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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180 PRACTICAL CONSIDERATIONS<br />
8.3.2 Time-varying channel and known symbol sequence<br />
Next consider the case of a time-varying channel and assume we know all the<br />
transmitted symbols. For simplicity, we assumed a symbol-spaced receiver and<br />
consider a single path channel with time-varying coefficient g{qT). We can model<br />
a vector of symbol-spaced received values r as<br />
r = Sg + n, (8.15)<br />
where S is a diagonal matrix with the known symbol values, g is a vector of the<br />
channel coefficient value at different times, and n is a vector of noise values.<br />
8.3.2.1 Filtering With the filtering approach, we use some or all of the received<br />
samples to estimate the channel coefficient at each moment in time. Using all the<br />
samples for each estimate, the vector of coefficient estimates is obtained by a matrix<br />
multiplication, i.e.,<br />
g = W f/ r, (8.16)<br />
where different columns of matrix W correspond to filters for estimating the channel<br />
coefficient at different times.<br />
Similar to MMSE linear equalization, MMSE channel estimation (also known as<br />
Wiener filtering) estimates the channel at time mT using<br />
where<br />
g(mï')=w H r, (8.17)<br />
w = C; 1 p = (SC fl S H + C n )- 1 p (8.18)<br />
C 9 = E{gg"} (8.19)<br />
p = E{rg*(kT)}. (8.20)<br />
The values for C g and p depend on how correlated the channel coefficient is from<br />
one symbol period to the next.<br />
The correlation between the channel coefficient at time mT and (m+d)T becomes<br />
small as |ef| becomes large. As a result, it is reasonable to only use received values<br />
in the vicinity of mT when estimating the channel at time mT. This gives rise to<br />
a transversal Wiener filter. Except at the edges, the coefficients are the same for<br />
different values of m.<br />
A simpler transversal filtering approach is the moving average filter. With this<br />
approach, the channel coefficient at time mT is estimated using<br />
where the number of filter taps is 2N + 1.<br />
N<br />
g{mT) = Σ s*{m)r{m'T), (8.21)<br />