Design of long-period PIN code in spread spectrum anti-jamming communication system
Spread spectrum communication is an effective and commonly used anti-jamming communication method. It is the main means of military communication. It is divided into basic technologies such as direct sequence spread spectrum, frequency hopping, linear frequency modulation and time hopping, and hybrid technologies composed of a combination of basic technologies. All technologies The design of the pseudo code is related to the anti-interference performance of the system. The pseudo-random sequences commonly used in existing spread spectrum communication systems are m-sequence, Gold-sequence, Walsh-sequence, M-sequence, and C / A codes (coarse / intercepted codes) and fine codes (P codes) commonly used in satellite communications. In these sequences, the P code has excellent performance and the longest code period. At a clock rate of 10.23 MHz, the code time period is about 266 days. Based on the study of the principle of P code, this paper proposes a pseudo-random sequence generation method with longer period and good security performance, which can be used in the wartime satellite measurement and control communication. 1.2 Design basis of code sequence The generation of pseudo-random sequence can be realized by linear or nonlinear shift register. Because m-sequences have good pseudo-randomness, small m-sequences are used in the design of GOLD, C / A, P and other PN sequences, so m-sequences are the basic sequence of spread spectrum communication. 3. Experimental simulation results The correlation characteristics of the generated long-period PN sequence are simulated. The auto-correlation characteristics are shown in FIG. 3, and the cross-correlation characteristics are shown in FIG. 4. Ningbo Autrends International Trade Co.,Ltd. , https://www.ecigarettevapepods.com
1 PN code design principle
1.1 Design principles In spread-spectrum anti-jamming communication systems, the design of the code mainly considers the performance of the relevant characteristics of the code, the confidentiality of the code (code complexity), and code capacity. Specific requirements are as follows:
(1) Strong autocorrelation characteristics The code synchronization in the system is often realized by the correlation characteristics of the codes. This requires the autocorrelation performance of the codes to have a sharp autocorrelation distribution characteristic.
With two sequences {ai} and {bi} of length N, i = O, 1, ..., N-1, the autocorrelation function of the sequence is defined as: 
In practical applications, the autocorrelation function of the pseudo-random sequence in spread spectrum communication is required to be binary, that is, the autocorrelation function Ra (j) is: 
In the formula: N is the sequence autocorrelation peak, which is equal to the sequence period, that is, N = 2n-1; σ is the sequence autocorrelation sidelobe value, which satisfies σ <
For the sequences {ai) and {bi}, i = O, 1, ..., N-1, orthogonal is defined as: 
(3) Large code capacity From the above analysis, it can be known that in a multi-user system, the number of orthogonal codes determines the system capacity. Therefore, it is desirable to select a code sequence with a large capacity when designing a spreading code.
(4) Good confidentiality Spread spectrum communication systems are often used in military communications, so when designing codes, the following methods are often used: to reduce the DC power of the code, to make the number of "O" and "1" in the code balanced and equal; increase the period of the code ; Adopt nonlinear shift register to realize code sequence.
The m sequence is a code sequence with a period of N = 2n-1 generated by the n-level linear shift register, is the abbreviation of the longest linear shift register sequence, and has excellent autocorrelation characteristics. Its generating principle is shown in FIG. 1. 
The characteristic polynomial is: 
In the formula: ci is called the feedback coefficient, and the value is 0 or 1; 1 means to participate in the feedback; O means not to participate in the feedback. Whether the shift register can generate m sequences is determined by the value of the feedback coefficient; the code period is determined by the number of shift registers; the linear complexity of the sequence directly determines the security performance of the spread spectrum system, and the principle of linear generation of m sequences is analyzed As long as the continuous 2n-1 symbols of the sequence can be intercepted, the value of the coefficient ci can be given, so that the m sequence is completely deciphered. In practical systems, the output of several stages of the shift register or the output of several different m-sequences are often combined in a non-linear manner to produce a non-linear sequence that is difficult for the jammer to crack. In this paper, this method is used, referring to the construction principle of P code, a method of generating a spreading sequence code with a long period and high complexity is proposed.
2 Long-period code design In this paper, a PN sequence with a code clock period greater than one year and related performance close to the P code is designed according to needs. Its principle is shown in Figure 2. 
The characteristic polynomials of the four 12-level linear shift registers in Figure 2 are: 
Four m sequences with a code period of 4095 bits are generated.
According to the principle of composite code generation, the modulo 2 addition of several code sequences that are mutually prime in code length can form a composite code sequence with a longer period, and the length is the product of several code lengths. The four m sequences are truncated separately. The method used is to truncate the number of symbols of X1a and X2a to 4 092; truncate the number of symbols of X1b and X2b to 4 093; and then truncate the truncated sequences X1a and X1b and X2a and X2b are respectively added modulo 2 to obtain a long period code with a length of 4 092 × 4 093, and then the long period code is truncated to cut out the X1 and code with a number of symbols of 15 345 000 b X2 with the arity of 15 345 037 b, then add the two truncated sequences of X1 and X2 to modulo 2 to obtain a longer sequence X, and finally X and modulo 2 to add the m sequence Y generated by the 3-level linear shift register , Constructed as a new PN code.
The PN sequence generated by this method has good correlation performance, large capacity, and long code period.
Assuming a clock frequency of 10.23 MHz, the number of symbols is 1 648 287 149 355 000 b, and the symbol time period is greater than 5 years. 
Fig. 3 (a) and Fig. 4 (a) are correlation characteristics of 4 095-bit m-sequence. As can be seen from Figure 3 (a), the maximum auto-correlation value is 4 095 when the code phase is zero, and the side lobe value is -1; as can be seen from Figure 3 (b), the maximum cross-correlation value is 479, The ratio to the maximum autocorrelation is about 10%.
Fig. 3 (b) and Fig. 4 (b) are correlation characteristics of P codes. The maximum value of the autocorrelation is 250 000, the maximum value of the side lobe is 15 000, and the average value of the side lobe is 500; the maximum value of the cross correlation is 4 652, and the ratio to the maximum value of the autocorrelation is about 1.8%.
Fig. 3 (c) and Fig. 4 (c) are related characteristic diagrams of long-period codes generated by the method in this paper. The maximum value of the autocorrelation is 250 000, the maximum value of the side lobe is 14 400, and the average value of the side lobe is 400; the maximum value of the cross correlation is 4 650, and the ratio to the maximum value of the autocorrelation is 1.8%.
It can be seen from the above comparative analysis that the long-period codes have similar correlation characteristics with the P codes. Although the autocorrelation is slightly worse than the m sequence, it has better cross-correlation performance.
4 Conclusion On the basis of studying the design principles and principles of spread spectrum communication PN sequences, a method for generating pseudo-random spreading sequences with a code period greater than 5 years and a good correlation performance at a clock frequency of 10.23 MHz is proposed. This method truncates and composites four 4 095-bit m sequences to obtain an intermediate sequence, and then performs a composite operation with a 7-bit m sequence to re-expand the period of the PN sequence. After simulation verification, the PN sequence designed by this method has excellent correlation performance, long period, simple and flexible implementation, and conforms to various principle characteristics of pseudo-random sequence codes.