mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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MORE MATH 21<br />
1.4.2 Channel<br />
The model used in the previous section is extended to allow for multiple transmit<br />
and receive antennas. The received vector (N r receive antennas) can be modeled<br />
as<br />
N,. L-l<br />
r W H Σ Σ 8^ι (0 (ί - re) + n(í), (1.45)<br />
¿=i *=o<br />
where g¿ is a vector of medium response coefficients, one per receive antenna.<br />
Also, unless otherwise indicated, all vectors are column vectors.<br />
In general, the medium responses from transmit antennas in different locations<br />
will have different path delays. We can handle this case by modeling all possible<br />
path delays and setting some of the coefficient vectors to zero.<br />
By substituting (1.33) into (1.45), we obtain the following model for the received<br />
signal:<br />
where<br />
N t K-\ , . oo<br />
KOhÊEV^W Σ ^m{t-rnT)sf{m)+n{t), (1.46)<br />
ΐ=1 fc=0 m=-oo<br />
is the channel response.<br />
e=o<br />
(1.47)<br />
1.4.2.1 Noise and interference models Here the noise model is extended for multiple<br />
receive antennas, and more general noise models are considered. We will still<br />
assume the noise has zero mean, i.e.,<br />
m n (i) 4 E{n(i)} = 0, (1.48)<br />
where boldface is used for column vectors. All vectors are JV r xl.<br />
The noise may be colored, meaning that there may be correlation from one time<br />
instance to another as well as from one antenna to another, and the covariance<br />
function may be a function of time. For multiple receive antennas, the correlation<br />
is defined as<br />
C„(íi,í 2 ) 4 E{[nft!) - m„(ti)][n(ta) - m n (i 2 )] H }, (1.49)<br />
where superscript "H" denotes conjugate transpose (Hermitian transpose). If t\ =<br />
t 2 + T and the correlation depends on both t 2 and τ, then it is considered nonstationary.<br />
If it only depends on τ, it is stationary and is then written as C n (r).<br />
We will still assume the noise is proper, also known as circular. With circular<br />
Gaussian noise, the I and Q components of n(i) are uncorrelated and have the same<br />
autocorrelation function, i.e.,<br />
E{n r (Í!)n;(í 2 )} = E{n i (í 1 )n*(í 2 )} = (0.5)C n (í 1 ,í 2 ) (1.50)<br />
E{n,.(tiK(t 2 )} = E{ni(iiK(t 2 )} = 0. (1-51)