Home Networking Basis: Transmission Environments and Wired/Wireless Protocols

3.9.1 Coaxial Cable Insertion Loss and Impulse Response Models

function [ht,h]=abcd2hcx(a,b,c,d); d=a; r=75; sz=length(a); h=2*r*ones(sz,1)./(r*(r*c+d)+(r*a+b)); h(sz+1:2*(sz-1))=real(h(sz-1:-1:2))-sqrt(-1)*imag(h(sz-1:-1:2)); ht=real(ifft(h));

3.9.2 Splitter Input-to-Output Model

function [a,b,c,d]=splitio(f,z0); l1=4e-5; l2=1e-7; k1=0.9997; k2=0.9997; a=0.707; r=220; C=4.5e-12; lf=length(f); W=2*pi*f'; a10=ones(lf,1)/a/k1; b10=j*W*l1*a*(1-k1^2)/k1; c10=ones(lf,1)./(j*W*l1*a*k1); d10=ones(lf,1)*a/k1; a3=ones(lf,1); b3=zeros(lf,1); c3=j*C*W; d3=a3; a1=a10.*a3+b10.*c3; b1=a10.*b3+b10.*d3; c1=c10.*a3+d10.*c3; d1=c10.*b3+d10.*d3; a2=j*W*l2*(2*(1+k2)*z0+r)+r*z0-(1-k2^2)*W.^2*l2^2; b2=j*W*l2*r*z0-(1-k2^2)*W.^2*l2^2*(r+z0); c2=2*j*W*l2*(1+k2)+r; d2=2*j*W*l2*(1+k2)*(r+z0)+r*z0; a=a1.*a2+b1.*c2; b=a1.*b2+b1.*d2; c=c1.*a2+d1.*c2; d=c1.*b2+d1.*d2; delt=j*W*l2*(1+k2)*(r+2*z0)+r*z0; a=a./delt; b=b./delt; c=c./delt; d=d./delt;

3.9.3 Splitter Output-to-Output Model

function [a,b,c,d]=splitoo(f,z1); l1=4e-5; l2=1e-7; k1=0.9997; k2=0.9997; a=0.707; r=220; C=4.5e-12; lf=length(f); W=2*pi*f'; zm=a^2*z1; a1=zm+j*W*l2; b1=j*W*l2*(1+k2).*(j*W*l2*(1-k2)+2*zm); c1=ones(lf,1); d1=zm+j*W*l2; a=b1+a1*r; b=r*b1; c=C*(r+b1)-(1-a1).^2; d=b1+a1*r; delt=r+b1; a=a./delt; b=b./delt; c=c./delt; d=d./delt;

3.9.4 Coaxial Cable Wiring Channel Model

f=[1:1025]/1025*1.5e8; l1=100; l2=25; l3=35; z0=75; z1=75; load c6.mod load c59.mod [a1,b1,c1,d1]=abcdcx(f,c6(:,1),c6(:,2),c6(:,3),c6(:,4),c6(:,5),l1); [a2,b2,c2,d2]=abcdcx(f,c6(:,1),c6(:,2),c6(:,3),c6(:,4),c6(:,5),l2); [a3,b3,c3,d3]=abcdcx(f,c6(:,1),c6(:,2),c6(:,3),c6(:,4),c6(:,5),l3); [as1,bs1,cs1,ds1]=splitoo(f,z1); [as2,bs2,cs2,ds2]=splitio(f,z0); [chip1,h1]=abcd2hcx(a1,b1,c1,d1); y1=20*log10(abs(h1(1:1025))); at1=a1.*as1+b1.*cs1; bt1=a1.*bs1+b1.*ds1; ct1=c1.*as1+d1.*cs1; dt1=c1.*bs1+d1.*ds1; [chip2,h2]=abcd2hcx(at1,bt1,ct1,dt1); y2=20*log10(abs(h2(1:1025))); at2=at1.*a2+bt1.*c2; bt2=at1.*b2+bt1.*d2; ct2=ct1.*a2+dt1.*c2; dt2=ct1.*b2+dt1.*d2; [chip3,h3]=abcd2hcx(at2,bt2,ct2,dt2); y3=20*log10(abs(h3(1:1025))); at3=at2.*as2+bt2.*cs2; bt3=at2.*bs2+bt2.*ds2; ct3=ct2.*as2+dt2.*cs2; dt3=ct2.*bs2+dt2.*ds2; [chip4,h4]=abcd2hcx(at3,bt3,ct3,dt3); y4=20*log10(abs(h4(1:1025))); a=at3.*a3+bt3.*c3; b=at3.*b3+bt3.*d3; c=ct3.*a3+dt3.*c3; d=ct3.*b3+dt3.*d3; [chip,h]=abcd2hcx(a,b,c,d); y5=20*log10(abs(h(1:1025))); figure(2) plot(f,y1,'k',f,y5,'k') figure(3) plot([1:1025]/2/1.5e8,chip(1:1025),'k')

3.9.5 Ingress Noise Model

psize=2049; nsub=500; perc=0.5; f=[0:psize-1]/2048*50e6; f(1)=0.00001; %define shortwave radio bands mask1l=5.5e6; mask1h=6e6; mask2l=7e6; mask2h=7.5e6; mask3l=9e6; mask3h=9.8e6; mask4l=11.5e6; mask4h=12e6; mask5l=13.5e6; mask5h=14e6; mask6l=14.8e6; mask6h=15e6; mask7l=17.5e6; mask7h=18e6; mask8l=21.5e6; mask8h=21.8e6; %define 30 random peaks rloc1=rand(1,30)*50e6; rloc2=rand(1,30)*50e6; rloc3=rand(1,30)*50e6; rloc4=rand(1,30)*50e6; rloc5=rand(1,30)*50e6; rloc6=rand(1,30)*50e6; rloc7=rand(1,30)*50e6; rloc8=rand(1,30)*50e6; %noise floor nsfllog=-40; nsflflog=ones(1,psize)*nsfllog; nsflf=10.^(nsflflog/10); %radio background noise level, e-filed efildlog=34.5-20; efildflog=ones(1,psize)*efildlog; epowflog=efildflog-44.5; epowf=10.^(epowflog/10); %radio interference noise level, random e-field erfildflog=rand(1,psize)*45; %spectrum mask erfmask=ones(1,psize)*0.1; for i=1:psize if f(i)>mask1l & f(i)<mask1h erfmask(i)=1; end if f(i)>mask2l & f(i)<mask2h erfmask(i)=1; end if f(i)>mask3l & f(i)<mask3h erfmask(i)=1; end if f(i)>mask4l & f(i)<mask4h erfmask(i)=1; end if f(i)>mask5l & f(i)<mask5h erfmask(i)=1; end if f(i)>mask6l & f(i)<mask6h erfmask(i)=1; end if f(i)>mask7l & f(i)<mask7h erfmask(i)=1; end if f(i)>mask8l & f(i)<mask8h erfmask(i)=1; end for j=1:30 if f(i)>rloc1(j)-100e3 & f(i)<rloc1(j)+100e3 erfmask(i)=0.2; end if f(i)>rloc2(j)-100e3 & f(i)<rloc2(j)+100e3 erfmask(i)=0.3; end if f(i)>rloc3(j)-100e3 & f(i)<rloc3(j)+100e3 erfmask(i)=0.4; end if f(i)>rloc4(j)-100e3 & f(i)<rloc4(j)+100e3 erfmask(i)=0.5; end if f(i)>rloc5(j)-100e3 & f(i)<rloc5(j)+100e3 erfmask(i)=0.6; end if f(i)>rloc6(j)-100e3 & f(i)<rloc6(j)+100e3 erfmask(i)=0.7; end if f(i)>rloc7(j)-100e3 & f(i)<rloc7(j)+100e3 erfmask(i)=0.8; end if f(i)>rloc8(j)-100e3 & f(i)<rloc8(j)+100e3 erfmask(i)=0.9; end end end erfildflog=erfildflog.*erfmask; %conversion at 10 MHz erpowflog=erfildflog-44.5; erpowf=10.^(erpowflog/10); %sum of background and interference noise power epowf=epowf+erpowf; %field to power: propotional to the power of wavelength epowf=epowf.*(10e6./f).^2; epowft=perc*epowf+nsflf; f(1)=0; nfilt=fir2(900,f/max(f),sqrt(epowft)); [h,w]=freqz(nfilt,1,1024); px=[1:1024]/1024*50e6; py=20*log10(abs(h)); plot(px(102:1024),py(102:1024),'k'); grid xlabel('Frequency (Hz)') ylabel('Noise Level (dBµV)')

3.9.6 Channel Capacity Calculation

coaxmod; h2=(abs(h(1:1024))).^2; nmdl; n2=(abs(h(1:1024))).^2; df=max(f)/1025; f1=ceil(1025*42e6/1.5e8); f2=ceil(1025*52e6/1.5e8); for psd=0:50 chacap(psd+1)=sum(log(1+10^(psd/10).*h2(f1:f2)./n2(f1:f2)))*df/log(2); end px=[0:50] figure(3) plot(px,chacap,'k'); grid xlabel('Transmit Signal Level (dBµV)') ylabel('Channel Capacity (Bits/Sec)')