MRRS-2008 S.vmposiu1Pl Proceedings. Kiel'. Ukraine, September 22-24, 2008

The Effect of Amplitude Fades on a ForwardTransmission System Using a DS CDMA

Abdel-Rahman AI-Qawasmi #, Ayman Al-Iawama *

H Communications and Electronics Department

Philadelphia University

P.O.Box: 1 Amman 19392 JordanQawasrni@philadelphia.edu.jo

* Electrical Engineering Department

Mutah University

Karak-Jordan61710P.O. Box (81)

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III. GENERATION OF GOLD DSSSS

n=-rYJ

n=-cr.;

Given the input modulator symbol vn

n =... -1,0,1,2,... ,vn E {I,-I}, the signal waveform in the

where hTp (t) is a pulse of duration Tp , r n =nTp , and

vn is a code sequence that defined by

Vn(k)(t) = IVnhTp(t-nT)

nth time instant Tn'·.· < T_1 < TO < T1 < T2 < ... < Tn < ...,is [2j

""-I ( ) (v n +l)h ( )Sn t-Tn = r;; T t-Tn

v2 p

The kth transmitter's output signal S(k) (t) is given by

;x; «k) 1)S(k)(t) = ~ v n + h (t-nT _a(k)~)

n~OCJ J2 Tp f n

where ~ is the duration of the addressable time delay bin,

Tf is the frame time (Tf »Tp ) and a~k) is called the

addressable pulse position shift. The elements a~k) of the

sequence are chosen from a finite set {-(Q-l)/2, (Q-3)/2 ... (Q­

1)/2], where Q=Tf / ~ and Q»l [2].

The generation process will be assigned for one user

(k =1). Suppose now that user sends a data signal u(t) that

represents a pulse train of positive and negative pulses

II. INTRODUCTION

Spread-spectrum access techniques allow multiple signalsoccupying the san1C frequency radiu frcqu~ncy (I:F)bandwidth to be transmitted simultaneously withoutinterfering with one another. One of the applications of spreadspectrum (SS) communication technology is cellular mobileradio, exploits fourth and fifth benefits to provide resistance tosignal interference from multiple transmission paths andpotentially higher bandwidth efficiency in multiple accesscommunication than in other technologies. In DS/CDMAsystems, the narrowband message signal is multiplied by avery large-bandwidth signal called spreading signal [1].

In IS-95, the code sequences from individual users and thepilot sequence are multiplied by the base station-specific in­phase and the Quadrature spreading sequences. The separationof users is achieved by employing orthogonal signals. This, inturn, is done by assigning one of the N Hadamard sequencesof duration N to spread each codeword of the inner code. Aswe know, the use of orthogonal sequences limits themaximum number of users that can access the system becausethe base station that receives and recognize a newly accessinguser must assign its a Hadamard sequence. Pseudorandom SSsignals may increase the interference effect when tow or moreusers have a chip time collision at the detection process. Butthe it is not considerable comparing to the effect of amplitudefades. In this paper, first, we will give a full analysis of Goldsequence spread spectrum generation. Second, we will studythe effect of fade amplitudes on the detection process usingpilot-aided Rake receiver.

ay_lawarna@yahoo.comI. Abstract- In this paper, we a study the effect of using

pseudorandom sequence spread spectrum signal (Gold

sequence) on the generation and detection process of a DS The spread spectrum signal set) can be represented as aCDMA system with fade amplitudes. The forwardtransmission in the 18-95 system is assigned to individual sequence of signal waveforms sn (t -TJ [2],base stations using orthogonal (Hadamard) sequences to each rYJ

of them. The uses of pilot-aided Rake receiver gives a ~~

conditional bit error probability that dose not depend on the set) = L...J Sn (t - Tn)

number of user and the effect of fade amplitudes decreasesthe probability of error. This phenomenon can be where ...T -1 < To < T1 < ... < Tn < ...compensated by increasing the normalized energy per oneuser.

978-1-4244-2689-8/08l$15.00 ® 2008 IEEE

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MRRS-2008 5,vmposiu1JJ Proceedings. Kiev, lila'nine, September 22-24, 2008

u(t) = {I,-I,I,I,-I,...} then the spread signal an can be

generated by mapping the spreading sequences

a =ao,a1,' .. ,an E {I,-I} . Then the transmitted signal for

one user (see formula 3 and 4) without repeating of eachsymbol is

an =aPilot anThe transmitted signal is

set) =r PilotSPilot (t) + }'S(t)

where rand r Pilot are weight coefficients.

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L 30

rpi/ot(t) = rPi/ot 'La/ 'LhTp(t-nTp -an -0/)

1=1 n=OL

X cos[2Jifc (n - 51) + q?/] + 'L ~I (t) (11)1=1

and_ L 30 (v

n+ 1)

r(t)-rfra/~ J2 xhl/t-nTp-anTn)

x cos[2Jifc (n - 51) + q?1 + t/J] (12)

'inl =r Pilotal sin ({JI + ({JI

30 V + 1x'Lr n~ hTp(t-nTp-anTn) xsin(q?,)

n=O v2The first terms are due to the pilot signal and the second

terms are due to given cell user's signal.

The value of vn should be as large as possible without

where ~I (t) are AWGN processes, a l are fade amplitudes,

51 are delays, and ({JI are phase shifts.

The amplitudes delay are assumed to be 110 Rayleighrandom variables having the probability density functions

1 ( I, '\

Pb(a1,a2 ,",aL ) = -exp -Tp N 'L a I2

/ NoJ2 1=1

Assuming free noise channel and perfect coherent detection,the quadrature outputs of pilot signal despreader depending onthe estimated time delay of a given path are

i nl = r pilot a I cos ({J I + q? I

30 V +1x 'Lr n~ h7~ (t-nTp -anTn) x COS(tp/)

n=O v2

ret) = rpilot (t) + ret)here

IV. RECEIVING OF OSSSS USING PILOT-AIDED RAKE

RECEIVER

The received signal containing signals of user set) and a

pilot signal SPilot (t) is

exceeding the period over which al and q?1 remain relatively

(7) constant. Then

" 1 30 "

111/ ~ 31~Zn/

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S(t) = 'Lu(t)hrp(t-Tf -anL\)n=-'Y)

The transmitter's output signal set) is given by for binary

one

where Tp = Tf for single user.

We suppose that the rate r =1/ N repetition code is used,

that is, vn = uLn / N J' and that the phases are random variables

uniformly distributed on the interval [O,21T] and known to

both transmitter and receiver.Without loss of generality we assume that the phase

t/JPilot of the pilot signal is equal to zero. The pilot signal is30

Spilot(t) = J2'LhTp (t-nTp -apilotTn)n=O

where aPilot is the pilot's BPSK sequence.

The user's sequences are the product of those of the pilot

and of the user -specific sequence an' That is,

The resulting OS COMA for bit stream

un =vnan ={ 1,-1, 1, 1,-1,-1... }an using PPH COMA

for positive one and a sequence of gold sequence. Theaddressable pulse position shift will be

a31 ={I 0000100010001010001100011 010 II} .

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MRRS-2008 Symposium Proceedings, Kiev, L'kraille, September 11-24, 1008

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TABLE 1 PROBABILITY OF ERROR CALCULATED FROM EQUATION (32)

is

YI = 30 1 30 •

~(Znl-31 ~Znl)2

As mentioned above, all weight coefficients should bechosen such that all users have the same SNR at the receiverinput. The first user conditional bit error probability is upper­bounded (see formula 21) by

1 (L )Ph <-exp -30L If!2 1=1 lj/ -lj/Pilot

From equation 27, it is clearly shown that the probability oferror depends on the normalized average power of the signal.This result is very interesting and it shows that the problem ofamplitude fades can be negligible if the normalized energyincreased and be nearly equal to the normalized energy of thepilot signal. Of course this result is true only by assuming theabsent of noise and no delays in the channel.

Number 30 which describes the number of chips in Goldsequence, shows that by increasing this number, theprobability of bit error decreases by exp(- N) times.

1 30 1 30

(17) a l2 =-L(Znl-- L Znl)2 .

60 n=O 31 n=O

The decision statistics at the output of L-path demodulator8},1 = 1,2,.· ·,L,

" 1 ~,_f.LQI ~ 31~Znl

The Neyman-Pearson criterion uses

for calculating the decision statistics Y1 • Although, the

variances a l2 are not known to the receive, we can estimate

the directly from (14) and (15):

2 1 30" "2 1 30 '-' __ 2

(JI = 60~(Znl-f.LIl) + 60~(Znl-f.LQI) (I 8)

The pilot-aided coherent Rake receiver for the kth userconsists of L fingers [2]. The pilot sequence tracking loopestimates the timing delay of a given path to remove the pilotBPSK spreading, giving rise to the quadrature components

Znl and Znl . The decision statistics at the output of L-path

demodulator is2 30

YI =-2 LZnl' 1=1,2,.· ·,L (19)a l n=O

." " "2 2TakIng a l = a l ' ({JI = ({JI and a l =a l ' the statistics

YI are independent conditionally Gaussian given al with

expectation

E(YI)={ 4Pel , if HI is true, (20)

-4Pel' if H_1 is true

where

V. THE EFFECT OF FADE AMPLITUDES ON Ph

Assuming zero delays t51 = 0 , the variances a l2

is

H2

The conditional bit error probability is upper- bounded by

p" (al ,a2 ,'" ,aL ) < !exp(- 30I Pel ) (24)2 1=1

y2a 2 f/2

Pel '-- aI2 [If!-':C:Pilot{] =~~r~ilot (21)

is the lth path SNR per chip, and If =r 2is the normalized

average power of the signal (5), then

Pel =If -IfPilot

The decision rule Y depends

statistics from L path demodulator

HIde! L >

y= LYI 01=1 <

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on the sum of decision

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If~)

VJPilot =15 VJPilot =14 lJlpilot =13

15 #DIV/O! 1.52951E-07 0.000277

15.1 1.32E-66 5.46124E-07 0.000377

15.2 4.93E-34 1.57727£-06 0.00049915.3 3.55E-23 3.86953£-06 0.00064615.4 9.52E-18 8.35085E-06 0.00081715.5 1.72E-14 1.62652E-05 0.00101515.6 2.55E-12 2.91473E-05 0.00123915.7 9.09E-ll 4.87678E-05 0.00149215.8 1.32E-09 7.70601E-05 0.00177115.9 1.06E-08 0.000116041 0.00207916 5.63E-08 0.000167731 0.002414

16.1 2.2E-07 0.000234088 0.00277616.2 6.85E-07 0.000316945 0.00316516.3 1.79E-06 0.000417969 0.00357916.4 4.09E-06 0.000538631 0.00401916.5 8.35E-06 0.000680184 0.00448316.6 1.56E-05 0.000843659 0.00497

16.7 2.71E-05 0.00102986 0.0054816.8 4.42E-05 0.001239376 0.00601116.9 6.86E-05 0.001472589 0.006562

17 0.000102 0.001729689 0.007132

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MRRS-2008 S.vmposillm Proceedings. Kiev, Ukraine, September 22-24.2008

Figure 2. Upper bounds of the error probability Ph for a downlink DS

CDMA system that operates in an L-path Rayleigh channel,

1- a l2=0.1,2-a~ =0.2,3- a; = 0.3 and 4- a~ =0.4

REFERENCES

[1] Viterbi,A.J., "CDMA Principles of Spread Spectrum Communication,"Reading, MA,Addison-Wesely,1995.

[2] Kamil Sh.Z., "Theory of Code Division Multiple AccessCcommunication," Wiley Interscience.[3] William Stallings, "Wireless Communications and Networks," PearsonEducation, 2002.[4] Bernard Sklar, "Digital Communications, Fundamentals andApplications," Prentice Hall, second edition, September 2004.[5] Simon Haykin, "Communication Systems", John Wiley & Sons, thirdedition, 199-1.[6] Dinan, E.H. "Spreading Codes for Direct Sequence CDMA andWidedband COMA Cellular Networks," IEEE Communications, vol. 36, No 9,pp. 48-54, September 1998.[7] Jimenez, A.F. and Zigangirov K.Sh. , "On Coherent Reception ofUplink Transmitted Signals in the DS CDMA System" IEEE Trans. OnInformation Theory, Vol. IT-45, No 7, pp. 2655-2661, November 1999.

VI. CONCLUSIONS

General analysis of received signal has been introduced andit was shown that the main sources of ambiguous are fadeamplitudes and AWGN of the system.

The uses of pilot-aided Rake receiver gives a conditionalbit error probability that dose not depend on the number ofuser [equations (21) and (24)].

The effect of fade amplitudes decreases ~ and this

phenomenon can be compensated by increasing thenormalized energy per one user (28).

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Normalized energy If

IIG: "1 II rr;lillrrg0.5 +H+--t-++++

I++++-+,11-++++-t-H!~'++j++illl+-1.J'H~::~+~' t-H~-lt-;:'-+~I!++=R1'++1!!~'~~I:I:! ::':I::~!

i 0.4 I I,',I. III. ~~ ~ I 1 "I II '~ 0.3 )I 11-

:ii I "~. j 1[:I.e I~ 0.2 -+++-H-+-+-+++-++-1.-H~++-hIlh--"t-+i++,++ ++-+-+--W"H-t-t-f+++H++,+-tI

1

!~

Q. I. <' ' 11 i IIIII

0.1 ~ ~l~~, IIII TI

, I III \ I . ,

o -++++"I"'I"'.Ft-+t~-t++++++-+++++++++++-H-++++++H++++++++1lUill, I U

Considering nonzero AWGN, the probability of bit error atthe output of correlator will be

1 [( a2

))Ph < -exp N If _ I

2 IfPilot -If (No + Noc)/Tp

where N is the number of chips in each bit.

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