AWGN的离散时间基带等效模型 Degree of freedom X( x y xb m]=xr[m]+jxo[m] 外回=网+圆{x咧=y四+ ns[m]=n, [m]+ ing ['m 噪声部分的统计特性n[m]~(0,N) a Given the bandwidth b and the time duration t the degree of freedom is 2BT. R,n]=Rn]=8[n] Rm[n]= 後照k季的 AWGN Channel ML decoding a Discrete-time model a At the receiver, maximum likelihood decoding is y[m]=x[m]+w[m] y=(l[]…y[N decoder where m=1…N,wm-(a=N2) a ML decoding algor a Encoding x'=arg maxpyf1v (24(2AD a In AWGN channel, this is equivalent to n Data transmission rate is rake bitslchannel use x=arg max 後照大季 x0後人手AWGN的离散时间基带等效模型 xb m yb m nb m yb m= xb m+ nb m nI nQ nInQ R n = R n = R N0  n, n =0       b I Q b I Q  xb m = xI m + jxQ m   y m = y m + jy m n m = n m + jn m  噪声部分的统计特性 nb m ~ (0,N0) 2 17 X (t) t → t → X t → ◼ Given the bandwidth B and the time duration T, the degree of freedom is 2BT. Degree offreedom 18 AWGNChannel ◼ Discrete-time model ym = xm+wm, where m = 1,,N, wm~ (0,  2 = N 2) 0 ym wm xm encoder ◼ Encoding Message i1,2,,  xi = (xi 1,, xi N) log  Data transmission rate is R = 2 bits/channel use N ML decoding ◼ At the receiver, maximum likelihood decoding is applied. ◼ ML decoding algorithm decoder y = (y1,, yN) iˆ ( ) * k for all xk x = arg max p y x ◼ In AWGN channel, this is equivalent to 2 k x * = arg max y − x for all xk 19 20