an environmental robust pn code acquisition

7/27/2019 An Environmental Robust Pn Code Acquisition

1/13

- 1 -

AN ENVIRONMENTAL ROBUST PN CODE ACQUISITIONARCHITECTURE IN DS-CDMA SYSTEMSHae-Sock Oh, Dong-Seog Han, and Chang-Joo Kim

School of Electronic Electrical Engineering, Kyungpook National University.Korea

Electronics Telecommunications Research Institute, KoreaPhone: +82-53-950-6609. Fax: +82-53-950-5505, E-mail:

[email protected]

Abstract-An adaptive double-dwell acquisition system of pseudo-noise (PN)sequences is presented for direct-sequence spread-spectrum (DS-SS) systems.

Since existing acquisition systems have a fixed threshold value, they are unable to

adapt to various mobile communication environments. Accordingly. this results in a

high false alarm rate or low detection probability. Therefore, an adaptively varying

threshold scheme is proposed through the use of a constant false alarm rate

(CFAR) algorithm well known in the field of detection. By deriving formulas for the

detection probability, faise alarm rate and mean acquisition time of proposed

adaptive system, its performance was analyzed and compared to an existing one.

The results showed that the proposed adaptive double-dwell acquisition system

provides a better performance than conventional systems.

I. INTRODUCTIONSPREAD-spectrum communication systems have been used for military purposes

since the 1960s. They are now commonly used all over the world and have been

adopted for use in CDMA, IS-95 system and so on. which selected direct-sequence

spread-spectrum (DS-SS) technology from among several spread-spectrum

communication methods. Current mobile communication systems are being

constructed on a global level. therefore the systems are needed that can guarantee

the performance of mobile terminals despite various kinds of geographical features

and other environments.

The effective acquisition of a spread-spectrum signal is a significant aspect of

mobile communication systems has been studied extensively. It is essential to

acquire a spread-spectrum signal both quickly and accurately in order to provide

high quality communication services.


2/13

- 2 -

Typical acquisition methods include serial, parallel and hybrid systems. Since a

common serial acquisition system[1] has a long acquisition time and low detection

probability, a parallel acquisition system was proposed[2]. However, since this

system also requires very complex hardware, a hybrid method[3] was then

suggested. This compromise between serial and parallel acquisition methods was

able to improve the performance in terms of the acquisition time and detection

probability, and lower hardware complexity of the parallel-type system. In addition,

a multiple-dwell system was created[4] for fast acquisition and low false locks.

This type of system has a lower hardware complexity than that of the hybrid

method. The common thing among multiple-dwell systems is their double-dwell

system related to their performance and hardware complexity. However, all these

conventional acquisition methods use a fixed threshold value, accordingly these

systems have problems with varying detection probabilities (PD) and false alarmrates (PFA) according to the surroundings. When the conventional systems decide a

threshold value, the system tests some threshold values many times by simulation

in a specific environment. After these tedious iterations, the system adopts a

sub-optimum threshold value. As a result, these systems are unable to provide a

sufficient quality of service to customers due to their lack of adaptability to various

environments.

To solve this problem. here, the threshold value of acquisition system is varied

adaptively using a constant false alarm rate (CFAR) algorithm [5]. which is well

known in the field of detection. Therefore ~he proposed system is able to

accommodate a variety of mobile communication environments. The performance is

analyzed and compared to the existing ones by deriving equations PD and PFA for

the proposing system.

This paper is organized as follows. Section II describes the acquisition scheme, and

in Section III presents the expressions for deriving the detection probability and

false alarm rate using the proposed adaptive threshold value method. The numerical

results are presented and the proposed system compared with a conventional

double-well system in Section IV. and the findings and conclusions are then

discussed in Section V.

II. SYSTEM DESCRIPTIONThe system under consideration in this paper is a double-dwell serial search

scheme that consists of two matched filter (MF) correlators connected in serial

manner. Referring to Fig. 1 it consists of two adaptive detectors (ADs). The first

detector has a short correlation tap size and the second detector has a longer

correlation tap size than that of the first one.


3/13

- 3 -

By constructing the correlation tap sizes in this manner, the acquisition system can

reject cells which is not in phase quickly. The shorter correlation tap size is, the

more false alarm results. To compensate this problem, the second detector has a

long correlation tap size. Therefore. if the threshold value of the detector is

controlled properly, a double-dwell system reduces a mean acquisition time and

also can have high detection probability.

The system operation is as follows. From Fig. 1. the received PN signal plus noise

and any interference arrive at each adaptive detector. If the first AD indicates that

the present cell is the correct cell, then the second AD starts working. Also if the

second AD indicates synchronization, then the decision is made to stop the search.

In contrast, if a detector fails to indicate that the present cell is correct, then the

relative time delay of the local PN signal is retarded by T C where TC represents

chip time. In this case the next cell is then examined repeatedly. Therefore thedistributions of the two AD outputs are independent. Usually the value of is 0.5

or 1. In this paper, was set to 1.

Fig. 1. Adaptive double-dwell acquisition scheme.Fig. 2 shows a block diagram of an AD. The first and second detectors have

structures as in Fig. 2. The difference between each detector is its correlation tapsize. Generally, the correlation tap size of the first detector is short, whereas that

of the second detector is long due to considerations of the mean acquisition time

and detection probability. i.e. N1


4/13

- 4 -

Fig. 2. Block diagram of adaptive detector.For the adaptive operation of the decision processor, the cell-averaging constant

false alarm rate (CA-CFAR) algorithm is used from among several CFAR algorithms

due to its low hardware complexity. The threshold value of the comparator in theAD is updated in accordance with the magnitude of the incoming signals as shown

in Fig. 2. Accordingly, the outputs of the correlator are sent serially into a shift

register of length M+1. The first register. denoted as Y, stores the output of the

test phase. The following M registers, denoted by Zj,j = 1,2, ,M and called as the

reference window, store the outputs of the previous M phases. The variable X is

the summation of the value in the window. Using variable X, the system estimates

the background noise power level of the incoming signals.

The values in the window are summed and scaled by Ti(i=1, 2), where Ti is set

according to the desired false alarm rate from the CA-CFAR algorithm. Therefore,

the adaptive threshold value of an AD is TiX. The correlators in Fig. 2 are I-Q

non-coherent matched filters.

III. ANALYSIS OF SYSTEMIn the derivation of the detection probability and false alarm rate for a typical

non-fading additive white Gaussian noise (AWGN) channel, the same assumptions of

[2] are used, namely, 1) there is only one sample corresponding to the correct

phase (one H1 cell only), 2) all samples are independent. 3) the correlation tap

sizes Ni >>1, i=1,2, are selected such that the correlation of the received sequence

and local code is about zero when they are not in phase (H0 cells), and 4) the

uncertainty region is the full code length L.


5/13

- 5 -

The received signal can be written as

where is the received code offset, C(t) is the PN sequence, is uniformly

distributed random phase (0 < 2 ), n is carrier frequency in rad/s, S is

received signal power, and n(t) is AWGN with a zero mean and one-sided power

spectral density of N0 in W/Hz. Fig. 3 illustrates the structure of the matched filter

shown in Fig. 2.

Fig. 3. I-Q noncoherent matched filter.

Fig. 4. Matched filter correlator of Fig. 3.Referring to Figs. 2 and 3, it can be shown that the probability density function

(pdt) of the H1 sample is a non-central chi-square distribution with two degrees of

freedom, which can be expressed as [2]


6/13

- 6 -

where noise variance is 2

n = N0NiTc/2, mean signal power is m2

= Ni2

Tc2S a n d I0

() is modified Bessel function of the first kind and zero order.The pdf of the H0, samples is a central chi-square distribution with two degrees of

freedom and can he expressed as [2]

Since the reference signals in the window cells can be assumed to be noise signals

(H0 cells) [5], the pdf of values Zj in the window cells is the same as the H0

distribution. Also the pdf of H0 cells can be written as an independent distribution

of G(1, 22

n), where G(,) is the Gamma distribution. Hence, the pdf of Zj is

X= M

i= 1 Z

j h as the pdf of G( M

i= 1 1 , 2

2

n ), the random variable X is

written as G(M, 2n2

). The pdf of the window cells. f(x), is

where ( ) is the Gamma function.With the CA-CFAR algorithm, the detection probability of the ith, i=1,2,AD, PDi, is


7/13

- 7 -

where Q(, ) represents the Marcum's Q-function. In (7) the Marcum's Q-function is

difficult to compute accurately. Plus if the equation of detection probability is

transformed to an infinite summation form, it will not be effective for deriving

results because there are infinite factorials. Accordingly. (7) can be approximated to

a Gaussian Q-function [6]. As a result, the equation of the detection probability of

an AD can be represented as

With the CA-CFAR algorithm, the false alarm rate of the ith(=1, 2)AD, PFAi, is

Since the correlator outputs of the first and second ADs are independent. the

detection probability of the system is the product of each AD's detection

probability. Hence, the probability of actually detecting the correct cell is


8/13

- 8 -

The false alarm rate of the system Is

In (11), since the parameters Ti and Mare constant values, the false alarm rate of

the proposed system is constant regardless of the signal-to-noise ratio (SNR).

Since the false alarm rate of the system is the product of each AD's false alarm

rate, the adaptive double-dwell system increases the detection probability with a

fixed the false alarm rate. This is another merit of the adaptive system.

The mean acquisition time of the proposed system is

where L is the length of PN sequence and K is a penalty time constant.

IV. NUMERICAL RESULTSTo confirm the performance of the proposed adaptive double-dwell system, its

detection probability, false alarm rate and mean acquisition time were determined

with various parameters. The proposed system was also compared with a

non-adaptive conventional double-dwell system. Due to the complexity of the

integration in (8), the results in this section were made using 'approximate

integration' method. All the results assumed an AWGN channel and used a chip time

Tc=10-6

[sec], PN sequence length L = 1023 and penalty time constant K=1000.

Fig. 5 shows the detection probability of the proposed system according to various

correlation tap sizes (N1. N2) of AD and Eb/N0[dB] when PFA is 10-3

and M is 20.

Here. Eb/N0 means signal-to-noise ratio per chip (SNR/chip). When the correlation

tap size of the first and the second AD is 96 and 128. the detection probability is

maximized. Fig. 6 shows the detection probability for different M's when N1 is 96.

N2 is 128 and PFA is 10-3

. The detection probability is increased when the window

cell size is increased and the increasing rate is reduced as M increases.


9/13

- 9 -

The detection probability of proposed system according to the false alarm rate is

presented in fig. 7 when N1 is 96. N2 is 128 and M is 20. It shows that the

detection probability is increased when the false alarm rate is increased as

expected CA-CFAR algorithm.

Fig. 5. Total probability of detection relative to correlation tap size.

Fig. 6. Total probability of detection with different Al s.


10/13

- 1 0 -

Figs. 8 and 9 present the comparison of the detection probability and the false

alarm rate between proposed system and conventional one. While the conventional

system uses a suboptimum threshold value when Eb/N0 is -5 . the false alarm rate

is 10-3, and the correlation tap size of the first and the second correlators are 96

and 128. respectively. From Fig. 8. the detection probability of the proposed

system is superior to that of the conventional system all over the SNR per chip

ranges. Referring Fig. 9. the false alarm rate of conventional system is extremely

increased and exceedingly varies according to Eb/N0. Therefore, the conventional

system cannot detect PN sequence efficiently.

In Fig. 9. since the false alarm rate of the proposed system is constant according

to Eb/N0, the system operates stably for various signal powers. Because system

operators can control this false alarm rate arbitrarily, it can be chosen adaptively

for some purpose. Fig. 10 shows the mean acquisition time of proposed systemaccording to various correlation tap size from the results of fig. 5. When the

correlation tap size of the first and the second AD is 96 and 128. the mean

acquisition time is minimized. But the mean acquisition time converges when Eb/N0

is over -10 as the detection probability approaches 1. Fig. 11 presents the

comparison of mean acquisition time between proposed and conventional systems

based on the detection probability and the false alarm rate of Figs. 8 and 9. The

proposed system has better performance about all over the ranges. Although a

conventional system shows somewhat better performance when Eb/N0 is over - 5 .

this is because the term related to the false alarm rate in (12) has been removed

when the false alarm rate of a conventional system goes to 0 over -5 while the

false alarm rate of proposed system is fixed, 0.001, by CA-CFAR algorithm.

Fig. 7. Total probability of detection with different PFAs.


11/13

- 1 1 -

Fig. 8. Comparison of PDs between proposed and conventional system.From the results of this section. while the performance of conventional system

varied dramatically relative to the surroundings, the proposed system maintained a

fixed false alarm rate along with a robust acquisition performance regardless of the

received signal powers. Therefore, it is apparent that the proposed system should

be considered for future mobile communication systems.

V. CONCLUSIONSThis paper derived formulas for an adaptive double-dwell acquisition system in a

non-fading AWGN channel and used the resulting detection probabilities and false

alarm rates to compare the performance of proposed system with that of a

conventional system with a fixed threshold value. Using the formulas derived for

determining the detection probability, false alarm rate and mean acquisition time,

the proposed system was analyzed relative to correlation tap sizes and window cell

sizes. The detection probability of the proposed system increased with the

increasing window cell sizes and the false alarm rate. By adopting the CA-CFAR

algorithm to the acquisition system, the threshold value is updated according to the

magnitude of the incoming signals, thereby improving the system performance.

Keeping the false alarm rate constant and controlling the false alarm rate

arbitrarily, the proposed system is able to produce robust performance regardless

of the surroundings.


12/13

- 1 2 -

Fig 9. Comparison of PFA between proposed and conventional system

Fig. 10. Mean acquisition time of proposed system according to the correlation tapsize.


13/13

- 1 3 -

Fig. 11 Comparison of mean acquisition time between proposed and conventionalsystems.

REFERENCES[1] A. Polydoros. C. L. Weber, "A Unified Approach to Serial Search Spread

Spectrum Code Acquisition - Part I : General theory," IEEE Trans. Commun.. vol.

COM-32, no. 5. May 1984.

[2] E. A. Sourour, S. C. Gupta, "Direct-Sequence Spread-Spectrum Parallel

Acquisition in a Fading Mobile Channel," IEEE Trans. Commun.. vol. COM-38. no. 7.

July 1990.

[3] W. Zhuang. "Noncoherent Hybrid Parallel PN Code Acquisition for CDMA Mobile

Communications." IEEE Trans. Veh. Technol., vol. VT-45, no. 4. Nov. 1996.

[4] D. M. Dicarlo. C. L. Weber, "Multiple Dwell Serial Search Performance and

Application to Direct Sequence Code Acquisition." IEEE Trans. Commun.. vol.

COM-31. no. 5, May 1983.

[5] N. Levanon. Radar Principles, New York John Wiley & Sons, Inc., 1988.

[6] I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, New

York Academic Press. Inc., 1980.

an environmental robust pn code acquisition

Documents