CC BY
9Journal of Siberian Federal University. Engineering & Technologies 1 (2011 4) 35-39
УДК 621.384 191
Comparative Analysis
of Phase-lock Control System Algorithms
for Spread-spectrum Signal Receiver
Evgeny V. Kuzmin*
Siberian Federal University, 79 Svobodny, Krasnoyarsk 660041 Russia 1
Received 4.02.2011, received in revised form 11.02.2011, accepted 18.02.2011
This paper investigates noise-immunity of phase-lock control system for spread-spectrum minimum shift keying signal receiver in case of adjacent channel interference influence. Four algorithms of phase-lock control system are suggested and described. Statistic simulations of signal processing in involved system are given.
Keywords: Spread-spectrum signal, minimum shift keying, signal from adjacent channel, phase synchronization system, statistical modeling, comparative analysis.
Introduction
Spread spectrum signals withminimum shift keying (MSK) are w idtly uce d inmodern radio navigation systems (RNS). Serviceability on long distances Dmax «1000km makes a demand to RNS, to hase rasliyr terge vahie of receiver's dynamic rcngt(more tMnSOhffi). ffigh accuracy of cootdrnait measuring m a" workinv ties ov RNS, iequireg iavrsei^ntm0 nsgori)hms afpMse-lock eontaol nysiem of MSSS-tignai reeriver, nelsla;l:i provides plase shift mnasuremenft with roel-mean-tquare (tmnSiSg en"sos e^aSS then stunaSS:otnoien raiso tlunshold equals to -40 dB (in the band of MSK-signal)andincase of adjaceut thanncl interference influencegdisturbing sognaiCrom another radio-range beacon) [1].
The aim of this article: noise-immunity investigation for suggested algorithms of phase-lock control system for MSK-signal receiver in case of adjacent channel interference influence.
Describing and comparative analysis oS phase-loik congrot (fitem algorithms cervlSs
SSseai realizetion ef MSKieisnuI, nifanal from adjacent channel (SAC) and additive white Gaussian noise (AWGN) can be described as [2, 3]:
y (t ) = s (t - *,)(t)>
(1)
S(t -T1)=kt{¿(i -t,)exe[j'(F*(/0 ±Fd)t-cp,)]},
* Corresponding author E-mail address: kuzminev@mail.ru
1 © Siberian Federal Un iversity. A ll rights reserved
here s(t -ts) and s (t -t/) are MSK-signal and SAC with delays ts and z's accordingly; y = JP//Ps -ratio «SAC/signal»,.Ps and P/ _ powersofsignal andSAC a^c^t^^dii^gly; E, (t) - A^^C^^^; py - carrier frequency; FS - frequeoayDopplerstift; a^ -startrngphase of signal; S(t -ts) - complex envelope of MSK-signal:
S(t -zt)=D(t - z,)J2F, opp[jQ(t -zt)], (2)
where D(t -t ) = ±1 - the information signal imposed on navigation signals for information transfer
t
about differential corrections for GNSS users; 0(t) = —Jd(t')dt' - function, which determines angle
2T o
N-1
modulation, d(t) = ^dt rect(t - iT), (dt} - pseudorandom sequence (PRS) of N-length, T - one's bit
i=0
PRS duration, rect(t) - square pulse with T duration. Disturbing signal from adjacent channel has similarly mathematics description, anddifferent parameters (including informationsignal D(t - t/) ).
Digital phase-lock control system (PLCS) structure chart of MSK-signal receiver is presented on Fig. 1. Values y,. = y(t,) (tt = iA/, i = 0,1,..., At - sampling interval) are incoming observations to digital phase-shift discriminator (DPD), which comes from an exit of analog-digital converter (ADC)
[1, 4].
Reference signals of carrier frequency is cos 6.) = cos(2n( f0 ± Fd (k)). and sin®,(k) = cos(2n(f0 ± Fd(k))t. come into supporting inputs of DPD. These signals are formed by digital synthesizer (DS) and based on frequency Doppler shift estimation Fd() in each k-period of filtering. Reference signals Q. = sin 0,. and I. = cos 0,, which are synchronous with quadrature components of MSK-signal, formed by delay lock system. Quadrature components of bandwidth compressing signal (after MSK-detection) are formed by summarizing of multiplications of quadrature components of realization (1) and reference signals It, Qt and integration on intervals t e[kTp,(k + 1)Tp], k = 0,1,..., (T - MSK-signal's period). Time of one cycle radio-range beacon transmition equals Tc = 25Tp. Error signal which is proportion to phase mismatch forms in compliance with algorithm:
Zd (k) = sign (Z1 (k )>2 (k) = D (k) Z2 (k), (3)
where sign (x) - sign function, D(k) - estimation of information signal D(t-ts ) on k-period of filtering, z1(k) and z2(k) - quadrature components of correlation, computing on interval t e[kTp,(k + 1)Tp]. Error signal Zd (k) comes into digital filter (DF). Output signal of DF used to control signals cos 6, (k) and sin 61 (k) frequencies.
Model of PLCS is presented on Fig. 2, where Zd (9) - discrimination characteristic of DPD; Tt -time constant of integrator; K= KFKS - instantaneous element, taking account of transfer constants of digital filter KF and digital synthesizer KS.
Frequency Doppler shift estimation on k-period of filtering is forming in compliance with algorithm [1]:
F; (k)=k i zd (k)+x (k -1)+Tz* (k -1)]. (4)
Fig. 1
a I I
y(1
ADC y „ DPD (k), DF
cos Ôi (k ) sin Ô, (k )
9, ( k)
i (k)
h cp, ( k ) --- ---' ^ 1 pTi x{ k ) |
2 K p J* (k ) K
Fig. 2
Analysis of statistic simulation data ofPLCS (Fig. 2) shows, that algorithm (3) is well-behaved if rated value yms[ = 40dB, on the assumptsoo oh user's top speed equais lf= c io0)-ii/l( tiea-h f-f^^l of frequency Doppler shift Fde-p=0,2Hz)- signai-tsapoise satlo ahoesholW g = -40<itland cwpSure probability Pc — 1. Noise-immunity increase of PLCS (ymax >40dB) can be achieved by using a separate chant^ foo s= information si=npf ssi tins caie ihe algorithnt (3) can be empHfietl Pitt0 written as Pt-a:- = z2 (=i. Contdquentfy -hast; ase tlm foilowlng ways of frequency Doppler shift estimation:
K\Zd(k) + x(k-l)+TTZAk-l)\M '=),
FF
( p \
f{M~1)
v p
M ' = 0,
(5)
F№ =
K\Zd{k) + x{k- l)+PT-Zd{k-1)1 M'= i
p p
y(M~1)
y p_
-<p,
2T T
^-(M-l)-TTc-T T
^-A4'=0,
(6)
where M' = (M/2)-]M/2[, H - integer part separation operation, M = 1+]Tp(k-l)/Tc[ - MSK-signal cycle number.
Statistic simulation results of PLCS in case of adjacent channel interference and AWGN influence are presented in table 1. Results are the following: average and RMS values of phase and frequency errors of tracing in steady-stateregime (SR). Numberofstatisticalexaminationequalsto 103.
Table 1. PLCS statistic simulation results
Z (k) sign( Z1(k )) Z2(k ) Zj (k) = z2{k) Zj (k) = z2{k) Zj (k) = z2{k)
Fj () ) К() 4( )
9sr, rad 0 0 0 0
rad 0,09 0,09 0,45 0,08
F., Hz 0 0 0 0
^ HZ 0,035 0,035 0,039 0,028
Y , dB > max5 40 75,6 54 80
Conclusion
The best for PLCS in case of adjacent channel interference influence is algorithm (6), which provides phase error of tracing RMS a « 0,08 rad with capture probability Pc ^ 1, Fdmax = 0,2 Hz, signal-to-noise ratio threshold q = -40dB and ymax = 80dB.
Acknowledgements
The author would like to thank the following persons: prof. V. N. Bondarenko; prof. V. I. Kokorin; L. A. Deeva; associate prof. V. A. Vyahirev.
These investigations are realized with the help of grant № 08-08-00849-a of Russian Foundation for Basic Research (RFBR) and program of scientific and educational evolution program for Siberian federal university.
Reference
1. Kuzmin E. V. Accelerated Phase-lock-loop Frequency Control Methods of User's Equipment in Perspective Radio Navigation Systems / E. V. Kuzmin // Journal of Siberian Federal University. Engineering & Technologies 3 (2008 1). (Журнал Сибирского федерального университета. Серия «Техника и технологии». Том 1, №3. С.276 - 286.).
2. Кузьмин Е. В. Методы равновесовой обработки шумоподобных сигналов с минимальной частотной манипуляцией / Е. В. Кузьмин // Электронное издание «Журнал радиоэлектроники» РАН № 9, 2007 - Режим доступа: http://jre.cplire.ru/jre/sep07/2/text.html
3. Кузьмин Е. В. Сравнительный анализ алгоритмов слежения за фазой шумоподобного сигнала при воздействии структурно-подобной помехи / В.Н. Бондаренко, Е.В. Кузьмин // Сб. науч. тр. «Соврем. пробл. радиоэл.». - Красноярск: ИПК СФУ, 2008. - С. 31 - 34.
4. Кузьмин Е. В. Реализация и исследование цифровой системы фазовой синхронизации приемоиндикатора широкополосной радионавигационной системы / Е.В. Кузьмин, Я.И Сенченко // Современные проблемы радиоэлектроники: сб. науч. тр. - Красноярск: Сибирский федеральный ун-т; 2010. - С. 188-192.
Сравнительный анализ алгоритмов слежения за фазой шумоподобного сигнала
Е.В. Кузьмин
Сибирский федеральный университет, Россия 660041, Красноярск, пр. Свободный, 79
В статье исследуется помехоустойчивость системы фазовой синхронизации приёмника шумоподобного сигнала с минимальной частотной манипуляцией при воздействии структурно-подобной помехи. Предложены и описаны четыре алгоритма слежения за фазой шумоподобного сигнала с минимальной частотной манипуляцией. Представлены результаты статистического моделирования рассматриваемой системы.
Ключевые слова: шумоподобный сигнал, минимальная частотная манипуляция, фазовая синхронизация, статистическое моделирование.
