Solve the following problem:
Consider a deterministic MISO (NT, 1) channel with AWGN and channel vector h. The received signal in any signal interval may be expressed as
y = hs + η
Where y and η are scalars.
a. If the channel vector h is known at the transmitter, demonstrate that the received SNR is maximized when the information is sent in the direction of the channel vector h, i.e., s is selected as s = (h*/||h|| )s’
(The alignment of the transmit signal in the direction of the channel vector h is called transmit beam forming.)
b. What is the capacity of the MISO channel when h is known at the transmitter?
c. Compare the capacity obtained in (b) with that of a SIMO channel, when the channel matrix h is identical for the two systems.