A method for calculating the bit error rate of artificial noise-assisted MIMO systems under imperfect channels

Abstract

The present invention discloses a method for calculating the bit error rate of an artificial noise-assisted MIMO system under a non-perfect channel. Through the method in which the communicating parties mutually send channel pilot sequences, both the transmitting and receiving ends obtain the main channel estimation information. The transmitting end performs QPSK modulation on the confidential binary information data, and then generates zero-space artificial noise and a precoding matrix according to the main channel state information estimated by the transmitting end, and transmits the artificial noise together with the confidential signal after the precoding processing. The receiving end obtains the main channel state information according to the pilot signal of the transmitting end and generates a deprecoding matrix, decodes the confidential signal, and finally decodes the confidential signal using the maximum likelihood detection method. The artificial noise technology of the present invention increases the difference in noise levels between the receiving end and the illegal eavesdropping end, and improves the confidentiality of communication under a non-perfect channel.

Description

Technical Field

[0001] The present invention belongs to the technical field of physical layer security of wireless communication systems, and more specifically, relates to a method for implementing an artificial noise-assisted MIMO system under an imperfect channel. Technical Background

[0002] The broadcast characteristic of the wireless communication channel makes the information of the secure communication link extremely vulnerable to eavesdropping by illegal terminals. The ultra-dense node heterogeneous network deployment of 5G and future 6G communication systems and the wireless sensor nodes with limited computing resources in the order of hundreds of billions lead to a sharp increase in the complexity of key management based on cryptographic security mechanisms. This makes it difficult to guarantee high-speed transmission, low latency, and high security requirements under the cryptographic security system, and it has become impossible to support classical security mechanisms that rely on computing.

[0003] Physical layer security technology is the key technology to achieve secure information transmission in wireless communication systems. Different from the traditional upper-layer encryption mechanism that completely relies on the confidentiality of keys and strong computing, physical layer security aims to utilize the randomness of the wireless channel (such as random fading, signal interference, environmental noise, etc.), uniqueness, and advanced signal processing technology to adaptively optimize system resources, establish a dominant channel with advantages, and prevent illegal users from stealing confidential information from the received signals while ensuring reliable communication between the transceiver, so as to achieve the purpose of reliable and secure communication transmission of the system. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for implementing an artificial noise-assisted MIMO system under an imperfect channel, aiming to improve and verify the secrecy performance of MIMO communication under an imperfect channel from the physical layer.

[0005] To achieve the above purpose, the present invention uses the communication parties to mutually send pilots to obtain channel state information. The transmitting end Alice generates null space artificial noise and a precoding matrix based on the estimated channel state information, and the receiving end Bob generates an equivalent channel based on the estimated channel state information and performs decoding. Finally, the maximum likelihood detection method is used to decode the received signal and calculate the bit error rate.

[0006] The technical solution of the present invention is: a method for calculating the bit error rate of an artificial noise-assisted MIMO system under an imperfect channel, the method comprising:

[0007] Construct a transmitting end Alice with M antennas, a receiving end Bob with N antennas, and L eavesdropping ends Eve i , 1≤i≤L, with K antennas, and construct a channel between Alice and Bob where d ab is the distance between Alice and Bob, and H abis the instantaneous small-scale fading channel between Alice and Bob, and γ represents the fading coefficient of the channel; construct the channel between Alice and Eve i between where d ae,i is the distance between Alice and Eve, and H ae,i is the instantaneous small-scale fading channel between Alice and Eve i ;

[0008] Bob sends the pilot data X bp = diag(x 1 , x 2 , …, x i , …, x N ), and the pilot data Y a received by Alice is:

[0009] where is the additive white Gaussian noise, and H ba represents the main channel state information, and I M represents the diagonal identity matrix;

[0010] Alice performs channel estimation through the received pilot signal to obtain the estimated main channel state information The difference between the estimated channel state information and the true channel is E ba , that is E ba represents the channel estimation error matrix; Alice performs singular value decomposition on the estimated channel, where is 's null space, that is U 1 and U 0 represent unitary matrices, and D represents 's singular values; take the first r columns of as the precoding matrix

[0011] of the confidential signal, and the artificial noise signal is where the confidential signal is and the artificial noise signal is P is the power allocation ratio of the confidential signal, α is the proportion of the artificial noise power, and r is the number of data streams;

[0012] The received signals of Bob and Eve i are y b and y e,i respectively, where

[0013]

[0014]

[0015] where n b is the additive white Gaussian noise of the channel between Alice and Bob, and n e,i is the additive white Gaussian noise of the channel between the i-th eavesdropper and Alice, and x a is the final transmitted signal mixed with artificial noise, and γ is the path fading coefficient;

[0016] To increase the reliability of Bob's decoding, Alice sends the pilot sequence X ap = diag(x 1 , x 2 , …, x i , …, x r ), and the pilot data Y b received by Bob is:

[0017]

[0018] where is the additive white Gaussian noise;

[0019] Alice performs channel estimation through the received pilot signal to obtain the estimated equivalent main channel state information The difference between the estimated equivalent channel state information and the true equivalent channel is E ab , that is Then Bob decodes y b to obtain y B as:

[0020]

[0021] Similarly, the equivalent eavesdropping channel state information of Eve i is Eve i decodes y e,i to obtain the decoded signal y E,i as:

[0022]

[0023] The data detected by Bob and Eve i through the maximum likelihood method are respectively and Compare with u, so as to calculate the bit error rate of the MIMO system for Bob and Eve i in the non-perfect channel.

[0024] Generally speaking, the following beneficial effects can be achieved through the present invention:

[0025] For the MIMO communication scenario under imperfect channels, the present invention enables Alice and Bob to mutually transmit pilots to obtain channel state information. The transmitted signal constructed by Alice includes artificial noise and valid signals. Among them, the artificial noise is used to improve the communication security performance of the system. Through the estimated signal state information, singular value decomposition is performed to respectively obtain the precoding matrices of the secure signal and the artificial noise. Bob generates a decoding precoding matrix based on the estimated equivalent channel state information and decodes the signal. Finally, maximum likelihood detection is used for decoding, and the bit error rate is calculated. Description of the Drawings

[0026] Figure 1 is the communication system model of the present invention;

[0027] Figure 2 is the flowchart of the steps of the present invention;

[0028] Figure 3 is the influence of the system bit error rate on the signal-to-noise ratio under different numbers of transmit antennas;

[0029] Figure 4 is the influence of the system bit error rate on the signal-to-noise ratio under different numbers of receive antennas;

[0030] Figure 5 is the influence of the system bit error rate on the signal-to-noise ratio under different power allocation ratio antennas;

[0031] Figure 6 is the influence of the system bit error rate on the signal-to-noise ratio under different distances. Detailed Embodiments

[0032] Consider the Figure 1 bidirectional communication system model as shown. The system constructs a transmitter Alice with M antennas, a receiver Bob with N antennas, and L eavesdroppers Eve i (1 ≤ i ≤ L) with K antennas, and constructs the channel between Alice and Bob where d ab is the distance between Alice and Bob, and H ab is the instantaneous small-scale fading channel between Alice and Bob; constructs the channel between Alice and Eve i where, d is the distance between Alice and Eve, and H ae,i is the instantaneous small-scale fading channel between Alice and Eve ae,i to i Eve.

[0033] The flow chart of the system is as Figure 2 shown in

[0034] Bob sends the pilot data X to Alice bp = diag([x 1 , x 2 , …, x i , …, x N ), and the pilot data Y received by Alice a is

[0035]

[0036] where is the additive white Gaussian noise;

[0037] Alice performs channel estimation based on the received pilot signal to obtain the estimated main channel state information The difference between the estimated channel state information and the true channel is E ba , that is Alice performs singular value decomposition on the estimated channel where is 's null space, that is Take 's first r columns as the precoding matrix of the confidential signal Therefore, Alice constructs the transmitted confidential signal as The artificial noise signal is where the confidential signal is The artificial noise signal is P is the power allocation ratio of the confidential signal;

[0038] Bob and Eve i 's received signals are y b and y e,i , respectively, where

[0039]

[0040]

[0041] where n b is the additive white Gaussian noise of the channel between Alice and Bob, and n e,i is the additive white Gaussian noise of the channel between the i-th eavesdropper and Alice, and x a is the final transmitted signal mixed with artificial noise, and γ is the path fading coefficient.

[0042] To increase the reliability of Bob's decoding, Alice needs to send the pilot sequence X to Bob ap= diag([x 1 , x 2 , …, x i , …, x r ), and the pilot data Y received by Bob b is

[0043]

[0044] where is additive white Gaussian noise.

[0045] Alice performs channel estimation through the received pilot signal to obtain the estimated equivalent main channel state information The difference between the estimated equivalent channel state information and the true equivalent channel is E ab , that is Then Bob decodes y b to obtain y B which is

[0046]

[0047] Similarly, for Eve i the equivalent eavesdropping channel state information is Eve i decodes y e,i to obtain the decoded signal y E,i which is

[0048]

[0049] Therefore, the signal-to-noise ratio SNR B of Bob i and the signal-to-noise ratio SNR E,i of Eve

[0050]

[0051]

[0052] The data detected by Bob and Eve i through the maximum likelihood method are respectively and Compare with u to calculate the bit error rate of Bob and Eve i in the MIMO system under imperfect channels.

[0053] Since the artificial noise is designed to be aligned with the null space of the channel, it has no impact on the communication link transmission. The artificial noise will reduce the information decoding ability of potential eavesdropping nodes, thereby improving the secure transmission performance of the wireless communication system. At the same time, by reasonably designing the transmission direction of the secure signal, Hae P can significantly improve the quality of Bob's received confidential information. We can see that as α decreases, the transmission power of the confidential signal decreases, while the power of the artificial noise signal increases, resulting in a decrease in the signal-to-noise ratio (SNR) E and SNR B with the illegal receiver. This shows that reducing the transmission power of the confidential signal has an adverse effect on the information reception quality at both Bob's end and Eve's end. As long as Alice designs a reasonable power allocation ratio α, a dominant channel can be established in the communication link, and Eve will not be able to decrypt any confidential information. At the same time, it can also be seen that if α is too small (α → 0), the energy of the confidential signal is insufficient to support information transmission, resulting in the interruption of normal communication; if α is too large (α → 1), Alice almost uses all the power to transmit the confidential signal, and the role of artificial noise can be ignored at this time. Without taking other security measures, the entire communication system will have no security at all.

[0054] The data detected by Bob and Eve through the maximum likelihood method are respectively and where

[0055]

[0056]

[0057] By comparing with u, the bit error rates of Bob and Eve in the MIMO system under imperfect channels can be calculated.

[0058] The following is illustrated with a specific embodiment. The signal is modulated and demodulated by QPSK. Without necessary explanation, the number of data streams r is 1, the path fading coefficient γ is 2, the signal power allocation ratio α is 0.5, and the distance d from Alice to Bob ab is 2 m, and the distance d from Alice to Eve ae is 2 m.

[0059] Figure 3 The bit error rates of the system with different numbers of transmit antennas as a function of the signal-to-noise ratio are simulated. The number of antennas of Bob and Eve is 1. At the same number of transmit antennas, as the signal-to-noise ratio increases, the bit error rates of Bob and Eve decrease; at the same signal-to-noise ratio, the larger the number of transmit antennas, the smaller the bit error rate of Bob, but it has little effect on Eve. That is to say, when the number of transmit antennas is greater than the number of receive antennas, the change in the number of transmit antennas has little effect on the bit error rate of Eve. Therefore, the bit error rate of the system can be reduced by increasing the number of transmit antennas without affecting the bit error rate of Eve.

[0060] Figure 4The bit error rate of the system with different numbers of receiving antennas as a function of the signal-to-noise ratio is simulated. Here, the number of transmitting antennas is 16. As the signal-to-noise ratio increases, the bit error rates of Bob and Eve decrease; at the same signal-to-noise ratio, the larger the number of receiving antennas, the smaller the bit error rates of Bob and Eve. At low signal-to-noise ratios, due to the influence of noise, the system cannot transmit and receive normally.

[0061] Figure 5 The bit error rate of the system with different power allocation ratios and numbers of antennas as a function of the signal-to-noise ratio is simulated. Here, the number of transmitting antennas is 4 and the number of receiving antennas is 2. As the signal-to-noise ratio increases, the bit error rates of Bob and Eve decrease; at the same signal-to-noise ratio, the larger the power allocation ratio, the smaller the bit error rates of Bob and Eve. When the power allocation ratio is 0, that is, all the transmitting power is used to transmit artificial noise, the bit error rates of Bob and Eve are 0.5.

[0062] Figure 6 The bit error rate of the system with different power allocation ratios and numbers of antennas as a function of the signal-to-noise ratio is simulated, where ab d ae = d = d, the number of transmitting antennas is 16, and the number of receiving antennas is 2. As the signal-to-noise ratio increases, the bit error rates of Bob and Eve decrease; at the same signal-to-noise ratio, the smaller the distance, the smaller the bit error rates of Bob and Eve. It can be seen from the figure that the influence of distance on Bob's bit error rate is greater than that on Eve's bit error rate.

Claims

1. A method for calculating the bit error rate of an artificial noise-assisted MIMO system under an imperfect channel, the method comprising: Construct a transmitter Alice with M antennas, a receiver Bob with N antennas, and L eavesdroppers Eve i , 1≤i≤L, the number of its antennas is K, and the channel between Alice and Bob is constructed where d ab is the distance between Alice and Bob, H ab is the instantaneous small-scale fading channel between Alice and Bob, γ represents the fading coefficient of the channel; construct Alice and Eve i Channels between Among them, d ae,i is the distance between Alice and Eve, H ae,i From Alice to Eve i The instantaneous small-scale fading channel between Bob sends pilot data X to Alice bp =diag(x1,x2,…,x i ,…,x N ), Alice receives pilot data Y a for: in is additive white Gaussian noise, H ba Indicates the main channel status information, I M represents the diagonal identity matrix; Alice uses the received pilot signal to perform channel estimation and obtain the estimated main channel state information. The difference between the estimated channel state information and the actual channel is E ba ,Right now E ba represents the channel estimation error matrix; Alice performs singular value decomposition on the estimated channel, in, yes The null space of U1 and U0 represent unitary matrices, and D represents The singular values ​​of The first r columns of are used as the precoding matrix of the confidential signal The secret signal constructed and transmitted by Alice is The artificial noise signal is The confidentiality signal is The artificial noise signal is P is the power allocation ratio of the confidentiality signal, α is the proportion of artificial noise power, and r is the number of data streams; Bob and Eve i The received signals are y b and e,i ,in, Among them, n b is the additive white Gaussian noise of the channel between Alice and Bob, n e,i is the additive Gaussian white noise of the channel between the ith eavesdropper and Alice, x a is the final transmitted signal mixed with artificial noise, and γ is the path fading coefficient; In order to increase the reliability of Bob's decoding, Alice sends a pilot sequence X to Bob. ap =diag(x1,x2,…,x i ,…,x r ), the pilot data Y received by Bob b for: in, is additive Gaussian white noise; Alice uses the received pilot signal to perform channel estimation and obtains the estimated equivalent main channel state information The difference between the estimated equivalent channel state information and the actual equivalent channel is E ab ,Right now Then Bob b Decode to get y B for: Similarly, Eve i The equivalent eavesdropping channel state information is Eve i For e,i Decode to get the decoded signal y E,i for: Bob and Eve i The data detected by the maximum likelihood method are and Will Compare with u to calculate Bob and Eve i Bit error rate of MIMO system under imperfect channels.

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