p=R/W bits/s/Hz cret nsion,then the date rate R o=26 bits/s/Hz (2.17) which is the number of bits sent per two real dimensions(bits/2D). The average energy per symbol is E,=Ex;the average energy per second, i.e,the average power of x(),is P=E/T.Thus, P=2EW for PAM (2.17b) P=EW for OAM For the continuous-time channel,the signal-to-noise ratio(SNR)is defined as SNR=signal power noise power Nl For the discrete-time channel,the SNR is defined as (2E, =Ew No for PAM for QAM N。' where N is the dimension of the signal constellation under consideration. The relation PE/T shows that the SNR is changed.SNR-ET The channel capacity of a continuous-time band-limited AWGN channel is given by =Wlog:(1+SNR)=W+ b/s (2.18) (which is obtained with a Gaussian distribution overx().) The capacity of a real or complex discrete-time AWGN channel is given by E C=log:(1+SNR)=log,+N b/2D (2.19) regardless of whether it is real or complex.(The derivation of (2.19)is provided in Section 2.6.3) Since the channel supports W two-dimensional real symbols per second,the capacity is unchanged 下面研究PAM/QAM系统的性能，包括极限性能与未编码系统的错误概率。 2.6 Capacity of Diserete-Time Channels In this section,we will discuss the capacity of the discrete-time AWGN channel under 2-192-19  = R / W bits/s/Hz If the discrete-time channel sends b bits per real dimension, then the date rate R = b / T [b/s] for PAM or R = 2b / T [b/s] for QAM. In either case R = 2bW, so  = 2b bits/s/Hz (2.17) which is the number of bits sent per two real dimensions (bits/2D). ◼ The average energy per symbol is 2 | | E x s k =     E ; the average energy per second, i.e., the average power of x(t), is / P E T = s . Thus, P = 2EsW for PAM (2.17b) P = EsW for QAM ◼ For the continuous-time channel, the signal-to-noise ratio (SNR) is defined as 0 signal power noise power P SNR N W = = For the discrete-time channel, the SNR is defined as 0 2 2 0 2 , for PAM , for QAM s d N s E E E N SNR N E N      = = =    where N is the dimension of the signal constellation under consideration. The relation P = Es/T shows that the SNR is unchanged. 0 / E T s SNR N W = ◼ The channel capacity of a continuous-time band-limited AWGN channel is given by [ / ] 2 2 0 log (1 ) log 1 b s P C W SNR W N W   = + = +     b/s (2.18) (which is obtained with a Gaussian distribution over x(t).) The capacity of a real or complex discrete-time AWGN channel is given by [ / 2 ] 2 2 2 log (1 ) log 1 s b D E C SNR N   = + = +     b/2D (2.19) regardless of whether it is real or complex. (The derivation of (2.19) is provided in Section 2.6.3) Since the channel supports W two-dimensional real symbols per second, the capacity is unchanged. 下面研究 PAM/QAM 系统的性能，包括极限性能与未编码系统的错误概率。 2.6 Capacity of Discrete-Time Channels In this section, we will discuss the capacity of the discrete-time AWGN channel under