Adaptive modeling of a multipath communication channel. The use of threshold technology for assessing the impulse response of a communication channel Recommended list of dissertations

In a multipath channel, it is necessary to mitigate the effect of delayed beams, for example, using the following scheme:

Each element of the line delays the signal for a time Δ. Suppose that during the transmission of a single pulse, the receiver receives 3 pulses with an amplitude ratio of 1: 0.5: 0.2, following at equal time intervals Δ. This signal x(t) is described by counts: NS 0 = 1, NS 1 = 0.5, NS 2 = 0.2.

The signal at the filter output is obtained by summation, with weight coefficients b 0 , b 1 , b 2, signal x(t) and its detained copies:

Options b i must be chosen so that readings are obtained at the filter output y 0 = 1, y 1 = y 2 = 0 for input counts 1, 0.5, 0.2:

Solution b 0 = 1, b 1 = – 0.5, b 2 = 0.05. With these weighting factors

In the example considered, the equalizer parameters are calculated from the known channel impulse response. This characteristic is determined by the reaction of the channel to the “training” (tuning) sequence known to the receiver. With a large excess delay and a high level of multipath signal components, the length of the training sequence, the number of delay elements in the filter, and the signal sampling rate must be large enough. Because the real channel is not stationary, the determination of its characteristics and the correction of the filter parameters have to be repeated periodically. As the filter becomes more complex, its adaptation time increases.

Identifying channel characteristics

Correlation method for identifying impulse response

Filter output

Let the impulse response be described by three samples:

Model adequacy criterion - minimum error variance

Minimum variance conditions

This system, written in general form

is a discrete form of writing the Wiener - Hopf equation

With a signal x (t) such as white noise R x(τ) ≈ 0.5 N 0 δ(τ),

and the estimation of the impulse response is reduced to determining the correlation function R zx (τ).

Inverse channel equalizer

Knowing the channel response is not necessary to equalize it. The filter parameters can be selected according to the criterion of minimum variance D e mistakes e(t) = x(t) – x*(t), where x(t) - training sequence transmitted over the communication channel and generated in the receiver.

Ideal alignment of the channel response (at H k (ω) H f (ω) = 1) may be undesirable if the frequency response of the channel has deep dips: a very large gain will be required from the correcting filter at frequencies corresponding to the zeros of the channel transfer function, and noise will increase.

How the Viterbi equalizer works

Signal z(t) received when transmitting the training sequence x(t) is fed to the filter matched to the training sequence. The output of the matched filter can be considered an estimate of the channel impulse response.

A signal is detected representing a sequence of n bit. All 2 n possible binary sequences that could have been transmitted are generated at the receiver and passed through a filter - the channel model. The sequence is selected, the filter response to which is least of all different from the received signal.

of bandwidth // Proceedings of International Conference CLEO'00. 2000, paper CMB2, P. 7. 13. Matuschek N.,. Kdrtner F. X and Keller U. Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations ”IEEE J. Quantum Electron. 1997. Vol. 33, no. 3: R. 295-302.

Received by the Editorial Board November 12, 2005

Reviewer: Dr. Phys.-Math. Sciences, prof. Svich V.A.

Yakushev Sergey Olegovich, Art. Faculty ET KHNURE. Research interests: systems and methods for the formation of ultrashort pulses and methods for their modeling; semiconductor optical amplifiers of ultrashort optical pulses. Hobbies: sports. Address: Ukraine, 61166, Kharkov, Lenin Ave., 14.

Shulika Aleksey Vladimirovich, assistant of the Department of Physical Education and Science, KhNURE. Research interests: physics of low-dimensional structures, effects of charge carrier transfer in low-dimensional heterostructures, modeling of active and passive photonic components. Hobbies: traveling. Address: Ukraine, 61166, Kharkiv, Lenin Ave., 14, [email protected]

UDC621.396.2 .: 621.316.2 "

ESTIMATION OF THE PULSE CHARACTERISTICS OF THE COMMUNICATION CHANNEL BASED ON HIGHER-ORDER STATISTICS

V. A. Tikhonov, I. V. Savchenko

A computationally efficient method for estimating the impulse response of a communication channel using a third-order moment function is proposed. The computational complexity of the proposed method is compared with the method that uses fourth-order cumulants to estimate the impulse response. It is shown that in the presence of Gaussian and non-Gaussian noise, the proposed method provides a higher estimation accuracy.

1. Introduction

Intersymbol interference (ISI) caused by high-speed transmission digital signals, is, along with narrowband interference from similar digital systems operating on adjacent cores telephone cable, the main factor that reduces the reliability of the transmission of information in xDSL systems. The ISI correction method, optimal from the point of view of minimizing the error probability, based on the maximum likelihood rule, as well as methods using the Viterbi algorithm for maximum likelihood estimation of sequences, require estimation of the impulse response of the communication channel.

Higher-order statistics can be used for this purpose. Thus, the method of blind identification by estimating the channel impulse response from the received signal using fourth-order cumulants is described. Present 3 0

Lysak Vladimir Valerievich, Cand. physical-mat. Sciences, Art. pr. Department of FOET KNURE. Research interests: fiber-optic data transmission systems, photonic crystals, systems for the formation of ultrashort pulses, methods for modeling the dynamic behavior of semiconductor lasers based on nanoscale structures. Student, member of IEEE LEOS since 2002. Hobbies: sports, travel. Address: Ukraine, 61166, Kharkiv, Lenin Ave., 14, [email protected]

Sukhoivanov Igor Aleksandrovich, Doctor of Phys.-Math. Sci., Professor of the Department of Physical Education and Science, KhNURE. Head of the international scientific and educational laboratory "Photonics". Honorary Member and Head of the Ukrainian Branch of the Society for Laser and Optoelectronic Technology of the International Institute of Electronic Engineers (IEEE LEOS). Research interests: fiber-optic technologies, semiconductor quantum-well lasers and amplifiers, photonic crystals and methods for their modeling. Hobbies: traveling. Address: Ukraine, 61166, Kharkiv, Lenin Ave., 14, [email protected]

The paper proposes to use a third-order moment function to estimate the impulse response. This approach makes it possible to increase the accuracy of the estimation of the impulse response of the communication channel, and hence the efficiency of suppression of intersymbol interference in the presence of additive Gaussian and non-Gaussian interference. The proposed method has a lower computational complexity compared to while maintaining the identification accuracy in the presence of Gaussian noise. The condition for applying the proposed method is the non-Gaussian character of the test signals at the input x [t] and output y [t] of the communication channel, which must have a nonzero third-order moment function.

The aim of the study is to develop a method to improve the accuracy of estimating the impulse response of a communication channel in the presence of Gaussian and non-Gaussian interference, to reduce computational costs.

The tasks are: substantiation of the possibility of using the third-order moment function for calculating the discrete impulse response of the communication channel; obtaining an expression connecting the third-order moment function with a discrete impulse response; comparison of the efficiency of the proposed method and the method based on the application of the fourth-order cumulant for the estimation of the impulse response.

2. Estimation of the impulse response of the communication channel by the cumulant function of the fourth order

It is possible to estimate the characteristics of the communication channel by the received signal using higher-order statistics. In particular, the impulse response of a linear, time-invariant system with

discrete time can be obtained from the fourth-order cumulant function of the received signal, provided that the channel input is non-Gaussian.

3. Estimation of the impulse response of the communication channel by the third-order moment function

Let the signal z [t] be the sum of the transmitted signal y [t] transformed by the channel with discrete time and memory L +1 and the additive white Gaussian noise (AWGN) n [t]:

z [t] = y [t] + n [t] = 2 hix + n [t].

For ABGS, the kurtosis coefficient and the fourth-order cumulant function are equal to zero. Consequently, the cumulant function of the fourth order of the received signal z [t] is determined only by the cumulant function of the transmitted signal y [t] converted by the channel. The fourth-order cumulant function of a real centered process y [t] is expressed in terms of moment functions

X 4y (y [t], y, y, y) =

E (y [t] yy y) -

E (y [t] y) E (y y) - (1)

E (y [t] y) E (yy) -

E (y [t] y) E (yy),

where E (-) is the operation of mathematical averaging.

The first term in (1) is the fourth-order moment function, and the remaining terms are the products of correlation functions for some fixed shifts.

In the method of blind identification, to estimate the impulse response of a communication channel, a useful binary signal is processed, which has no statistical links. It has a uniform distribution with a non-zero one-stage fourth-order cumulant% 4X. Then the transformation of the fourth-order cumulant function by a linear system with a discrete impulse response ht is determined by the expression

X4x Z htht + jht + vht + u

It can be shown that in this case the impulse response of the communication channel is determined through the values of the cumulant function of the output signal z [t] 6:

where p = 1, .., L. Here, the values of the fourth-order cumulant function% 4z are estimated from the samples of the received signal sequence z [t] according to (1).

Consider the case when an additive non-Gaussian interference with a uniform probability density distribution is present at the channel output. The fourth-order cumulant function of such a disturbance is not zero. Consequently, the fourth-order cumulant function of the received useful signal z [t] will contain an interference component. Therefore, when estimating the impulse response of a communication channel using expression (2) at small signal-to-noise ratios, it will not be possible to achieve high accuracy of estimates.

To improve the accuracy of estimating the discrete impulse response of a communication channel in the presence of non-Gaussian interference, in this work it is proposed to calculate the values of the impulse response samples from the third-order moment function. The third-order moment function of a real process y [t] is defined as

m3y = shzu =

E (y [t] yy). W

The transformation of the third-order moment function by a linear system with a discrete impulse response ht, according to, is determined by the expression

m3y = Z Z Z (hkhlhn x

k = -w 1 = -that n = -that

x Wsx).

If the test signal x [t] is non-Gaussian white noise with non-zero asymmetry, then

m3x =

Ш3Х 55, (5)

where m3x is the third-order central moment of the signal at the channel input.

Substituting expression (5) into expression (4), we obtain

m3y = Z Z Zhkh1hn х k = -<х 1=-<х n=-<х)

x m3x5 5 =

M3x Zhkhk + jhk + v.

Taking into account that the moment function of the third order of a non-Gaussian noise with a uniform distribution is equal to zero, we obtain

m3z = m3y =

M3x Z hkhk + jhk + v (6)

Let the shifts j = v = -L. Then, under the summation sign in (6), the product of the impulse response coefficients of the physically realizable filter will differ from zero only for k = L, i.e.

m3z [-L, -L] = m3xhLh0. (7)

For shifts j = L, v = p under the sum sign in (6), the product of the impulse response coefficients will differ from zero only for k = 0. Therefore,

m3z = m3xh0hLhp. (eight)

Using expression (8) taking into account (7), we obtain the samples of the discrete impulse response through the values of the moment function:

m3z _ m3x h0hLhp _ m3z [_L, _L] m3xhLh ° h0

The counts of the third-order moment function m3z are estimated by averaging over the counts of the received signal sequence z [t] according to (3).

The methods for estimating the impulse response of the communication channel, based on the calculation of the third-order moment function and the fourth-order cumulant function, can be used in the case when a non-Gaussian test signal with non-zero kurtosis and asymmetry coefficients is used. It is advisable to use them in the case of Gaussian noise, for which the third-order moment function and the fourth-order cumulant function are equal to zero. However, the method proposed in the article has a much lower computational complexity. This is due to the fact that in order to estimate one value of the fourth-order cumulant function according to (1), it is required to perform 3N + 6N +13 operations of multiplication and addition. At the same time, to estimate one value of the third-order moment function, it will be required, according to (3), to perform only 2N +1 operations of multiplication and addition. Here N is the number of samples of the test signal. The rest of the calculations performed according to (2) and (9) will require the same number of operations for both methods.

4. Analysis of simulation results

The advantages of the proposed method for estimating the impulse response of a communication channel in the presence of Gaussian and non-Gaussian interference are confirmed by the results of experiments that were carried out by the method of statistical modeling. The ineffectiveness of the blind alignment method in the presence of Gaussian noise is explained by the fact that at

blind identification uses an equiprobably distributed signal. A two-level pseudo-random sequence has a kurtosis coefficient of 1 and a fourth-order cumulant of -2. After filtering by a narrowband communication channel, the signal is partially normalized, i.e. its kurtosis is close to the kurtosis of Gaussian noise, which is zero. The value of the fourth order cumulant approaches the value of the fourth order cumulant of the Gaussian signal, which is also zero. Therefore, at low signal / (Gaussian noise) ratios and in cases where the fourth-order cumulants of signal and noise differ insignificantly, accurate identification is impossible.

Experiments have confirmed that blind identification is ineffective at low signal-to-noise ratios. Through the model of the communication channel with a given discrete impulse response, the coefficients of which were 0.2000, 0.1485, 0.0584, 0.0104, a signal was passed in the form of a two-level pseudo-random sequence with a length of 1024 samples. A correlated Gaussian interference, as well as an ABGN, was added to the signal at the channel output. Amplitude response characteristic (ARC) of the communication channel model is shown by curve 1 in Fig. 1.

Rice. 1. True AFC and estimates of the AFC of the communication channel model, PSD of Gaussian interference

Hereinafter, the abscissa shows the values of the normalized frequency f "= (2f) / ^, where ^ is the sampling frequency. The power spectral density (PSD) of the correlated noise obtained with the help of the shaping autoregressive filter is shown in Fig. 1 by curve 2 According to (2), the discrete impulse response of the communication channel was estimated at large signal-to-noise and signal-to-noise ratios equal to 15 dB, as well as at lower signal-to-noise and signal-to-noise ratios equal to 10 dB and 3, respectively. dB Noise and interference were Gaussian Estimates of the frequency response of the communication channel corresponding to the found discrete impulse responses are shown in Fig. 1 (curves 3 and 4).

In this paper, it is shown that for identification of a communication channel using fourth-order cumulants at low signal-to-noise ratios, test non-Gaussian signals can be used, the kurtosis coefficient of which, even after normalization by the communication channel, is noticeably different from zero. In the simulation, a test signal with a gamma distribution was used with a shape parameter c = 0.8 and a scale parameter b = 2. The kurtosis coefficient of the signal at the channel input was 7.48, and at the channel output was 3.72.

In fig. 2 curves 1 and 2 show the frequency response of the communication channel model and PSD of the correlated interference. The signal-to-noise and signal-to-noise ratios were 10 dB and 3 dB, respectively. The noise and interference were Gaussian. The estimate of the frequency response of the communication channel, found from the estimate of the discrete impulse response (2), is shown in Fig. 2 (curve 3).

Rice. 2. True frequency response and frequency response estimates of the communication channel model, PSD of Gaussian interference

In the presence of Gaussian interference and ABGN in the communication channel, it is proposed to use a more computationally efficient identification method based on the use of the third-order moment function. In this case, it is necessary that the asymmetry coefficient of the test signal at the output of the communication channel be nonzero, i.e. differed from the asymmetry factor of the Gaussian noise. For statistical experiments, a test signal with a gamma distribution with a shape parameter c = 0.1 and a scale parameter b = 2 was used. The asymmetry coefficient of the signal at the channel input was 6.55, and at the channel output was 4.46.

The estimate of the frequency response of the communication channel model, found from the estimate (9) of the discrete impulse response, is shown in Fig. 2 (curve 4). Analysis of the graphs in Fig. 2 shows that the accuracy of estimating the frequency response using fourth-order cumulant functions and third-order moment functions is approximately the same.

The case of the presence in the communication channel simultaneously of white noise with Gaussian and non-Gaussian distribution was also considered. In statistical modeling, a test signal with gamma

distribution, with the shape parameter c = 1 and with the scale parameter b = 2. The kurtosis coefficient of the signal at the channel output was 2.9, and the kurtosis coefficient of interference with a uniform probability density distribution was equal to -1.2. The asymmetry coefficient of the signal at the channel output was 1.38, and the estimate of the noise asymmetry coefficient was close to zero.

Curve 1 in Fig. 3 shows the frequency response of the communication channel model, and curves 2 and 3 show the estimates of the frequency response of the communication channel using fourth-order cumulants (2) and the third-order torque function (9). The signal-to-noise ratio was 10 dB and the signal-to-noise ratio was 3 dB.

Rice. 3. True frequency response and frequency response estimates of the communication channel model

As can be seen from the graphs shown in Fig. 3, when using a method based on calculating fourth-order cumulants for identification of a communication channel, interference with a nonzero kurtosis coefficient at small signal-to-noise ratios significantly reduces the identification accuracy. At the same time, when a third-order moment function is used to identify a communication channel, interference with a zero asymmetry coefficient will not significantly affect the estimation accuracy of the impulse response at small signal-to-noise ratios.

5. Conclusion

For the first time, a method for estimating the impulse response of a communication channel using a third-order moment function is proposed. It is shown that the use of the proposed identification method can significantly reduce the effect of non-Gaussian interference on the estimation accuracy of the channel impulse response. In the case of Gaussian interference in the communication channel, the proposed method, in comparison with the method for estimating the impulse response from fourth-order cumulants, has a significantly lower computational complexity and can be used in the case of using a non-Gaussian test signal.

The scientific novelty of the research, the results of which are given in the article, lies in the fact that for the first time,

expressions for calculating the coefficients of the discrete impulse response of the communication channel from the values of the third-order moment function are derived.

The practical significance of the obtained results lies in the fact that the proposed identification method provides an increase in the accuracy of estimating the impulse response of a communication channel in the presence of interference, as well as a more effective suppression of intersymbol interference using the Viterbi algorithm and other methods that require preliminary estimation channel.

Literature: 1. R. Fischer, W. Gerstacker, and J. Huber. Dynamics Limited Precoding, Shaping, and Blind Equalization for Fast Digital Transmission over Twisted Pair Lines. IEEE Journal on Selected Areas in Communications, SAC-13: 1622-1633, December, 1995.2 G.D. Forney. Maximum Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference. IEEE Tr. IT, 363-378, 1972. 3. Forney G.D. The Viterbi Algorithm. Proceedings of the IEEE, vol. 61, n. 3, March 1978. P. 268-278. 4. Omura J. Optimal Receiver Design for Convolutions Codes and Channels with Memory Via Control Theoretical Concepts,

Inform. Sci., Vol. 3.P. 243-266. 5. Prokis J. Digital communication: Per. from English / Ed. D.D. Klovsky. M: Radio and communication, 2000.797 p. 6. Malakhov A.N. Cumulative analysis of random non-Gaussian processes and their transformations. M .: Sov. radio, 1978.376 p. 7. Tikhonov V.A., Netrebenko K.V. Parametric estimation of higher-order spectra of non-Gaussian processes // Automated Control Systems and Automation Instruments. 2004. Issue. 127.S. 68-73.

Received by the Editorial Board June 27, 2005

Reviewer: Dr. Sciences Velichko A.F.

Vyacheslav Tikhonov, Cand. tech. Sciences, Associate Professor of the Department of RES KNURE. Research interests: radar, pattern recognition, statistical models. Address: Ukraine, 61726, Kharkov, Lenin Ave., 14, tel. 70215-87.

Savchenko Igor Vasilievich, post-graduate student, assistant of the Department of RES KNURE. Research interests: methods for correcting intersymbol interference, higher-order spectra, non-Gaussian processes, linear prediction theory, error-correcting coding. Address: Ukraine, 61726, Kharkov, Lenin Ave., 14, tel. 70-215-87.

^ 3.7. Identifying channel characteristics

The identification of the characteristics of an object is to obtain its mathematical model based on an experimentally recorded response to a known input action. As a model, a linear filter is often used, described in different ways: by the transfer function H(s), impulse response h(t), differential or difference equation in usual or matrix form. The filter parameters are determined by selection or as a result of solving equations based on experimental data. The criterion for the adequacy of the model is most often the minimum variance of the error e(t) = z(t) – y *(t), where z(t) and y *(t) - signals at the outputs of the channel and filter (Fig. 17).

Consider a correlation method for identifying the impulse response of a filter that simulates a channel. Output signal y *(t) of the filter is the convolution of the input signal x(t) and impulse response h(t):

Suppose, for simplicity, that the impulse response is described by three samples, i.e. filter output

Rice. 17 explains the formation of this signal by summation, with weight coefficients equal to the values of the samples of the input signal, time-shifted discrete impulse responses of the filter. Highlighted components k-th count of the output variable. Error variance

Minimum variance conditions

May be represented as follows

where

System () written in general form

linking the impulse response of the channel with the autocorrelation function of the input signal and the function of cross-correlation of the input and output signals.

To obtain an adequate model of the object, the signal x(t) should be broadband and should not be correlated with interference n(t). A pseudo-random sequence is used as such a signal. Its autocorrelation function has the form of a short pulse and, like the autocorrelation function of white noise, can be approximately represented as R x(τ) ≈ 0.5 N 0 δ (τ). In this case, equation (17) is simplified:

(18)

and the estimation of the impulse response is reduced to determining the correlation function R zx (τ).

The solution of system (16) is complicated by the fact that it is often “ill-conditioned”: some equations turn out to be almost linearly dependent. In this case, minor changes in the experimentally found coefficients of the equations - discrete values of the correlation functions - lead to fundamentally different solutions, including those devoid of physical meaning. This situation is typical for "inverse" problems, when the mathematical model of an object is determined by its input and output signals (the "direct" task - determining the reaction of an object with known characteristics to a given input signal is solved without any complications). To obtain a practically realizable model, the form of the equations of dynamics or characteristics of the model is set on the basis of physical considerations, and the numerical values of the parameters of the model, at which it is most adequate to the object, are selected in different ways, comparing the behavior of the object and the model. This identification is called "parametric". The considered "nonparametric" identification method does not use any a priori information about the type of object characteristics.

Control questions.

1. What are the main indicators of the quality of the data transmission channel? What is channel volume.

2. How the application of error-correcting coding affects the spectral and energy efficiency of the channel.

3. What the theorems of Nyquist and Kotelnikov claim.

4. Imagine the response to a rectangular pulse of a channel that is a low pass, wide and narrow band pass filter.

5. How does the smoothing factor of the Nyquist filter affect the impulse response of the channel.

6. What factors determine the probability of a symbolic error.

7. What is the relationship between the signal-to-noise ratio and specific energy costs.

8. How does an increase in the volume of the alphabet of channel symbols affect the dependence of the probability of a symbolic error on the signal-to-noise ratio and on the specific energy consumption during amplitude-phase and frequency shift keying.

9. What is the difference between the concepts of technical and information speed of a data transmission channel

10. What is the bandwidth of the channel

11. What is the relationship between the maximum possible spectral efficiency of the channel and the specific energy consumption.

12. What is the theoretical value of the lower limit of unit energy costs.

13. Is it possible to correctly transmit messages with a high probability of errors in determining channel symbols

14. How the amount of information per character of the alphabet of the source is estimated

15. What is effective coding, what are its advantages and disadvantages

16. How the loss of signal power during transmission in free space is estimated

17. How the noise factor and effective noise temperature are determined

18. What phenomena are observed in a multipath channel

19. What parameters characterize a multipath channel

20. What is the relationship between time dispersion and channel frequency response

21. Explain the concepts of amplitude and frequency selective fading, Doppler shift and scattering.

22. Under what conditions does spectrum spreading increase the noise immunity of a multipath channel?

23. Explain the concept of parametric identification

Multichannel data transmission methods

Multichannel data transmission is the simultaneous transmission of data from many sources of information over one communication line, also called multi-station, or multiple, channel access, compression, multiplexing, channel division.

The main ways to split channels are as follows.

Frequency division (frequency division multiply access, FDMA): each subscriber is assigned its own frequency range.

Time division (time division multiply access, TDMA): the subscriber is periodically allocated time slots to transmit a message.

Code separation (code division multiply access, CDMA): each subscriber of a spread spectrum communication system is assigned a pseudo-random (pseudonoise - PN) code.

In the same system, different ways of distributing communication channels between subscribers can be used simultaneously. Separate communication channels can be permanently assigned to certain subscribers, or provided upon request. The use of public channels, provided for communication as needed (trunking principle), dramatically increases, with an increase in the number of channels, the capacity of the system. Systems with dynamic channel allocation are called demand-assignment multiple access (DAMA) systems. To reduce the likelihood of conflicts arising when several subscribers are simultaneously accessing the channel, special algorithms are used to control access to the channel.

We will consider the principles of channel separation in digital systems using specific examples.

^ 4.1. Time division of channels

in a wired communication system

In systems with time division multiplexing, sources and receivers of information are alternately connected to the communication channel (group path) by switches on the transmitting and receiving sides. One period of operation of the switch is a cycle (frame, frame), in which all sources are connected to the channel once. Source data is transmitted during a "time slot", a "window". Some of the windows in the cycle are reserved for the transmission of service information and synchronization signals for the operation of the switches.

For example, in the European digital telephone system, data from 30 subscribers make up the primary digital data stream, divided into frames. One frame with a duration of 125 μs contains 32 time windows, of which 30 windows are reserved for transmitting messages from subscribers, 2 windows are used for transmitting control signals (Fig. 18, a). 8 message bits are transmitted in one window. At a sampling rate of an audio signal of 8 kHz (sampling period 125 μs), the data transfer rate in the primary stream is 8000 ∙ 8 ∙ 32 = 2.048 Mbit / s.

Four primary digital streams are combined into one secondary stream, 4 secondary ones - into a 34 Mbit / s stream, etc. up to speeds of 560 Mbit / s for transmission over fiber. The equipment that provides the combining of streams and their separation at the receiving end is called "muldex" (multiplexer - demultiplexer).

Digital streams are transmitted over communication lines by channel codes that do not have a constant component and provide self-synchronization. To group multiple streams, the muldex performs the following operations:

Translation of channel codes in each input stream into BVN code with representation of binary symbols by unipolar signals,

Sequential interrogation of all input channels within one bit and the formation of a combined stream of binary symbols in the unipolar BVN code (Fig. 18, b, the moments of the survey are marked with dots),

The channel code representation of the binary symbols of the combined stream. In addition, framing words are inserted into the combined stream.

The transfer rates in different streams are slightly different. To match the speeds, an intermediate storage of the data of each stream is carried out until the moment of reading by synchronized pulses. The frequency of reading data in the stream is slightly higher than the frequency of their arrival. Such systems with the combination of asynchronous streams are called plesiochronous digital hierarchy. There are more complex systems with a synchronous digital hierarchy.

^ 4.2. Time-frequency division of channels in a GSM communication system

In a cellular communication system of the GSM standard, subscribers (MS mobile stations) exchange messages through base stations (BS). The system uses frequency and time division of channels. The frequency range and the number of frequency channels depend on the system modification. The channel separation scheme in the GSM - 900 system is shown in Fig. 19.

The transmission from the BS to the MS on the “forward” (downlink, forward, downlink, fall) channel and from the MS to the BS on the “reverse” (reverse, uplink, rise) channel is carried out at different frequencies separated by an interval of 45 MHz. Each frequency channel occupies a bandwidth of 200 kHz. The system is allocated the ranges 890-915 MHz (124 reverse channels) and 935-960 MHz (124 forward channels). Eight time division multiplexed channels operate alternately on one frequency, each within one time window of 576.9 μs duration. Windows form frames, multiframes, superframes, and hyperframes.

Long duration of the hyperframe (3.5 hours) is determined by the requirements of cryptographic protection. Superframes have the same duration and contain either 26 multiframes (26 ∙ 51 frames) when transmitting sync signals, or 51 multiframes (51 ∙ 26 frames) when transmitting speech and data. All frames contain 8 windows and have the same duration (about 4.6 ms). The system uses several types of windows with the same duration.

All windows of one frame are transmitted at the same frequency. When switching to another frame, the frequency can jump. This is done to improve noise immunity.

All transmitted information, depending on the type (speech, data, control and synchronization commands), is distributed over different logical channels and transmitted in separate "portions" in different windows - physical channels. In one window, data from different logical channels can be transmitted. Different types of windows are used to transmit information of different types. Guard intervals are introduced between the windows to eliminate the overlap of signals from different users. The length of the guard interval determines the maximum cell size (cell).

Logical channels are divided into communication and control channels.

Channels of connection (TCH - traffic channels) transmit voice and data at rates from 2.4 to 22.8 kbps. The system uses a source encoder of the PRE-LPC type (Linear Predictor Excited Coder). Its standard speech rate of 13 kbps is increased to 22.8 kbps as a result of channel coding.

Control channels are divided into 4 types.

"Broadcast" control channels they transmit from the BS sync signals and control commands necessary for all MS for normal operation. Each MS receives from the BS:

Synchronization signals for setting the carrier frequency on the FCCH (frequency correction channel),

The number of the current frame on the SCH (synchronization channel),

The BS identification number and the code that determines the sequence of the carrier frequency hops over the BCCH (broadcast control channel).

Common control channels (CCCH - common control channels) are used when establishing communication between BS and MS in the following order:

The BS notifies the MS of the call via the PCH - paging channel,

The MS requests from the BS, via the RACH (random access channel), the number of the physical channel for connecting to the network,

The BS issues the MS, on the AGCH (access grant channel), the permission to use the communication channel (TCH) or the dedicated individual control channel.

Dedicated individual control channels (SDCCH - stand-alone dedicated control channels) are used to transmit from the MS to the BS a request for the type of service and to transmit from the BS to the MS the number of the physical channel assigned to the MS and the initial phase of the pseudo-random sequence that determines the frequency hopping program for this MS.

Combined control channels (ACCH - associated control channels) are used to transmit control commands when the MS moves to another cell (FACCH channel - fast associated control channel) and to send information about the received signal level from the MS to the BS (via the SACCH channel - slow associated control channel).

In "normal" windows of the NB type, the transmitted information is located –114 bits. A 26-bit training sequence known to the receiver is used to estimate the impulse response of the communication channel in order to adjust the equalizer of the receiver,

Equalizing the characteristic of the communication channel, as well as for assessing the quality of communication and determining the time delay of the signal. At the window borders, TB (tail bits) end combinations are placed, at the end of the window - a GP guard period (guard period) of 30.46 μs duration. The steering flag (SF) bits indicate the type of information.

FB windows are designed to adjust the MC frequency. The 142 zero bits are transmitted as an unmodulated carrier wave. Repetitive windows of this type constitute the logical channel for setting the FCCH frequency.

SB windows are designed for time synchronization of MS and BS. Repetitive windows form a logical SCH synchronization channel. 78 information bits contain the frame number and BS identification code.

Type AB windows are designed to obtain permission for MS access to the BS. The sync bit sequence transmitted by the MS configures the BS to correctly read the next 36 bit sequence containing the service request. The guard interval in the AB window is increased to accommodate a large cell size.

^ 4.3. Code division of channels

in the communication system of the IS-95 standard.

The system is allocated the frequency ranges of 869-894 MHz for transmission of signals over the forward channel and 824-849 MHz for the reverse transmission. The frequency spacing between the forward and return channels is 45 MHz. The operation of the forward channel at one carrier frequency during speech transmission is illustrated in Fig. 21.

The sequence of binary symbols from the channel encoder is converted as follows:

- "scrambled" - summed modulo 2 with the individual code of the subscriber to whom the message is transmitted ("long" PSP),

- summed up with the Walsh sequence. Orthogonal Walsh sequences, which are the same for all BSs, divide one frequency channel into 64 independent channels,

- divided by a commutator (CM) into two quadrature streams I and Q.

The symbols in these streams modulate the quadrature components of the carrier waveform. To separate signals from different stations, symbols in quadrature streams are summed with "short" PSP- I and PSP- Q- BS identifiers.

The system uses unified data encoding equipment. GPS receivers are used to synchronize all BSs in time. The elementary PSP symbols are followed with a frequency of 1.2288 Msymb / s. Long memory bandwidth with a period of 41 days is formed by a register containing 42 bits. Individual subscriber codes are fragments of a long bandwidth that differ in initial phases. Short PSPs of 2/75 s duration are formed by shift registers containing 15 bits, and differ in different BSs by an individual shift relative to the moments of the beginning of two-second time intervals.

When summed with the output sequence of the encoder, having a frequency of 19.2 kbit / s, the long PSP is punctured to equalize the rates of the added sequences: every 64th symbol is taken from it. When the obtained sequence is summed with the Walsh codeword, one symbol of the sequence is converted into 64 Walsh chips, so that a digital stream at a rate of 1.2288 Msps is fed to the switch. Short memory bandwidths have the same symbol rate. Therefore, for the most efficient use of the frequency range, according to the Nyquist and Kotelnikov theorems, the spectrum of the sequence of symbols at the input of the band-pass modulator in the transmitter should be limited to the frequency 1.2288 / 2 MHz. For this purpose, a low-pass filter is installed at the input of the modulator with the boundaries of the pass and stop bands of 590 kHz and 740 kHz.

Each BS modulates a short PRB signal, issued on a special "pilot" channel. The MS, shifting the short PRP in time, finds the BS with the strongest pilot signal and receives from the BS via the synchronization channel the data necessary for communication, in particular, the system time value for setting its long code. After setting the long code, the MS can receive messages directed to it or start the procedure for accessing the BS on its own initiative. During operation, the MS monitors the level of the pilot signal and, when a stronger signal is detected, it switches to another BS.

Data that needs to be transmitted at high speed is divided into packets and transmitted simultaneously over different frequency channels.

In the return channel (Fig. 22), the transmitter power and signal-to-noise ratio are lower than in the forward channel. To improve noise immunity, the rate of the convolutional encoder is reduced to k / n= 1/3, the encoder outputs data at 28.8 kbps. The spectrum of this digital stream is expanded: each 6-bit data packet is replaced by one of 64 Walsh symbols, repeated 4 times. The character number is determined by the content of the data packet.

After expansion, the sequence of symbols is summed modulo 2 with the long PSP of the subscriber and is divided by the switch into two sequences: in-phase ( I) and quadrature ( Q), which, after summing with short PSPs, I and PSP- Q, modulate the in-phase and quadrature carrier waves. To reduce phase jumps, the quadrature modulation sequence is time-shifted by half the duration of an elementary symbol.