Parallel Gaussian channels. Consider two parallel complex Gaussian channels with channel gains h1 = 1 + j,
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Parallel Gaussian channels. Consider two parallel complex Gaussian channels with channel gains h1 = 1 + j, h2 = −3j and noise covariances N1 = 1, N2 = 2. Assume that the transmitter knows the channel characteristics.
(a) At “low” SNR, which of the two channels would you use?
(b) For what values of net input power P would you start using both channels?
(c) Plot the capacity as a function of net input power P using the waterfilling power allocation. Also plot for comparison the capacity attained if the transmitter does not know the channel characteristics, and splits power evenly across the two channels.
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