TABLE OF CONTENTS In the previous section, the design criteria maximize the diversity and coding gains for a fixed transmission rate and are based on the average PEP. We take here an alternative approach exploiting information theory results and aim to achieve the diversity-multiplexing trade-off, whose theoretical background has been outlined in Chapter 4.
Fast fading MIMO channels constitute a relatively simple situation with respect to slow fading channels. The reason for this is that the transmission capability over fast fading channels is described by a single quantity, which is the ergodic capacity
| (5.25) |  |
When the channel realizations are known to the transmitter (CSIT scenario), we already know that the transmission of independent streams in the directions of the eigenvectors of the channel matrix H decouples the system into n ? min{ n t, n r} parallel data pipes. For a total transmission rate R, each layer k can then be encoded using a capacity-achieving Gaussian code with rate R k such that 
R k = R, ascribed a power ? k( Q) (the eigenvalues of Q can be seen as the powers attached to each layer) and can be decoded independently of the other layers. The optimal power allocation 
is given by the water-filling allocation strategy in (4.7) described in Section 4.1. The resulting ergodic capacity is then written as (4.6)
| (5.26) |  |
with ?
