ThammasatInt. J. Sc.Tech..Vol.4.No.3. November1999
A NoncoherentPseudo-Noise Acquisition Schemefor Direct-sequence SpreadSpectrumSystemsUsingan Auxiliary Signal TaweesakSamanchuenand SawasdTantaratana Depaftmentof ElectricalEngineering, SirindhornInternational Instituteof Technology ThammasatUniversity,RangsitCampus,pathumthani ,l2l2l, Thailand e-mail: taweesak@si it.tu.ac.th,
[email protected]
Abstract We propose a noncoherentPseudo-Noise(PN) acquisitionscheme for Direct-Sequence Spread-Spectrum (DS/SS)systemsusingan auxiliarysignal,previouslyusedfor coherentacquisition. The proposedschemeconsistsof a phasealignmentdetectorand a voltagecontrolledctoct IVCC; loop, which is for updatingthe phaseof the local PN signaland the directionof update. performance of the proposed scheine is evaluated by simulation and compared with that of a conventional noncoherent fixed-dwell serial scheme. Results show that the proposed scheme acquires approximatelythreeto four times fasterthan the conventionalscheme.In addition,the varianceof the acquisitiontime of the proposesschemeis 20 to 40 times smallerthan that of the conventional scheme. 1. Introduction One of the major functions of a spreadspectrumsystem receiver is to generatea local pseudo-noise (PN) signal which is in synchronismwith the incoming PN signal. pN synchronizationis traditionally achievedin the two steps: coarse synchronization (called acquisition)and fine tuning (called tracking) There has been extensive research on acquisition,see[-9] for examples.Acquisition schemes may be coherent or noncoherent, dependingon whether the receiver knows the camier phase or not. Generally, the receiver generatesa local PN signal and verifies whether or not it alignswith the incomingpN signalto within a specifiedrange (normally within ?1, where I is the chip duration) by inspectingthe correlation result of the locally generatedand the incoming PN signals. If alignment is detected, the tracking circuit is initiated. Otherwise,the local PN signal updatesits phase, and the processcontinues. Acquisitioncan be
classifiedaccordingto the alignmentdetection or the phase update strategy (searchstrategy). Alignment detectionmay be of fixed-dwell, multiple-dwell,or sequential types. Somephase updatestrategiesare: serialsearch,Z-search. Recently, a new acquisitionscheme was proposed[10]. An auxiliary signal(insteadof the PN signal)was usedfor correlatingwith the incomingsignal. The auxiliarysignalis a linear combination of the PN signal and its shifted versions. By design,the cross-correlation ofthe auxiliaryand the PN signalhas a triangleshape with a periodequalthe periodof the PN signal. Such a cross-correlationfunction enables the receiverto identify the directionofphase update toward the synchronizedphase. The proposed scheme was used for coherent acquisition in
il 01.
In this paper,the idea of using an auxiliary signal is extendedto noncoherentacquisition. Section 2 describes the proposed scheme. Section3 evaluates the probabilitiesofdetection
1999 ThammasatInt. J. Sc. Tech', Vol.4, No'3, November
- -='
Iphasealignmentdetecrol-lll.fullJNli,n
to tracking
nT"
[t'to'
rl VCC LooP
!21i.-1,r\
t4i*_vr)
f{tn
x(t - t,)
+"=
yr)
a--7i;ti;,y-1
in,
d(t-t.++ts Figure l: The proposednoncoherentacquisitionscheme
and false alarm. Section 4 presents some simulation results. Finally, some concluding remarksaregivenin Section5. 2. The Proposed Scheme The proposed noncoherent acquisition systemis depictedin Figure 1. It consistsof two parts: voltage controlled clock (VCC) loop and phasealignment detector. The VCC loop uses advancedand delayed versions of an auxiliary signalfor correlatingwith the incomingsignal. The auxiliary signal a(l) is designedso that its cross-correlationwith the PN signal wilL indicatethe direction for updatingthe phaseof the auxiliary signal. The phase alignment detectordecideswhether the phasesuppliedby the VCC loop is within somespecifiedrangeof the phaseof the incomingPN signal. Note that phasealignmentdetectionusesa local PN signal to correlatewith the incomingPN signal.In the
following subsectionswe describethe auxiliary signal, the VCC loop, and the alignment detector. The input signalof the receiveris s0 = J2Pc(t - r) cos(a,t- 0) + n(t), (l) where c(/) is the PN signal, a;. and I are the carrier frequency and phase,P is the average power of the transmittedsignal, r is the phaseof itt" pN signaldue to propagationdelay, andn(t) is a zero-meanwhite Gaussiannoisewith power For spectrum density (PSD) of Nol2. convenience,we use the equivalent baseband signalof s(r),which is je + z(t1' u ( t 1= J 2 P r 1 ,- r l e
Q)
ThammasatInt. J. Sc. Tech.,Vol.4, No.3, November 1999
The carrier phase d is assumedto be a uniform random variable, and z(t) is a zero mean white Gaussianprocess with PSD of 2No. It can be written as jz,(t), z(t)= 2^111+
R"'(B)
(3)
where zp(t) and z1(t) are the real part and imaginary part of z(t), respectively. Let f be the phaseofthe local PN signaland auxiliary signal. The phasedifferenceis defined by €,=t-r. (4)
Figure2: The periodiccross-correlationR""(B)
&,@)
The function of an acquisition scheme is to obtain the phase estimate f such that the error e. is within somespecifiedrange suchas T"/2 , where 7. is the chip duration. 2.l Auxiliary Signil a(t) The auxiliary signal a(t) is defined by N-3
a ( t ) =I
z
Figure3: The periodiccross-correlation R,(B)
-l
f rr.r
l - -z l , l F r) , - i r , ) .
(5)
N-3L
whereN is the period of the PN sequence{c1}, : c1,,andc(t) is the PN signal given by i.e. c1,*1,1
This is plotted in Figure 2. Note that it is periodic with period N[, which is the sameas the periodofc(t). In the VCC loop, we generatea signal x(r) which is the difference between delayed and advancedversionsof a(t). Specifically,we let
- ? ) -" Q. 1 , o =o Q c(t\ =
- kT,), Lc*Pr,Q
k =_@
The cross-correlation of x(r) with c(l) is
where co = +1 is the l/h chip of the PN sequence. Note that c(t) has a period of NT". p, is the unit-amplituderectangularpulse shape in the interval[42"]. An important properry of a(t) is its crosscorrelationwith c(/) which is ,
(8)
(6)
t
n,,(F)= * lvlc
N't..
i
lc(t + B)x(t)dr :
/ \ / ".\ = R""V _+). * ,HR,"lp
(e)
which is shown in Figure 3. It is periodic with periodNI..
NI"
R,,(Bt=+
lcQ+fia(t)dt
tvrc x
2.2YCCLoop The VCC loop is the lower part of Figure 1. The function of this part is to control the phase of the local PN signal by controlling the phase ofthe auxiliary signal. The receivedsignal u(r) is correlatedwith x(r - t ^) and x(t - t * - *l .
wt=s+ _(N-l)2 4N
(N - l)Tc z
(N + t\7. < p^ < 2 (7)
The resultsof correlation are filtered by HtJ) and then sampledat t = mT", wherem = 10, 1,2, . ). For noncoherentacquisition,the canier
ThammasatInt. J. Sc. Tech.,Vol.4, No.3, November 1999
phase d is unknown. Note that noncoherent acquisition is more realistic than coherent acquisition,since d is normally not available during acquisition. To eliminate the unknown carrier phase,we form two products: one as the product of the real parts of the two signals after filters, and the other is the product of the imaginaryparts. The two productsare summed and invertedto obtain wlt,,-r,r). The VCC computesan estimated i,, of the phaseby updating the previous estimate f,,,-, Specifically,the updated using 4t,,,-,,r). estimateis t , , = t , , , + K r r . r ' w ( t n1, , r ) ,
Tt.trt
- i)dt. (r5) =+-'0.'i')r,rrr, ,lzPT,. *l; (k+l)?'c
tl2.k+l -
, 0o
0,
;r o 1a.3)
is
nT" A
(A.4)
for t,n.
The correlationcoefficientp of s1,aands2,a ^(
^
I
i
ot,ncz.n
(A.s)
p0
Therefore, sr,n and r2,R are approximately uncorrelated. Since they are jointly Gaussian, they are also statistically independent. Similarly, s,,, and s2.r are also independent. Therefore,s1is statisticallyindependentofs2. The quantity g(i,) can be written in terms ofj and yas s(t,r) = J2PT,,t1n,y, i1
nNoTr'-'
'
l
-
t
\ -\ I
/V+sm(/)ll
y>0 .v
