Shannon bound (Rayleigh) Shannon bound (AWGN) 2.5 2 1.5 1 0.5 0 15 SNR (dB) Figure 7.9.Capacity of the independent Rayleigh fading channel with CSIR.Assuming 1D signaling. Perfect channel-state information available to tro nsmiter and receiver Assume that the channel state information is available to both receiver and transmitter in a causal manner.Under the input-power constraint El]P,the capacity of the fading channel is given by =E, suplog( bits/2D (7.20) N。刀 where the supremum is over all nonnegative power assignments satisfying E,[P(v)]sP (7.21) The optimal power assignment P'(v)satisfies [Goldsmith97 o-(日-) (7.22) 11 ，y2% 0, Y<Yo 17 17 -10 -5 0 5 10 15 0 0.5 1 1.5 2 2.5 3 SNR (dB) Capacity (bits/symbol) Shannon bound (Rayleigh) Shannon bound (AWGN) Figure 7.9. Capacity of the independent Rayleigh fading channel with CSIR. Assuming 1D signaling.  Perfect channel-state information available to transmitter and receiver: Assume that the channel state information is available to both receiver and transmitter in a causal manner. Under the input-power constraint 2 [| | ] E k av x P  , the capacity of the fading channel is given by CSITR 0 ( ) suplog 1 s v P vv C N            E bits/2D (7.20) where the supremum is over all nonnegative power assignments satisfying   av ( ) Ev s Pv P  (7.21) The optimal power assignment * ( ) P v s satisfies [Goldsmith97] * 1 0 ( ) s N P v  v          (7.22) or * 0 0 av 0 1 1 , ( ) 0, P v s P               