Contents 5 Hrs ISI and zero-ISI condition (Refp380-381,p393-394) Design of BL signals for zero-ISI (Refp396-399) OFDM UESTC-Digital transmission thro BL AWGN channels Prof李晓峰 2
6.2 Design of BL signals for zero-ISI Most channels are practically BAND-LIMITED.Examples such as, Subscribe-line in a standard telephone system is limited to 4kHz. Uplink channel in GSM is for data from mobile user to the base and is a bandpass channel limited to 200kHz. The freq response of channel,C() 1.For BB,limited to some w,and C()=0,f>W 2.For PB,limited to some w about its central freq f,and C(f)=0,f-f≤W12 UESTC-Digital transmission thro BLAWGN channels Prof李晓峰 4
6.2 Design of BL signals for zero-ISI Think about the channel with BW of WHz. Case 1:W<Rs/2 三AU-z Flat?Impossible! -R -R/2 W Case 2:W=Rs/2 十2U-回 Flat?If and only if H(t)is rect. -R, -R/2 R -W UESTC-Digital transmission thro BLAWGN channels Prof李晓峰 7
6.2 Design of BL signals for zero-ISI Think about the channel with BW of WHz. Case 1:WRs/2 Flat?Many chances, once H(t)is complement about -R-m-R/2 公 R Rg/2. UESTC-Digital transmission thro BLAWGN channels Prof李晓峰 8
6.2 Design of BL signals for zero-ISI Think about the channel with BW of WHz. Case 1:WRs/2 Flat?Many chances, once H(t)is complement about -R.-F-R/2 R Rg/2. UESTC-Digital transmission thro BLAWGN channels Prof李晓峰 9
6.2 Design of BL signals for zero-ISI In the design of BL systems for zero-ISI,Raised-Cosine (RC)spectrum is widely used for H(). A RC spectrum and its time response are defined by, 0≤f八≤1-a)f H)-4} 1 2af 1-a)i(1+a)f0 respectively,where a is called the roll-off Hgc(f) factor and=Rs/2 called 6dB-BW. a=0.0 0.5 1.0 R/2 -2f6 -f6 2f0 UESTC-Digital transmission thro BLAWGN channels Prof李晓峰 11
6.2 Design of BL signals for zero-ISI In the design of BL systems for zero-ISI,Raised-Cosine (RC)spectrum is widely used for H(). A RC spectrum and its time response are defir hac(t) a=0.0 0.5 H)-4} 1 1.0 2af。 (-a 0 2 26 26 26 respectively,where a is called the roll-off HRc(f) 个 factor and=Rs/2 called 6dB-BW. a=0.0 2 and 0.5 1.0 R/2 hgc(t)= sin(2πft）cos(2afd） 2πft 1-(4aft)2 -2f6 -f6 2f0 UESTC-Digital transmission thro BLAWGN channels Prof李晓峰 12
6.2 Design of BL signals for zero-ISI In the design of BL systems for zero-ISI,Raised-Cosine (RC)spectrum is widely used for H(). From the figure,we read W-(1+a)Rs/2.a hac(t) controls the transition of the band.We note a=0.0 that: 0.5 1)Large a gives a smooth transition and requires large BW,while small a sharp transition and small BW. 2f 2 26 2)The RC spectrum for a-0 is exactly the LPF HRc(f) and BW reaches the minimum. a=0.0 2 3)The smoothness of transition band with 0.3 1.0 R/2 non-zero a is very important in practical implementation of filters. -2f6 +a2f0 UESTC-Digital transmission thro BLAWGN channels Prof李晓峰 13
Example:a passband channel of 600=Rs/2=[7200/log2(M)]/2 -2f0-0 267 log2(M)>=7200/(2*1500)=2.4, (1+a)Rs/2 Take M=8,and 8PSK.Rs=2400 Baud 3.Take W/2>=(1+a)Rs/2,that is1500>=1200(1+a), a<=1500/1200-1=5/4-1=1/4,Take a RC filter with a=0.25 4.The spectral efficiency is:Rb/W=7200bps/3000Hz=2.4bps/Hz UESTC-Quiz Prof李晓峰 18