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 163<br />
Figure 7.1<br />
MAPSD trellis diagram, three-path channel.<br />
are 0, 1,2, and 3. One possible transition is S t -i = 0, S t = 0. This corresponds to<br />
the sequence 6t-2 = +1> öt—i = +1, bt = +1. Notice from the trellis diagram that<br />
not all state transitions are possible, as the values for b t -i for states at times ί — 1<br />
and t must be consistent.<br />
Now we are ready to write the symbol metric in terms of state transition likelihoods.<br />
Recall the fact from probability theory that<br />
Ρτ{Α} = Σ PI{A\BÍ}PI{BÍ} (7.26)<br />
i<br />
where the ß; are independent and span the probability space. By defining the B¡<br />
to be the state transitions, the symbol metric in (7.25) becomes<br />
3 3<br />
P(bt-i = +1) = Σ Σ ϊΜ 5 «-! = m '> S * = m < 6 *-i = +1 > y i T }· ( 7·27 )<br />
Prom the trellis diagram, we see that half of the terms on the right-hand side will<br />
be zero, as the state transition and bt-i value are inconsistent. When they are<br />
consistent, we have the added requirement that bt-i = +1. Thus, we can write<br />
(7.27) as<br />
3 3<br />
P(6 t _! =+1) = J2 ^ Pr{5 t _i =m',S t = m,F T 1 }Tr(m',m)/(m',m,+l),<br />
τη'=0 m=0<br />
(7.28)<br />
where Tr(m', m) denotes a function based on the trellis that is 1 if the transition<br />
is valid and zero otherwise. The term I(m',m, +1) is 1 if the transition is valid<br />
and 6 t _i = +1. While the term Tr(m',m) is redundant in this case, we will find it<br />
useful later.