CC BY
10
Volovach V.I. Bo:itxum B.H. cand. sci. tech., assistant professor, head of department «Informational and electronic service department», FSBEIHЕ «Volga region state university of service» Russia, Togliatti
Anfalov K. V. ÄH^anoe K. B.
senior lector «Informational and electronic service department», FSBEIHЕ «Volga region state university of service» Russia, Togliatti
YflK 681.3.06
EVALUATION EFFICIENCY SERIAL INPUT IN SYNCHRONISM CONSTITUENTS SEQUENCE AT SERVICE DATA TRANSMISSION
This article is about using of M-sequences to synchronize the data transmission system in a busy telecom channel. The concept of expression and proposed for the determination of the coefficient of acceleration input system matching. Transmission equipment uses a noise-signal for the united transfer single messages and the main voice signal, but in connection with the united transmission of two useful signals in one-frequency channel issues arise noise immunity.
In the simultaneous transmission of two signals in one frequency channel to consider their mutual influence, which in fact can be compensated by including applying error-correcting coding.
For a correct choice of the service data signal to be determined, primarily, their maximum level, and a number of other features.
Substantiated and solved the problem of synchronization of the service data transmission system based on the noise-like signal recognition, given as a combined M- sequences.
There're expressions for determining the time based on correlation sequences. In the example values were calculated acceleration ratios for combination of sequences of different lengths and with different numbers of constituent sequences.
The calculation of the comparative rate of acceleration input in synchronism. The values of the combination coefficients for acceleration sequences of different lengths and with different numbers of constituent sequences.
The article considers the problem of synchronization transmission system based on the noise-like signals detection. Combined M- sequences were chosen as a noise-like signal. The solution of this problem allows determining the most effective noise-like sequences and methods for their generation. The article estimates different sequences and compares the system performance of synchronization by comparing acquisition times. The dependence of efficiency the synchronization system, parameters of combination sequences. A comparison of the effectiveness different methods obtaining the combination sequences based on analyzing the correlation properties sequences and the calculated acceleration factor enter in synchronism.
There is a logical block diagram implementing the principle combining the components of the sequences with the appropriate logic function. A block diagram of the correlator implements a combined search sequences.
In conclusion is formulated, in which method input data synchronization system based on a combination of sequences provides a significant gain in time compared with the conventional method with stepwise correlation length transmitted with the same sequences.
Keywords: systems of synchronization, combined sequences, M-sequences, methods of combining the sequence, evaluation time synchronization.
ОЦЕНКА ЭФФЕКТИВНОСТИ ПОСЛЕДОВАТЕЛЬНОГО ВВОДА В СИНХРОНИЗМ СОСТАВЛЯЮЩИХ ПОСЛЕДОВАТЕЛЬНОСТЕЙ ПРИ ПЕРЕДАЧЕ СЛУЖЕБНЫХ ДАННЫХ
В статье рассмотрено использование М-последовательностей для синхронизации системы передачи служебных данных по занятому телекоммуникационному каналу. Введено понятие и предложены выражения для определения коэффициента ускорения ввода системы в синхронизм. Показано, что устройство передачи служебных данных использует шумоподобный сигнал для совместной передачи названных данных совместно с полезным сигналом. При одновременной передаче двух сигналов в одном частотном канале следует учитывать их взаимное влияние, которое, в том числе может быть скомпенсировано применением помехоустойчивого кодирования. Для корректного выбора сигналов передачи служебных данных должен быть определен, прежде всего, их максимально допустимый уровень и ряд других особенностей.
Обоснована и решена задача синхронизации системы передачи служебных данных на основе распознавания шумоподобного сигнала, заданного в виде комбинированной М-последовательности. Определены наиболее эффективные методы формирования шумоподобных последовательностей для характерных случаев. Проведена сравнительная оценка различных последовательностей на основе анализа времени вхождения в синхронизм. Исследованы зависимости эффективности системы синхронизации от метода комбинирования и параметров комбинационных последовательностей. Вывод об эффективности предложенных методов формирования комбинационных последовательностей производится на основе сравнения корреляционных свойств полученных последовательностей.
Приведены выражения для определения времени вхождения в синхронизм системы передачи данных на основе корреляции между получаемой и эталонной последовательностью. Произведен расчет сравнительного коэффициент ускорения ввода в синхронизм. Определены значения коэффициентов ускорения для комбинационных последовательностей различной длины и с различным числом составных последовательностей.
Получена структурная схема, реализующая принцип комбинирования составляющих последовательностей с помощью соответствующей логической функции. Предложена структурная схема коррелятора, реализующая поиск комбинированной последовательности.
В качестве вывода формулируется, что метод ввода в синхронизм системы передачи данных на основе комбинирования последовательностей обеспечивает существенный выигрыш во времени по сравнению с обычным способом с пошаговой корреляцией при одинаковой длине передаваемых последовательностей.
Ключевые слова: коэффициент ускорения, система синхронизации, комбинационные последовательности, М-последовательности, методы комбинирования последовательностей, оценка времени синхронизации.
When building different data transmission systems we come acress the issue of synchronization of a transmitter and a receiver. Analyzing the transferability of information along the telecommunication channels [1, 2, 3], it was found that it is effective to use M-sequences as a synchronization signal [4].
A thorough analysis of the correlation properties of composite sequences showed that with the increase
of the lengths Ll and L2 periodic correlation function of the composite sequences in its form approximates to the periodic correlation function of M-sequence. Therefore, these composite sequences make rapid input of the system in synchronism impossible.
Non-linear sequences y" = 1, 2, ...,
L have the best synchronizing properties. We get
these sequences by combining K short sequences
{yjti}, O^Jwith lengths ^ .. Lk
respectively. With proper selection of component
sequences ..., {y>j K} and the way they are put
together (logical function) the length of the sequence is
''comb
K
= Z/j • L2 •... • LK = Lt,
(1)
/=1
and the correlation coefficient of the combined sequence{Xj} with any of the sequences {yji}, i = 1, ..., K will dramatically increase at values T, that
are multiples of the period of the component sequence {j }.
With other T the cross-correlation coefficient will have the same value, substantially smaller than when T = mL¡, m = 1, 2, ... Such combined sequences provide an opportunity to significantly accelerate the input of the system in synchronism.
The sequence obtained by using the logical function is non-linear. Correlation properties of this sequence
make rapid input in synchronism possible.
The degree of acceleration should be assessed by using the acceleration coefficient Ky . The value of the acceleration coefficient Ky can be calculated based on the following considerations.
Let the receiver that detects the input in synchronism consist of a single correlator and spends at each search step a time period equal to T^ . Then when applying the sequence {Xj} comb obtained from R of shorter sequences on the basis of
majority rule, the total search time of sync signal is:
T = (Li + L2 + ..Lr) £ = Li.
(2)
The coefficient Ky characterizing the acceleration to search the M-sequence {Xj} with the length Lcomb, to
of input in synchronism while using complex sequences the time determined by the formula (2): {X.}, is defined as the ratio of time L , T required
j ' comb im A
L T.
j¡r _ comb im
T'Y L.
im / / i
(3)
1=1
As it can be seen from the formula (3) the increase of the coefficient K, can be achieved both by increasing
the ratio
^ comb _ ¿=1
n A
» l.
a
x Li m
(4)
¿=1
and by the adjustment of time of integration T ' and tion sequence, and research time T , at which the value
j j o im i ' imp
Tim without increasing the probability of errors during Ky is maximum.
the search. Thus, we get the problem of choice of In [5] it is shown that to obtain a combined sequence
the lengthsLi of the components{y^}, i = l,...,i?, with the length number of components R, which form a synchroniza-
Lcomb ~ L1L2,...,LS
(5)
the length of the components of the sequences must be mutually prime numbers. Besides, the relation (5)
will be maximal in the case, when the lengths of the components of the sequences are close to the value,
'comb
L = ZL
"'comb '
(6)
Then the maximum value of the acceleration coefficient is
1 — T
K ~ — L R
y ~ n comb rpf ' im
(7)
The formula (7) shows that the integration time T.m ', which determines the probability of error during searching, mostly depends on the mutual correlation coefficient of the combined sequence with the constituent sequences {yy;1}; {>y:2>;—;€Vy;*> -
The best will obviously be the case when the coefficient of mutual correlation of sequences {X j} comb
T / T' =
with any of the components of the sequences, for example {y j , takes the maximum value at t multiple of the length of this sequence, and the same and significantly lower values for all other t.
The ratio of research time T and T ' can be
im im
expressed as [5]
AC AC
\2
(8)
where AC is the minimum difference between the received and reference signals at different t. Then the values of the coefficients of mutual correlation of the formula (7) can be written as:
1
R-1 f
K ~_L R
y r comb
AC' AC
V
(9)
AC' ,
As a rule, and the task of increasing Ky unity, i.e. to the problem of choosing a particular logical
function.
is reduced to forming that kind of sequence {Xj} comb, In [6] it is shown that, if the rule of choosing the for which this ratio would be as close as possible to value of a logical function is written as
/00 =
+ 1, if(;Vy;i; yy;2 yj;r )
contains less R/2 units; -1, ifOi;1; yj,2,-\yJ;R) contains more R/2 units,
(10)
this function allows to obtain in output sequence {Xj} comb the maximum percentage of each of the R of component sequences, regardless of the remaining sequences, i.e. to obtain a minimum cross distortion.
The function f (y) when R is odd is single and symmetric function of (y^; y^;...; ynr ).
The value of cross distortion depends not only on the selected logical function, but also on the type of component sequences. To minimize cross distortion these sequences must satisfy the following requirements:
AC'
1. The correlation functions of the component sequences should be similar to the correlation function of the noise.
2. Any two elements of the sequence must be not correlated between each other.
3. In each component sequences the number of units must equal the number of zeros.
When satisfying all three of the requirements the cross distortions, defined by the sequences are absent.
Thus
AC
= F(el),
(11)
where is the coefficient taking into account the
deterioration of the correlation properties of the signal obtained by combining the component sequences
function (10).
in accordance with the logic
For this function
1 — T
fr ~ _T R
y „ comb j,r • im
(12)
Then taking into account (11) and (12) the equation (9) for Ky takes the following form:
1
K =— L R y R
"'comb
f<R - D
(13)
When using M-sequences as components {y ~} The expression (13) defines the maximum value
none of the requirements 1-3 is met accurately. However, of the acceleration coefficient. As the lengths of real
in this case, even for small values of R the cross distor- sequences do not satisfy (13), the value can be calculated
tions determined by use of M-sequences will be negli- by the following formula: gible.
L,,
Ky =
L1 + L2 ... + LR
f<R - D
-1
(14)
The table 1 shows the values of acceleration ient K,
The lengths Lcomb of combined sequences {X}} coefficients for different R h Li. It also shows the comb, shown in table. 1, were found based on the conditions of using M-sequences with relatively prime periods ratio —. as components
K
y max
The lengths of combined sequences
Table 1.
R Lcomb + Z(3 +... + Lr JÇ y max Ky V max
3 651 =3-7-21 5,06 7,96 0,635
3 3255 = 7-5-31 19,53 23,11 0,845
3 27559 = 7-31-127 53,2 97,2 0,548
5 846199095= 60,500,0 447000 0,135
7-15-31-127-2047
-1
Table 1 show that the method of input in synchronism on the basis of sequences combinations provides a significant gain in time compared with the usual way. By usual way is meant step-by-step correlation with the same length of transmitted sequences.
In addition, the value of this gain, with appropriate choice of the number and lengths of the component sequences, is very close to its limit.
Fig. 1 illustrates the principle of combining the component sequences with the help of appropriate logic function.
We have R generators G, i =1, 2, ..., R, of the sequences {y;1} {y;,2};...; {y^ } with relatively prime lengths.
We denote these sequences as:
(yj;1; yj-1;1; yj-2;1 ; ... ; yj-l;1; ...),
O^i' yj-\-,2' yj-2;2 ' ••• ' y]-l;2 ' •")>
(yj;R ; yj-1;R ; yj-2;R ; ... ; yj-l;R ; ...),
wtere (y;;1; y;-.2; y,,R ) = 0 от 1.
j;R-
f-i,W ---
>—d
Dftaii&i ¡¿Ьяаг
SiEih. ¡j-ibsms
*
а)
b)
Fig. 1. Structural diagram illustrating: a) the principle of combining component sequences; b) searching of combined sequence
The values of the sequences at the output R of the generators can be written in the following matrix:
y yj —1;1; yj—2;1' ... ; yj-l;1 ... yj;2 ' yj—1;2; yj—2;2 ; ... ; yj—l;2 ...
У
j;R ; y j-1;R ; У j-2;R ;
У,- -
j-I ;R
(15)
At the moment of time l a vector column of the matrix (yj_n; yj-i-2 5 yj~ir )■ is delivered to the input of logical device. Each vector is assigned according to some rule the value of the logical function f (y) : +1 or -1.
To search the combined sequence the correlation device (Fig. 1 b) is used on which the input sequence {Xj} comb and one of the sequences {yJti}, i = l,...,R. are fed.
If the delay {Xj} kom6 is a multiple of the period of this reference sequence, then positive voltage appears at the output of the correlation device. The decision scheme in accordance with the sign and value of the output voltage of the correlator decides on the need to continue the search.
If the value exceeds some threshold,
then the decision scheme captures the convergence of sequences {X j }to the reference sequence with the
accuracy up to the period of the reference sequence and causes a switch providing another reference sequence feed on the correlator.
The search continues until all of the reference sequences will be accurately synchronized with the input sequence {X j}.
The work of the decision device is challenged by cross-distortion, giving extra components of voltage at the output of the correlation device.
After dropping in synchronism further synchronous communication is supported using the discriminator with delayed sync.
Further we use the method of obtaining {X j} comb from three components of sequences, since the increase in the number of component sequences Ky becomes much less Kymax . When applying three sequences as a logical function one should apply a logic "2 of 3" or
Xcomb=XY@YZ@XZ.
When forming Xcomb it is necessary to choose the components of the sequence so that:
1) K
= K '
y max y '
2) the selected component sequences make it easy to get trigger and timing pulses required for encoding and decoding devices.
To form a broadband signal and timing pulses with a repetition rate /Tim2 = fTimi / Lel as one of three sequences, it is necessary to take a sequence, the length of which is LA. To obtain trigger pulses that
start synchronization with the beginning of the code word, one needs to use the sequence with the length
L = L
words '
equal to the number of elements of the
code words as the second sequence. Further
L2= 2"-
Then the repetition rate of trigger pulses will be
1 = 2-1 = 15.
Tn =4, -¿words -to =127.15-U-10"3 =2,1 S
As the third sequence one can use the sequence with L3 = 1, i.e. a trigger, the input of which receives the frequency
f = 2Amwhere /Timi =900 Hz.
In this case Lcomb = 127-15 • 1 = 1905. Then the acceleration coefficient is
_ 127-15-1 7 ~ 127 + 15 + 1
fe-O
-1
1905 1
143 3,14
= 4,26;
1
Ä-i
X —_T R
jmax — ^ kom6
-1
1
= -1905 3
2/3
§<3-i)
-1
= 16.
Loss compared to the maximum possible acceleration is
K
y max
« 3,76.
It is unreasonable to use the sequence with length equal to 1.
Let us consider another case. Suppose that along the direct channel for the transmission of the elements of the code word we use the sequence obtained by summing up two sequences over module 2. These sequences are {11100010010} and {1111100110101} with lengths L1
11 and L2 = 13. The combined
Lcomb — L\
L2= 11
sequence will have the length • 13 = 143 and its correlation prop-
erties will be close to M-sequence. In this case, the transmission time of one element of the codeword is T, = L ,rn = 0,158 s, and the transmission time of the
el comb• 0 ' '
code word is Tk = Tdn= 2,37 p.
Then to form a synchronizing sequence using a logical function one needs to take the following sequences of lengths L1 = 11; L2 = 13; L3 = 15.
In this case L , = 11-13-15 = 2145, the coefficients
comb
are
1
r-1
K — — LR
y max — ^ comb
f<*-l>
= — 21452/3 3
f(3-D
= 17,6;
"'comb
Ky-
f^-i)
2145
11 + 13 + 15
f(*-i)
= 17,52.
The loss is
y y 17,6
We define the time of entering into synchronism for the sequence with the length L , = 11-13-15 = 2145.
comb
Suppose that the signal to noise ratio at the receiver
input is h^ = 0,04 and the probability of error when entering into synchronism is approximately 5-10-3. In this case, the research period will be T ~ 0,14 when
' r im
T0 = 1/ fTim ~ 1,1 ms. The maximum time of entering into synchronism by the method of step by step correlation
is ™™Tstepcorelation -¿-7^21,45-0,14-294 s..
When using the fast entering in synchronism method the time of entering is
max T
1иа.л •» stepcorelation
maxTcomb
К,
A comparison of the method of accelerated entering in synchronism with the usual step-by-step entering is made, provided that there is a synchronization by clock frequency.
When entering into synchronism the synchronization by clock frequency is practically missing. Therefore, after the next shift of the sequence and synchronization check the subsequent shift must be made by
(U I7'8,
. In this case
294 17,5
«16,8 s.
the time of entering into synchronism by step-by-step correlation is max Tstepcorelation = 8 L^ Tim.
When using the sequence derived with the help of logical function first a short sequence is entered. Its entering time, due to the lack of time synchronization, will also increase eight-fold.
After entering a short sequence, the rest can be shifted at a clock interval, as there already is a sync clock. Then
_ ^comt
^ 8 Zi[ + ¿2 "l"
f(*-i>
For the example considered above
(A =11; =13; Ц =15) 3,14
_ 8-2145 * ~ 8-11 + 13 + 15
(3-1)
= 47.
Therefore, ifthe synchronization by clock frequency a 47-fold win on time in comparison with the step-by-is missing the accelerated entering in synchronism gains step method of correlation. For example,
A£«-10dB; Tim~ 0,055s;
max T
stepcorelation = 8 Tim • Lœmb = 8 • 2145 • 0,055 » 945 s; 945
max ^c'omb =
47
20 s.
Along with the method of successive entering in component sequences are entered in synchronism
synchronism the method of parallel entering component simultaneously. The time of entering will be determined
sequences in synchronism can be offered. This requires by the longest component sequence, and the acceleration
three correlators and enter a taken sequence and one coefficient is of the components into each of them. Thus all three
If _ ^comb
ForZcomb=2145 К
46. When hi =-14dB.
max rc'omb
maxT.
stepcorel
K„
294
= 64 s.
In the absence of prior synchronization on clock frequency, the method of parallel entering in synchronism does not give a gain in time compared to the sequential method. Input method based on a
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