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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THE MATH 125<br />
We would then identify the best candidate using<br />
jb = arg min C m (io,j). (6.38)<br />
We would then store the path metric for state ¿o at time m,<br />
and update the path history<br />
P m (.ia) = C m (ia,jb), ( 6·39 )<br />
Qm(io) = [qm(io),Qm-l(jb)\- (6.40)<br />
This process would be repeated for each possible state i at time m. When finished,<br />
m would be incremented and overall process would be repeated.<br />
The last iteration would be at symbol period m^. After updating the path<br />
metrics and path histories, we would then determine which state has the best path<br />
metric:<br />
ib = arg min P m (i)- (6-41)<br />
i=0 ... Ns(m)<br />
The detected values would then be determined from Q m {ib)·<br />
We can shorten the path history at iteration m by only storing symbol values<br />
from m — (L — 2) and earlier, as the current state determines symbol values for<br />
times m through m — (L — 2) and the previous state determines the symbol value<br />
for time m — (L — 1).<br />
6.3.2 SISO TDM scenario<br />
Now let's consider MLSD for the SISO TDM scenario. The MLSD solution is<br />
the hypothetical sequence of symbols that maximizes the likelihood of the received<br />
signal, given the transmitted sequence equals the hypothesized sequence. Unlike<br />
the LE and DFE formulations, we will not assume that the received signal has been<br />
pre-processed by a filter matched to the pulse shape. However, we will find that<br />
the result can be expressed in terms of such pre-processing.<br />
We basically follow the derivation given in [Ung74]. Let S p denote the set of<br />
possible sequences. For a block of N s symbols with M-ary modulation, there are<br />
M N ' elements in the set. Using q to denote an hypothesized sequence, the MLSD<br />
solution is<br />
{s} = arg max Pr{r(í) Vt|s = q}. (6.42)<br />
qSSp<br />
Next we note that for a particular value of t = to, using model equations (1.27) and<br />
(1.23) gives<br />
ΛΓ,-1<br />
Pr{r(i 0 )|s = q} = Pr{n(t„) = r(t 0 ) - y/Ë~ s ]Γ h(t 0 - mT)q{m)}<br />
m=0<br />
1 rvn Í -Irfo) - ν^ΓΣ^Γο 1 Ht - mT)q{m)\*<br />
~ nN eXP 0 \ N 0<br />
Since the noise is assumed white, the likelihood of multiple received values is simply<br />
the product of the individual likelihoods. Working in the log domain, we end up