In this section, we present the capacity of wireless MIMO channels and show that it is greater than that of the wireline SISO channel.

The capacity of a communication channel is the maximum throughput at which data can be sent over the channel while maintaining a low probability of error. The capacity is measured in bits per channel use. Clearly, we would like to transmit over channels with high capacity.

Table 1: Diversity order and antenna gain for various spatial channels

The capacity of the wireline SISO channel (1.1) is given by [2]

(1.50)

where P is the transmission power

(1.51)

As we can see, for the wireline SISO channel, the capacity can be increased only if the transmission power is increased. This is not the case for wireless MIMO channels as shown next. The capacity of the wireless MIMO channel (1.39) is given by [1]

(1.52)

where

(1.53)

is the total transmission power radiating from the transmit antennas

(1.54)

and I is the identity matrix of size

(1.55)

"det" denotes the determinant of the matrix. Averaging (1.52) with respect to the Rayleigh distribution of the fading yields [1]

(1.56)

(It should be pointed out that the above expression is an approximation; however. for mid-to-high values of P it is a fairly accurate one). We define the multiplexing gain as

(1.57)

Under the same transmission power P, the multiplexing gain is

(1.58)

Thus, by using multiple antennas we can dramatically increase the throughput. If our main goal is power saving, and not increased throughput, we can use the MIMO architecture and have the same throughput as for the SISO channel, but with a much reduced transmission power. Usually, MIMO systems are used to simultaneously achieve both increased throughput and reduced power. In that case, we achieve multiplexing gain that is smaller than min{MN}.