TABLE OF CONTENTS Let us consider now a MISO system with n T transmit antennas, where the channels are time-invariant FIR filters. Using a block transmission with CP, in this case it is possible to derive the optimal transmission strategy in closed form. More specifically, assuming as optimization criterion the maximization of the mutual information, the optimal coding strategy was derived in [10] and is reported here below. We denote with N the block length (without the CP) and with L the channel order (equal to the CP length).
The optimal coding strategy for LTI channels is OFDM, with proper power/bit allocation across the sub-carriers;
Denoting by H j( k) the value assumed by the jth channel transfer function over the kth frequency bin, I u the set of sub-carriers where a nonnull power is loaded, and ? j( k) 2 the power allocated on the kth subcarrier in the jth transmit antenna, the power ? j( k) 2 is equal to
| (6.103) |  |
where ( x) + ? max( x, 0). The set of indices I u and the constant K, are such that the average power constraint is satisfied, i.e., 
;
If no channels have zeros on the grid z k = e j 2 ?k / N, with k integer, all antennas transmit over the same portion of the available spectrum (in other words, if...
