Method for capacity estimation of real communicational channels with PSKnsignals in presence of ISI and its application Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

METHOD FOR CAPACITY ESTIMATION OF REAL COMMUNICATIONAL CHANNELS WITH PSK-N-SIGNALS IN PRESENCE OF ISI AND ITS APPLICATION

Ilya M. Lerner,

Kazan National Research Technical University named after A.N. Tupolev-KAI, Kazan, Russia, aviap@mail.ru

Keywords: Capacity estimation, ISI, PSK-n-signals, bandpass filters, predistortion signals.

Volume of transmitted information exponentially increasing from year to year is a current trend of modern society that leads to the need for increasing the transmission speed of data transmission systems. This trend is the most pronounced among radio engineering data transmission systems, which currently operate under conditions of limited frequency resources and constantly increasing requirements to an effective frequency resource usage.

One of the most effective approaches to solving this problem is the conversion to the data transmission in the presence of intersymbol interference at radio engineering data transmission systems produced by their selective systems. Despite the attractiveness of this approach, its technical implementation is associated with a number of difficulties that can lead to an increase of complexity of the receiver itself along with an increase in the number of interfering symbols. This ultimately arises the issue not only about the expediency of its implementation, but also about its practical feasibility.

Since the increase in the alphabet of channel symbols leads to the need to increase the signal-to-noise ratio (SNR) in order to achieve a given signal reception quality, it is advisable to consider receiving algorithms based on utilizing frequency filtering to increase SNR and consequent use of multithreshold decision device at situation of strong ISI in communicational channel.

In this paper, we consider capacity of such channel with PSK-n-signals. A new method for capacity estimation was developed, which can be used to estimate ultimate capacity in the absence of noise when the decision device is a simply multi-threshold device and radio engineering data transmission systems operates in the presence of strong ISI.

The method has high accuracy and low computational complexity, which doesn't increase with the growth of size of PSK-n-signal constellation.

New properties of LTI systems that can be used to rise frequency efficiency of radio engineering data transmission systems were revealed.

Information about author:

Ilya M. Lerner, associated professor. candidate of physico-mathematical sciences, Kazan National Research Technical University named after A.N. Tupolev-KAI, Department of Radioelectronic and Quantum Devices, Kazan, Russia

Для цитирования:

Лернер И.М. Метод оценки пропускной способности реальных каналов связи с многопозиционными фазоманипулированными сигналами при наличии межсимвольных искажений и его применение // T-Comm: Телекоммуникации и транспорт. 2017. Том 11. №8. С. 52-58.

For citation:

Lerner I.M. (2017). Method for capacity estimation of real communicational channels with psk-n-signals in presence of ISI and its application. T-Comm, vol. 11, no.8, рр. 52-58.

T-Comm Том 11. #8-2017

Introduction

Volume of transmitted information exponentially increasing from year to year is a current trend of modern society that leads to the need for increasing the transmission speed of data transmission systems. This trend is the most pronounced among radio engineering data transmission systems (RDTS), which currently operate under conditions of limited frequency resources and constantly increasing requirements to an effective frequency resource usage [3].

One of the most effective approaches to solving this problem is the conversion to the data transmission in the presence of intersymbol interference (ISI) produced by selective systems presented at RDTS. Despite the attractiveness of this approach, its technical implementation is associated with a number of difficulties that can lead to an increase of complexity of the receiver itself along with an increase in the number of interfering symbols. This ultimately arises the issue not only about the expediency of its implementation, but also about its practical feasibility.

So widely used methods: zero-forcing filter (ZFF), zero-forcing equalizer (ZFE), linear minimum squared estimation (LMSE) equalizer and decision feedback equalizer (DFE) have a significant loss in noise immunity as opposed to optimal reception algorithms using the maximum likelihood (ML) criterion [1,2]. In some cases the first three methods of mentioned above cannot be realized for real channels [ 1 ] and as it was mentioned in [2J these methods are inadequate as compensators for the ISI on channels with spectral nulls, which may be encountered in radio transmission. The last one has the same problem as first three methods for channels, which may be encountered in radio transmission but with less effect. It should be noted that all of them do not lead to complete suppression of ISI and they provide good results only with minor ISI when amplitude frequency response has slow variation on magnitude [1,2].

As for ML algorithms (since they were constructed on Viterbi algorithm) their main disadvantage is the complexity of implementation, depending exponentially on the transmission speed and memory channel, which leads to the impossibility of their usage with a large alphabet of channel symbols. In the literature, various approaches to reducing the complexity of the Viterbi decoder for this case are considered: a decrease in channel memory by means of a preliminary linear correction, slightly distorting amplitude frequency response of the channel [3, 4], a shortened search of the most probable paths along the lattice [5,61; combination of two methods mentioned above [7,8]. However, the complexity of the receiver in this case decreases insignificantly, still remaining much more complex than a linear equalizer. One of the latest works in this direction shows that obtaining suboptimal algorithms based on ML algorithms leads to considerable computational complexity described by exponent law when the number of channel symbols exceeds 4 and/or in a case of high transmission rate [11-

In this case, one of the most interesting approaches to getting high speeds on radio communication channel is the usage of pre-distortion signals and receiving algorithms concerted with them.

Since the increase in the alphabet of channel symbols leads to the need to increase the signal-to-noise ratio (SNR) in order to achieve a given signal reception quality, it is advisable to consider receiving algorithms based on utilizing frequency filtering to increase SNR and consequent use of multithreshold decision device at situation of strong ISI in communicational channel. Their effi-

ciency is expedient to estimate the ultimate capacity of linear selective systems (capacity of channel in this particular case) in the absence of noise when the decision device is a multithreshold device. The last condition determines the efficiency limit for such RDTS.

It should be noted that using radio bandpass filters in the radio path of RDTS leads to additional ISI which influence is considered. So it would be better to obtain the solution of this problem for radio frequency signals.

Due to the fact that RDTS using multi-position phase-shift keying signals with n discrete states (PSK-/?-signals) are the most widely spread nowadays, we will solve this problem for RDTS of this class.

Problem Statement

In this case, capacity estimation is considered for a communication channel (Fig.l), which consists of a transmitter, a linear time invariant (LTI) system, a receiver and a decision device (DD).

In this work we assume that LTI system is tuned bandpass filters that possess the following properties: 1) © / 2Aii(1 >15 where

2Afi„ - the resultant bandwidth of LTI system, where a0 - the

average frequency of the tuned LTI system; 2) their amplitude frequence response possess an even symmetry and phase frequence response - odd symmetry with respect to We also

assume that receiver is an ideal phase detector similar to DD that does not introduce additional ISI.

ijf)

Transmitter LTI System Receiver DD

Fig. 1. The considered communication channel

We assume that each symbol of primary signal that impacts on the input of transmitter takes cquiprobably one of the n phase values of the signal constellation

= (jfc + 0.5vsign (||0-5»||-0.5n-0.25)-||0.5n||) A<pf, ■ (1)

Here k = l,n; |. - rounding operation to the nearest integer;

in accordance with the requirements to the PSK-n signal generated by the transmitter V takes zero for the PSK-/? signal with initial shift of the signal constellation ^ = o and v = i when

q>cs - n!n\ sign( . ) - signum function; A(ps, =2n!n ~ step between adjacent phase values of the signal constellation.

The PSK-n signal generated by the transmitter from the moment t = 0 can be represented as follows

V (0=i[iM''-ik,,H(>-)>p(/{cy+2er+sr - %))=

r»l

(2)

where /ePJ" - the number of transmitted radio pulses forming the PSK-n signal; / - resolution time is the minimum transmission lime of each of pulses when any primary symbol from any transmitted sequence can be reliably reconstnicted by DD from received channel symbol at the output of the LTI system at given playback quality; - Heaviside step function;

6 +q> > cou ~ "ie carner frequency of the PSK-n signal

equal to the average frequency of the tuned LTI system; p -constant phase shift at the frequency co{) introduced by tuned LTI system; 20r = y ((r -1) t^) - y/ {(r - 2) tm) - phase jump caused by the transmission of r-th radio pulse where V'(('-OO = 20' + 9r and v{(r-2)t„J) = 29,_t+$r_t ~ initial phases of r"' and (,*-radio pulses of PSK-n signal at the output of transmitter; (/-/((^-2)/,.., ) = ?>„ if/'= 1 because we assume

that before the start of transmission, until the moment t = 0, LTI system is in a steady state and harmonic oscillation

expf^tty + tp^-ipo)) ac,son lts input-

For considered case the resolution time / must correspond to the minimum time when the following condition is true

Here arr - the permissible phase settling error at the output

of LTI system, which is related to the liducial permissible settling error by the relation aa =erfiri)/ApI(; a„ (rrr.,) — measured settling phase error at the output of LTI system for the rlh radio pulse when it ends; y (/■/ ) - the measured value of slowly varying

phase of the r1'1 radio pulse at the output of LTI system obtained by a receiver at moments >■>

J rva

In this case PSK-n signal at the output of a LTI system starting from the time t = 0 according to the superposition principle and results of [9] can be represented in the form

■C (f) = Z (,r) ■exp (/oy) = k (;©0) exp (j (co0i -<p„))x

(4)

where Xr = (l-S(1(/)) ifr=l;

if f— 2,1 and/=i(,_(/_i)/(B)Jn(,_(/_i)fim); B,{i) - settling function [9]; Z{/) - complex envelope of the transient

process caused by the passage of the PSK-n signal through LTI system; ¿(y'w,() = /t{yw(l)exp(/tp„) -complex transmission coefficient of a tuned LTI system, where we assume k(jm„) =1;

q.\

The signal at the output of the receiver, based on equation (4), is defined as

The recovery of the primary signal is made by DD based on the decision rule

wm(>(7)

where f(k',r) {rtj^-^aj, «,„„<0.5^,.

The last of these conditions is necessary to ensure the uniqueness of the DD solution and it is obvious that in the absence of noise

Analyzing results of 110] we can conclude that for considered channel capacity determination may be formulated as the maximum information transmission rate on the communication channel with equivocation produced by IS1 where maximum is taken over all possible sources of in formation used as input to the channel.

In this case, equivocation produced by IS! is easy to consider using resolution time in the following equation form for capacity channel estimation

(8)

where the second multiplier in equation is maximum entropy of source and / is taken at the condition a —> 0.5A<p■

Thus, it is necessary to determine the resolution time / of

LTI system to estimate the capacity of considered channel, which requires an analysis of the occurring transient process caused by the PSK-n signals transmission.

Problem Solution

Analyzing (6) and (7), we conclude that in order to get estimation of tns it is required to determine a combination of the values

of the transmitted phase jumps when the settling time for a given value of the permissible phase settling error will be the greatest of any of the transmitted radio pulses.

First of all it is necessary to obtain an expression that allows us to estimate measured settling phase error at the end of the Mh radio pulse at the LTI system output. For this we assume in (4):

' = K,> ¿{K>) = M, exprj- ■ n -and then we divide both sides of the equation by exp( /(4, +0,)) ■

As a result, we get the following equation

/

M, exp(ya,) = exp(-/x,. ) + y,»

r-1

where ^=¿20,-

After a scries of simple transformations over (9) with respect to argument of complex amplitude on the left-hand side of the equation, the relation for the ai definition has the form

tanK, = -£y, sin/

y, +Zr,cosx,

ÎL

' S

(10)

where 'g sin%r - Sc = y\ + £yr cos%r*

r=l r=|

Using (10), we estimate the combinations of transmitted phase jumps that provide the greatest settling times of slow varying phase on the output of LTI system for each rf-th (d -2,1) radio pulse of the PSK-n signal for a given permissible phase settling error a >m - For this, in the equation (10) we replace the variables:

/ by dt 20, by 20^, t„ by tmt, a, by where

«U =CV siS«K and as 3 result' we

get

tan aimt = -sin u / pd + cosp,

S^ S[

(11)

where

ßd=1f'fL

i'i

c tan a

820

S[ ¿P(cosn, +5:

(12)

M

■S<ß] cos¿/t + Ssß] sin//, =0 5.'f V^.cos/i,. I + 5;

(13)

V i"

■

%cßx cos+ Stß, sin//[ = 0 Seß2 cos/i, + Ssß, sin p, =0

(14)

cot 2Ö„

K=Xß,sin Mi' s'c=ßj+Zß, cos w ■

/-1

Let us test the obtained expression for the extremum. Since a0 <0.5 and n>2, then a<«72, therefore, it is advisable to

use the dependence tana^ instead of a in the analysis.

Analyzing (II), the equation allowing determining the partial derivatives with respect to all phase jumps of the transmitted radio pulses can be represented as

sin 20...

(¿4

I I±A + A

Vfei_

Ä + cos 20„

{,t-1

±A+A

where f = \,d ■

In this case, the set of equations with the solution determining the combinations of phase jumps providing maximum settling time for a given value of the permissible phase settling error for considering the d-th radio pulse, because of (12), takes the form

where y = j 0;! for \/q, so the last condition produce "+ " signs before p (for / = l,d—I) in the last expression of (16). The concrete value of a sign before p. is defined by concrete value of Sq in considered realization of sequence j^j.

Producing a number of simplest transformations over (¡6) with respect to 28ma , we obtain

(17)

=tan<2^ usinS <16>'

Pj \ (=1

We transform the equation cot 20. (17) and after the simplest transformations we obtain

tan apn, - ~

(18)

(#

Analyzing the system (13), we conclude that it can be the following

S'A cos//,, + S'Jl, sin pd =0 0

Wewill find a solution of (14) when v/i, *(), f = \,d since

otherwise the moments of time will be considered when the slowly varying phase at the LTI system output reaches a stationary value. It is possible only in one case, according to [9]: at the end of the transient process r oc.

From (14) and (11) the following relation follows

cot |i, = cotjii =... = cot jt,, = -Ss /Sc = tan afm. (15)

Analyzing (15), we can make the following conclusions:

1)20 = as wl^re 5 = i0; 1} if b = \,d -1;

2) cot20mjlj =tanaiH„-

We use the obtained results and (11) to get an expression that allows determining the maximum settling time for a given value of the permissible phase settling error for each of the transmitted radio pulses starting with the second.

After trans form at ion ctg20m„ = tg a'pm using the first conclusion mentioned above, we get the follow ing result

The resulting equation (18) allows determining the maximum settling lime ^ ^ for given permissible phase settling error at the

output of LTI system for any d-th (d = 2,/} transmitted radio pulse. In order to obtain /nm for d-th transmitted radio pulse we

have to solve 2'1" equations formed using equation (18) with 2'1 1 different realization of and to choose the greatest solution.

In the presence of damped oscillations for settling function, the greatest solution from the set of solutions of each equation of 2d l equations for d-th transmitted radio pulse which were obtained using expression (18) must be chosen. It should be noted that the generated PSK-n signals at the input of LTI system do not generally have jumps 20mBX =jrs where s = {0; l} as 20raiKi

equals to the phase jump from the discrete set of jumps of the PSK-n signal operating at the input of LTI system. However, in the dynamic operation mode values of effective phase jumps determined as v-',,,, } <JUC to the inertial properties of

the selective systems can take any values in the range -2n ... 2ir, which causes the correctness of the obtained results.

We use 77(f) = -arctan((l-2fio(r))tan0) PI for the slowly

varying phase of the transient process at the output of LTI system caused by the phase jump of the harmonic oscillation from —0 to +0 where 0 e (0;,t/ 2] to determine the longest settling time of

a slowly varying phase for the first radio pulse tmm (in the general case) for a permissible phase settling error. We transform this equation assuming n{tv) = 9y+v, 0 = 0V where ve[-;r/2;,T/2]

is the phase settling error at the observation time ty of the peak or

cavity of the settling function and using the substitution Z?(1(/r) = l±A where A > 0 is the peak or cavity value with respect to the stationary value equal to unity, here "+" if there is the peak and "-" if there is the cavity. As a result, we get

2Atan 8 (19)

l + tan:0(l±2A)>

An optimum analysis of (19) has shown that it is achieved under condition

1 (20)

v=± arctan

e.

= arctan -

Vl±2A

And the greatest phase settling error in this case is A

= + arctan

(v1±2a)

___ (21)

sVl±2A,

As seen from (21), to determine the maximum settling time, it is necessary to determine the time instant t" when jvj <a

begins to be realized and then to detenuine two discrete phase jumps 20y corresponding to the considered PSK-n signal, w hich

coiTesponds most closely to (20). It is necessary to solve the equation using the obtained results with respect to B0 (/mri J

K + "arctan ((' - 2Bo '(U ))tan K ) ' (22)

Then it is necessary to determine >r" using the obtained

results and the solution of (22).

The transposition principle operates for LTI system. Therefore, in determining the resolution time tres, it is possible to take

into account a finite number of radio pulses m, which we will call the effective memory of LTI system. In this case (3) in the part a will be with an accuracy of 8

5 >

(23)

end of the second stage of establishment for correct operation of the DD. The smallest value ce providing the end of the second

stage is called a critical errora^,- Obviously, atn! is defined as

follows

acril =rnk)(ic-jyi|)<0.5Atp„. (26)

The greater part of the change in the slowly varying phase at the output of LTI system corresponds to the first stage as compared to the third stage, the smaller value is taken by a ■ Thus,

this gives an additional upper limit on the choice of aml as

arm < « ,„, ■

(27)

Method verification and Results of its Application

Presented method (see equation (8), (IS) — (27)) and (6) are used to verify the method. The accuracy is estimated by determining the greatest difference taken in the absolute magnitude between the resolution time t№ determined using (24) and the resolution time tni 1 determined by numerical simulation (6) and calculation a (t using (3) with substitution / by? '.

at \ res / rts fjh

As LTI system we consider the following bandpass filters with identical bandwidth: 1) a single stage and two staged filter on coupled circuits with different degrees of coupling [9, p.30]; 2) three circuits filter with two coupled of them (see scheme [9,p.I62]).

According to [9] expression for short frequence response for the filter of the first type is determined as

(28)

Thus, the definition of the resolution time for LTI system with the constraints given above and the obtained results leads to the solution of the follow ing problem

(24)

Let us consider additional restrictions connected with the features of the considered transient process in LTI system. Thus, from the analysis of (6) it follows that when

M'O-y'K.H*';2*-). (25)

where yf(rtm) ~ the value of the initial phase of the (r +1)-th

radio pulse of the PSK-n signal at the output of the transmitter, stepwise change of the slowly varying phase of the signal at the output of LTI system will be observed.

This feature will be considered in more detail to determine the associated restrictions in the application of the results. In this case, the establishment of a slowly varying phase at the output of LTI system occurs in three stages, what follows from the analysis of (6). At the first stage, a slowly varying phase is established from q, „,(«„,) to ±tt ("+" if (*„,)> 0 and if

) < 0 ), at the second there is a jump from ±n to ~n . The third stage is its establishment from +/r to the value (fr+l)Cj)" Therefore, the resolution time must provide the

(1 + j&ccf + A2

where A ~ degree of circuit coupling; A a — generalized detune; p - number of stages of considered filter. And according to [9] the settling function of such tunned filter is determined as: for p = 1

(29)

5o(i) = l—exp(-oc)fcos /4x+-^sin /fx j> for p = 2

B„(x) = l-exp(-x)x

1-

1 + A'

2A3

Ax cos + 1 +

\ + A2 1+ A2

2 A2

2 A

Ax sin Ax

,(30)

where x = AQt - non-dimensional time where AQ = Afi0 / a, -

half of bandwidth of one circuit, a - coefficient indicating how

many times the circuit bandwidth must be changed to achieve the resultant filter bandwidth. For one staged filter with degree of circuit coupling A = 1 aA = 1.414 and for A = 2.41 aA = 3.11J for

two staged-for A = 1 =1.13.

According to [9] expression for short frequence response for the filter of the second type is determined as

k(jAa) -

[(1+jAa)3

(31)

where k- ratio of circuit damping of coupled circuits to the third one. For a- = 2 (the widely spread case in practice) the settling function of such a tunned filter is determined as:

S0(*) = l ^exp(-2jc)+-^-exp(-x)sin Ax^ (32>

For aA = 2 for A=\!3 and a% = 6.64 for .4 = 6.

The numerical simulation for ! - 200 and m = 4 and m = 5 using (23), (19) - (22) for considered bandpass filters has shown that to achieve accuracy of ¿><10 " it is sufficient to take into account four or five radio puises when an —> 0.5 (cases when a0 < 0.5 also include) for n > 9. For greater accuracy, it is neces-

saiy to increase m. Some of simulation results are presented in Table 1 and Table 2. As it can be seen from these tables the obtained method provides high accuracy of determination of the resolution lime with the number of discrete states « £ 9 and, consequently, high accuracy of determining the considered communication channel capacity under given limitations.

The dependences of the specific capacity ( C = C,,, /2AF„ [bits/(l Iz*s)], where 2AK = 2AO, / 2k ) on the

number of discrete states for considered in this paper LTI systems with the same bandwidth were obtained using the presented method and using (29), (32). They are presented in Fig, 2.

It can be seen from the Fig. 2 that as the number of discrete states exceeds 80 the capacity changes insignificantly. Every dependence has its own maximum, which reaches with finite number for finite value of number n of discrete states. From Fig. 2 it can be seen that 1) the smaller is the value of the parameter

then the bigger value of specific capacity will be; 2) capacity also depends on frequency response of LTI.

1

10 20 30 40 50 60 70 SO 11 100

Fig, 2. Dependence of the specific capacity on the number of discrete states of the PSK-n signal for a channel with a LTI system for given fiducial permissible settling error a(l - 0.4999- LTI system: I - a single

stage filter on coupled circuits, a degree of circuit coupling A = 1;

2 - three circuits filter, a degree of circuit coupling A = yj3, K-2;

3 - two staged filter on coupled circuits, a degree of circuit coupling A=l; 4 — a single stage filter on coupled circuits, a degree of circuit coupling A =2.41; 5 - three circuits filter, a degree of circuit coupling A = 6.

Table 1

Simulation results for two-staged filter on coupled circuits with A = I

Degree of coupling A Number of discrete states n Fiducial permissible settling error a0 Error % Effective LTI memory m

I 9 0.4999 0.25 4

15 0.067

32 0.0468

100 0.0018

Table 2

Simulation results for a single stage filter on coupled circuits, A = 2.41

Degree of coupling A Number of discrete states n Fiducial permissible settling error an Error I^OLH^/tfV.', % Effective LTI memory m

9 0.4999 0.1312 4

15 0.0617

32 0.03

100 0.0015

Conclusion

We can conclude the following:

1. The new method of capacity estimation for considered channel presented in this paper has a high accuracy. The error of the method, which on the is less than 0.5% for the number of discrete states equal 9 and more and effective memory m = 4.

2. Every dependence of capacity on number of discrete states has its own maximum, which reaches with finite value for finite value of number n of discrete states. Besides the smaller is the value of the parameter then the bigger value of specific capacity will be and capacity also depends on frequency response of LTI.

References

1. Mordvinov, A.E. (2008), Possibility of increasing the frequency efficiency of communication lines due to the use of signals with mutual interference of symbols: dissertation [Issledovanie vozmozhnosti povysheniia chastotnoi effektivnosti linii sviazi za schet ispol'zovaniia signalov s vzaimnoi interferentsiei simvolov: dis. ... kand. tech. natik], Moscow, MEl(TU), 150 p.

2. Proakis, .I.G. (2000), Digital Communications, 4"1 ed., McGraw-Hill, N.Y., 928 p.

3. Qurcshi, $., Newhall, E. (1973), "Adaptive Receiver for Data Transmission over Time-dispersive Channels", IEEE Trans, No. 3, pp. 448-457.

4. Falconer, D.D., Magee, F.R, (1973), "Adaptive Channel Memory Truncation for Maximum Likelihood Sequence Estimation", BSTJ, No. 9, pp. 1541-1562.

5. Clark, A.P., Harvey, J.D., Driscoll, J,P, (1978), "Nearmaxi-mum Likelihood Detection Process for Distored Digital Signals", The Radio and Electronic Engineer, No.6, pp. 301-309,

6. Clark, A.P., Najdi, N.Y., Fairfield, F.J. (1983), "Data transmission at 19.2 kbits/s over telephone circuits". The Radio and Electronic Engineer, No, 4, pp. 157-166.

7. Vac hula, G.M.. Hill, F.S. (1981), "On Optimal Detection of Rancl-limited PAM Signals with Excess Band with", IEEE Trans, No. 6, pp. 886-890.

8. Weselowski, K. (1987), "An Efficient DFE ML Suboptimal Receiver for Data Transmission Over Dispersive Channels using Two-Dimensional Signal Constellation", IEEE Trans, No. 3, pp. 336-339.

9. Evtyanov, S.L (1948), Transient processes in the receiver-amplifier circuits [Perehodnye processy v pnemno-usilitel'nyh shemah \ Svjaz'izdat, Moscow, 221 p.

10. Shannon, C.E. (1948), "A mathematical theory of communication", Bell Syst. Tech. J., No. 3, pp. 379-423.

МЕТОД ОЦЕНКИ ПРОПУСКНОЙ СПОСОБНОСТИ РЕАЛЬНЫХ КАНАЛОВ СВЯЗИ С МНОГОПОЗИЦИОННЫМИ ФАЗОМАНИПУЛИРОВАННЫМИ СИГНАЛАМИ ПРИ НАЛИЧИИ МЕЖСИМВОЛЬНЫХ ИСКАЖЕНИЙ И ЕГО ПРИМЕНЕНИЕ

Лернер Илья Михайлович, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ, Казань, Россия, aviap@mail.ru

Аннотация

Объем передаваемой информации возрастает экспоненциально из года в год, что является тенденцией современного общества. Это приводит к необходимости увеличения скорости передачи данных систем передачи информации. Наиболее выражено это среди радиотехнических систем передачи информации, которые в настоящее время работают в условиях ограниченных частотных ресурсов и постоянно увеличивающихся требований их эффективного использования. Одним из наиболее эффективных подходов к решению этой проблемы является переход к передаче информации при наличии межсимвольных помех в радиотехнических системах передачи информации. Несмотря на привлекательность этого подхода, его техническая реализация связана с рядом трудностей, которые могут привести к увеличению сложности самого приемника при увеличении числа интерферирующих символов. В конечном итоге возникает вопрос не только о целесообразности реализации, но и о его практической осуществимости самого приёмника. Поскольку увеличение алфавита символов канала приводит к необходимости увеличения отношения сигнал / шум для достижения заданного качества приема сигнала, целесообразно рассмотреть возможность использование алгоритмов приема на основе использования частотной фильтрации и последующее использование многопорогового решающего устройства в ситуации сильных межсимвольных искажений, вызванных избирательными системами в канале связи. Производится оценка пропускной способности такого канала при использовании ФМн-n-сигнала. Для этого был разработан новый метод оценки пропускной способности, который можно использовать для оценки предельной пропускной способности при отсутствии шума, когда решающее устройство является простым многопороговым устройством, а радиотехнические системы передачи информации работают в присутствии сильных межсимвольных искажений. Метод имеет высокую точность и низкую вычислительную сложность, которая не увеличивается с ростом размера сигнального созвездия рассматриваемых сигналов.

Ключевые слова: пропускная способность, избирательные системы, ФМн-п-сигналы, повышение частотной эффективности. Литература

1. Мордвинов А.Е. Исследование возможности повышения частотной эффективности линий связи за счет использования сигналов с взаимной интерференцией символов: дис. канд. техн. наук (051204) дата защ. 12.10.08, дата утв. 21.05.09. МЭИ(ТУ). 150 с.

2. Proakis J.G. Digital Communications, 4th ed., N.Y.: McGraw-Hill, 2000, 928 p.

3. Qureshi S., Newhall E. Adaptive Receiver for Data Transmission over Time-dispersive Channels // IEEE Trans, 1973, No. 3, pp. 448-457.

4. Falconer D.D., Magee F.R. Adaptive Channel Memory Truncation for Maximum Likelihood Sequence Estimation // BSTJ, 1973, No. 9, pp. 1541-1562.

5. Clark A.P., Harvey J. D., Driscoll, J.P. Nearmaximum Likelihood Detection Process for Distored Digital Signals // The Radio and Electronic Engineer, 1978, No.6, pp.301-309.

6. Clark A.P., Najdi N.Y., Fairfield, F.J. Data transmission at 19.2 kbits/s over telephone circuits // The Radio and Electronic Engineer, 1983, No. 4, pp. 157-166

7. Vachula G.M., Hill, F.S. On Optimal Detection of Band-limited PAM Signals with Excess Bandwith // IEEE Trans, 1981, no. 6, pp. 886 -890.

8. Weselowski K. An Efficient DFE ML Suboptimal Receiver for Data Transmission Over Dispersive Channels using Two-Dimensional Signal Constellation // IEEE Trans, 1987, no. 3, pp. 336-339.

9. Евтянов С.И. Переходные процессы в приемно-усилительных схемах. М.: Связьиздат, 1948. 221 с.

10. Shannon C.E. A Mathematical Theory of Communication // Bell System Technical Journal, 1948, vol. 27, pp. 379-423, 623-656.

Информация об авторе:

Лернер Илья Михайлович, к.ф.-м.н., доцент кафедры РЭКУ, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ, Казань, Россия