In this exercise we study the price of channel inversion.
1. Consider a narrowband Rayleigh flat fading SISO channel. Show that the aver- age power (averaged over the channel fading) needed to implement the channel inversion scheme is infinite for any positive target rate.
2. Suppose now there are L> 1 receive antennas. Show that the average power for channel inversion is now finite.
3. Compute numerically and plot the average power as a function of the target rate for different L to get a sense of the amount of gain from having multiple receive antennas. Qualitatively describe the nature of the performance gain.