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COMMUNICATIONS
CAPACITY ESTIMATION OF REAL COMMUNICATIONAL CHANNELS WITH APSK-N-SIGNALS IN PRESENCE OF ISI
DOI 10.24411/2072-8735-2018-10065
Ilya M. Lerner,
Kazan National Research Technical University named after
A.N. Tupolev-KAI, Kazan, Russia, aviap@mail.ru
Sergey M. Chernyavskii,
Kazan National Research Technical University named after Keywords: Capacity estimation, ISI, APSK-N-signals,
A.N. Tupolev-KAI, Kazan, Russia, chernyavskii.39@mail.ru 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.
The alternative approach which allows to create the radio data transmission systems that function in the conditions of strong intersymbol interference caused by linear selective systems of radio path, in the absence of their compensation, is the appropriate choice of the channel symbol duration time, with regard to the resolution time of linear selective systems. In this paper, we consider capacity of such channel with amplitude phase shift keying signal with N discrete states. A new method for capacity estimation was developed, which can be used to estimate potential capacity in the absence of noise when the decision device is a simply multithreshold 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 constellation size of amplitude phase shift keying signal with N discrete state. Also it can be used for capacity estimation of such channels for phase shift keying signal with n discrete state, when additional constraints on its envelop are required
Information about authors:
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
Sergey M. Chernyavskii, professor, doctor of physico-mathematical sciences, Kazan National Research Technical University named after
A.N. Tupolev-KAI, Department of Automation and Control, Kazan, Russia
Для цитирования:
Лернер И.М., Чернявский С.М. Оценка пропускной способности реальных каналов связи с АФМН^-сигнапами при наличии МСИ // T-Comm: Телекоммуникации и транспорт. 2018. Том 12. №4. С. 48-55.
For citation:
Lerner I.M., Chernyavskii S.M. (2018). Capacity estimation of real communicational channels with APSK-N-signals in presence of ISI. T-Comm, vol. 12, no.4, рр. 48-55.
Introduction
One of the major problems known during all history of a radio communication has always been and remains the problem of finding the ways of maximum possible reduction of the frequency bandwidth used for transmission of an information signal, which will provide the necessary speed, and correctness of information transfer [1].
At the moment the efficiency of information transfer in real communication systems is increased by using of mult ¡position signals, noise immunity coding and reduction of protective frequency intervals [1, 2|. At the same time the transmission is always earned out by independent (not interfering) symbols. The requirement of absence of symbol interference restricts a choice of channel symbol duration [11.
However due to the annual increase of information volume which is transmitted through the radio engineering data transmission systems (RDTS) and continuous increase in requirements imposed to effective use of the frequency resource, the abovestated approach to creating the latest communication systems is ineffective [ 1 ]
At the same lime, if in case ofcreation of RDTS we do not require the absence of the intersymbol interference (¡SI) in the linear selective systems of a radio path, then it is possible to achieve the best results in this direction [1]. However application of algorithms of optimum signal processing or the similar approaches in the receivers working in real time had already become inexpedient in ease of a small number of interfering characters [1,2],
So, the computational complexity of the optimal (using the maximum likelihood criterion) algorithms for receiving signals under 1SI conditions is growing exponentially with an increase in the number of interfering symbols [1,2].
Using the suboptima! algorithms of receiving which initially reduce 1SI level (by using zero-forcing filter, or linear minimum squared estimation equalizer, or decision feedback equalizer) and then performing the optimal signal processing in the absence of communication channel memory [1-3] is also not without drawbacks. According to papers [2, 3], such methods lead to a large loss in noise immunity in comparison with the optimal receiving methods; dependence of their noise immunity on the shape of amplitude frequency response (AFR) of communication channel, particularly when it is subjected to considerable variations on magnitude. These properties are the most strongly manifested when using these algorithms in radio channels, what does not allow achieving high noise immunity for RDTS [2,3].
The alternative approach which allows to create the RDTS that function in the conditions of strong IS1 caused by LSS of radio path, in the absence of their compensation, is the appropriate choice of the channel symbol duration time, with regard to the resolution time of LSS |4, 5].
Papers |6, 7] concerned with phase RDTS with phase-shift keying signals with n discrete states (PSK-«-signals) which implements such operation mode shows that there are the ranges of channel symbol time duration (so-called «transparency windows») and within these ranges the error probability per channel symbol (SER - symbol error rate) caused by IS! in bandpass fillers of linear radio path equals zero. The same papers slate that this can be applied for increasing maximum transmission rate and, consequently, spectral efficiency. In connection with this fact, the results obtained in [4J can be considered a lower bound of capacity.
Therefore, it is interesting to consider data transfer in such RDTS thai use amplitude phase-shift keying signals with N discrete stales (APSK-jV-signals). It is caused by wider opportunities provided by application of such signals.
At the same time, it is expedient to use estimation of such channel capacity in the noise abscnce as criterion for evaluation of efficiency of this operating mode, what allows to evaluate potential efficiency of the considered systems.
Problem Statement
In this case, capacity estimation is considered for a communication channel, which consists of a transmitter, a linear time invariant (LTl) system, a receiver and a decision device (DD).
In this work we assume that LTl system is a set of tuned bandpass filters that possess the following properties:
A) First case, when we use results of paper [81: 1) ft),, / 2Aii„ > 15 where 2Aii„ - the resultant bandwidth of LTl
system, where co0 - the average frequency of the tuned LTl system; 2) their amplitude frequence response possess an even symmetry and phase frequence response - odd symmetry with respect
tO ft,,,.
R) Second case, when we use results of paper [9]: considered bandpass filters have polynomial approximation AFR with ftj, / o), >1.21 where ox, - the upper and lower frequency
of filter bandwidth.
We also assume that receiver is an ideal phase detector similar to DD that does not introduce additional ISI.
We assume that each symbol of primary signal takes equiprobably one of A1' = m :< n values of primary alphabet which represents a signal constellation with m different values of amplitude and n different values of initial phase.
The values of the initial phases of the concerned signal constellation are defined by the following expression
= (it+vsign (|0.5«| - 0.5 « - 035 J-1[0.5n||) Aq) „» 0)
and the values of the amplitudes of the signal constellation are defined by the expression
iip=pAM„+Mln. (2)
Here k=l,n', p = l,m', ||, | — rounding operation to the nearest integer; sign( .) - signtim function; -2n!n - step between adjacent phase values of the signal constellation; I'e [0;0.5] ~ denotes the initial phase shift of the signal constellation px = 2xvi n; = (Mm - Mm) / m -step between adjacent amplitude values of the signal constellation; Min~ initial amplitude shift of the signal constellation.
The APSK-7V signal on the transmitter output from the moment / = 0 (from the moment of transmission start) can be represented as follows
f M
+l(,-(/-]),jM,exp(y>,)),
(3)
where I e №— the number of transmitted radio pulses forming the APSK.-/V signal; f - resolution time: 1) in the absence of
"transparency" windows, it is the minimum transmission time of
radio pulses when any primary symbol from any transmitted sequence can be reliably reconstructed by DD from received channel symbol at the output of the LT1 system at given playback quality; 2) in the presence of such windows tKS is a set that includes moments of time that define the start t , and the end /
end/
{f = \,K,K- numbers of "transparency" windows, the biggest moments oftime correspond to large values of window number/) of each transparency windows and the boundary time thminJ - the
greatest time, from which any primary symbol from any transmitted sequence can be reliably reconstructed by DD from received channel symbol at the output of the LTl system at given playback quality; - Heaviside step function; COu - the carrier frequency of the APSK-V signal equal to the average frequency of the tuned LTl system; <p{] —constant phase shift at the frequency
o)a introduced by tuned LTl system; Mr and у = V 0 +<p ~
<H
amplitude and initial phase ofr"1 radio pulse of APSK-/V signal at the output of transmitter, consequently, where ® - a phase jump
caused by transmission of ¿/-ill radio pulse.
We assume that before the start of transmission, until the moment f = 0, LTl system is in a steady state mode and harmonic oscillation M(Jexp(y{oV + (p4.-ф„)} acts on its input.
For considered case, the resolution time must correspond
to the time when one of the following inequalities becomes an equality and the other one is true,
«,,„, ^ |«„„ )| = V„, (''',, )~Гг\ } (4)
Here apm and д - the pemiissible phase and amplitude settling errors at the output of LTl system, which are related to theirs fiducial permissible settling error by the relations alt = a^! A^
and consequently; ajrt„) and Д„„(г/гга) -
measured settling phase and amplitude errors at the output of LTl system for the r" radio pulse when it ends, consequently; '//„„ (nr„)and ~ measured values of slowly varying
phase and envelope of the r radio pulse at the output of LTl system obtained by a receiver at moments rt, ■
In this case APSK-jV signal at the output of a LTl system starting from the time / = 0 according to the superposition principle and results of [8] can be represented in the form
х(л/„[1-Я0(/)]ехр(у>к)+ (5)
Mr [a, ('-(>■ -1)0 - B0(t - rtm)]exp(yy,) +
r=l
where Z(/} - complex envelope of the transient process caused by the passage of the APSK.-jV signal through LTl system; Jt(/ш„} = Jt(/w0)exp( /ф„) - complex transmission coefficient of
a tuned LTl system, where we assume A(y<»0) = i; Д, (/) — settling function for tuned LTi, defined by the following expression [8]
' 2 Jt(./4)
w here /)(r) - complex envelope of LTl step response. For case B
analogical function of settling function is h (;), which has the
same meaning and properties, differs only in a designation [9]. In this paper under ¿f(l(i), we mean both designations.
Signals for measured slowly varying phase and envelope on the output of the receiver, based on equation (5), are defined as
V„„(i) = argZ(/), (?)
The recovery of the primary signal is made by DD based on the decision rule
= 1
(9)
where
к ' e 1, n : f(k \ r ) = mio | Vm (4«} ~ ¥k | i ¿V \
. Conditions
p'1 e 1, m :/( p\r) = min \Mm (rt№.)■- M p\< &p
required to ensure the uniqueness of the DD solution are the following for phase a<m < 0.5Aand for amplitude A^ < 0.5
and it is obvious that in the absence of noise « -»0.5Aand
Analyzing results of [6, 7, 10J we can conclude that capacity determination for considered channel may be formulated as the maximum information transmission rate on the communication channel with equivocation produced by ISI in the absence of errors during recovery by DD, where maximum is taken over all possible sources of information used as input to the channel. In this case, the distribution of primary symbols in information sequence should be equiprobable, since other distribution will not change the maximum information transmission rate
In this case, equivocation produced by ISI is easy to consider using resolution time in the following equation form for capacity channel estimation
(Ш)
where the second multiplier in equation is the maximum entropy of source and t is taken af the condition a —> 0.5Aw ,/—>».
FCS ptff 'Si
In the case of presence of "transparency" windows, we should talk about a number of estimates of channel capacity. Obviously, upper c and lower bounds ¿j of channel capacity in this
case, according to (10), have the forms
1 . ~ , 1
<4 =~lo&«; C^ =СД ^ =--log,« ■
' I/ ' fviiiwf
(11)
Upper Cltpw and lower bounds Chww of channel capacity w hen /:th transparency window is used have the forms
C,„,„, =CJ =-10g:«; = —log:» ■ <i2>
L
of
Thus, it is necessary to determine the resolution time /
LTl system to estimate the capacity of the considered channel, which requires an analysis of the occurring transient process caused by the APSK-W signals transmission.
Problem Solution
From expressions (7) - (9) it follows that in order to get estimation of / first of all it is required to determine resolution time
for envelope trei and for slowly varying phase tr, considering
the possible presence of "transparency" windows, for given values of permissible amplitude and phase settling errors, consequently. In this ease, the resolution time t will be determined as follows:
tt'S
1) in the absence of "transparency" windows /„, = max {/,„„ };
2) in the presence of "transparency" windows trcs=ir, rv„, > taking into account that * = maxi/t , u. , i. where t -
c ' Wit/ P""^ ('floimul,, ''(niiiw/j. j baiinlg,
is the boundary time for envelope; tboand - is the boundary time
for slowly varying phase.
To estimate resolution time / it is required to determine a
combination for first case and a set of combinations for second case of the values of the transmitted phase jumps and amplitudes for each d-th (d = i^/j information symbol, which for given values of a,m and ¿^ ensure that: 1) the ¿/-th symbol greatest settling times for envelope and slowly varying phase on the LTl output in the absence of "transparency'1 windows and 2) in the presence of "transparency" windows the greatest number of windows with the smallest time duration (the greatest settling time for each window, determines its start and the smallest settling time determines its end) and the greatest boundary time for the ¿/-Hi symbol is provided. Next, in this paper, problem of determining these conditions will be called the settling time problem.
Obviously i/ / -> oo then the settling time for slowly varying phase for t/-lh symbol / / and the settling time for envelope for t/-th symbol tM _> / . The speed of this tendency
depends on inertial properties of LTl system.
First of all we need to obtain an expression that allows us to estimate the considered measured settling errors at the end of the d-th radio pulse at the LTl system output. For this we assume in (5): ' = K' 2 K ) = [>,+ A™ )>xp(/[y, + (ltw})) ■ and then we divide both sides ol the equation by exp{ / ( ojJ + yt j j • As a result, we get the following equation for Z(lt,A
[M, + A„„ (^„)]exp (./«„, (ltm )) = V MrB, exp (-.//,,) ■
r=0
where ^ = y ©; h = B{l ({/-/•+1) ) -*((/- );
After a series of simple transformations (13), the expression for the |a (It has the form
|A»,("™)| = [X -M^os^-Ai, cos (/,„,}] +
^ t-r 0 '
+2\ ?.M,Br V + »„(ft«)))
V r=0 r=0 * _
(14)
and the relation for the a (h )—
ms v V« /
f^MX sin(^)
^A^cos [zr)+MtB,
s.
(16)
where 5 sin(Zr). S = M,B, cos(Xr) •
r=0 r=0
Obviously, two last obtained expressions are also valid for the case, when d-tb symbol is considered. For this we have to substitute the following set of equalities in expressions (14) and (15):
/ = d,d=U;t;= ¿©„
¥=r+l
s; = X MX Mzl). 5;=+E ma cos(x')
Let us lest the obtained expression (14) for the extremum for ¿/-th symbol with the respect to Hn (dtm), using substitution (16).
Determination of conditions in which the expression reaches the extremum will be made only at stationary points. This is due to the following reasons: 1) settling function is a smooth function, what we can conclude, analyzing expression (6); 2) singular critical point is excluded from consideration, when & (di: ) = -M.
and a,,.. (t/f, .,) is unspecified, because in this case ¿(dt\ = Q
and therefore DD will not be able to make the correct decision according to (9).
In this case, the solution of the problem formulated above is the solution of equation c|A;iji (di, )|/3«,„ {dtm) = Q • Partial derivative necessary in this equation can be represented in the following form using (14), (16)
(I
à 11 cos a,„, ) s Mr K sin X'r + sin «,„, {dtn., ) V MrBr cos x'r
- M,
and the solution of the equation s|am< (dt^ )\jda^ «„) = 0
(17)
takes the form
X'^Â sin
sin/;
x MBr cos/; A/A + z KK C0S2;
(18)
Analyzing expressions (15), (18), taking into account substitution (16) and results of paper f 11 ], we conclude the following: the greatest values of measured settling phase corresponds to the greatest amplitude errors at the output of LTl system.
Let us test expression (15) for the extremum for ¿/-th symbol with the respect to phase jumps ©,,0,,...©^, using (16) and substitution b = ß | to determine combinations of transmitted
phase jumps j@ . | (/) = ],</) that solves the settling time problem. Here ti/: is a set of settling moments of time and boundary
time in general case which are the solution of settling time problem with the respect to J.
Determination of conditions in which the expression reaches the extremum we will be made only at stationary points. Application of this approach to the solution Of this problem is due to Ihe folio wings facts: 1) in the dynamic operation mode values of «effective» phase jumps determined as y lrtv )-/r can any
values in the range -2n ... 2n due to the inertia! properties of the selective systems; 2) eq. (15) is a smooth and bounded function in domain of function where |aml[dtv £apm <nl2> because
an <0,5 and n> 2 , Therefore, it is advisable to use the dependence tana,,,, [dt¥j) instead of am[dtVj) in the analysis.
For this ease, the equality allowing determining the partial derivatives with respect to all phase jumps of the transmitted radio pulses can be represented as
iii n h-1
_ / , v S[ V MrB cos y' M, B sin y'
dxma^idt^ r r ' r ' r
S®.
(20)
cot % = cotX\ = = cot= -S, I Sc = tan a\,m ■ (23)
Analyzing (23), we can make the following conclusions:
-{GjlJ if A =
nil-a.
if h = d
(24)
Let us test the expression (15) for the extremum for i/-th symbol with the respect to amplitudes Ma, Mr...Mr using (16) and
substitution [}>- % I , to determine combinations of transmitted amplitudes jAi„n j (ft = O.i/) that solve the settling time problem. Here tM is a set of settling times and boundary lime in general case which are the solution of settling time problem with the respect to{A./J.
Determination of conditions in which the expression reaches the extremum will be made only at stationary points as previous test. In this case, the set of equations which determines the condition for the existence of an extremum considering the d-th radio pulse takes the form
(19)
In this case, the set of equations which determines the condition of the existence of an extremum considering the i/-th radio pulse, because of (19), takes the form
sin co»(Ä)=g
S sin (i,, J - ¿Xm cos(/,,_> 0 5,5,', =0
(25)
ScMtlB„ COS+ S,M0B9 sin Xo = 0 i i 5 X MA + S, £ MrBr sin xr = o
r=il r=t
KlLKk «»£ + sin x, - 0
r=0 0
[Stf* 0
= m„ (dtVj)»tan aim = sign (V„„ [dt^)-/,/) tan a,,,,, •
Analyzing the system (20), we conclude that it can be the following
B, (Se cos X\ + S, sin x,) = 0 (22)
Bj icosx^i+S,sinXj ,)=0
We will find a solution of (22) when VB #0, tc = i,i/-l
since otherwise the moments oftime will be considered when the slowly varying phase at the LT1 system output reaches a stationary value. It is possible only in one case, according to [8|: at the end of the transient process.
From cq. (21), (22) the following relation follows
where t = V 0a
q-r* t
; s =S"| , . ; , .
c c>X,=Xr * =z,
tan a..
—g- = tan am (dtMj ) = tan a"m = sign (y„„ (dtMj )-ya)
From eq. (25) the following relations follow tan ^0 = tan x = ...=tmXi t = 5 / Se = - tan ,
sx- o.
Analyzing (26), we can make the following conclusions: = {0:1]
0.. =
-a.
if h = ],d-1 if h = d
(26)
(27)
(28)
and B'j =0 or S = 0 ■ Analyzing the last two conditions, we conclude that the iirst condition corresponds tci^P =-a" and the
um j pm
second one takes place only in one case when / —> co, which
'' <
bas no practical realization.
Analyzing expressions (28) and (24) and taking into account that a" -a' that follows from the previous results of this work,
[mi Jim 1
we conclude that
JTS„S.
= {0:1}
71 „ —+ 0
pK
if h = \,d-\ if h = d
(29)
Since there is no any condition connected with determination of amplitudes values, thus, we can come to the conclusion that there is no combination of amplitudes satisfying the solution of the above problem of searching for an extremum inside the set (2), Obviously in this case the solution should be sought on the boundaries of the set (2), which are the smallest and the greatest amplitudes, so it can represented as
where u . = AM,, + M
A - dim ens ion less coefficient A lor
f
//-th symbol, where ^
= I, + 1 '
Ms
M,,
(31)
Af+'iL^00"
r=0 \
where A = A M B ■
* F 111 I n rf>
+ X ^ ■
Using the following trigonometric transformation
( it-1 ^ ii-i an + S n
\ / tf=r+l ,
r
cos^0
1-r 4-1
A + S
1
f| n<r q=r-t-l J q=r+1
where ^cosxs , equation (31) takes the form
cot©„,: = -
* A, + P,
(32)
We transform the equality tana^ = cot©Mj
P.,-,
(34)
= [(ßwcosQ,,^ - A,,Mmia(B'J-cos ad)) + + (ft_, sine^ + ^M^sin«,)'],
We use the obtained results (24), (30), expression (15) with the respect to substitutions (16), and g _ g I to get an ex-
r r\, =r
pression that allows determining in general ease a set r'M of settling moments of time and boundary time for </-th symbol which is a final solution of settling time problem for slowly varying phase. After transformation cot0;J, = tanaMJ we get the following result
( j-\ /
calO^-E^sinl ©,,„+ X *s„\
nO V uvr+l J!
where
-A4)/
toK + Q.1-1 cos0
i m ;
phj
r=Q If=r+1
Producing a number of simplest transformations over (32) with respect to ©f , we obtain
(33)
considering (32) and using (33), afier the simplest transformations we obtain the
expression
2 xaB
tan-l = tan a = + , -
From analysis of expression (34) the estimation algorithm for the rf-th symbol settling time for slowly varying phase is the following: for given value of permissible phase settling error we have to solve different y' (2'/+l -1) equations formed by combinations of phase jumps and amplitudes and a sign value before the fraction on the right side of (34). Then we compare the obtained solutions and choose the final one in accordance with the rule given at problem statement of settling time problem.
We use the obtained results (24), (29), (30), expression (14) with the respect to substitutions (16), g"= g
'L-m,
A/m = k (dtal )| 10 £et 311 expression that allows determining in
general case a set / of settling times and boundary time for d-th
utf
symbol which is a final solution of settling time problem for envelope. As a result we get
& ' = X n »AM^BI+A^M^B; r
r-0 ./ '■ I
From analysis of expression (35) the estimation algorithm for the i/-th symbol settling time for slowly varying phase is the following: for given values of permissible phase and amplitude settling errors we have to solve different equations.
Then we compare the obtained solutions and choose the final one in accordance with the rule given at problem statement of settling time problem.
Analysing equations (34) and (35), we conclude that all their sets produced by combinations of phase jumps (24) and amplitudes (30) for lsl to (c/-l) - th symbol are presented in sets of
equalities (34) and (35) for the ¿-th symbol.
As it was mentioned above £/->/-> co then /' -> / ,
Vfj 'tar
t i and the speed of this tendency depends on inertia I
properties of LT1 system. Therefore, in determining the resolution time t, ¡1 is possible to take into account a finite number of radio
pulses G, which we will call the size of effective memoiy of LTl system, in this case, alter estimating the size of the effective memory G, we can determine the resolution time for the envelope and phase using (34), (35) taking into account that d -G and then a resolution time of LTI system. After that we can estimate the capacity of considered channel according to expressions (10)- (12).
The following algorithm can be used to estimate the size of effective memory G:
1) Determine the estimation of first window start time /' = max fr' */' i (?' * /' ~ first window start time for envelope and slowly varying phase, consequently) for the first symbol in the presence of "transparency windows" or settling time
=max|^., J hi their absence, using expressions (34) and
(35) and amplitudes M0 - = wAA/, + Mih; =MITj„ =AA-/j + Mm• This choice of concrete values of amplitudes
follows from the results of paper [I11
2) For a given value of error e when h -/ I <£ we use the
following rule to estimate G
Gel,/: R(1-Aim
lim
t-rs
il^l-il^l]
TS 0 r-G '
estimate ■£s, where Fr = B,\
or
?r = B>A
' ^Sit. ■ ftfl
J=C
. The last inequality follows from
majorized series theory application to equation to (13) in the following form A/_Zkvcxp(-./Zr)|<A/_Zlf:l' We appr°Xi" mate the series remainder Jlt, by the sum of infinite decreasing
If I
geometric progression RM G • where
G" (TWIX j j^r
COMMUNICATIONS
V = maxexclude fractions,where or take
local minimum equal to zero, q - G + \,/J ■ For practical realization estimation of G based 011 the above rule has the following form
G =
(36)
s{\-V)V
where j" . — ceil rounding operation; g^ = 3, /7=10 using
greater values for both parameters is not recommended due to rapid striving | /-* | to zero.
Finally, since amplitude manipulation does not affect the trajectory of slowly varying phase changing, but only its speed, then the limitations of this method is the same as for a PSK-n-signal ¡4]. Thus, the additional upper limit on the choice of a is
a,„„ < mio I) <0-5A<p„ • (37)
Field of application
The obtained method can be used in following fields:
1) To estimate the capacity of the considered channel with APSK-zV-signal.
2) To estimate the capacity of the considered channel with phase shift keying signal with n discrete stales, considering the restrictions on the minimum signal energy.
3) To optimize the construction of a radio path.
Acknowledge
The reported study was funded by RFBR according to the research project № 18-37-00440.
References
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ОЦЕНКА ПРОПУСКНОЙ СПОСОБНОСТИ РЕАЛЬНЫХ КАНАЛОВ СВЯЗИ С АФМН-М-СИГНАЛАМИ ПРИ НАЛИЧИИ МСИ
Лернер Илья Михайлович, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ,
Казань, Россия, aviap@mail.ru
Чернявский Сергей Меерович, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ,
Казань, Россия, chernyavskii.39@mail.ru
Исследование выполнено при финансовой поддержке РФФИ в рамках научного проекта № 18-37-00440
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. Альтернативным подходом, позволяющим создавать радиотехнические системы передачи информации, которые функционируют в условиях сильных межсимвольных искажений, возникающих в линейных избирательных системах радиотракта, при отсутствии их компенсации, является соответствующий выбор длительности канального символа, осуществляемый с учетом разрешающего времени линейных избирательных систем. Производится оценка пропускной способности такого канала при использовании АФМн-п-сигнала. Для этого был разработан новый метод оценки пропускной способности, который можно использовать для оценки потенциальной 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. Данный метод может также использован для анализа рассматриваемых каналов, когда используются ФМн-п-сигналы, при накладывании ограничений на поведение их огибающей, в частности для ограничения минимальной мгновенной мощности сигнала для увеличения достоверности приема.
Ключевые слова: пропускная способность, избирательные системы, АФМн-п-сигналы, повышение частотной эффективности.
Литература
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Информация об авторах:
Лернер Илья Михайлович, к.ф.-м.н., доцент кафедры РЭКУ, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ, Казань, Россия
Чернявский Сергей Меерович, д.ф.-м.н., профессор кафедры Автоматика и управление, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ, Казань, Россия
