In this chapter, we will look at the capacity of MIMO fading channels and discuss transceiver architectures that extract the promised multiplexing gains from the channel. We particularly focus on the scenario when the transmitter does not know the channel realization. In the fast fading MIMO channel, we show the following:

• At high SNR, the capacity of the i.i.d. Rayleigh fast fading channel scales like nmin log SNR bits/s/Hz, where nmin is the minimum of the number of transmit antennas nt and the number of receive antennas nr. This is a degree-of-freedom gain.

• At low SNR, the capacity is approximately nrSNR log2 e bits/s/Hz. This is a receive beamforming power gain.

• At all SNR, the capacity scales linearly with nmin. This is due to a combination of a power gain and a degree-of-freedom gain.

Furthermore, there is a transmit beamforming gain together with an opportunistic communication gain if the transmitter can track the channel as well.

Over a deterministic time-invariant MIMO channel, the capacity-achieving transceiver architecture is simple (cf. Section 7.1.1): independent data streams are multiplexed in an appropriate coordinate system (cf. Figure 7.2). The receiver transforms the received vector into another appropriate coordinate system to separately decode the different data streams. Without knowledge of the channel at the transmitter the choice of the coordinate system in which the independent data streams are multiplexed has to be fixed a priori.