Low-complexity code tracking loop with chip-level differential detection for DS/SS receivers

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0 IEE 2000

E1ecfrunic.s Letters Onliiie No: 20001434 DOI: IO. 104Y/el:20001434

Qiaii Liang (Hrior.rin Bidding 1804#, Mohile Cornniiinicntiun Lrih., Department of Electronic EnRineering, Slinnghoi JiiiotunR Univer:dg,

Hirii.r.Arin Rood /954#, S l ~ m ~ ~ l i i i i , Peuple’k Repirhlic qf Chinii, 200030) E-mail: gianliang@mail .com

1.5 June 2000

Refcrenccs

1 BRAND, A.E., and AGHVAMI. NI.: ‘Performance or ii joint CDMAI PRMA protocol for mixed voiceidata transmission for lhird generation mobile communication’, IEEE J-SAC, 1996, 14, (9), pp.

1698-1707

‘Speech and voiceband data performance requircmcnts for future public land mobile tclecotnintinication sytcms (FPLMTS)’. Rccomnicndation ITU-R M.1079, 1994

3 GOODMAN, D.J., and WEI, s.x.: ‘Efficiency of packct rcservation multiple access’, IEEE 7 h i . s . I’ehic. Techno/., 1991, 40, (I), pp.

170-176 2

Low-complexity

code tracking loop with

chip-level differential detection for DS/SS

receivers

Jia-Chin

Lin

A ncw code tracking loop is proposcd for direct-sequence sprcad- spectrum communications. The main rcatures of such a techniquc are its lower complexity together with its good tracking performance. Analytical expressions Cor the error characteristic are derivcd and timing jitter is evaluatcd by computer simulation.

Introduction: Direct-scquence spread-spectrum code-division mul-

tiple access (DSICDMA) has rccently become the most popular system for commercial applications. Code tracking is onc of the most important functions in DSISS receivcrs, and substantial effort has gone into solving this problem [I, 21. A differcntially coherent dclay-locked loop has also been proposed [3]. However, it cannot deal with data modulation, and can thus only be used in ranging applications. In addition, migration towards digital imple- mentation of modems is currently onc of the main trends in communications systems [4]. In this Letter, a fully digital low- complexity code tracking loop suitable for recent comniercial applications is proposed. I

I

e-iw,t I I

1425111

Fig. 1 Proposed code fraclciny loop with cliip-level ilijj‘krenjiril ilefecfiori

Signal model and sysfem clescril,tion: For bandlimited DSISS com-

munications [4], the complex envelope of the modulatcd signal can be expressed as s ( t ) = =Z; a aij,jiM c ~ , , , ~ , ~

gdt

- mT,.), where ni = *1

represents BPSK information-bcaring symbols, T and T, are thc symbol duration and chip interval, respectively, A4 = T/(T,) is the proccssing gain, c, = +I is the ith chip value of the PN code, N is the code length, and l?nlN are the intcger quotient and n7 modulus N , respectively.

gdf)

is the transmitted chip-shape, lhe Fourier transform of which is G7(f) = T,dG,vU), where GN(f) is the frequency response of the Nyquist raised-cosine filtcr. It can be shown that the baseband power spectral density (PSD) of the signal s(t), being proportional to IG,v(f)12, is constrained to the interval i ( 1

+

a)/2TC wherc a is the roll-off factor of thc raised-cosine

2040

ELECTRONIC

pulse. In the receiving end, the baseband equivalent j(t) of the signal at the input of the DSiSS noncoherent down-converter is y ( f )

= ,s(t)

+

rz’(t), whcre n’(t) = n’<.(t)

+

jn’<(t) is complex AWGN the

qnadraturc components of which own thc PSD S,,” = N0/2P, P

being the I F signal power. The complex representation of the baseband signal at the output of the chip-matched filter with its transfer function dGNU) is therefore r(f) = e‘e E,;;= ~ rzt,>!ihf

ci,,,i,vg(t -

m r . )

+

n”(t), where the PSD of the noise components is

now S,,”y) = (NoGN(f))/2P, and the PSD of the overall pulse shape is GU) = T,GN(f). Thc oversainpler samples r(f) at the instants f, = (IC

+

E/<)T, and tk+li2 = (/c

+

E/,

+

112)r. (i.e. sampling rate 2/73, wherc E~ is the kth normalised chip timing error. The integer- instant samples rj< = r(&) arc fed into the following information detection processes, while thc half-integer-instant samples =

~ . ( t ~ + ~ / ? ) are exploited in the tracking loop. Note that the actual processing rate of both thc information detection processcs and the code tracking subsystem is exactly I sample/chip. The half- integer-instant saniples given by rk+li2 = r[(lc+E,.

+

1/2)T,] are mul- tiplied by the complcx conjugate of its one-chip-delay replicas. We take the real part and then multiply by the difference (ix. cii+linrcli.iN - cikiNriII.IiN) of the two local differential sequences. Thc

resultant samples are fed into the branch filters hk which are first- order lowpass filters with bandwidth 0, and the following transfer function: Hll(z) = l-a/(l-az I), a = exp(-2nB,TC), whcrc B/, may be of the same order or magnitude as l / T . The error signal at the input of the NCO can thus be expressed by

= R ~ { T . ~ + I 2’

r i - ~ }

2 x [ c I ~ I ~ ~ , ( c I ~ + I I ~ - c l k ~ I I , ~ ) ] 8 / ~ k

It is assumed that code acquisition has been accomplished (i.e.

I E ~ . ~

5 112). Therefore, thc intcgration inherently performed by the NCO can be represented by the following loop cquation:

- yeh, where y is the NCO sensitivity. The average loop error characteristic can be defined as q ( ~ ) = <E{e&,, = E, Vk}>, whcrc thc operator <.> indicates time-averaging. Since thc bandwidth ol‘ the branch filters is comparable with l/T (hence, much narrowcr than

UT),

for = E after somc manipulations, the loop error characteristic can be rewritten as

=

Thc error characteristics of the DDLL [4] and the proposed technique derived from the above statistical analyses and using Monte Carlo methods on a computer arc shown in Fig. 2. It is

obvious that the simulation results are very close to the theoretical oncs, and that the proposed technique has a slightly narrower error characteristic and a slightly higher slope at E = 0.

1 .o 0.8 0.6 5 0.4 v) .-

?

0.2 1 0 0 8 -0.2

8

-0.4 -0.6 -0.8 -1 .o

-

I I -2 -1 0 1 2

normalised chip timing error

j425121

Fig. 2 Sirnulrited loop error ~1iri~ai~~eri.stic.s qf DDLL [ 4 ] rind ~ ~ r i i l ~ o s e d techniqire cmd fho.ve oblriined by theorefical oiidysi,?

Theoretical: - - - - proposed Simulated: X DDLL

+

proposed DDLL

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References Stendy-stcite tiniing jitter: Sincc thc ovcrall chip shape is given by

g(ET,.) = sin(m)/m cos(nc~~)/l-(2m)~, the slope A of thc loop crror characteristic at E = 0 can be found to bc

3 x 0 2 +8 cos( -) 7rN -8 cos( -) 2 37rm(l - 9~1') sin(37icu/2) - 2 ( 1 - 27n') cos(3.rra/2) 97i2(1 - $)(l - Dn"2 ( 2 ) By exploiting the above analysis and thc standard linear loop analysis, the normaliscd chip timing jitter c m be derived. Only the

simulation results of thc RMS normalised chip timing jitter with the DDLL [4] and the proposed techniqtie are rcportcd in Fig. 3. It can bc sccn that the pcrformance difference between the DDLL [4] and the proposed technique is very slight.

I I

-10 -5 0 5

E,/No, dB

_1425131

Fig. 3 R M S norniali,sed chip tirning error U / UI1I.I. (4J rid p r t p s e r l

technique hy computer siniulrrtion

-0- proposed (B,,T,. = 0.01) . . . . _. 'I . . . proposcd (BLT( : 0.02)

-+- DDLL (B,T,. = 0.01)

X- DDLL (B,T,. = 0.02)

Comnpkxity cornpctrison: Except for the common components

employed in both the comparcd schcmcs, the proposed techniquc needs only one real corelator (including thc branch filter hkj, two real multipliers, onc addcr and one delay element, whilc thc DDLL [4] requircs four rcal correlators, four real multipliers, three adders and one delay clcmcnt. As a result, the proposcd technique achieves significant complcxity rcduction.

Conc/n,sion: A low-complcxity code tracking loop has bccn proposed by taking advantage of chip-level differential detcction. Analytical expressions for thc crror characteristic are derivcd and the timing jitter has bcen cvaluated by computer simulation. Acknowledgment: This work was supported by Project X9-E-FA06- 2-4 from Ministry ol' Education, Taiwan, Rcpublic of China. 0 IEE 2000

Electronics Letters Online No: 20001425 1101: IO. 1049/e/:20~JOI425

Jia-Chin Lin (Rni. 312, Microelectronics and Infornnition Systems Rescuvch Center, N(rtionn1 Cliino 1 iriig Universitj~. I(I0l Trr-tL~ueh

Rood, Ilsin-Chii 300. Toiivon, I<qnib[ic of Chino)

E-mail: jiachinOcic.nctu.cdu.tw

7 .lune 2000

GILL, W.I : 'A comparison oC binary dclay-lockcd loop implementiitions', IEllE 7 i . ~ i i ~ . Aero.~p. l:lcctron. Sysr., 1966, 2, pp. 415-424

POLYOORCIS. A., and WEIIER. C.L.: 'Analysis and optimization of corrclative cock Lracking loop in sprcad spectrum systems', IEEE

T ~ ~ ~ ~ ~ . ~ .

c

~

19x5,

~

33, pp.

~

30 43

~

.

,

FAN. C.-C., and TSAI, L : 'A differentially coherent dclay-locked loop

Cor spread-spectrum tracking rcceivers', IEEE Coinnitin. L ~ r t . , 1999, 3, pp. 282-284

GAUDENLI, R.D., LUISE, M., and V I O L A , R.: 'A digital chip timing recovery loop for hand-limited dircci-scqucncc spread-spcctrnm signals', I I X E rrrms. Coninnin., 1993, 41, pp. 1760-1769

Nonlinear space-time decorrelator for

multiuser detection in non-Gaussian

channels

T.C. Chuah, B.S. Sharif and O.R. Hinton

A space-time detection scheme conihining nonlincw dccorrelators

imd anteniia array is invcstigatcd for jointly mitigating moltiple access inlcrfcrcncc, mdlipath fading and impulsive noisc. Monte Carlo simulation results of the proposed space-iime detector are presented io justify the relative merits of nonlinear signal processing techniques in the spatial-temporal domain.

Introtlidon; Thc last few dccadcs havc witncsscd trcincndous

progress in multiuser detection [I] as the driviiig techuology for direct-scqucncc codc-division niultiplc-acccss (DS-CDMA) communications. A kcy assumption of these works has becn the use of the Gaussian model for the ambient noise. Unfortunately, the wireless enviromncnts arc oftcn corruptcd by interferencc that exhibits impulsive statistics [2]. Since linear detection schemes

often perform poorly in impulsive noise, this motivates the use of nonlinear signal processing techniques. In addition, the urban propagation cnvironmcnts producc multipath fading that dcgrades sigiial quality. Antenna array tcchniques have been round attrac- tivc in mitigating multipath fading. In [3], a spacc-timc detector based on thc linear tlccorrclator [4] combincd with spatial filters has been investigated. However, a recent study has shown that the lcast squares-based decorrelator is extremely susceptible to the presence of impulsive noise [5]. This Letter examines a space-timc structure by combining the nonlinear decorrelator with adaptive spatial filters.

Signol nzorlcl; In this Letter we consider ii synchronous CDMA

system tinder flat Fading channels, i.e. whcre multipath propagation does not induce temporal delays, but angular spreads. In addition, we assnnic a slowly varying chauncl so that thc channel parameters are considered as conslants. For K users and an icI-clc-

ment receiving array, the received signal iit the rnth antenna ele- ment during the ith symbol of intcrval T is captured by chip- matched filtering and thcn sampled ai the chip rate l/T,:

IC L ,f-m,j(i) = & h ( i ) ~ $ c ( z ~ , , ~ < / k i

+

? l n l , 3 ( i ) > k = 1 1=1 j = l , , , . , N (1) or in vector form I< L r7".(Ij = A k t J a ( i j s h

C~icl,~~al

+

1 i T T L ( i j E

c N ,

k = 1 1=1 'fJ2 = 1 , . . . ,114 ₍₂₎ where N is the processing gain with NT, = T and L is thc number

of multipaths in cach user's channel. With respect to the lctb user,

A k , bk(i) E { f l } , E {tli'ilv} and

si,/

denote. the transmitted amplitude, ith incormation bit, normalised sigiiaturc codc for the jtli chip, complex channel gain of the lth path, respectivcly. s/% = [slk ... ,y(,l]'' and nJij = [n,,z,l(i)

...

n,,?,N(ij]T arc thc vcctor of inde- pendent zcro-mean complex spatially and temporally white ambient noise which is being modcllcd a s a-stable random proccsses