A robust directional modulation method with switch relaxation

Abstract

The present invention relates to a robust directional modulation method with switch relaxation, and relates to the field of communication technology. A random selection of transmission signals is introduced at the transmitting end, and a basic model of the relaxation phase is first built. The original coordinate system is rotated to the direction of the user's desired signal using a coordinate system rotation method, and the target constellation point is split into real and imaginary parts in the coordinate system obtained after the rotation, minimizing the transmission power of the transmitting end, converting the optimization problem into a convex optimization problem for solution, and reconstructing the transmission signal vector of the transmitting end according to the obtained optimal vector. The method of the present invention is applicable to the case where there is a bounded error in the azimuth angle estimation value between the desired user and the transmitter under a line-of-sight channel. The random selection of transmitting antennas is introduced at the transmitting end to further reduce the probability that the useful signal is intercepted by the eavesdropping user in the channel, thereby enhancing the secure transmission performance of the communication system.

Description

Technical Field

[0001] The present invention relates to a robust directional modulation technology with switched relaxed phase constraints, and in particular to a method for robust directional modulation with switched relaxed phase constraints. The method is applicable to situations where there is a bounded error in the azimuth angle estimation value between a desired user and a transmitter in a line-of-sight channel. The method introduces random selection of transmitting antennas at the transmitting end to further reduce the probability that useful signals are intercepted by eavesdropping users in the channel, thereby enhancing the secure transmission performance of the communication system. Background Art

[0002] With the deepening of research on multi-antenna wireless physical layer security technology, the emerging array antenna transmission technology has emerged. Recently, more and more scholars have begun to study the emerging array antenna directional modulation technology to achieve secure transmission at the physical layer. The basic model can be seen in the attached Figure 1 The transmitter consists of several antenna arrays. By appropriately adjusting the phase of the signals sent to each antenna array, the signal received in the direction of the legitimate user is enhanced while the signal strength in the undesired direction is suppressed. As a result, the signal received in the direction of the legitimate user is an ideal constellation, while the signal received by the eavesdropper in other directions is disrupted.

[0003] like Figure 2 As shown in the figure, consider a model in which the receiver's azimuth angle estimation has bounded error. In this case, applying a robust directional modulation technique with relaxed phase constraints can enable more desired symbols to be detected by the receiver, but this approach does not optimize the decoding performance of legitimate users. Furthermore, introducing random selection of transmit antennas at the transmitter can further reduce the user's average bit error rate, thereby making the transmission of private information more secure.

[0004] To achieve high-speed and efficient data transmission, a basic mathematical model of robust directional modulation with relaxed phase switching is constructed under bounded channel errors. The optimal weight vector is solved using the Convex Optimization (CVX) toolbox, and the average bit error rate (BER) of users is calculated and observed under different signal-to-noise ratios (SNRs) and angle estimation errors. Finally, it is shown that the robust modulation method with switching can further reduce the BER of users compared to the robust modulation method without switching, regardless of the ergodic SNR or angle estimation error. Summary of the Invention

[0005] Technical problems to be solved

[0006] In order to avoid the shortcomings of the prior art, the present invention proposes a robust directional modulation method with switch relaxation.

[0007] Technical Solution

[0008] A method for robust directional modulation with switch relaxation is characterized by the following steps:

[0009] Step 1: Introduce random selection of the transmitted signal at the transmitter and use the coordinate system rotation method to express the real and imaginary parts of the noise-free signal at the receiver:

[0010]

[0011]

[0012] Among them, τ is the random selection vector of the transmitting antenna; ω is the transmitting signal vector; s i is the expected signal of user i; y i , n i Represent the signal received by user i and the additive white Gaussian noise respectively; (Re{z i},Im{z i}) is the coordinate of the target constellation point after the rotation of the coordinate system, and o is the product of the corresponding parameters of the two vectors;

[0013] For the sake of brevity, the definitions are:

[0014]

[0015] in, represents the estimated value of the normalized channel of the i-th user relative to the transmitter; Δh i represents the difference between the actual value and the estimated value of the normalized channel of the i-th user relative to the transmitter, that is, the channel error of the i-th user relative to the transmitter; h(θ i ) represents the actual value of the normalized channel of the i-th user relative to the transmitter;

[0016] Step 2: After completing the real and imaginary part expressions, split the noise-free received signal at the receiving end into real and imaginary parts:

[0017]

[0018]

[0019] in, e i =Δh i s i ; Respectively represent The real and imaginary parts of e iR , e iI Represents e i The real and imaginary parts of ω; R ,ω I represent the real and imaginary parts of ω respectively; ω1=[ω I ; -ω R ],ω2=[ωR ;ω I ];

[0020] Step 3: Establish a basic model of the relaxation phase and simplify the model:

[0021]

[0022] Further, it can be simplified to:

[0023]

[0024]

[0025]

[0026]

[0027] Among them, η i is the minimum signal-to-noise ratio constraint for the i-th user; N0 is the noise power, which is set to the same value here; θ represents the angle between the desired signal direction and the relaxed phase boundary;

[0028] Step 4: Vector e i Derivation of the upper bound of the module:

[0029]

[0030] It can be found that the vector e i and the channel error vector Δh i have the same upper bound ε i , so we can solve for the vector e i The upper bound of is obtained and the above inequality is scaled, thereby transforming the optimization problem into a convex optimization problem.

[0031] Step 5: Translate the inequalities in the model into vectors e i The upper bound ε i Scale the link and transform it into a convex function;

[0032]

[0033]

[0034] Step 6: Minimize the transmit power at the transmitter to ensure that the target constellation point of the received signal of any user falls within the relaxed phase region;

[0035]

[0036]

[0037]

[0038] ω1=Πω2

[0039]

[0040] Step 7: Convert step 6 into a convex optimization problem and solve it using the CVX toolkit. Reconstruct the transmitting signal vector ω at the transmitter based on the obtained optimal vector ω1.

[0041] A computer system, characterized in that it includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method.

[0042] A computer-readable storage medium is characterized by storing computer-executable instructions, which are used to implement the above method when executed.

[0043] Beneficial effects

[0044] The present invention provides a method for robust directional modulation with added switch relaxation. By adopting a method for robust phase modulation with added switch relaxation, random selection of transmitted signals is introduced at the transmitting end, thereby reducing the average bit error rate of users. Compared with traditional methods, this method can show better performance and better ensure the security of signal transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0046] Figure 1 Schematic diagram of multi-beam multicast directional modulation;

[0047] Figure 2 Schematic diagram of receiver angle error;

[0048] Figure 3 is a curve chart showing the change of the user's average bit error rate with the minimum signal-to-noise ratio at the receiving end;

[0049] Figure 4 This is a graph showing how the average bit error rate of users changes with the upper bound of the angle estimation error. DETAILED DESCRIPTION

[0050] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0051] The present invention provides a robust directional modulation method based on relaxed phase constraints with switches. The method uses Quaternary Phase Shift Keying (QPSK) as a modulation method. The solution process mainly includes the following steps:

[0052] Step 1: Use the coordinate system rotation method to express the real and imaginary parts of the noise-free signal at the receiver:

[0053]

[0054]

[0055] Among them, τ is the random selection vector of the transmitting antenna; ω is the transmitting signal vector; s i is the expected signal of user i; y i , n i Represent the signal received by user i and the additive white Gaussian noise respectively; (Re{z i},Im{z i}) is the coordinate of the target constellation point after the rotation of the coordinate system; for the sake of simplicity, it is defined as:

[0056]

[0057] in, represents the estimated value of the normalized channel of the i-th user relative to the transmitter; Δh i represents the difference between the actual value and the estimated value of the normalized channel of the i-th user relative to the transmitter, that is, the channel error of the i-th user relative to the transmitter; h(θ i ) represents the actual value of the normalized channel of the i-th user relative to the transmitter.

[0058] Step 2: After completing the real and imaginary part expressions, split the noise-free received signal at the receiving end into real and imaginary parts:

[0059]

[0060]

[0061] in: e i =Δh i si ; Respectively represent The real and imaginary parts of e iR , e iI Represents e i The real and imaginary parts of ω; R ,ω I represent the real and imaginary parts of ω respectively; ω1=[ω I ; -ω R ],ω2=[ω R ;ω I ].

[0062] Step 3: Establish a basic model of the relaxation phase and simplify the model:

[0063] If the noise-free signal received by the receiver is pushed into the relaxed phase region, the following inequality relationship needs to be satisfied:

[0064]

[0065] Further, it can be simplified to:

[0066]

[0067]

[0068]

[0069]

[0070] Among them, η i is the minimum signal-to-noise ratio constraint for the i-th user; N0 is the noise power, which is set to the same value here; θ represents the angle between the desired signal direction and the relaxed phase boundary;

[0071] Step 4: Vector e i Derivation of the upper bound of the module:

[0072]

[0073] It can be found that the vector e i and the channel error vector Δh i have the same upper bound ε i , so we can solve for the vector e i The upper bound of is obtained and the above inequality is scaled, thereby transforming the optimization problem into a convex optimization problem.

[0074] Step 5: Translate the inequalities in the model into vectors e i The upper bound ε iScale the link and transform it into a convex function;

[0075]

[0076]

[0077] Step 6: Minimize the transmit power at the transmitter to ensure that the target constellation point of the received signal of any user falls within the relaxed phase region;

[0078]

[0079]

[0080]

[0081] ω1=Πω2

[0082]

[0083] Step 7: The above problem is a convex optimization problem and can be solved using the CVX toolkit. The transmitted signal vector ω of the transmitter is reconstructed based on the obtained optimal vector ω1. Then, the position of the target constellation point is locked and it is determined whether it is in the same quadrant as the expected signal. This is used as a basis to determine whether the current experiment has a bit error.

[0084]

[0085] Among them, n1,…n i ,…n K Respectively represent the additive Gaussian white noise received by user K, satisfying the complex Gaussian distribution with mean 0 and variance 1; if y i In s i The projection in the direction is greater than times s i , which means that the signal received by the receiver is in the same quadrant as the expected signal, which means that user i currently has no bit error, otherwise a bit error has occurred;

[0086] Step 8: First, fix the upper bound of the angle estimation error and perform experiments with small signal-to-noise ratios at the receiver. Keeping all other variables the same, perform multiple experiments at each signal-to-noise ratio. Calculate the user's average bit error rate at the current signal-to-noise ratio based on the number of bit errors, and compare the performance with traditional methods. Second, fix the minimum signal-to-noise ratio at the receiver and perform experiments with the upper bound of the angle estimation error. Keeping all other variables the same, perform multiple experiments at each angle estimation error. Calculate the user's average bit error rate at the current upper bound of the angle estimation error based on the number of bit errors, and compare the performance with traditional methods.

[0087] Example 1:

[0088] The robust directional modulation method based on relaxed phase constraints provided by the present invention comprises the following steps of constructing and solving the robust optimization problem:

[0089] Step 1: Consider the following scenario: there is one transmitter in space, and the base station is equipped with four antennas. There are three target users, each with a single antenna. Assume that the estimated azimuth angles between the three users and the transmitter are 30°, 90°, and 120°, respectively. However, the azimuth angles estimated using the Capon algorithm inevitably have errors. Assume that the upper bound of the error between the estimated angle and the actual value is 0.5°.

[0090] First, build a basic model of the relaxation phase and use the coordinate system rotation method to rotate the original coordinate system to the direction of the desired signal of user i:

[0091]

[0092]

[0093] Among them, τ is the random selection vector of the transmitting antenna; ω is the transmitting signal vector; s i is the expected signal of user i, here we take QPSK signal; y i , n i Represent the signal received by user i and the additive white Gaussian noise respectively; (Re{z i},Im{z i}) is the coordinate of the target constellation point after the rotation of the coordinate system; for the sake of simplicity, it is defined as:

[0094]

[0095] in, represents the estimated value of the normalized channel of the i-th user relative to the transmitter; Δh i represents the difference between the actual value and the estimated value of the normalized channel of the i-th user relative to the transmitter, that is, the channel error of the i-th user relative to the transmitter; h(θ i ) represents the actual value of the normalized channel of the i-th user relative to the transmitter.

[0096] Step 2: After the coordinate system rotation is completed, the target constellation point is split into real and imaginary parts in the coordinate system obtained after the rotation;

[0097]

[0098]

[0099] in: e i =Δh i si ; Respectively represent The real and imaginary parts of e iR , e iI Represents e i The real and imaginary parts of ω; R ,ω I represent the real and imaginary parts of ω respectively; ω1=[ω I ; -ω R ],ω2=[ω R ;ω I ];

[0100] Step 3: Establish a basic model of the relaxation phase and simplify the model:

[0101] If the noise-free signal received by the receiver is pushed into the relaxed phase region, the following inequality relationship needs to be satisfied:

[0102]

[0103] Further, it can be simplified to:

[0104]

[0105]

[0106]

[0107]

[0108] Among them, η i is the minimum signal-to-noise ratio constraint for the i-th user; N0 is the noise power, which is taken as 1 here; θ represents the angle between the desired signal direction and the relaxed phase boundary, that is, 45°;

[0109] Step 4: Vector e i Derivation of the upper bound of the module:

[0110]

[0111] It can be found that the vector e i and the channel error vector Δh i have the same upper bound ε i , so we can solve for the vector e i The upper bound of is obtained and the above inequality is scaled, thereby transforming the optimization problem into a convex optimization problem.

[0112] Step 5: Translate the inequalities in the model into vectors e iThe upper bound of is scaled and transformed into a convex function;

[0113]

[0114]

[0115] Step 6: Minimize the transmit power at the transmitter to ensure that the target constellation point of the received signal of any user falls within the relaxed phase region;

[0116]

[0117]

[0118]

[0119] ω1=Πω2

[0120]

[0121] Step 7: The above problem is a convex optimization problem and can be solved using the CVX toolkit. The transmitted signal vector ω of the transmitter is reconstructed based on the obtained optimal vector ω1. Then, the position of the target constellation point is locked and it is determined whether it is in the same quadrant as the expected signal. This is used as a basis to determine whether the current experiment has a bit error.

[0122]

[0123] Among them, n1,…n i ,…n K Respectively represent the additive Gaussian white noise received by user K, satisfying the complex Gaussian distribution with mean 0 and variance 1; if y i In s i The projection in the direction is greater than times s i , it means that user i currently has no bit error, otherwise a bit error has occurred;

[0124] Step 8: First, fix the upper bound of the angle estimation error to 0.5 and perform experiments with small signal-to-noise ratios at the receiver. Keeping all other variables constant, perform 10,000 experiments at each signal-to-noise ratio. Calculate the user's average bit error rate at the current signal-to-noise ratio based on the number of bit errors, and compare the performance with traditional methods. Second, fix the small signal-to-noise ratio at the receiver to 0 dB and perform experiments with the upper bound of the angle estimation error. Keeping all other variables constant, perform 10,000 experiments at each signal-to-noise ratio. Calculate the user's average bit error rate at the current upper bound of the angle estimation error based on the number of bit errors, and compare the performance with traditional methods.

[0125] like Figure 3As shown in , under different signal-to-noise ratio constraints of the receiver, the application of the phase-robust modulation method with switch relaxation can further improve the error performance of the legitimate user compared with the phase-robust modulation method without switch relaxation. Figure 4 As shown in the figure, under different upper bounds on the azimuth estimation error, the phase-robust modulation method with switched relaxation can provide the receiver with stronger decoding capabilities. Therefore, introducing random selection of transmit antennas at the transmitter can further reduce the probability of private information being misdetected at the receiver.

[0126] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present invention, and these modifications or replacements should all be included in the scope of protection of the present invention.

Claims

1. A robust directional modulation method with switch relaxation, characterized in that Here are the steps: Step 1: Introduce random selection of the transmitted signal at the transmitter and use the coordinate system rotation method to express the real and imaginary parts of the noise-free signal at the receiver: Among them, τ is the random selection vector of the transmitting antenna; ω is the transmitting signal vector; s i is the expected signal of user i; y i , n i Represent the signal received by user i and the additive white Gaussian noise respectively; (Re{z i },Im{z i }) is the coordinate of the target constellation point after the rotation of the coordinate system, and o is the product of the corresponding parameters of the two vectors; For the sake of brevity, the definitions are: in, represents the estimated value of the normalized channel of the i-th user relative to the transmitter; Δh i represents the difference between the actual value and the estimated value of the normalized channel of the i-th user relative to the transmitter, that is, the channel error of the i-th user relative to the transmitter; h(θ i ) represents the actual value of the normalized channel of the i-th user relative to the transmitter; Step 2: After completing the real and imaginary part expressions, split the noise-free received signal at the receiving end into real and imaginary parts: in, e i =Δh i s i ; Respectively represent The real and imaginary parts of e iR , e iI Represents e i The real and imaginary parts of ω; R ,ω I represent the real and imaginary parts of ω respectively; ω1=[ω I ; -ω R ],ω2=[ω R ;ω I ]; Step 3: Establish a basic model of the relaxation phase and simplify the model: Further, it can be simplified to: Among them, η i is the minimum signal-to-noise ratio constraint for the i-th user; N0 is the noise power, which is set to the same value here; θ represents the angle between the desired signal direction and the relaxed phase boundary; Step 4: Vector e i Derivation of the upper bound of the module: It can be found that the vector e i and the channel error vector Δh i have the same upper bound ε i , so we can solve for the vector e i The upper bound of is obtained and the above inequality is scaled, thereby transforming the optimization problem into a convex optimization problem. Step 5: Translate the inequalities in the model into vectors e i The upper bound ε i Scale the link and transform it into a convex function; Step 6: Minimize the transmit power at the transmitter to ensure that the target constellation point of the received signal of any user falls within the relaxed phase region; ω1=Πω2 Step 7: Convert step 6 into a convex optimization problem and solve it using the CVX toolkit. Reconstruct the transmitting signal vector ω at the transmitter based on the obtained optimal vector ω1.

2. A computer system, characterized in that include: One or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method of claim 1.

3. A computer-readable storage medium, characterized in that Computer-executable instructions are stored, and when the instructions are executed, they are used to implement the method of claim 1.

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