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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66 ZERO-FORCING DECISION FEEDBACK EQUALIZATION<br />
where r = Q H x. Because Q is orthonormal, e is complex Gaussian with zero mean<br />
and covariance iV () I.<br />
Since R is upper triangular, we can detect SK with no ISI. We then subtract the<br />
influence of SK on the r and detect SK-\- The process continues until all symbols<br />
have been detected. Mathematically,<br />
K-\<br />
Vk„ = i-fe,, - Σ<br />
ñ ( fc n,fc)Sfc (3.46)<br />
fc=fc„ + l<br />
Sk,, = detect(j/fc„,\/^rñ(fc(),fco)), (3.47)<br />
where R(r, c) denotes the element in row r and column c of R.<br />
Now suppose N r > N t . To reduce the number of equations, we initially perform<br />
matched filtering, giving<br />
H"x, (3.48)<br />
which can be modeled as<br />
y \= A/ËT(H H H)S + H H n. (3.49)<br />
Notice that the noise on y is no longer uncorrelated, but now has covariance<br />
7V()H H H. So, before performing QR factorization, we need to whiten the noise.<br />
This can be done by multiplying by square matrix F H , which can be obtained by<br />
Cholesky decomposition of (Η Η Η)"\ i.e., FF H = (H^H)" 1 .<br />
3.5 AN EXAMPLE<br />
In practice, the ZF DFE is usually not used, as it tends to enhance the noise. Thus,<br />
we will wait until Chapter 5 to discuss an example.<br />
3.6 THE LITERATURE<br />
As DFE is revisited in Chapter 5, we will only mention references related specifically<br />
to this chapter.<br />
The idea of connecting the FBF prior to the FF can be found in [Ari92]. In<br />
synchronous CDMA, triangularization and ZF DFE is developed in [Due93].<br />
For block equalization, Cholesky factorization is applied to triangularize the<br />
channel after matched filtering in [Cro92]. In [Kal95], Cholesky factorization is<br />
motivated by the desire to whiten the noise after matched filtering.<br />
PROBLEMS<br />
The idea<br />
3.1 Consider the Alice and Bob example. Suppose instead that r\ = —1 and<br />
Γ2 = 4. Also, so = +1.<br />
a) What is the value of ζ λ with ZF DFE?