04104-106通信原理II第五讲

04104-106IIMarch27,20071X!YP(YjX)XYYXI(X;Y)=H(X)¡H(XjY)=H(Y)¡H(YjX)I(X;Y)I(X;Y)=H(X)YXI(X;Y)H(X)YXBPSK1210000I(X;Y)=0:5bits=symbol1Y5000bit1bit5000bit210000(X1;X2;¢¢¢;X10000)2500025000¡1210000M=25000MMYMlog2M=5000bits10.5bitfXigfYig9I(X;Y)(bits/symbol)P(YjX)I(X;Y)P(X)I(X;Y)=H(Y)¡H(YjX)=¡XYP(Y)lnP(Y)+XX;YP(X;Y)lnP(YjX)P(Y;X)=P(YjX)P(X)P(Y)=PXP(X;Y)=PXP(YjX)P(X)I(X;Y)XC=maxP(X)I(X;Y)ShannonCapacity12BinarysymmetricalchannelBSCX2f0;1gY2f0;1gP(Y=1jX=1)=P(Y=0jX=0)P(Y=1jX=0)=P(Y=0jX=1)=¹¹C=1¡h2(¹)=1+¹log2¹+(1¡¹)log2(1¡¹)bits=symbolX3GaussianchannelAWGNyx0zy=x+n()xnS=E[x2]SNR=E[x2]E[n2]=S¾2p(yjx)=1p2¼¾2e¡(y¡x)22¾2vH(v)=¡E[lnp(v)]¡E[logP]P(v)=p(v)dv¡lnP=¡lnp(v)¡lndv=1H(v)=¡E[lnp(v)]dvI(u;v)=H(u)¡H(ujv)=E[¡lnp(u)du]¡E[¡lnp(ujv)du]=E[¡lnp(u)]¡E[¡p(ujv)]I(x;y)=E[¡lnp(y)]¡E[¡lnp(yjx)]¡lnp(yjx)=12ln2¼¾2+n22¾2lnp2¼¾2+12=lnp2¼e¾2I(x;y)=H(y)+lnp2¼e¾2H(y)y0ySyxnSy=S+¾2E[v2]0H(y)y0lnp2¼e(S+¾2)bitC=log2p2¼e(S+¾2)¡log2p2¼e¾2=12log2(1+SNR)bits=symbol(1)04AWGNAWGNx(t)y(t)=x(t)+n(t)Bn(t)¡B·f·BN02¾2=N0Bx(t)y(t)jfj·By(t)SNR=S¾2BISIRs=2BTs=1Rs=12Bx(t)=Pkxksinc(t¡kTsTs)sinc(t¡kTsTs)TsEs=E[x2k]TsEs=STsE[x2k]=ShMF(t)=1Tssinc(tTs)2yk=xk+nknk0N02Ts=N0B=¾2ykE[x2k]E[n2k]=S¾2xk!yk12ln(1+S¾2)xk12ln(1+S¾2)2B2B£12ln(1+S¾2)C=Blog2(1+SNR)bps(2)(1)bits/symbol(2)bits/secondsymbol50·tT12b1b21b1s1(t)2b2s2(t)x(t)=b1s1(t)+b2s2(t)x(t)s1(t);s2(t)b1;b2x(t)s1(t)s2(t)r1=ZT0x(t)s1(t)dt=b1E1+b2E12r2=ZT0x(t)s2(t)dt=b2E2+b1E21E1=RT0s21(t)dtE2=RT0s22(t)dts1(t)s2(t)E12=E21=RT0s1(t)s2(t)dt½,RT0s1(t)s2(t)dtpE1E2r1;r2b1;b2s1(t)s2(t)s1(t)6=Ks2(t)Kr1;r2b1;b2RT0s1(t)s2(t)=0r1=b1E1b1r2=b2E2b2NNsi(t);i=1¢¢¢Nsi(t)sj(t);j6=ifsi(t)g(1)FDM(2)TDMCDM3