N.-Q. LIU ET AL. 269

From (15), not only the threshold, but the number of

FFT points has connection with false alarm probability.

And the probability increases with the increasing values

of M. Therefore, the number of the chosen FFT points in

actual system is limited, and the false probability and the

searching range of the frequency offset are in contradict-

tion.

For the PMF-FFT capture system the detecting prob-

ability [4, 5] is

DinPMF-FFT

()2(, ),Pk QNSNRGkfc

d

(16)

Suppose the preset threshold c=30, at this time PFA =

3.9210-5, the information rate Rb=1kpbs, the period of

the PN code N=10240, the input SNR SNRin = -25 dB.

The relation between the detecting probability and the

Doppler offset before and after the improvement is

shown in Figure 5.

From Figure 5, the PMF-FFT algorithm expands the

right detecting probability in the frequency domain. And

the probability is bigger after windowing process than

before. So the windowing method improves the detecting

probability of the PN code acquisition.

This paper uses the single stay acquisition decision, so

the average acquisition time is

D

Acq d

D

2(2)( 1)(1)

2

Pq kP

TP

FA

(17)

Here q is the number of code offset units to be

searched, q=KN; d

is single stay time. The stay time

will be Ts by using parallel matched filters, but it is at the

cost of huge hardware resource. So it is the serial way

that is chosen in this design and the stay time is XTs; k is

the number of decisions approving the happening of false

alarm. So false alarm penalty time is d

k

. If k = 10, the

relation between PMF-FFT algorithm and the Doppler

frequency offset before and after the improvement is

shown in Figure 6. Figure 7 shows the connection of

algorithm and the input SNR before and after improve-

ment.

05001000150020002500 3000 35004000 45005000

0. 8

0. 82

0. 84

0. 86

0. 88

0. 9

0. 92

0. 94

0. 96

0. 98

1

多普勒频偏f

d

/Hz

检测概率P

D

K

2

=0， 未加窗

K

2

=1， 汉宁窗

K

2

=1.7，改进窗

in

1ms

10240

25dB

b

T

N

SNR

2

2

2

Figure 5. Relationships between probability of detection of

improved algorithm and Doppler shift.

0 1 234 56

x 10

4

75

80

85

90

95

100

105

多普勒频偏f

d

/Hz

平均捕获时间T

Acq

/ms

K

1

=0, K

2

=0

K

1

=0, K

2

=1.7

K

1

=1.7,K

2

=1.7

1

10240

25

b

in

Tms

N

SNR dB

1

1

1

2

2

2

Figure 6. Average capture time of original and improved

algorithm under Doppler shift.

-40 -35 -30 -25-20 -15 -10 -5 0 5

10

1

10

2

10

3

10

4

10

5

输入信噪比SNR

/dB

平均捕获时间T

Acq

/ms

K

1

=0, K

2

=0

K

1

=0, K

2

=1.7

K

1

= 1.7,K

2

=1.7

1

1

1

2

2

2

b

d

1ms, 10240

30, 59.5kHz

TN

cf

Figure 7. Average capture time of original and improved

algorithm under different SNR.

7. Conclusions

This paper analyses basic theory of the PMF-FFT PN

code acquisition algorithm. For the Scalloping Loss, it

focuses on the windowing function method and improves

the structure, reducing the influence of the Scalloping

Loss. What is more, it proposes an equivalent method

equipped with easier structure. For the loss brought by

PMF fixed low-pass properties, it chooses the windowing

process to the received data. Theoretical analysis results

show that, after windowing twice, the algorithm im-

proves detecting probability and reduces average acquisi-

tion time compared with the original one, improving the

capacity of resisting disturbance.

REFERENCES

[1] M. Sust, R. Kaufman, F. Molitor and A. Bjornstor,

“Rapid Acquisition Concepts for Voice Activated CDMA

Communication,” IEEE Globecom’ 90, 1990, pp.

1820-1828.

[2] G. J. R. Povey and J. Talvitie, “Doppler Compensation

and Code Acquisition Techniques for LEO Satellite Mo-

bile Radio Communications. IEEE Fifth Internation Con-

ference on Satellite Systems for Mobile Communications

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