A method for constructing a set of frequency hopping sequences without collision region

Abstract

The application discloses a construction method of a collision-free frequency hopping sequence set, solves the problems of low complexity and limited sequence length of the collision-free frequency hopping sequence, and expands the application scenario of the collision-free frequency hopping sequence. The application constructs an encryption base sequence based on TOD information and a local key to improve the complexity and other statistical characteristics of the frequency hopping sequence, then extends the base sequence into an orthogonal frequency hopping sequence family, and constructs the collision-free frequency hopping sequence set through periodic superposition value and frequency mapping. The generation method not only retains the high security of the encryption sequence, but also realizes the collision-free construction of the sequence, and thus has good comprehensive performance. On this basis, the frequency hopping pattern construction method of the system is updated in time through TOD information, the frequency allocation strategy is adjusted, the security and concealment of the frequency hopping sequence can be improved, and the anti-frequency aiming interference, anti-frequency tracking interference and anti-multipath interference capabilities of the communication system are enhanced.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and specifically relates to a method for constructing a collision-free frequency hopping sequence set with high security. Background Technology

[0002] In frequency-hopping communication systems, frequency-hopping sequence analysis and design are core technologies. Designing high-performance frequency-hopping sequences requires good Hamming correlation characteristics and statistical properties such as uniformity, randomness, and complexity. Frequency-hopping communication systems using collision-free frequency-hopping sequences allow for a certain synchronization delay between users, eliminating the impact of multi-user multiple access interference within this delay range, thus having a wide range of applications.

[0003] The definition of aperiodic Hamming correlation is: in the frequency slot set Construct frequency hopping sequence set , Include The length of the strip is The sequence. For any It has Hamming-related functions.

[0004]

[0005] for Non-periodic Hamming correlation:

[0006]

[0007] in According to The operation is performed, and only positive delays are considered.

[0008] Definition of collision-free zone:

[0009]

[0010] The theoretical community of aperiodic Hamming correlation (Liu-Hong-Zeng-Zhou boundary) is: If yes The collision-free region frequency hopping sequence set on the above, then the collision-free region Must satisfy

[0011]

[0012] Currently, there are methods for constructing collision-free frequency hopping sequence sets with optimal Hamming correlation. However, these methods are either too simple to construct or have limited period lengths, thus restricting the practical application of collision-free frequency hopping sequences. Frequency hopping sequences possess good statistical properties such as uniformity, randomness, and complexity, which can effectively improve the resilience of communication systems against complex interference and malicious attacks. Most current methods for constructing collision-free frequency hopping sequences are based on the full permutation of matrices or sequences, neglecting statistical properties and resulting in poor security. Summary of the Invention

[0013] This invention aims to address the problems of low complexity and limited sequence length in collision-free frequency hopping sequences, thereby expanding their application scenarios. To solve this problem, this invention proposes a real-time construction method based on system Time of Day (TOD) information and a local key, which improves the statistical properties of the frequency hopping sequence, such as its complexity. Furthermore, by periodically updating the system's frequency hopping pattern using TOD information, the frequency allocation strategy is adjusted, enhancing the security and stealth of the frequency hopping sequence.

[0014] The technical solution adopted in this invention is as follows:

[0015] A method for constructing a collision-free frequency hopping sequence set includes the following steps:

[0016] Step 1: After performing an XOR operation on the system's real-time time (TOD) information using the local key, the binary data is converted to a multi-base representation, generating a multi-valued encrypted base sequence. ;

[0017] Step 2: Use 0 to The vector formed by all permutations The base sequence is expanded to generate a sequence family consisting of M orthogonal frequency hopping sequences;

[0018] Step 3: Orthogonal frequency hopping sequence with For periodic superposition and through arrive Frequency mapping Obtain the frequency hopping sequence set of the collision-free region ;

[0019] in, Indicates the number of available frequency slots. Indicates size is The set of frequency slots, positive integers These represent the sequence length, number of sequences, and size of the collision-free region frequency hopping sequence set to be constructed, respectively.

[0020] Furthermore, the collision-free zone frequency hopping sequence set sequence length From the number of sequences The length of the extracted TOD is determined by:

[0021] .

[0022] Furthermore, the size of the collision-free zone is:

[0023] ,

[0024] Collision-free zone frequency hopping sequence set relative time delay Less than or equal to the size of the collision-free zone .

[0025] Furthermore, the collision-free zone frequency hopping sequence set The statistical properties of each sequence in the base sequence are derived from the base sequence. Decide.

[0026] The beneficial effects of this invention are as follows:

[0027] (1) The present invention uses a collision-free zone frequency hopping sequence construction method based on TOD information and local key, which solves the multiple access interference problem of quasi-synchronous communication system on the one hand, reduces the amount of computation on the other hand, and can generate frequency hopping sequences of arbitrary length, ensuring the security and concealment of frequency hopping information.

[0028] (2) The present invention can update the frequency hopping pattern construction parameters of the system and change the carrier frequency allocation strategy, making the signal difficult to detect and track, and greatly improving the communication system's ability to resist frequency aiming interference, frequency tracking interference and multipath interference.

[0029] (3) Frequency hopping sequence set of the present invention The length of the collision-free region is optimal with respect to the non-periodic Hamming correlation theory bound. Attached Figure Description

[0030] Figure 1 To construct a collision-free frequency hopping sequence set for this invention The structural block diagram.

[0031] Figure 2 This is a structural block diagram of the base sequence module in this invention.

[0032] Figure 3 This is a structural block diagram of the sequence extension module in this invention.

[0033] Figure 4 This is a non-periodic Hamming correlation distribution diagram of the frequency hopping sequence with a collision-free region size of 2 constructed in this invention.

[0034] Figure 5The randomness test results are for the collision-free frequency hopping sequence set constructed in this invention, which has 12 frequency slots, a collision-free region size of 3, and a sequence number of 3.

[0035] Figure 6 The uniformity test results are for the collision-free frequency hopping sequence set constructed in this invention, which has 12 frequency slots, a collision-free region size of 3, and a sequence number of 3.

[0036] Figure 7 The complexity test results for the collision-free frequency hopping sequence set constructed in this invention, which has 12 frequency slots, a collision-free region size of 3, and a sequence number of 3. Detailed Implementation

[0037] The present invention will now be further described with reference to the accompanying drawings.

[0038] A method for constructing a collision-free frequency hopping sequence set, wherein, using Indicates the number of available frequency slots. Indicates size is The set of frequency slots, positive integers These represent the sequence length, number of sequences, and size of the collision-free region frequency hopping sequence set to be constructed, respectively.

[0039] like Figure 1 As shown, the construction process includes three parts: constructing the base sequence, sequence expansion, and frequency slot mapping, as detailed below:

[0040] First, the local key is used to encrypt the TOD information to generate a base sequence. ,like Figure 2 As shown.

[0041] Next, as Figure 3 As shown, the sequence expansion vector ranges from 0 to... The full permutation of . Expanding the vector through the sequence. , for the base sequence Expand the elements in the sequence to obtain M sequences of length . Sequence families composed of orthogonal sequences , .

[0042] Finally, for the frequency hopping sequence set Based on the position of each element For periodic superposition and through frequency mapping M collision-free frequency hopping sequences are obtained, and the set of these M collision-free frequency hopping sequences is the collision-free frequency hopping sequence set. .

[0043] The frequency hopping sequence for each user is: Collision-free zone frequency hopping sequence set Obtain the collision-free region frequency hopping sequence matrix through frequency slot mapping. Subscript It is the position of an element in the sequence. Representing different users, and satisfying . Indicates from arrive One-to-one mapping and They represent the modulus respectively Operations and Modulus Calculation.

[0044] Furthermore, the collision-free zone frequency hopping sequence set Depend on Composed of sequences, sequence length The length is determined by the segmented TOD information.

[0045] Collision-free zone frequency hopping sequence set The size of the collision-free zone is : .

[0046] Collision-free zone frequency hopping sequence set Applied to quasi-synchronous systems, This is a set of frequency hopping sequences for each user. The synchronization delay and information transmission delay of each user are controlled within the low-collision zone, ensuring that the frequency hopping patterns of each user are orthogonal to each other, thereby eliminating multiple access interference between users.

[0047] The theoretical bound (Liu-Hong-Zeng-Zhou bound) of this method is: if there is no collision region frequency hopping sequence set yes The above A length of The frequency-hopping sequence constitutes the collision-free region. have

[0048]

[0049] Due to the lack of a collision zone It is an integer, therefore and Equivalent. If If we take the equal sign, then It is the set of collision-free frequency hopping sequences that are approximately optimal in the theoretical community of non-periodic Hamming correlation.

[0050] The definition of nonperiodic Hamming correlation is: for Non-periodic Hamming correlation

[0051] in,

[0052] All subscript operations are performed according to... Operational, The operation is division Calculation of remainders.

[0053] The method described above yielded the following results. The proof is as follows: This relates to the theoretically optimal set of collision-free frequency-hopping sequences in the aperiodic Hamming correlation domain.

[0054] for The delay is Nonperiodic Hamming correlation:

[0055]

[0056] if ,because , so

[0057] if and ,but .

[0058] Therefore, the collision-free region frequency hopping sequence set exist There is no collision on top. Size of the collision-free zone: This satisfies the equality requirement in theoretical circles, therefore Regarding the theoretical optimality.

[0059] Q.E.D.

[0060] In this method, multiple users control the carrier frequency using different frequency-hopping sequences and communicate within a shared frequency band according to certain rules. The system uses collision-free frequency-hopping communication technology to eliminate multiple access interference between users within a certain time delay range, ensuring communication reliability. Furthermore, the construction rules for the collision-free frequency-hopping sequence destroy the pseudo-randomness of the sequence. A high-security collision-free frequency-hopping sequence construction method using TOD information to periodically update the key ensures that the frequency-hopping pattern continuously changes according to different rules, improving the security and concealment of communication information.

[0061] Here is another example:

[0062] A method for constructing a collision-free frequency hopping sequence set, wherein, Indicates the number of available frequency slots. Indicates size is The set of frequency slots, positive integers These represent the sequence length, number of sequences, and size of the collision-free region frequency hopping sequence set to be constructed, respectively.

[0063] The sequence transition matrix consists of several A vector consisting of all permutations of .

[0064] like Figure 1 As shown, the construction process of the collision-free frequency hopping sequence set consists of three stages: 1. Constructing the base sequence, 2. Sequence expansion module, and 3. Frequency slot mapping module. Wherein:

[0065] 1. The implementation process of constructing the basis sequence is as follows: Figure 2 As shown, specifically: the local key encrypts the TOD information bit by bit, and performs a base conversion to generate a base sequence of alphabet size M. At the same time, each processing For each segment of TOD information, the key is updated by XORing the TOD with the local key, thus increasing the complexity of the frequency hopping sequence.

[0066] 2. The specific implementation process of sequence expansion is as follows: Figure 3 As shown: using numbers from 0 to... The vector formed by all permutations , with the encrypted base sequence Add them together to get A frequency hopping sequence, in which , .

[0067] 3. The specific implementation process of frequency slot mapping is as follows: Frequency hopping sequence set Elements at different positions are superimposed with different values, and frequency mapping is used. Obtain the frequency hopping sequence set of the collision-free region .

[0068] The frequency hopping sequence for each user is: Collision-free zone frequency hopping sequence set Obtain the collision-free region frequency hopping sequence matrix through frequency slot mapping. Subscript It is based on the position of the element in the frequency hopping sequence according to TOD. Representing different users, Indicates from arrive One-to-one mapping and They represent the modulus respectively Operations and Modulus Calculation.

[0069] Furthermore, the collision-free zone frequency hopping sequence set Depend on Composed of sequences, sequence length The length of the frequency hopping sequence is determined by the length of the intercepted TOD. .

[0070] Collision-free zone frequency hopping sequence set The size of the collision-free zone is : .

[0071] Collision-free zone frequency hopping sequence set Applied to quasi-synchronous systems, This is a set of frequency hopping sequences for each user. The synchronization delay and information transmission delay of each user are controlled within the low-collision zone, ensuring that the frequency hopping patterns of each user are orthogonal to each other, thereby eliminating multiple access interference between users.

[0072] The theoretical community (Liu-Hong-Zeng-Zhou's community) defines it as: if there is no collision region frequency hopping sequence set yes The above A length of The frequency-hopping sequence constitutes the collision-free region. have

[0073]

[0074] Due to the lack of a collision zone It is an integer, therefore and Equivalent. If If we take the equal sign, then It is the set of collision-free frequency hopping sequences that are approximately optimal in the theoretical community of non-periodic Hamming correlation.

[0075] The definition of nonperiodic Hamming correlation is: for Non-periodic Hamming correlation

[0076] in

[0077] All subscript operations are performed according to... Operational, The operation is division Calculation of remainders.

[0078] To verify the effectiveness of this method, the uniformity, randomness, and complexity are defined below:

[0079] (1) Uniformity

[0080] Uniformity refers to the property of frequency hopping being evenly distributed within the frequency hopping band. Good uniformity ensures that each carrier is selected with equal probability, thereby improving the system's immunity to electromagnetic interference. The uniformity of the frequency hopping code sequence can be described in two categories:

[0081] One-dimensional uniformity: The system operates at every frequency number The probabilities are equal, therefore , .

[0082] Two-dimensional uniformity: The probability of each frequency pair occurring consecutively is equal, i.e., the frequency pairs are equal in probability. The frequency number appears after it appears. The joint probabilities should be equal, therefore , .

[0083] Uniformity is usually adopted The sequence performance is verified using a test method. According to Pearson's theorem, when performing a one-dimensional homogeneity test, take... Indicates a length of In the frequency hopping sequence, the frequency number The number of occurrences is then used to define the chi-squared test value as:

[0084]

[0085] As a test theory (i.e. hypothesis) A measure of how well it conforms to reality. sufficiently large ( In the case of ), the statistic always follows a set of degrees of freedom. of Distribution. Under the assumption If calculated below Worth having Then in the horizontal Accept .

[0086] Similarly, when performing a two-dimensional uniformity test, take Indicates a length of Frequency number pairs in the frequency hopping sequence The number of occurrences is then used to define the chi-squared test value as:

[0087]

[0088] As a measure of how well a theory matches reality. When the number of degrees of freedom is sufficiently large, the statistic always follows a sequence of degrees of freedom of 1. of Distribution. Under the assumption If calculated below Worth having Then in the horizontal Accept .when When the degrees of freedom for testing are large enough, Reference values ​​can be obtained from empirical formulas:

[0089]

[0090] (2) Randomness

[0091] Randomness, also known as independence, is used to characterize whether the statistical correlation between two random variables is significant. Good randomness ensures that the frequency number is not recursive, guaranteeing that the frequency hopping communication system has good confidentiality and anti-interference capabilities, meaning that non-cooperative receivers cannot predict the current frequency hopping number based on previously intercepted frequency numbers.

[0092] Currently, another method is typically used to address the randomness of sequences. The test method is the contingency table test. The specific process of this method is as follows: Truncate the data to a length of... sequence segment and its shift sequence segment ,in , The frequency hopping codes in the extracted frequency hopping sequence are grouped into pairs according to their order.

[0093]

[0094] Calculate the number of occurrences of each frequency pair and denote it as . ,make ,use express The probability of occurrence. When the independence assumption holds, , express The probability of occurrence express The probability of occurrence. This can be obtained using the maximum likelihood method. , express The estimated value, Therefore, the randomness test statistic is:

[0095]

[0096] (3) Complexity

[0097] The complexity of a random sequence is defined as the minimum number of stages of the equivalent linear feedback shift register that generates the sequence. Complexity reflects the frequency-hopping sequence's resistance to interference and decryption. If the sequence generation is sufficiently complex, it can ensure that a complete frequency-hopping sequence is difficult to obtain even with observations of a limited number of frequency samples. This is crucial for communication systems with high requirements for resisting various attacks.

[0098] To distinguish the complexity of the sequence proposed in this method from that of chaotic sequences, fuzzy entropy (FuEn) is used as a measure of sequence complexity. This method utilizes the property of entropy as a measure of the randomness of chaotic motion; therefore, FuEn can distinguish the complexity of chaotic frequency-hopping sequences that commonly used linear complexity cannot, and the verification process is insensitive to the verification parameters. A larger FuEn value indicates higher complexity.

[0099] The approximate entropy (ApEn) is defined as: given an integer non-negative integers and positive real numbers and real sample space First, define dimensional vector group ,in ,but dimensional vector and maximum distance for

[0100]

[0101] For each , Satisfy the first indivual dimensional vector The maximum distance is less than number of vectors

[0102] according to ,definition

[0103]

[0104] Then ApEn can be defined as

[0105]

[0106] In one embodiment, setting parameters , , The base sequence generated by TOD and the key is as follows: ,

[0107] The new sequence obtained after the sequence shifting in step 2, and the orthogonal frequency hopping sequence set formed by the new sequence and the base sequence:

[0108]

[0109] The collision-free frequency hopping sequence set obtained after step 3:

[0110]

[0111] It can be verified that this sequence set is a collision-free frequency hopping sequence set with a sequence length of 25 and a sequence number of 4, on a frequency slot set size of 12, and a collision-free region size of 2. Nonperiodic Hamming correlation in relative time delay The maximum value distribution chart below is as follows Figure 4 As shown, the maximum value of its aperiodic Hamming correlation in the collision-free region is as follows:

[0112] .

[0113] Furthermore, the detection results of the randomness, uniformity, and complexity of the sequences in this sequence set are as follows: Figure 5 , Figure 6 and Figure 7 As shown. The collision-free frequency hopping sequence set constructed in this invention exhibits stable performance, maintaining high levels of randomness, uniformity, and complexity.

[0114] In summary, this invention proposes a method for constructing a collision-free frequency hopping sequence set, which can ensure that the frequency hopping patterns are orthogonal to each other within a certain relative time delay range, thereby eliminating multiple access interference in frequency hopping multiple access communication.

[0115] Because the length of the frequency hopping sequence set constructed by the method of the present invention is only related to the length of the base sequence. Therefore, by setting the appropriate TOD information length and key, a collision-free frequency hopping sequence of arbitrary length can be constructed.

[0116] Because the present invention not only uses keys to increase the complexity of the sequence during the construction process, but also updates the frequency hopping pattern construction parameters of the system and changes the carrier frequency allocation strategy, the signal is difficult to detect and track, which greatly improves the communication system's ability to resist frequency aiming interference, frequency tracking interference and multipath interference.

[0117] This invention solves the problems of low complexity and limited sequence length of collision-free frequency hopping sequences, expanding their application scenarios. Based on TOD information and a local key, this invention constructs an encrypted base sequence to improve the statistical properties of the frequency hopping sequence, such as complexity. Then, the base sequence is expanded into a family of orthogonal frequency hopping sequences, and a collision-free frequency hopping sequence set is constructed through periodic superposition values ​​and frequency mapping. This generation method retains the high security of the encrypted sequence while achieving collision-free sequence construction, thus exhibiting excellent overall performance. Furthermore, by periodically updating the frequency hopping pattern construction method using TOD information and adjusting the frequency allocation strategy, the security and concealment of the frequency hopping sequence can be improved, enhancing the communication system's resistance to frequency aiming interference, frequency tracking interference, and multipath interference.

Claims

1. A method for constructing a set of collision-free zone frequency hopping sequences, characterized in that, The method comprises the following steps: Step 1: XOR operation is performed on the system real-time time TOD information using the local key, and then the binary is converted to multi-base to generate a multi-value encrypted base sequence ; Step 2: using 0 to a vector consisting of all permutations The motif sequence is expanded to generate a sequence family consisting of M orthogonal frequency hopping sequences; Step 3: Each orthogonal frequency hopping sequence is... The periods are stacked sequentially. and through arrive Frequency mapping Obtain the frequency hopping sequence set of the collision-free region , It is a one-to-one mapping; wherein, denotes the number of available frequency slots, denotes a set of frequency slots of size , and positive integers denote the sequence length, the number of sequences, and the size of the collision-free zone, respectively.

2. The method of claim 1, wherein, The set of collision-free zone frequency hopping sequences The sequence length Is determined by the number of sequences And the truncated TOD length: 。 3. The method of claim 1, wherein, The size of the collision-free zone is: ， Collision zone free frequency hopping sequence set Relative latency Less than or equal to collision zone size .

4. The method of claim 1, wherein, Collision free zone hopping sequence set The statistical properties of each sequence are determined by the base sequence .

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