single hop or multiple hops, modeling the sky-wave channel as a multipath channel.

[0018] Preferably, the establishment of a mathematical model for the user location-based precoding scheme, base station selection, and achievable rate distribution in step 2 of the present invention includes the following:

[0019] Let x m (t) is the analog baseband signal sent by base station m, and the analog baseband signal received by receiver ξ is

[0020]

[0021] Where t represents time, τ is the temporary variable of integration, is the time-varying channel impulse response from base station m to receiver ξ, x mis the transmitted signal of base station m, dτ represents τ as the integrand, z ξ (t) is Gaussian white noise;

[0022] Using OFDM system, define N c 、N g 、T s is the number of subcarriers, cyclic prefix length, and sampling interval; then, T c =N c T s and T g =N g T s Set N as the duration of OFDM symbol and cyclic prefix respectively. v subcarriers are used to transmit data;

[0023] definition and Δf = 1 / T c h m,ξ (t,τ) and the subcarrier spacing; then, for the sub-information sent by base station m, the demodulated signal on the kth subcarrier from base station m to receiver ξ on the lth symbol is

[0024]

[0025] in is the channel frequency response from base station m to receiver ξ on the kth subcarrier of the lth symbol, is the transmitted signal component from base station m to receiver ξ on the kth subcarrier of the lth symbol, z m,ξ,l,k is a complex Gaussian random variable with zero mean and variance n0, and

[0026]

[0027] is the channel frequency response from base station m to receiver ξ at the lth symbol and kth subcarrier;

[0028] The shortwave channel is modeled as a wide-sense stationary uncorrelated scattering channel; let f c is the carrier frequency; considering the time-varying nature of the shortwave channel, the operating frequency needs to be adjusted according to the real-time ionospheric state; each base station is equipped with a uniform linear array, and f is set om is the highest operating frequency of base station m, then the spacing between adjacent antenna units of base station m is in represents the wavelength corresponding to the highest operating frequency, and c is the speed of light;

[0029] set up and are the azimuth and elevation angles of the departure path respectively. Assume that there is P between the receiver ξ and the base station m.m,ξ separable multipaths, define τ m,ξ,p,n is the time delay of the pth path from base station m to the nth antenna of receiver ξ, expressed as

[0030] τ m,ξ,p,n =τ m,ξ,p,1 +(n-1)Δτ m cosθ azi,m,ξ,p cosθ ele,m,ξ,p (28)

[0031] in is the time it takes for light to pass through two adjacent antenna units of base station m. To make the expression more concise, let Ω m,ξ,p =cosθ azi,m,ξ,p cosθ ele,m,ξ,p ;

[0032] The time-varying channel impulse response from receiver ξ to the nth antenna of base station m is expressed as

[0033]

[0034] in is the imaginary unit, f m is the operating frequency of base station m, α m,ξ,p (t) represents the complex gain random variable; since the earth's surface and ionosphere are rough, assume that there is Q in the p-th path from base station m to receiver ξ m,ξ,p subpaths, these subpaths have the same propagation delay, sending and arrival azimuth and elevation angles; α m,ξ,p (t) is expressed as

[0035]

[0036] where β m,ξ,p,q 、φ m,ξ,p,q and υ m,ξ,p,q are the gain, initial phase and Doppler shift of the qth path respectively; assuming φ m,ξ,p,q Obey the uniform distribution on [0,2π); when Q m,ξ,p →∞,α m,ξ,p The amplitude of (t) follows a Rayleigh distribution;

[0037] According to formula (3) and formula (5), we can get

[0038]

[0039] in

[0040]

[0041] represents the direction cosine Ω m,ξ,pThe corresponding direction cosine on the kth subcarrier; defines the path gain

[0042]

[0043] Here, the direction cosine Ω of each separable path is m,ξ,p and path gain β m,ξ,p Considered as partial CSI;

[0044] The transmitted signal of base station m is expressed as

[0045]

[0046] Among them, P m and s m are the transmission power and symbol of base station m, respectively, and s m is a random variable with zero mean and unit variance, f m,k represents the precoding vector of base station m on the kth subcarrier; the achievable rate R of base station m sending sub-information m to receiver ξ on the kth subcarrier m,ξ Expressed as

[0047]

[0048] Where n0 is the noise power.

[0049] Considering that the corresponding original signal can be correctly restored only when all sub-signals are correctly received, the ergodic achievable rate of the entire system is expressed as

[0050]

[0051] where w∈{0,1} M×1 Indicates the status of the base station, [w] m =1 means the mth base station is selected, otherwise it is not selected, N v is the number of subcarriers used to transmit data;

[0052] Assume that each eavesdropper is equipped with a single antenna to receive and combine information from various channels. Formula (12) reveals the relationship between the receiver rate and its position. In this case, the eavesdropper's rate is related to its spatial position. By making good use of the sparsity of the angle domain channel, the area of ​​the receiving area is made smaller, which ensures the communication of legitimate users while reducing the eavesdropper's communication rate. Assuming that the positions of the user and eavesdropper are u and e, respectively, the system's security rate is expressed as

[0053] R sec =[R u -R e ] + (37)

[0054] where Ru and R e denote the traversal rates of the user and the eavesdropper respectively.

[0055] Under the constraints of the minimum number of base stations selected, the maximum transmit power of a single base station, and the two-norm of the precoding vector, the user rate is maximized by optimizing the precoding vector, transmit power, and base station selection scheme. The optimization problem is mathematically expressed as:

[0056]

[0057] The constraint C1 indicates that at least κ base stations must be in working state, and the constraint C2 indicates that the transmission power of each base station should be less than the maximum value P max ,Constraint C3 indicates that the precoding scheme of a single base station antenna array must meet the power constraint.

[0058] Preferably, solving the precoding problem of each base station in step 3 of the present invention specifically includes:

[0059] According to formula (5), formula (8) and formula (11), we can get

[0060]

[0061] in is α m,ξ,p The complex conjugate of .

[0062] Definition a m,ξ,k is the channel gain from base station m to receiver ξ on the kth subcarrier, expressed as

[0063]

[0064] The expected value of the achievable rate of the channel from base station m to receiver ξ on the kth subcarrier is a m,ξ,k The monotonically increasing function maximizes the achievable rate of each sub-information by maximizing the channel gain of each sub-information;

[0065] The goal is to maximize the channel gain under the constraint of the two-norm of the precoding vector. The optimization problem is modeled as

[0066]

[0067] Define the following matrix

[0068]

[0069] According to formula (6), we get

[0070]

[0071] According to formula (9) and formula (19), P2 is converted into

[0072]

[0073] Using the relaxation method, ignoring rank(F) = 1, it is obvious that P2.1 is a convex semidefinite program, which is solved using CVXPY; the optimal F is defined as m,k The matrices and their corresponding maximum gains are and If the solution F m,opt If the rank is one, the solution is globally optimal. If not, the first column of its left singular matrix is ​​output.

[0074] Preferably, the precoding design of the present invention in a perfect CSI scenario is:

[0075] By assuming that the base station obtains perfect CSI, a precoder based on the minimum mean square error (MMSE) criterion is used; the following optimization problem is established

[0076]

[0077] in s m,k ,ζ m,k 、y m,k 、 f m,k 、h m,k are the MMSE-based precoding vector of base station m on the kth subcarrier, the transmitted signal, the auxiliary variable for power normalization, the received signal, the temporary variable, and the channel frequency response. Therefore, we can get

[0078]

[0079] Among them, m,k =||h m,k ||2.

[0080] Preferably, selecting a suitable base station according to the user location in step 4 of the present invention specifically includes:

[0081] Maximize the user's traversal rate by optimizing the base station selection; define R ξ (w) is the ergodic achievable rate of the receiver ξ obtained by CVXPY under the base station selection scheme w, then problem P4 is expressed as

[0082]

[0083] Solve P4, we have The case where constraint C1 is satisfied; for the M base station scenario, the complexity of the exhaustive search is very high when k is relatively small, which is O(2 M );

[0084] 6.1 Calculate the rate of all sub-information according to formula (11);

[0085] 6.2 Arrange the results in step 6.1 from largest to smallest and define b(i) as the index number of the i-th base station;

[0086] 6.3 Initializing w opt =0 M ;

[0087] 6.4 For m = 1 ~ κ, assign [w opt ] b(m) =1;

[0088] 6.5 output w opt .

[0089] Preferably, the power optimization of the selected base station in step 5 of the present invention specifically includes:

[0090] To optimize the transmit power of each selected base station, a heuristic solution is to set the transmit power of each base station to the maximum, thereby maximizing the user's rate. Considering that the user's traversal rate is determined by the smallest of all sub-information, the power of the base station with the lowest channel gain is maximized, while reducing the power of other base stations until the traversal rate of each sub-information is the same. This problem is expressed as

[0091]

[0092] Use binary search to solve P5.

[0093] initialization m min =0,ε=inf, where m=1,2,3,...,M; let, w m =1, Calculate R according to formula (11) m,ξ ,like but m min =m, where m=1,2,3,...,M; if m≠m min , calculated by binary search Returns the optimized transmit power

[0094] The beneficial effects of the present invention are:

[0095] By introducing the Nelder-Mead-based optimization algorithm, the user and capacity maximization under the physical layer security constraints is achieved. Specifically, the beneficial effects of the present invention include:

[0096] 1. The precoding design of the present invention can maximize the ergodic achievable rate of the skywave massive MIMO system under perfect CSI and imperfect CSI conditions;

[0097] 2. The base station selection design of the present invention can select the appropriate base station for the user, thereby maximizing the user's traversal reachable rate. On the other hand, the multi-base station joint scenario can further increase the sparseness of the spatial distribution of the traversal reachable rate, further improving security performance.

[0098] 3. The base station transmission power design of the present invention can reduce the base station transmission power while ensuring the user's traversal reachable rate, thereby reducing the eavesdropper's traversal reachable rate and improving the traversal reachable security rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 The flowchart of the planning method of the anti-eavesdropping system based on multi-station collaboration of the present invention.

[0100] Figure 2 Schematic diagram of a system scenario in an embodiment of the present invention.

[0101] Figure 3 2 is an angle relationship diagram in an embodiment of the present invention.

[0102] Figure 4 The figure shows the relationship between the number of base station antennas and the traversal achievable rate under partial CSI and perfect CSI scenarios.

[0103] Figure 5 This is a diagram showing the relationship between the number of different base station antennas and the traversal reachable rate under the base station selection algorithm and exhaustive search method of the present invention.

[0104] Figure 6 A graph showing the relationship between different maximum transmit powers and traversal achievable rates for partial CSI and perfect CSI scenarios is shown.

[0105] Figure 7 This is a diagram showing the relationship between different maximum transmit powers and traversal achievable rates under the base station selection algorithm and exhaustive search method of the present invention.

[0106] Figure 8 This is a spatial distribution diagram of the traversable achievable rate for a single base station 1 in a single-antenna scenario.

[0107] Figure 9 Schematic diagram of the change in the proportion of effective receiving area with the number of antennas.

[0108] Figure 10 Schematic diagram of the change of effective receiving area ratio with transmission power.

[0109] Figure 11 Schematic diagram of the change of traversal safe rate with the number of antennas.

[0110] Figure 12 Schematic diagram of the change of traversal safe rate with transmission power. DETAILED DESCRIPTION

[0111] For a given user location, the core network calculates the azimuth of the corresponding base station's main beam and instructs the base station to intersect its beam within a small area encompassing the user. Only terminals within this area can simultaneously receive multiple channels of information and combine them to recover the original information. Users outside this area lack at least one channel of information and cannot complete the combination, thus losing access to the original information.

[0112] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0113] A skywave massive MIMO secure communication method based on multi-station collaboration includes the following steps:

[0114] Step 1: Describe the roles of various elements in the multi-station collaborative skywave secure communication method and the relationships between them;

[0115] The description includes:

[0116] like Figure 1 As shown in the figure, a communication system consisting of a source, a core network, M base stations, and a user is established. The source sends the original message to the core network. The core network divides the original message into M sub-messages and sends them to M base stations via optical cables. Each base station sends the sub-message to the user via the skywave channel. Finally, the user combines the corresponding sub-messages to restore the original message. At the same time, the eavesdropper can eavesdrop on the communication content by receiving the signal.

[0117] Skywave channels transmit information through reflections from the ionosphere. The ionosphere is divided into three layers: the D layer, the E layer, and the F layer. The E and F layers are the ones that can reflect signals.

[0118] The D layer is 50 to 90 kilometers above the ground and only exists during the day. It disappears at night. The free electron density in the D layer is low. The D layer absorbs signal energy, causing channel attenuation, but does not reflect signals.

[0119] The E layer is 90 to 130 kilometers above the ground. The free electron density of the E layer is higher than that of the D layer. It is the lowest layer that can reflect sky wave signals. The E layer does not completely disappear at night.

[0120] The F layer is more than 130 kilometers above the ground. It is divided into F1 and F2 layers during the day and merges into a single layer at night. The F layer has the highest degree of ionization, and most sky-wave communications are achieved through reflections from the F layer. The transmitted signal usually reaches the receiver from different angles and with different signal strengths after a single hop or multiple hops, modeling the sky-wave channel as a multipath channel.

[0121] Step 2: Build a mathematical model for the distribution of precoding schemes, base station selection, and achievable rates based on user location.

[0122] Includes the following:

[0123] Let x m (t) is the analog baseband signal sent by base station m, and the analog baseband signal received by receiver ξ is

[0124]

[0125] Where t represents time, τ is the temporary variable of integration, is the time-varying channel impulse response from base station m to receiver ξ, x m is the transmitted signal of base station m, dτ represents τ as the integrand, z ξ (t) is Gaussian white noise;

[0126] Using OFDM system, define N c 、N g 、T s is the number of subcarriers, cyclic prefix length, and sampling interval; then, T c =N c T s and T g =N g T s Set N as the duration of OFDM symbol and cyclic prefix respectively. v subcarriers are used to transmit data;

[0127] definition and Δf = 1 / T c h m,ξ (t,τ) and the subcarrier spacing; then, for the sub-information sent by base station m, the demodulated signal on the kth subcarrier from base station m to receiver ξ on the lth symbol is

[0128]

[0129] in is the channel frequency response from base station m to receiver ξ on the kth subcarrier of the lth symbol, is the transmitted signal component from base station m to receiver ξ on the kth subcarrier of the lth symbol, z m,ξ,l,kis a complex Gaussian random variable with zero mean and variance n0, and

[0130]

[0131] is the channel frequency response from base station m to receiver ξ at the lth symbol and kth subcarrier;

[0132] The shortwave channel is modeled as a wide-sense stationary uncorrelated scattering channel; let f c is the carrier frequency; considering the time-varying nature of the shortwave channel, the operating frequency needs to be adjusted according to the real-time ionospheric state; each base station is equipped with a uniform linear array, and f is set om is the highest operating frequency of base station m, then the spacing between adjacent antenna units of base station m is in represents the wavelength corresponding to the highest operating frequency, and c is the speed of light;

[0133] set up and are the azimuth and elevation angles of the departure path (e.g. Figure 2 Assume that there is P between the receiver ξ and the base station m. m,ξ separable multipaths, define τ m,ξ,p,n is the time delay of the pth path from base station m to the nth antenna of receiver ξ, expressed as

[0134] τ m,ξ,p,n =τ m,ξ,p,1 +(n-1)Δτ m cosθ azi,m,ξ,p cosθ ele,m , ξ,p (52)

[0135] in is the time it takes for light to pass through two adjacent antenna units of base station m. To make the expression more concise, let Ω m,ξ,p =cosθ azi,m,ξ,p cosθ ele,m,ξ,p ;

[0136] The time-varying channel impulse response from receiver ξ to the nth antenna of base station m is expressed as

[0137]

[0138] in is the imaginary unit, f m is the operating frequency of base station m, α m,ξ,p (t) represents the complex gain random variable; since the earth's surface and ionosphere are rough, assume that there is Q in the p-th path from base station m to receiver ξ m,ξ,p subpaths, these subpaths have the same propagation delay, sending and arrival azimuth and elevation angles; αm,ξ,p (t) is expressed as

[0139]

[0140] where β m,ξ,p,q 、φ m,ξ,p,q and υ m,ξ,p,q are the gain, initial phase and Doppler shift of the qth path respectively; assuming φ m,ξ,p,q Obey the uniform distribution on [0,2π); when Q m,ξ,p →∞,α m,ξ,p The amplitude of (t) follows a Rayleigh distribution;

[0141] According to formula (3) and formula (5), we can get

[0142]

[0143] in

[0144]

[0145] represents the direction cosine Ω m,ξ,p The corresponding direction cosine on the kth subcarrier; defines the path gain

[0146]

[0147] Here, the direction cosine Ω of each separable path is m,ξ,p and path gain β m,ξ,p Considered as partial CSI;

[0148] The transmitted signal of base station m is expressed as

[0149]

[0150] Among them, P m and s m are the transmission power and symbol of base station m, respectively, and s m is a random variable with zero mean and unit variance, f m,k represents the precoding vector of base station m on the kth subcarrier; the achievable rate R of base station m sending sub-information m to receiver ξ on the kth subcarrier m,ξ Expressed as

[0151]

[0152] Where n0 is the noise power.

[0153] Considering that the corresponding original signal can be correctly restored only when all sub-signals are correctly received, the ergodic achievable rate of the entire system is expressed as

[0154]

[0155] where w∈{0,1} M×1 Indicates the status of the base station, [w] m =1 means the mth base station is selected, otherwise it is not selected, N v is the number of subcarriers used to transmit data;

[0156] Assume that each eavesdropper is equipped with a single antenna to receive and combine information from various channels. Formula (12) reveals the relationship between the receiver rate and its position. In this case, the eavesdropper's rate is related to its spatial position. By making good use of the sparsity of the angle domain channel, the area of ​​the receiving area is made smaller, which ensures the communication of legitimate users while reducing the eavesdropper's communication rate. Assuming that the positions of the user and eavesdropper are u and e, respectively, the system's security rate is expressed as

[0157] R sec =[R u -R e ] + (61)

[0158] where R u and R e denote the traversal rates of the user and the eavesdropper respectively.

[0159] Under the constraints of the minimum number of base stations selected, the maximum transmit power of a single base station, and the two-norm of the precoding vector, the user rate is maximized by optimizing the precoding vector, transmit power, and base station selection scheme. The optimization problem is mathematically expressed as:

[0160]

[0161] The constraint C1 indicates that at least κ base stations must be in working state, and the constraint C2 indicates that the transmission power of each base station should be less than the maximum value P max ,Constraint C3 indicates that the precoding scheme of a single base station antenna array must meet the power constraint.

[0162] Step 3: Solve the precoding problem for each base station;

[0163] Specifically include:

[0164] According to formula (5), formula (8) and formula (11), we can get

[0165]

[0166] in is α m,ξ,p The complex conjugate of .

[0167] Definition a m,ξ,kis the channel gain from base station m to receiver ξ on the kth subcarrier, expressed as

[0168]

[0169] The expected value of the achievable rate of the channel from base station m to receiver ξ on the kth subcarrier is a m,ξ,k The monotonically increasing function maximizes the achievable rate of each sub-information by maximizing the channel gain of each sub-information;

[0170] First, we analyze the precoding problem in the case of partial CSI;

[0171] The goal is to maximize the channel gain under the constraint of the two-norm of the precoding vector. The optimization problem is modeled as

[0172]

[0173] Define the following matrix

[0174]

[0175] According to formula (6), we get

[0176]

[0177] According to formula (9) and formula (19), P2 is converted into

[0178]

[0179] Using the relaxation method, ignoring rank(F) = 1, it is obvious that P2.1 is a convex semidefinite program, which is solved using CVXPY; the optimal F is defined as m,k The matrices and their corresponding maximum gains are and If the solution F m,opt If the rank is one, the solution is globally optimal. If not, the first column of its left singular matrix is ​​output.

[0180] The specific process can be found in Algorithm 1.

[0181]

[0182] Secondly, precoding design in a perfect CSI scenario:

[0183] By assuming that the base station obtains perfect CSI, a precoder based on the minimum mean square error (MMSE) criterion is used; the following optimization problem is established

[0184]

[0185] in s m,k ,ζ m,k 、y m,k 、 f m,k 、h m,k are the MMSE-based precoding vector of base station m on the kth subcarrier, the transmitted signal, the auxiliary variable for power normalization, the received signal, the temporary variable, and the channel frequency response. Therefore, we can get

[0186]

[0187] Among them, m,k =||h m,k ||2.

[0188]

[0189] Step 4: Select an appropriate base station based on the user's location; specifically:

[0190] Maximize the user's traversal rate by optimizing the base station selection; define R ξ (w) is the ergodic achievable rate of the receiver ξ obtained by CVXPY under the base station selection scheme w, then problem P4 is expressed as

[0191]

[0192] Solve P4, we have The case where constraint C1 is satisfied; for the M base station scenario, the complexity of the exhaustive search is very high when k is relatively small, which is O(2 M );

[0193] Because the traversal rate depends on the slowest sub-message, an efficient method is proposed to reduce the algorithm complexity. Because the traversal rate is an increasing function of the channel gain of each sub-message, all sub-messages are arranged from largest to smallest, and the first k are selected.

[0194]

[0195] Step 5: Optimize the power of the selected base station. Specifically include:

[0196] To optimize the transmit power of each selected base station, a heuristic solution is to set the transmit power of each base station to the maximum, thereby maximizing the user's rate. Considering that the user's traversal rate is determined by the smallest of all sub-information, the power of the base station with the lowest channel gain is maximized, while reducing the power of other base stations until the traversal rate of each sub-information is the same. This problem is expressed as

[0197]

[0198] Use binary search to solve P5. See Algorithm 4 for the specific process.

[0199]

[0200]

[0201] A skywave massive MIMO secure communication system based on multi-station collaboration, comprising:

[0202] A description module is used to describe the role of each element in the multi-station collaboration-based skywave secure communication method and the relationship between them;

[0203] Establish a module for establishing a mathematical model for precoding schemes, base station selection, and achievable rate distribution based on user location;

[0204] Precoding module, used to solve the precoding problem of each base station;

[0205] Base station selection module, used to select a suitable base station according to the user's location;

[0206] The power optimization module is used to optimize the transmission power of the base station.

[0207] A specific embodiment of the present invention is as follows, and the system simulation adopts Python language. The following embodiment examines the effectiveness of the multi-station coordinated skywave massive MIMO secure communication system designed by the present invention.

[0208] This section demonstrates the effectiveness of the proposed algorithm through simulation results. First, the user rate of the proposed algorithm is compared with that of the exhaustive search method. Then, the regional distribution characteristics of the receiver rate are analyzed and the reception area of ​​the proposed method is compared with that of a single base station omnidirectional antenna coverage scenario. Finally, the traversal safety rate performance of the proposed method is analyzed. Figure 3 The parameter settings are given. 100 user locations are randomly generated within the simulation area 90-120E-20-50N. The azimuth angle can be calculated based on the geometric relationship between the base station and the user locations.

[0209] Figure 4 and Figure 6The following diagram shows the user rate changes under different parameter settings for both partial CSI and perfect CSI scenarios. It can be seen that the user rate increases with increasing the number of antennas and transmit power. This is because the former improves energy efficiency and concentrates energy, while the latter increases the received signal-to-noise ratio. Furthermore, a smaller κ value leads to a higher user rate, as the user rate is determined by the slowest of all sub-messages. Therefore, a smaller κ value corresponds to a higher rate for the slowest sub-message. Furthermore, the performance under partial CSI approaches that under perfect CSI. This is because in shortwave skywave channels, the angular domain spread is generally limited, and the energy of multiple arrival paths is already very small.

[0210] Figure 5 and Figure 7 The performance comparison of the achievable rate under the proposed base station selection algorithm and the exhaustive search method is plotted. It can be seen that the performance of the proposed algorithm is very close to that of the exhaustive search algorithm, which demonstrates the effectiveness of the proposed algorithm.

[0211] Figure 8 This figure shows the spatial distribution of the traversal rate in a single-base station (base station 1) single-antenna scenario. As shown in (a), a very low rate area appears in the lower left corner. This is the quiet zone for shortwave communication, where no shortwave signals are reflected. From the lower left corner to the upper right corner, a ring with a slightly lower rate than the surrounding area can be seen. This is because the lower left corner of the ring has two paths from the F layer reflection, while the upper right corner has one path from the F layer and one from the E layer reflection. Further out, the traversal rate increases again, due to the addition of the second sky hop, which has the shortest propagation distance. The third sky hop is not clearly visible in the figure due to its low signal strength. At longer distances, the traversal rate decreases further due to spatial loss. Sub-figures (b) and (c) show the scenarios with 8 and 128 antennas, respectively. It can be seen that the beam becomes narrower, while the main lobe energy is higher. Sub-figure (df) plots the scenario with four base stations for the same number of antennas. It can be seen that in the multi-base station scenario, the receivable area is further reduced, demonstrating the security performance of the proposed solution.

[0212] Figure 9 and Figure 10 The figure shows how the effective reception area ratio changes with the number of antennas and transmit power. As the number of antennas increases, the effective reception area ratio first increases and then decreases. This is because when the number of antennas is small, while coverage is wide, the overall rate is relatively low. As the number of antennas increases, the beam becomes narrower, the energy is more concentrated, and the effective reception area ratio gradually decreases. As the transmit power increases, the effective reception area also increases. This is because when the signal-to-noise ratio at the receiver improves, the traversal rate can meet the threshold in more areas.

[0213] Figure 11 and Figure 12 The traversable secure rate is plotted as a function of the number of antennas and transmit power. It can be seen that the traversable secure rate increases with the number of antennas. However, the increase in transmit power is slower. This is because increasing transmit power increases both the user and eavesdropper rates, making it less noticeable in the final traversable secure rate. Furthermore, the proposed power optimization algorithm outperforms the heuristic transmit power design scheme in terms of traversable secure rate. This is because the proposed power optimization algorithm can reduce the base station's transmit power while maintaining user rates, thereby reducing the eavesdropper rate. Furthermore, the secure rate is highest when κ = 2. This is because two beams are sufficient to form a relatively small effective reception area, and adding more beam crossings will not provide any significant improvement. Performance is particularly poor when κ = 4. This is because it cannot prevent users from being in any blind spots, lacking flexibility.

[0214] The present invention has been described above in an illustrative manner using embodiments. Those skilled in the art should understand that the present disclosure is not limited to the embodiments described above, and that various changes, modifications, and substitutions may be made without departing from the scope of the present invention.

Claims

1. A skywave massive MIMO secure communication method based on multi-station collaboration, characterized in that: The steps include: Step 1: Describe the roles of various elements in the multi-station collaborative skywave secure communication method and the relationships between them. The description includes: Establish a communication system consisting of a signal source, a core network, M base stations, and a user. The signal source sends the original message to the core network. The core network splits the original message into M sub-messages and sends them to M base stations via optical cables. Each base station sends the sub-message to the user via a skywave channel. Finally, the user combines the corresponding sub-messages to restore the original message. Meanwhile, an eavesdropper can eavesdrop on the communication content by receiving the signal. Skywave channels transmit information through reflections from the ionosphere. The ionosphere is divided into three layers: the D layer, the E layer, and the F layer. The E and F layers are the ones that can reflect signals. The D layer is 50 to 90 kilometers above the ground and only exists during the day. It disappears at night. The free electron density in the D layer is low. The D layer absorbs signal energy, causing channel attenuation, but does not reflect signals. The E layer is 90 to 130 kilometers above the ground. The free electron density of the E layer is higher than that of the D layer. It is the lowest layer that can reflect sky wave signals. The E layer does not completely disappear at night. The F layer is located at an altitude of more than 130 kilometers above the Earth's surface. It is divided into the F1 and F2 layers during the day and merges into a single layer at night. The F layer has the highest degree of ionization, and most skywave communications are achieved through reflections from the F layer. Transmitted signals typically reach the receiver from different angles and with different signal strengths via a single or multiple hops, modeling the skywave channel as a multipath channel. Step 2: Build a mathematical model for the user location-based precoding scheme, base station selection, and achievable rate distribution. This includes the following: Let x m (t) is the analog baseband signal sent by base station m, and the analog baseband signal received by receiver ξ is Where t represents time, τ is the temporary variable of integration, is the time-varying channel impulse response from base station m to receiver ξ, x m is the transmitted signal of base station m, dτ represents τ as the integrand, z ξ (t) is Gaussian white noise; Using OFDM system, define N c 、N g 、T s is the number of subcarriers, cyclic prefix length, and sampling interval; then, T c =N c T s and T g =N g T s Set N as the duration of OFDM symbol and cyclic prefix respectively. v subcarriers are used to transmit data; definition and Δf = 1 / T c h m,ξ (t,τ) and the subcarrier spacing; then, for the sub-information sent by base station m, the demodulated signal on the kth subcarrier from base station m to receiver ξ on the lth symbol is in is the channel frequency response from base station m to receiver ξ on the kth subcarrier of the lth symbol, x m,ξ,l,k is the transmitted signal component from base station m to receiver ξ on the kth subcarrier of the lth symbol, z m,ξ,l,k is a complex Gaussian random variable with zero mean and variance n0, and is the channel frequency response from base station m to receiver ξ at the lth symbol and kth subcarrier; The shortwave channel is modeled as a wide-sense stationary uncorrelated scattering channel; let f c is the carrier frequency; considering the time-varying nature of the shortwave channel, the operating frequency needs to be adjusted according to the real-time ionospheric state; each base station is equipped with a uniform linear array, and f is set om is the highest operating frequency of base station m, then the spacing between adjacent antenna units of base station m is in represents the wavelength corresponding to the highest operating frequency, and c is the speed of light; set up and are the azimuth and elevation angles of the departure path respectively. Assume that there is P between the receiver ξ and the base station m. m,ξ separable multipaths, define τ m,ξ,p,n is the time delay of the pth path from base station m to the nth antenna of receiver ξ, expressed as in is the time it takes for light to pass through two adjacent antenna units of base station m. To make the expression more concise, let The time-varying channel impulse response from receiver ξ to the nth antenna of base station m is expressed as in is the imaginary unit, f m is the operating frequency of base station m, α m,ξ,p (t) represents the complex gain random variable; since the earth's surface and ionosphere are rough, assume that there is Q in the p-th path from base station m to receiver ξ m,ξ,p subpaths, these subpaths have the same propagation delay, sending and arrival azimuth and elevation angles; α m,ξ,p (t) is expressed as where β m,ξ,p,q 、φ m,ξ,p,q and υ m,ξ,p,q are the gain, initial phase and Doppler shift of the qth path respectively; assuming φ m,ξ,p,q Obey the uniform distribution on [0,2π); when Q m,ξ,p →∞,α m,ξ,p The amplitude of (t) follows a Rayleigh distribution; According to formula (3) and formula (5), we can get in represents the direction cosine Ω m,ξ,p The corresponding direction cosine on the kth subcarrier; defines the path gain Here, the direction cosine Ω of each separable path is m,ξ,p and path gain β m,ξ,p Considered as partial CSI; The transmitted signal of base station m is expressed as Among them, P m and s m are the transmission power and symbol of base station m, respectively, and s m is a random variable with zero mean and unit variance, f m,k represents the precoding vector of base station m on the kth subcarrier; the achievable rate R of base station m sending sub-information m to receiver ξ on the kth subcarrier m,ξ Expressed as Where n0 is the noise power; Considering that the corresponding original signal can be correctly restored only when all sub-signals are correctly received, the ergodic achievable rate of the entire system is expressed as where w∈{0,1} M×1 Indicates the status of the base station, [w] m =1 means the mth base station is selected, otherwise it is not selected, N v is the number of subcarriers used to transmit data; Assume that each eavesdropper is equipped with a single antenna to receive and combine information from various channels. Formula (12) reveals the relationship between the receiver rate and its position. In this case, the eavesdropper's rate is related to its spatial position. By making good use of the sparsity of the angle domain channel, the area of ​​the receiving area is made smaller, which ensures the communication of legitimate users while reducing the eavesdropper's communication rate. Assuming that the positions of the user and eavesdropper are u and e, respectively, the system's security rate is expressed as R sec =[R u -R e ] + (13) where R u and R e denote the traversal rates of the user and the eavesdropper respectively; Under the constraints of the minimum number of base stations selected, the maximum transmit power of a single base station, and the two-norm of the precoding vector, the user rate is maximized by optimizing the precoding vector, transmit power, and base station selection scheme. The optimization problem is mathematically expressed as: The constraint C1 indicates that at least κ base stations must be in working state, and the constraint C2 indicates that the transmission power of each base station should be less than the maximum value P max ,Constraint C3 indicates that the precoding scheme of a single base station antenna array must meet the power constraint; Step 3: Solve the precoding problem for each base station; specifically, According to formula (5), formula (8) and formula (11), we can get in is α m,ξ,p The complex conjugate of Definition a m,ξ,k is the channel gain from base station m to receiver ξ on the kth subcarrier, expressed as The expected value of the achievable rate of the channel from base station m to receiver ξ on the kth subcarrier is a m,ξ,k The monotonically increasing function maximizes the achievable rate of each sub-information by maximizing the channel gain of each sub-information; First, we analyze the precoding problem in the case of partial CSI; The goal is to maximize the channel gain under the constraint of the two-norm of the precoding vector. The optimization problem is modeled as st||f||≤1. Define the following matrix According to formula (6), we get According to formula (9) and formula (19), P2 is converted into stC1:F≥0, C2:tr(F)≤1. Using the relaxation method, ignoring rank(F) = 1, it is obvious that P2.1 is a convex semidefinite program, which is solved using CVXPY; the optimal F is defined as m,k The matrices and their corresponding maximum gains are and If the solution F m,opt If the rank is one, the solution is globally optimal. If not, the first column of its left singular matrix is ​​output. Step 4: Select a suitable base station based on the user's location; specifically: Maximize the user's traversal rate by optimizing base station selection; define is the ergodic achievable rate of the receiver ξ obtained by CVXPY under the base station selection scheme w, then problem P4 is expressed as stC1:||w||0≥k. Solve P4, we have The case where constraint C1 is satisfied; for the M base station scenario, the complexity of the exhaustive search is very high when k is relatively small, which is O(2 M ); 6.1 Calculate the rate of all sub-information according to formula (11); 6.2 Arrange the results in step 6.1 from largest to smallest and define b(i) as the index number of the i-th base station; 6.3 Initializing w opt =0 M ; 6.4 For m = 1 ~ κ, assign [w opt ] b(m) =1; 6.5 output w opt ; Step 5: Optimize the power of the selected base station; specifically include: To optimize the transmit power of each selected base station, a heuristic solution is to set the transmit power of each base station to the maximum, thereby maximizing the user's rate. Considering that the user's traversal rate is determined by the smallest of all sub-information, the power of the base station with the lowest channel gain is maximized, while reducing the power of other base stations until the traversal rate of each sub-information is the same. This problem is expressed as Use binary search to solve P5. initialization m min =0,∈=inf, where m=1,2,3,...,M; let, w m =1, Calculate R according to formula (11) m,ξ ,like but Where m=1,2,3,...,M; if m≠m min , calculated by binary search Returns the optimized transmit power 2. The skywave massive MIMO secure communication method based on multi-station collaboration according to claim 1, characterized in that: Precoding design in perfect CSI scenarios: By assuming that the base station obtains perfect CSI, a precoder based on the minimum mean square error criterion is adopted; Establish the following optimization problem in s m,k ,ζ m,k 、y m,k 、 f m,k 、h m,k They are the precoding vector based on the MMSE criterion of base station m on the kth subcarrier, the transmitted signal, the auxiliary variable for power normalization, the received signal, the temporary variable, and the channel frequency response, which can be obtained Among them, m,k =||h m,k ||2.

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