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 IDEA 153<br />
Traditionally, we still call it MAPSD, even though strictly speaking its ML symbol<br />
detection. In general, ML detection can be viewed as a special case of MAP<br />
detection in which a symbol or sequence values are assumed equi-likely.<br />
7.1.2 Soft information<br />
So far, we have concentrated on recovering the binary symbols being transmitted.<br />
In reality, we are interested on underlying information being sent. Often a code is<br />
used that relates the information to the transmitted symbols. Consider the Alice<br />
and Bob example in Table 1.1, in which there are three possible messages. Notice<br />
that two binary symbols are used to represent the message. Because two binary<br />
symbols can represent up to four messages, there is one pattern that is not used<br />
(s\ = —1, S2 = +1). This fact can be used when decoding the message.<br />
In the Alice and Bob example, when we perform MAPSD, the detected values are<br />
Si = —1, S2 — +1, an invalid combination. That means there is an error somewhere<br />
in the detected sequence. But where? To answer this question, we need to know<br />
more than just the detected symbol values. We need to know how confident we are<br />
of each symbol value.<br />
Soft information generation is about assigning a confidence level or likelihood to<br />
each symbol value. Ideally it is a function of the likelihood that a symbol equals<br />
a certain value, given the received signal (Pr{s 2 = +1|τ~})- But wait a minute. In<br />
the previous subsection, we used symbol metrics related to symbol likelihoods in<br />
MAPSD. In fact, they were proportional to symbol likelihoods. Thus, if we are<br />
using MAPSD, then we can use the symbol metrics as the soft information!<br />
7.1.2.1 Using soft information But what do we do with the soft information?<br />
Consider the Alice and Bob example in Table 1.1. Suppose we use MAPSD and<br />
form the symbol metrics given in Table 7.1. Notice that the symbol metrics for the<br />
two symbol values do not add to one. That is because we used metrics proportional<br />
to a posteriori likelihoods. Though not necessary, we could normalize each pair by<br />
its sum to get likelihoods that add to one.<br />
To decode the message using the soft information, we form message metrics<br />
by multiplying the symbol metrics corresponding to a particular message. For<br />
example, to form a metric for message 1, we would multiply the symbol metrics<br />
L(s 1 = +1) = 0.96975 and L(s 2 = -1) = 0.90783, giving 0.8804. We would need to<br />
form metrics for all possible messages, as shown in Table 7.2. The decoded message<br />
is the one with the largest metric, in this case message 3, which is correct.<br />
Table 7.1<br />
Examplo of MAPSD symbol metrics<br />
Symbol Metric Value<br />
L(s 1 = +1) 0.96975<br />
L(si = -1) 1.4529<br />
LÍS2 = +1) 1.5149<br />
L(s 2 = -1) 0.90783