It has been shown by many authors that there exists a tremendous gain to be had when using
MIMO technology. One approach to quantify these gains is through the use of information theory.
The best way to approach this is to consider the scalar channel first. For this case the system capacity
is given as [38]
(Bps/Hz) (9.25)
where h is the channel response and SNR is the signal-to-noise ratio at the receiver antenna. Note that
this type of channel is commonly called SISO, single-input-single-output. As we increase the number
of receiver antennas the system capacity increases and thus we have the following assuming M
receive antennas.
(Bps/Hz) (9.26)
Note this type of channel is commonly called SIMO, single-input-multiple-output. The performance
gain shows up as an increase logarithmically in the average capacity. The flip side to this previous
example is a system that uses N transmit antennas.
(Bps/Hz) (9.27)
Now this type of channel is commonly called MISO, multiple-input-single-output. Normalizing
by N forces the total transmit power to be fixed.
Next we discuss the famous capacity equation, where N is the number of transmit antennas and M
is the number of receive antennas.
(Bps/Hz) (9.28) C4 log2 c det aIM
SNR
N
# H # H*bd
C3 log2 c1
SNR
N
# aN
i1
Zhi Z2 d
C2 log2 c1 SNR # aM
i1
Zhi Z2 d
C1 log2 [1 SNR # ZhZ2]
502 CHAPTER NINE
Modulation
Data In
x1
x2
x3
y1
y2
y3
MIMO
Receiver
Demodulation
Data Out
h11
h12 h13
FIGURE 9.
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