This document discusses the capacity of fading channels with channel side information. It presents the following key points: 1) When the channel is known at both the transmitter and receiver, the optimal strategy is water filling for power adaptation and variable rate coding to achieve capacity. 2) When the channel is only known at the receiver, having channel information at the transmitter does not provide any additional capacity benefit if fading is independent and identically distributed and transmit power is constant. 3) Suboptimal strategies like channel inversion aim to maintain a constant received signal-to-noise ratio but suffer capacity losses, especially under severe fading conditions.

1. Capacity of Fading Channels With Channel Side Information Goldsmith, A.J. Varaiya, P.P. California Inst. of Technol., Pasadena, CA; IEEE Transactions on Information Theory Publication Date: Nov 1997 On page(s): 1986-1992 Volume: 43, Issue: 6 203

5. Channel Known at Tx & Rx J. Wolfowitz, Coding Theorems of Information Theory , 2nd ed. New York: Springer-Verlag, 1964. Channel Capacity Set of Discrete Memoryless channels Probability of channel being in state s

6. Channel Known at Tx & Rx AWGN Channel Capacity ( Received SNR  ) Channel Bandwidth define: then: Fading Channel Capacity

8. Channel Known at Tx & Rx

9. Channel Known at Tx & Rx

13. Sub-optimal (Channel Inversion) Constant Received SNR Channel is no longer a fading channel It becomes AWGN

14. Sub-optimal (Truncated Channel Inversion)

16. Capacity in log-normal Fading

17. Capacity in Rayleigh Fading

18. Capacity in Nakagami Fading