basis function,and it can be implemented by a correlator.See Fig.2.2. Tp1(0 x(t) fo Tp2(0 ox ↑p Figure 2.2 The correlative demodulator The computation in (2.2)can be more easily implemented by a matched filter since it can be a x0.0dh=xo)*.(T-儿 where"*"denotes convolution operation.Matched-filter demodulator is illustrated in Fig. 2.3. p1(T-0 pMT-用 Figure 2.3 The matched-filter demodulator 2.2 The Ideal AWGN Channel The continuous-time ideal band-limited AWGN channel is modeled by 0=x(0+n0 where()is the channel input signal with an average power of P and a positive-frequency bandwidth of W Hz,and n(t)is AWGN with one-sided p.s.d.No. 02-3 basis function, and it can be implemented by a correlator. See Fig. 2.2. 0 () T  dt  0 () T  dt  0 () T  dt  x1 x2 xN φ1(t) φ2(t) φN(t) x(t) Figure 2.2 The correlative demodulator The computation in (2.2) can be more easily implemented by a matched filter since it can be written as 0 ( ) ( ) ( )* ( ) T n n t T x t t dt x t T t   = = −  where “*” denotes convolution operation. Matched-filter demodulator is illustrated in Fig. 2.3. φ1(T-t) φN(T-t) x(t) x1 xN Figure 2.3 The matched-filter demodulator 2.2 The Ideal AWGN Channel The continuous-time ideal band-limited AWGN channel is modeled by y(t) = x(t) + n(t) where x(t) is the channel input signal with an average power of P and a positive-frequency bandwidth of W Hz, and n(t) is AWGN with one-sided p.s.d. N0. 0 W fc W -fc