The design of an improved matched filter in DSSS-GMSK system

Transcription

1 Journal of Physics: Conference Series PAPER OPEN ACCESS The design of an improved mached filer in DSSS-GMSK sysem To cie his aricle: Mao Wei-ong e al 16 J. Phys.: Conf. Ser View he aricle online for updaes and enhancemens. This conen was downloaded from IP address on 13//18 a 1:8

2 8h Inernaional Conference on Advanced Infocomm Technology (ICAIT 15) Journal of Physics: Conference Series 679 (16) 1 doi:.88/ /679/1/1 The design of an improved mached filer in DSSS-GMSK sysem Mao Wei-ong, Zheng Lin-hua, Xiang Liang-jun, Wang Tan College of Elecronic Science and Engineering, Naional Universiy of Defense Technology,Changsha, China,73 address : @qq.com Absrac. This paper inroduces he principle of DSSS-GMSK sysem, analyses he superioriy of GMSK modulaion over MSK modulaion. Accord ha he mehod of de-spread before demodulaion can effecively improve he capabiliy of he sysem wih spread specrum gain, his paper researches an improved mehod wih mached filer o de-spread and demodulae he DSSS signals. The local PN code is modulaed wih GMSK modulaion before being correlaed wih received signal, hen we can ge he synchronous PN code, de-spread and demodulae he signal. MATLAB simulaion shows ha his mehod is more efficien han he mehod of demodulaion before despread in low SNR environmen. 1. Inroducion Spread-specrum sysem has been widely used wih he advanage of low probabiliy of being capured, srong abiliy on ani-jamming, high resolving power of disance and he power of random sochasic locaion by muli-user. As a working mechanism of spread-specrum sysem, direc sequence spreadspecrum (DSSS) uses BPSK/QPSK/MSK as is common mode of modulaion. GMSK modulaion, which is an improvemen on MSK modulaion, uses a Gaussian low pass filer before MSK. GMSK modulaed signals have more ighly band limi han oher consan envelope signals, so ha hey are more suiable. The advanage of DSSS sysem is he spread specrum gain o he signal. To ge he gain, he signals mus be de-spread before demodulaion. DSSS-BPSK/QPSK/MSK sysems all use he mehod of despread before demodulaion o manage he signals. The local PN code is made correlaion calculaion wih received signals by mached filer, hen we can ge he correlaion peak, which could help us ge he synchro PN code and demodulae he signals. Bu in GMSK modulaed sysem, we could no ge he correlaion peak by using he same mehod. To solve his problem, lieraure [] and lieraure [5] boh use he mehod of demodulaion before de-spread o process he received signals. Bu his mehod could no efficienly use he spread-specrum gain. The sysem could no work well in low SNR environmen. In order o efficienly use he spread-specrum gain, his paper researches an improved mehod wih zero IF direc correlaor o demodulae he DSSS signals, analyses and emulaes he principle and capabiliy of he sysem.. Principle and capabiliy of DSSS-GMSK modulaion Conen from his work may be used under he erms of he Creaive Commons Aribuion 3. licence. Any furher disribuion of his work mus mainain aribuion o he auhor(s) and he ile of he work, journal ciaion and DOI. Published under licence by Ld 1

3 8h Inernaional Conference on Advanced Infocomm Technology (ICAIT 15) Journal of Physics: Conference Series 679 (16) 1 doi:.88/ /679/1/1.1. Principle of DSSS-GMSK modulaion GMSK Gaussian-filered minimum-shif keying is a kind of modulaion scheme wih consan envelope, which develops from MSK. The principle of GMSK modulaion is ha he signals go hrough a Gaussian low-pass filer before MSK modulaion. The impulse response of he Gaussian filer is defined as follows: p p h ( ) = exp[( - ) ] (1) a a Where a = ln B B is he 3dB bandwidh of he Gaussian filer. If he widh of a pulse is T, hen BT is he normalized 3dB bandwidh. We can obain he frequency impulse signal of he Gaussian filer: æ p Bb æ T ö ö æ p Bb æ T ö ö g ( ) = Q ç ç - - Qç ç + øø è ln è ø ø è ln è () 1 exp ( - x ) dx. p Suppose ha he ransmiing daa muliplied by PN sequence is ak (ak Î {-1,1}) hen he phase of he modulaed signals is shown as follows: p ( k +1)T T f (k ) = [å ak g ( - nt - )]d (3) T ò k Where Q ( x ) = òx Where kt (k + 1)T. The frequency of he carrier wave is f c, hen he GMSK modulaed signal is produced afer IF modulaion: s ( k ) = cos ( p f c k + f ( k ) ) = cos ( p f c k ) cos f ( k ) - sin ( p f c k ) sin f ( k ) ().. Capabiliy analysis of GMSK modulaed signals GMSK is an improvemen on MSK. Figure 1 gives he BER performances and frequency specrum for GMSK and MSK modulaed signals. Alhough he error rae performance of GMSK modulaed signal is less han MSK modulaed signal, bu he gap is quie small. Figure shows ha wih respec o MSK modulaed signals, GMSK modulaed signals have a more compac specrum and faser band aenuaion. So GMSK has a broader developmen prospec. BER MSK GMSK BT=.16 GMSK BT=.3 GMSK BT= SNR(dB) Figure 1. BER comparison of GMSK and MSK. Normalized 3dB bandwidh is a very imporan parameer of GMSK modulaed signals. From figure we can see ha he specrum srucure of GMSK modulaed signals is closely relaed o BT value. The smaller he BT value, he more compac he frequency specrum. When BT +, he GMSK modulaed signals change ino MSK modulaed signals. BT value will also have an impac on he error rae of GMSK modulaed signals. Figure 1 also shows ha he BER performance will be geing worse as BT value decreases. So, BT value usually is.3 in GSM sysem.

4 8h Inernaional Conference on Advanced Infocomm Technology (ICAIT 15) Journal of Physics: Conference Series 679 (16) 1 doi:.88/ /679/1/1 Figure. Frequency specrum of GMSK and MSK. 3. Improved mehod wih mached filer o de-spread and demodulae he DSSS signals Two mehods are used for he signal processing a he receiving erminal of he DSSS sysem: de-spread before demodulaion and demodulaion before de-spread. In high SNR environmen, he wo mehods boh have good BER performances. Bu in low SNR environmen, he mehod of de-spread before demodulaion has a beer BER performance because his mehod could effecively use he spread specrum gain. A he receiving erminal, we mus ge he he synchronous PN code before despread he received signals. Common mehods o ge synchronous PN code are sliding correlaion and mached filer. The principle of mached filer is ha we use he PN code as he coefficiens of he filer o filer he received signals. The resul will be sen o he hreshold decider. If he resul is larger han he hreshold value, he PN code is synchronous. In DSSS-BPSK sysem, signals a he receiving erminal is shown as follows: s( ) = Pc ( - ) cos(w' + f ' ) (5) Where c( ) is he PN code muliplied by ransmied daa. is he ime delay. w is he frequency of ' he received signal f ' is he iniial phase which can be se o zero. The impulse response of he mached filer is: h( ) = c( NTc - ) where NTc NTc is he period of PN code. Afer DDC, he signals will be sen o he mached filer. The resul is ha: y ( ) = s ( ) * h( ) = ò s (l )h( - l )d l =ò - NTc (6) Pc(l - )c( NTc - + l ) cos(dwl )d l Where Dw is he variaion of he carrier frequency. The correlaion peak could be found from he resul. However, he GMSK modulaed signals are shown as formula(), he resul of he signals correlaed wih PN code is ha: z ( ) = cos ( Dw + f ( ) ) * h ( ) = ò cos ( Dwl + f (l ) ) h ( - l )d l =ò -NTc (7) cos ( Dwl + f (l ) ) c (NTc - + l )d l We can no find he correlaion peak from formula(8), hen we can no ge he synchronous PN code and 3

5 8h Inernaional Conference on Advanced Infocomm Technology (ICAIT 15) Journal of Physics: Conference Series 679 (16) 1 doi:.88/ /679/1/1 despread he received signals. To solve his problem, his paper researches an improved mehod wih mached filer o de-spread and demodulae he DSSS signals. Figure 3 shows he process of he mehod. The local PN code, which modulaed by GMSK mode firs, is se as he coefficien of he mached filer. Then he mached filer is used o filer he received signals. Daa I Daa Q Ä Ä ( g) ò ò ( g) GMSK modulae Å PN code generaor demodulae hreshold clock Figure 3. Process of he improved mehod. Assume ha he carrier is synchronous, afer DDC, he GMSK In-phase daa and Quadraure daa of he signals are ha: si ( ) = A cos(f ( )) sq ( ) = A sin(f ( )) Where f ( ) = p é (9) () T ù å a g ( - nt - ) úû d. Assume he period of he PN code is k, hen he T ò êë n n local GMSK modulaed signals are ha: r ( ) = cos(f ( )), kt (11) The oupu of he mached filer is ha yi ( ) = s ( ) * ri ( ) = ò s (l )ri ( - l )d l = Aò - ktc cos(f (l )) cos(f ( - l ))d l (1) yq ( ) = s ( ) * rq ( ) = ò s (l )rq ( - l )d l = Aò - ktc cos(f (l )) sin(f ( - l ))d l (13) Then he peak value is ha z ( ) = yi ( ) + yq ( ) (1) If z ( ) is larger han hreshold value, hen he local PN code is synchronous. According o he correlaion peak values in each symbol period, we can demodulae he received signals.. Simulaion resuls Assume ha signal ransmission rae Rb = 8kHz PN code period k = 18 hen PN code ransmission rae is.mhz The sampling rae is 1 imes he code ransmission rae. Time delay is se o be 8 sampling duraion. Carrier is synchronous a he receiving erminal. We can ge he simulaion resuls wih he inpu SNR of -6dB : 1 The oupu of he mached filer is shown as Figure. From Figure we can see he correlaion peak clearly. Then we can ge he synchronous PN code by seing a suiable hreshold value.

6 8h Inernaional Conference on Advanced Infocomm Technology (ICAIT 15) Journal of Physics: Conference Series 679 (16) 1 doi:.88/ /679/1/1 8 X: 8 Y: Figure. Oupu of he mached filer. Figure 5 shows he correlaion peak afer de-spread. Since every symbol has 1536 sampling poins, he correlaion peak will appear every 1536 sampling poins. We can ge he sending signals hrough he posiive and negaive of every peak value x Figure 5. Correlaion peak afer de-spread. 3 Figure 6 shows he BER performances of he wo mehods. The mehod his paper researched has a beer BER performance han he mehod of demodulaion before de-spread in low SNR environmen. de-spread before demodulaion demodulaion before de-spread Figure 6. BER performances of he wo mehods. 5

7 8h Inernaional Conference on Advanced Infocomm Technology (ICAIT 15) Journal of Physics: Conference Series 679 (16) 1 doi:.88/ /679/1/1 5. Summary This paper inroduces he principle of DSSS-GMSK sysem, analyses he GMSK modulaed signals. According o he special form of he GMSK modulaed signals, wih he hough of de-spread before demodulaion, his paper improves he mached filer. Simulaion resuls show ha we can ge he correlaion peak from he filer oupu and despread he signals. When inpu SNR is -6dB, he BER can be -5. References [1] Hanwen Cao, Friederike Maier, Andreas Wilzeck and Thomas Kaiser 1 DSSS Differenial GMSK Wih Space-Time Modulaion for Robus Mobile Daa Links IEEE Wireless Communicaions and Neworking Conference: PHY and Fundamenals [] SHIGA.S, IKEGAHI.T Digial Mached Filer Deecion of GMSK/DSSS Signal IEEE In. Symp. an Personal, Indoor and Mobile Radio Communicaion pp [3] LOU Li 199 The Emulaion and Analysis of GMSK Digial Modulaion Modern Elecronics Technique Vol 1 pp [] Liang Xianming Realizaion of Demodulaion and Despread Technology for GMSK Spread Specrum Signal Telecommunicaion Engineering Vol 5 pp [5] Yasuhiro yano, Hisao Tachika and Tadashi Fujino 1996 Performance of DS/GMSK/PSK Modern Using Four-phase Correlaor IEEE.Radio Communicaion Deparmen, Informaion Technology R&D Cener, Misubishi Elecric Corp 6