Research on Physical Layer Encryption Technology of HST 5G communication system with spatial permutation modulation

In high-speed train (HST) communication, the application of 5G technology is of great importance. The massive multi-input multi-output (massive MIMO) technology in HST communication has advantages, but there are problems of inter-channel interference and multiple antennas synchronization. Spatial modulation has been widely used as a technology to solve this problem. In order to ensure the security of the HST wireless communication system, a hyperchaotic antenna-index spatial permutation modulation (HASPM) is proposed by combining chaos theory on the basis of spatial modulation technology. Aiming at the problem of reduced spectrum efficiency in traditional encryption algorithms due to pre-shared keys, channel information and noise interference, the proposed HASPM physical layer encryption scheme can improve above shortcomings on the basis of secure communication. The multipath fading effect is reduced, the bit error rate (BER) performance is greatly improved, and the system security and reliability are thus guaranteed. The evaluation results of calculation analysis and simulation on the scheme verified the feasibility and effectiveness of the proposed scheme.

applications for railway scenes on dedicated frequency bands for railway communication [2]. Table 1 shows the comparison between 5G-R and existing railway communication methods. GSM-R is limited by the limitations of 2G technology narrowband communication, and its transmission rate and delay performance are unsatisfactory [3]. LTE-R uses two physical layer technologies, orthogonal frequency division multiplexing (OFDM) and multiple input multiple output (MIMO). OFDM can independently process signals in each subchannel to eliminate interference to the maximum extent. MIMO can generate multiple parallel independent channels to increase the data transmission rate of LTE-R without increasing bandwidth [4]. However, neither of these two methods can provide massive user connections, extensive signal coverage, and realtime video surveillance technologies to meet the requirements of intelligent railway dispatching and safety assurance. In addition to its excellent rate and delay performance, 5G-R can also use layer encryption uses the physical characteristics of wireless communication system to achieve secure communication, which can greatly improve the security level of the system. A classic three-terminal eavesdropping model (Alice-Bob-Eve model) for physical layer security was proposed in [8], including a transmitter (Alice), a legitimate receiver (Bob) and an eavesdropper (Eve). Massive MIMO can use multiple transmitting antennas to enhance the confidentiality of communication system, so its combination with communication encryption is natural [9]. The concepts of eavesdropping channel and confidentiality have promoted the research of physical layer security of wireless communication systems [10,11]. There have been a number of phased progress in the study of wireless system security performance [12][13][14][15][16]. Literature [17] and [18] gave a general representation method for the channel security capability of multi-antenna eavesdropping under the constraint of the input matrix. A suboptimal beamforming scheme based on Markov bound was proposed in [19]. In this scheme, transmitter must know the prior knowledge of the receiver channel. The physical layer security of the massive MIMO system is configured when the eavesdropper has a large number of antennas in [20]. This scheme requires a minimum level of noise. To improve the physical layer security of the channel under the classical eavesdropping model, transmission antenna selection scheme is analyzed in [21]. The security of the physical layer for new generation of wireless communication systems was further discussed in [22]. In a secure multi-antenna system, sends noise to the empty space of the receiving end to confuse Eve, but this method does not guarantee the absolute security of communication channel.
This article proposes a physical layer encryption scheme for Massive MIMO system based on spatial permutation modulation (SPM). A space-modulated multi-antenna transmission scheme is proposed in [23] The activation state of the signal transmitting antenna creates a new modulation dimension. To break through the limitation of the number of transmitting antennas in traditional SM scheme, a joint mapping spatial modulation scheme was proposed in [24] and [25]. MIMO systems show better confidentiality than single-antenna systems in [26]. SPM scheme was proposed in [27], which modulates data bits into permutation vectors, and the antennas are activated according to the vectors in continuous time. This article applies SPM technology to wireless communication encryption. In order to further improve the security, chaos theory is applied to key extraction, a key generation algorithm is designed, and keys are used to protect antennas combination and mapping modes antenna combination and mapping modes (ACMM) and interfere with spatial constellation. Finally, HASPM method is proposed for information encryption and modulation.
The main contributions of the paper are as follows.

1)
A new HASPM is proposed for spatial modulation scheme for massive MIMO wireless communication. This scheme uses the antenna sequence generated by hyperchaotic mapping to encrypt the spatial modulation information.
2) Using SPM technology, compared with traditional physical layer security solutions, the system can be designed with mature discrete mathematics domain knowledge, and it has high compatibility, reliability and flexibility.
3) The chaos theory is applied to key generation, and a new key generation algorithm is proposed to further improve the security of the physical layer encryption system.

4)
Carry out theoretical research on the proposed scheme, analyze its complexity, randomness and reliability, and perform simulation to illustrate the advantages of the scheme. The rest of the paper is organized as follows. The second section introduces the 5G-R scenario massive MIMO technology and SPM model, and briefly describes the main ideas of the proposed scheme. The third section introduces the HASPM scheme in detail from three aspects: key generation, spatial modulation and signal reception. The fourth section gives the superiority analysis and simulation results. The fifth section summarizes the paper.  channel and support higher data rate [28]. Therefore, it can also significantly improve spectrum efficiency and energy efficiency in addition to the advantages of traditional MIMO [29], and can simplify the access control layer design and further reduce the system delay, it can be seen that massive MIMO can significantly improve the transmission performance of 5G-R. 5G-R will provide emerging railway services beyond existing railway technologies, such as real-time video surveillance and train multimedia dispatch. HST is considered as a typical application scenario for 5G due to its short time delay, real-time video monitoring and a large number of sensing requirements for railway internet of things sensors. T2T communication can provide emergency communication between trains when the T2I communication network is interrupted. As the train speed continues to increase and the distance between the workshops continues to decrease, the available braking time of the train is greatly reduced. Therefore, there are higher requirements for transmission rate and network delay. 5G applies network layering technology, allowing devices to communicate directly without involving infrastructure. Network layering technology for 5G applications allows devices to communicate directly without involving infrastructure. The characteristics of high speed and low latency enable it to meet the requirements of T2T communication.
In order to intuitively show the advantages and development prospects of 5G-R scenarios, compare it with the existing HST communication technology in table 2, and summarize the advantages and disadvantages of various technologies. In addition to its advantages in transmission rate and delay, 5G technology also has the advantages of convenient upgrade and low cost. Therefore, HST communication will focus on LTE-R and 5G-R in the future.
As shown in Figure 2, the integrated cab can implement T2T communication and T2I communication. On this basis, MEC paradigm is applied to the existing train control system, and TDAP is constructed for on-site analysis of train data. The functions of the four parts are as follows.

SPM scheme
In classic communication-eavesdropping In the encryption technology of the wireless communication system model, ACMM is stored in the antenna index, which is compared with ACMM according to book, and the spatial modulation is realized by SPM scheme in the information bit. SPM scheme selects appropriate phase vectors, activates transmitting antennas corresponding to the vectors in a continuous time to disperse the space signal as shown in figure2.
In consideration of system security, the proposed system scheme adopts three-level encryption, which respectively correspond to the keys K1, K2, and K3 generated by hyperchaotic Henon mapping. The first level of encryption is to use K1 to select the appropriate ACMM in the book. The second level of encryption uses K2 to disrupt the correspondence between ACMM and the memory address in the book. The third level of encryption is to use SPM for threedimensional modulation. Bob can decrypt the information by combining the keys and performing reverse operations in corresponding order.
Different transmitting antennas carry out signal propagation with different gains, the SPM receiver can thus detect the data symbols by identifying the most-likely combination of the fading gain and constellation symbol.

Hyperchaotic Henon key generation algorithm
5G-R scenario wireless channel has many inherent properties at the physical layer, such as randomness, reciprocity, and location specificity. these properties make it possible to extract keys from channel's properties. As shown in the figure 3, the process of extracting keys from channel state information can be roughly divided into channel detection, measurement quantification, information adjustment and privacy amplification. Channel measurement is a method for Alice and Bob to collect channel measurement values. Channel state information is obtained by alternately transmitting signals and evaluating them. Since the channels are reciprocal, the difference between measured values observed by both parties is very small. Measurement quantization is to quantize the result measured in the previous step into a vector and convert it into the form of data encoding, and then the preliminary keys can be obtained. Since the complete consistency of the channel measurement between two parties cannot be guaranteed, errors often occur during the measurement process, and the obtained preliminary keys cannot match each other. Therefore, information coordination is required. Information exchange through a common channel and key synchronization is achieved through coding error correction, ensuring that the keys generated respectively are the same. Privacy amplification is a method to eliminate the correlation between parts of information for the key intercepted by the opponent.
To ensure the security of generating keys based on channel information, it is necessary to perform high-dimensional mapping on keys extracted from channel information, chaotic systems have the characteristics of randomness, unpredictability, and high sensitivity to initial values and system parameters. In this paper, the generalized Henon chaotic mapping is selected. It has two positive Lyapunov exponents, it is thus called a hyperchaotic map. Compared with Lorenz chaotic and chen chaotic, Lyapunov exponents of hyperchaotic Henon mapping are not the largest, but only it has two positive Lyapunov exponents, which shows that it has good randomness compared to the other two chaotic systems. In addition, Henon mapping only needs two multiplications for each iteration, while Lorenz mapping needs to solve a set of differential equations. Therefore, hyperchaotic Henon mapping can generate keys faster and ensure the encryption rate. The mathematical expression is as follows.
where m, n are system parameters. u, v, and w are variables.
When the parameters meet the conditions 1.54<m<2,0<|n|<1, mapping is in a hyperchaotic state. When two parameter values are m=1.65 and n=0.15, two largest Lyapunov exponents of the chaotic system are 0.689 and 0.693.
Keys extracted from the wireless channel is used as the initial value of the chaotic system to carry out the operation to generate a new chaotic sequence, and then use an appropriate quantization method to quantize the disordered sequence into a binary sequence, and three binary sequences respectively constitute the key K1, K2, K3.

Antenna mapping and spatial permutation modulation
The SPM scheme selects appropriate phase vectors, activates transmitting antennas corresponding to the vectors in a continuous time to disperse the space signal, and changes the antenna activation sequence from original simultaneous activation at the same time and different positions to sequential activation at different moments and different positions determined by the vectors. For example, when two antennas are activated at two consecutive times, in addition to the information conveyed by the quadrature amplitude modulation (QAM) signal, space modulation transmitters use permutation sets composed of permutation vectors for modulation. Bit '0' indicates that the selection is vector [1,2] T , where the order of antenna activation is that the first antenna is As mentioned earlier, the number of transmitting antennas is Nt. In the process of spatial modulation using permutation vectors, assuming that there are p elements that need to be arranged, then ANt,p is a set of all p elements arranged in the Nt space. For example, the representation of the permutation set A3,1 and A3,2 are as follows.
In order to obtain keys through permutation vectors to facilitate the spatial modulation of the information, permutation vectors representing the constellation are corresponding to binary digital codes, and F permutation vectors with smallest Hamming distance dmin are selected from ANt,p and combined into a permutation set subset ANt,p(F,dmin). SPM spatial signal is generated from specific permutation vectors selected from the subset ANt,p(F,dmin) according to data bits. Table 3 shows permutation sets in different situations. Compared to the number of modulated bits 2 log t N     of SM spatial signal, the number of modulated bits of SPM spatial signal has a logarithmic relationship with the dimension of the permutation vector used, that is 2 log F     . The more permutation vectors contained in ANt,p(F,dmin), the more bits can be modulated by reducing the Hamming distance. Therefore, bit error rate performance and modulation rate can be balanced by adjusting F and dmin. When transmitter is equipped with more antennas, the number of permutation vectors that meet conditions will also increase, so SPM can be easily applied to a massive MIMO system.
For the selection of the permutation vector set, first define all permutation vectors that meet conditions as a candidate pool. Define other vectors whose Hamming distance from the permutation vector is less than dmin as its neighbors. The permutation vector with fewest neighbors is selected, and its neighbors are removed from the candidate pool. If the number of permutation vectors in the expected permutation set is more than F, increase dmin and perform repeated screening until a permutation set that meets requirements is selected.
In practical applications, according to scenarios and user requirements, corresponding replacement subsets will be pre-arranged in transmitting and receiving antennas. SPM modulates v bit information contained in keys into a replacement vector v = [v1, v2, …, vt] T ∈ ANt,p(F,dmin), so that each antenna is activated at the corresponding time. Figure 4 shows the flow chart of the HASPM scheme, which is divided into four steps and introduced later.  Figure 4: Flow chart of HASPM scheme.
First, the keys K1, K2, and K3 generated by the algorithm are used to select the applicable ACMM from the book and disrupt the relationship between the ACMM and the address storage, and finally perform space replacement modulation on it.
Secondly, the correspondence between ACMM and address storage can be established by the selection of the key K1, and each ACMM has a different address storage corresponding to it. The number of transmitting antennas is Nt, and the number of different antenna combinations is as follows.
Since the transmitting antenna is a group of three, Nt must be a multiple of three. When the modulation order is L, the number of different mapping modes on the three antennas is (3L)!. So the book is composed of Ntc(3L)! different ACMMs stored in the same number of storage addresses. The key K2 is used to disrupt the previously described relationship between the ACMM and the storage address. This operation makes it extremely difficult to obtain the correct corresponding relationship and prevents eavesdropper from intercepting the correct ACMM. At the same time, this operation ensures that the length of the binary sequence composing K1 does not exceed log2(Ntc(3L)!). By using the key K2 for corresponding address interference, the key space is increased to Ntc(3L)!, and the security of the system is further improved.
In actual applications, usually only part of the book is used instead of the entire content to reduce the complexity of the system caused by the correspondence, but for eavesdropper, without knowing which part of the content is used, they can only try to search the entire space increases the difficulty of interception.
Then, after determining the relationship between the ACMM and the storage address, the information stream to be transmitted needs to be mapped to the activated antenna, and the antenna activation needs to be spatially modulated. The HASPM scheme proposed in this paper uses SPM to spatially modulate information bits. The traditional modulation technology only maps a certain number of bit streams to constellation punctuations, and transmits information through different antennas. The modulation type is easily intercepted and therefore leads to information leakage. Different from the traditional modulation strategy, the proposed HASPM scheme combines chaos theory and applies the physical layer-based SPM method to modulate partially activated antennas. The antenna activation sequence determined by key K3 will be used for SPM of information to realize the whole process from modulation to transmission. In the process of information transmission, rather than all antennas being activated, this solution thus has better energy efficiency. The information bit is a group of three bits and is mapped to a signal. The first bit selects the transmitting antenna to be activated, and the second two bits select the position of the constellation punctuation on the antenna. The transmitting antennas are divided into group Nt/3 by ACMM, and each group has three antennas. ACMM determines the constellation plot of each group. When a different ACMM is used, the activated antenna and the selected modulation type will change accordingly. For eavesdropper, it becomes more difficult to obtain the correct constellation diagram and modulation method, thus ensuring the security of information transmission.
Finally, the information is transmitted through the wireless network and demodulated after being received at the receiving end. The received signal is detected by the detection algorithm, and then the decryption operation opposite to the encryption operation is performed to obtain the original information.

Minimum mean square channel estimation decoding
After receiving the coded and modulated signal, the signal receiving antenna must decode the received information to obtain the original correct signal. To perform the decoding operation, the serial number and constellation punctuation of the activated antenna at the transmitting end must be obtained in advance. Because different transmitting antennas use different gains for signal propagation, the signal receiver can detect data information according to the combination of attenuation gain and constellation signal. Then use the minimum mean square error estimation monitoring scheme to decode the constellation symbols. The signal received by the energy detection method decision device is as follows.
where i is the antenna serial number, Pi is the constellation punctuation of the antenna transmission, K is the channel gain, Ei is the channel noise, and Si is the activation state of the antenna.
Since the transmitting antenna and the receiving antenna have already performed wireless channel information detection and exchange during the key generation phase, the channel state information is known, and the data detection operation can be performed when the antenna is in the active state. Considering that the frequency selection channel signal model should be more accurately expressed as follows.
Where Ki is the gain of the i-th antenna. In order to detect the activated antennas, N antennas are selected according to the channel signal energy. Using the introduced energy detection method, the serial numbers of N activated antennas can be known. The next step is to use the minimum variance estimation detection method to decode the constellation of the activated antenna, and then perform the opposite operation to the original information encrypted by the transmitting antenna to obtain the correct information.

Performance analysis and simulation
Theoretical analysis and simulation experiment were used to verify the feasibility and advantages of the proposed scheme in this section. The channel information is fully known to the transmitter and receiver, so the keys can be properly synchronized. In this paper, the key is generated by hyperchaotic Henon mapping, and the spatial modulation is carried out by HASPM scheme.

Complexity analysis
The security of the ACMM mapping process depends on two encryption processes corresponding to the three keys. Process 1 is that K1 selects an ACMM, whose opposite relationship with memory address is disorganized by K2. Process 2 is that K3 transforms the spatial distribution of information into the temporal distribution.
In first process, the main calculation of decrypting intercepted information focuses on finding the selected ACMM. For Eve without a key to get the original information, every ACMM in the book should be tried, so the computational complexity is Ntc(3L)!. Bob can obtain the correct mapping mode according to the received key and directly obtain the correct ACMM. Table  4 shows the comparison of the calculation amount of the legitimate receiver and the For Eve, in the case of the same modulation order and different antenna numbers, the amount of calculation increases by 2-3 orders of magnitude with the double increase of the number of antennas, and the amount of calculation increases sharply with the increase of the multiple of antennas. In the case of the same number of antennas and different modulation orders, every time the modulation order increases by 1, the amount of calculation will increase by 2-3 orders of magnitude. It can be seen that the amount of calculation of Eve increases drastically with the increase of the modulation order and the number of transmitting antennas, but Bob only needs to use the key to perform addressing operations to obtain the correct original information.
In second process, Constellation punctuation completes the conversion of information from space to time after the key K3 modulation. The constellation punctuation of quadrature phase shift keying (QPSK) modulation is four points on the quadrant angle bisector with a distance of 1 from the origin. If Eve can intercept the complete spatially modulated signal, then its BER is as follows.  (6) where Pr is the probability of the original signal rotating to other quadrants.
Analysis shows that the combination of the two encryption processes can effectively prevent the original information from being intercepted. Eve cannot identify the modulation type through higher order statistics, which is the most widely used modulation classification method. In addition, the security of the encryption algorithm also depends on the randomness and consistency of the key.

Random analysis
Regarding the security of wireless communication, the key used for communication must have enough randomness to ensure the irregularity of cracking the key. The most commonly used test in the world is fifteen different test indicators designed by the National Institute of Standards and Technology (NIST), including frequency test, test operation, and entropy test. The standard suite uses a specific test algorithm to obtain a value between 0 and 1 indicating the degree of difference by comparing the measurement results of the sequence to be tested and the degree of difference between the ideal sequence. The test will only be performed when this value is greater than the significance level a=0.01. After repeated test statistics and calculations, the results shown in Table 5 can be obtained. It can be seen from the table that the test values are significantly higher than the significance level, and 8 items of test values exceed 0.5, so the key stream sequence generated by the super chaotic mapping has enough randomness, and the hyperchaotic Henon algorithm is safe.
The ZUC algorithm is a candidate algorithm recommended by the international organization 3GPP as the third set of international encryption and integrity standards for 4G wireless communications. Adding the ZUC algorithm to the NIST test comparison, it can be seen that the test value of the algorithm proposed is higher than the ZUC algorithm in most test items, there is even a huge lead in four tests (Serial, Longest Runs of ones, Approximate Entropy and Fast Fourier Transform). It shows that hyperchaotic Henon algorithm has obvious advantages over traditional encryption algorithms.
In a traditional 36×36 MIMO system, Nsdo=1. In the same situation when using the HASPM scheme, each group of transmitting antennas only activates one antenna at a time, and the receiving antennas are all activated, so Nsdo=25. As Nsdo increases in wireless communication, its multipath fading effect decreases, so with the same SNR, BER decreases as Nsdo increases. Moreover, in massive MIMO system, the number of receiving antennas increases, and the interference between the transmitting antennas is reduced, the receiving antennas can thus receive signals more effectively.
The figure 5 shows the comparison between the HASPM scheme and the traditional digital modulation method QPSK when the number of antennas, coding algorithms, and decoding algorithms are the same.
It can be seen from the figure that Eve's BER is always maintained at about 0.5 with different received signal-noise ratio (SNR), the BER remains high. It is impossible to decode the intercepted information to obtain the correct Communication information. On the other hand, compared with QPSK digital modulation, the Bob's BER performance of proposed scheme is much better. When the modulation type is QPSK and the bit error rate is 10 -2 and 10 -4 , the performance gain is 2dB and 3.3dB respectively. From the curve trend, the BER improves more obviously as the SNR increases.

Conclusions
In this paper, we proposed a new physical layer encryption scheme HASPM, which uses hyperchaotic mapping and spatial permutation modulation are used to prevent eavesdropping by eavesdropper with large-scale receiving antennas and improve the security of massive MIMO system. First, the proposed scheme uses hyperchaotic Henon mapping to generate keys, encrypts the correspondence between ACMM and storage address and the modulation method, and improves the security of the communication system. Secondly, only one antenna in each group is activated at a time on the transmitting antenna side, the multipath fading effect is thus reduced and the problem of mutual interference of transmitted signals among different channels is solved. Finally, the complexity, randomness, and reliability of the system are verified. The huge number of antenna combination modes and modulation methods make it impossible for eavesdropper to obtain the original information they strive for even if they have a sufficient number of receiving antennas. The receiver can decode the signal according to the key and easily receive and decode the original information. Therefore, the key and channel information are transmitted and exchanged when the information is transmitted, and do not need to be shared in advance. The physical layer security encryption is realized with a more concise calculation.
Compared with the traditional massive MIMO modulation scheme, the multipath fading effect is reduced, the BER performance is greatly improved, and the system security and reliability are thus guaranteed. Theoretical analysis and experimental results also show the proposed solution can further improve the security of the wireless communication system compared with the traditional MIMO physical layer security solution. In general, the scheme proposed in this paper has a good guarantee in terms of complexity and security, improves the security of the wireless communication system, and in terms of information transmission, it can reduce channel interference and improve the BER performance.