-Shannon bound(Rayleigh with CSITR) Shannon bound (Rayleigh with CSIR) -Shannon bound (AWGN) 3 意2 以 00 5 0 10 15 20 SNR(dB) (b) Figure 7.11.Capacity of the flat Rayleigh fading channel with CSIT and CSIR (a)1D signaling.(b)2D signaling Unavailable channel-state information: In the absence of channel-state information at both transmitter and receiver,for i.i.d. states h the full solution is available for circularly complex distribution of In fact.it has bee wn that the capacity-achieving distribution has a discrete iid.power and irrelevant phas .No general closed-form is known for this dist ibution:however,asymptoti results are available.Specifically,for relatively low values of the average signal-to-noise ratio (SNR)<8dB.only two signaling levels x=0 and x=va and with respective probabilities (1-P.P)suffice.where ap =P )and hence the optimum modulation scheme is on-off. Clearly,the capacity-achieving codes in this case deviate markedly from Gaussian codes which achieve capacity when CSI is available either to the receiver or to both receiver and transmitter. 7.3.3 Capacity of the Independent Fading Channels with Constrained-Constellation Capacity with BPSK signaling With BPSK modulation and coherent detection,the discrete-time model of a independent flat-fading channel is given by 2020 -10 -5 0 5 10 15 20 0 1 2 3 4 5 6 7 SNR (dB) Capacity (bits per 2D symbol) Shannon bound (Rayleigh with CSITR) Shannon bound (Rayleigh with CSIR) Shannon bound (AWGN) (b) Figure 7.11. Capacity of the flat Rayleigh fading channel with CSIT and CSIR. (a) 1D signaling. (b) 2D signaling  Unavailable channel-state information: In the absence of channel-state information at both transmitter and receiver, for i.i.d. states {hk} the full solution is available for circularly complex distribution of {hk}. In fact, it has been shown that the capacity-achieving distribution has a discrete i.i.d. power |Xk| and irrelevant phase. No general closed-form is known for this distribution; however, asymptotic results are available. Specifically, for relatively low values of the average signal-to-noise ratio (SNR)<8dB, only two signaling levels x=0 and x   and with respective probabilities (1 , )  P P   suffice, where av P P )    ; and hence the optimum modulation scheme is on-off. Clearly, the capacity-achieving codes in this case deviate markedly from Gaussian codes, which achieve capacity when CSI is available either to the receiver or to both receiver and transmitter. 7.3.3 Capacity of the Independent Fading Channels with Constrained-Constellation  Capacity with BPSK signaling With BPSK modulation and coherent detection, the discrete-time model of a independent flat-fading channel is given by