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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING The main types of code sequences of modern communication and navigation systems. Reference data
Encyclopedia of radio electronics and electrical engineering / Reference materials The article describes the main types of code sequences used in modern communication and navigation systems. The given parameters are considered from scientific and practical points of view, with references to modern research in this area. The choice of a pseudo-random code sequence in a radio engineering information transmission system is very important, since the gain of the system processing, its noise immunity, and sensitivity depend on its parameters. With the same length of the code sequence, the system parameters may be different. Systems using complex noise-like signals have been in use for over 50 years. The well-known advantages of noise-like signals, such as high noise immunity with respect to high-power narrow-band interference, the possibility of separating subscribers by code, secrecy of transmission, high resistance to multipath propagation, and even high resolution in radar and navigation measurements, predetermined their use in various communication systems. and location determination. Due to what parameters of noise-like signals does their application have a number of wonderful properties and can they be improved? Characteristics of noise-like signals An important parameter of a system using noise-like signals is the processing gain. Processing gain (BO) indicates the degree to which the signal-to-noise ratio is improved when converting the noise-like signal received by the receiver into the desired information signal. This procedure is called compression or despreading. According to the classical definition, VO is equal to: VO \u10d XNUMX Lg [Cк /FROMи]Where Ск - the frequency of the pseudo-random sequence chips, chip/second. Си - information transfer rate, bit/second. By this definition, a system that has an information rate of 1 Mbps and a chip rate of 11 Mchips/sec (meaning that each bit of information is encoded with a pseudo-random sequence of 11 bits) will have a RR of 10,41 dB. This result means that the operability of the information transmission system will remain with the same BER if the useful signal at the input decreases by 10,41 dB. In conventional commercial noise-like radio modems, such as Arlan, Wavelan, and the like, the highest priority is often given to the speed of information transmission, rather than stealth or noise immunity. Since the instructions of the Federal Communications Commission in the United States (FCC) for such devices provide for a minimum VO value of 10 dB, and also allocated the minimum allowable bandwidth of one channel (which imposes restrictions on the maximum repetition rate of chips Cк), then the length of the pseudo-random code sequence must be at least 11 chips per bit. If we increase the length of the code sequence to 64 chips per bit (this is the maximum possible length for the well-known NPS Z87200 processor from Zilog), then with the same chip repetition rate of 11 Mchip/sec, the processing gain will be 10Lg (64) = 18,06 dB , the information transfer rate will decrease by 64/11 = 5,8 times. To be used in a NPS system, code sequences must have certain mathematical and other properties, the main of which are very good autocorrelation and cross-correlation properties. In addition, the code sequence must be well balanced, that is, the number of ones and zeros in it must differ by no more than one character. The last requirement is important to exclude the constant component of the information signal. The DSSS receiver compares the received code sequence with its exact copy stored in memory. When it detects a correlation between them, it switches to the information receiving mode, establishes synchronization, and starts the operation of decoding useful information. Any partial correlations can lead to false positives and disruption of the receiver, which is why the code sequence must have good correlation properties. Consider the concept of correlation in more detail. Autocorrelation and cross-correlation function The correlation properties of the code sequences used in NPS systems depend on the type of the code sequence, its length, the repetition rate of its symbols, and its symbol-by-symbol structure.(1). In general, the autocorrelation function (ACF) is determined by the integral: Y (t ) = ∫f(t)f(t-t )dt and shows the connection of the signal with a copy of itself, shifted in time by τ. The study of the ACF plays an important role in the choice of code sequences in terms of the lowest probability of establishing false synchronization. The cross-correlation function (CCF), on the other hand, is of great importance for code division systems such as CDMA, and differs from the CCF only in that there are different functions under the integral sign, and not the same one: Y (t ) = ∫f(t)g(t-t )dt The FCF shows, thus, the degree of correspondence of one code sequence to another. To simplify the concepts of ACF and VKF, one can represent the value of a particular function as the difference between the number of matches A and mismatches B of symbols of code sequences when they are compared character by character. To illustrate this example, consider the autocorrelation function of an 11-chip long Barker code sequence that has the following form: 1 1 1 0 0 0 1 0 0 1 0 A character-by-character comparison of this sequence with its own copy is summarized in a table.
A graphic representation of the ACF of this Barker sequence is shown in the figure:
Such an ACF can be called ideal, since it does not have side peaks that could contribute to false signal detection. As a negative example, consider any arbitrary code sequence, for example: 1 1 1 0 0 0 1 1 1 0 0 Having carried out the calculations corresponding to the previous example, we obtain the following graphical representation of the autocorrelation function, shown in the figure:
Side peaks of 7 and 3 units can lead to false alarms of the system if such a sequence is used for signal distribution. For high-speed NPS systems intended for information transmission, but not for code separation of subscribers, Barker codes are usually used, which have good autocorrelation properties. With the help of computer simulation, the so-called Willard codes (2) were found, which, with the same length as the Barker codes, sometimes have better correlation properties. Barker code sequences with a length of more than 13 symbols are unknown, therefore, to obtain a larger VO, greater noise immunity, as well as for code separation of subscribers, sequences of a greater length are used, a significant part of which form M-sequences. M-sequences One of the best known phase shift keying signals are signals whose code sequences are maximum length sequences or M-sequences. To build M-sequences, shift registers or delay elements of a given length are usually used. The length of the M-sequence is 2N-1, where N is the number of shift register bits. Various options for connecting the discharge outputs to the feedback circuit give a certain set of sequences. The ACF of the M-sequence is -1 for all delay values, except for the region 0±1, where its value varies from -1 to the value 2N-one. In addition, M-sequences have another interesting property: each sequence has one more 1s than zeros. A lot of literature is devoted to the methods of formation and characteristics of M-sequences, so we will not dwell on this in detail. To explore the capabilities of the new PRISM chipsetTM Harris Semiconductor conducted a practical study of short M-sequences and Barker codes in order to find the optimal ones from the point of view of the autocorrelation function (3). As part of this study, an M-sequence of length 15 was analyzed and has the form: 111 1000 1001 1010 As it turned out, it has worse autocorrelation properties than the 13-character Barker sequence of the following form: 1 1111 0011 0101 A practical view of the ACF of the M-sequence is shown in the figure:
For comparison, the ACF of a Barker code sequence of length 13:
The oscilloscope clock is shown at the top of the photo. As can be seen from the photographs, the M-sequence has several large side peaks, which can significantly degrade the receiving quality of the NPS system, and can sometimes lead to false signal detection. As it turned out in the course of further research, if two zeros are added to the 13-character Barker code sequence, then the ACF of the resulting sequence 001 1111 0011 0101 will be much better than the described ACF of the M-sequence, which also consists of 15 symbols. ACF of the newly obtained sequence:
Short M-sequences are thus significantly inferior to Barker sequences in terms of autocorrelation properties, despite a better balance of zeros and ones. Of the most well-known systems using M-sequences, we can name a mobile communication system with a code division of subscribers CDMA and a global navigation system GPS. The CDMA system uses three code sequences. The first of them, used to synchronize the operation of all equipment, has a variable length N ≈ (32÷131)103 characters. The second M-sequence has a maximum length N=242-1 and is used to identify subscriber stations from the base station. The third sequence is used to transmit useful information between the base and subscriber stations and is one of the Walsh sequences. Walsh sequences (the rows or columns of the Hadamard matrix act as them) have the property of orthogonality with respect to each other. From a mathematical point of view, orthogonality means that in the absence of a time shift between Walsh sequences, their dot product is zero. From the point of view of radio engineering, this makes it possible to eliminate mutual interference in the transmission of information from the base station to several subscriber stations and thereby dramatically increase the throughput of the communication system (5). This advantage of orthogonality takes place only in the case of accurate synchronization of the transmission of sequences to all subscribers. Precise synchronization of CDMA base and subscriber stations is carried out mainly with the help of the global navigation system GPS. In addition to Walsh sequences, other orthogonal sequences are used in communication systems: Digilok and Stiffler sequences. In addition to M-sequences as such, composite code sequences have found application in communication systems, which are combinations of M-sequences and have some specific properties. The most famous and used of them are the Gould sequences. Gould's code sequences are formed using a simple sequence generator based on two shift registers of the same capacity and have two advantages in relation to M-sequences. First, the generator of code sequences, built on the basis of two shift registers of length N each, can generate, in addition to the two original M-sequences, N more sequences of length 2N-1, that is, the number of generated code sequences is significantly expanded. Secondly, Gould codes can be chosen so that the CCF for all code sequences received from one generator will be the same, and the value of its side peaks is limited. For M-sequences, it cannot be guaranteed that the side peaks of the CCF will not exceed a certain predetermined value. Gould code sequences are used in global navigation systems such as GPS. The so-called "rough" code (C/A - clear/acquisition) uses a Gould sequence of 1023 symbols, transmitted at a clock frequency of 1,023 MHz. The exact code (P - precision), which the military and special services have access to, uses an extra-long composite sequence with a repetition period of 267 days and a clock frequency of 10,23 MHz. In addition to Gould's composite sequences, Kasami sequences are most commonly used. New Technologies The M-sequences, Gould's, Kasami's sequences mentioned in this article refer to sequences having a linear formation algorithm. The main disadvantage of such sequences is their predictability and the lack of transmission secrecy associated with it. Non-linear sequences are more unpredictable. Recently, a number of publications have appeared on the generation of noise-like signals using the phenomenon of dynamic chaos (4). The phenomenon of dynamic chaos is that the motion of a deterministic dynamic system under certain conditions has all the properties of a broadband chaotic process. At the same time, the fundamental feature of the algorithms that describe this phenomenon is their non-linearity, and the feature of the generated time process is its non-periodicity. This opens up the possibility of searching for a new class of random sequences for use in radio engineering systems for various purposes: broadband chaotic SHCS signals, which to a greater extent meet the requirements for pseudo-random sequences. Conclusion Mobile systems of the third generation, which are already being developed within the framework of international European programs, will use broadband signals generated by pseudo-random sequences. In particular, WCDMA or broadband CDMA, developed by Ericsson, was chosen as the basic standard for UMTS - Universal Mobile Telecommunications System. More than twenty projects are known that unite, to one degree or another, all developed telecommunications companies and leading universities in the world, which are trying to solve the problem of global world communications of the future from different angles (6). In the distant future, obviously, every inhabitant of our planet will have its own terminal, which is small in size and provides its owner with all available types of communications - from a video phone to access to the global information system. And there is a high probability that in such systems code separation of subscribers using pseudo-random sequences will be used. Literature
Author: Malygin Ivan Vladimirovich; Publication: library.espec.ws
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