Tutorial 17 & Partial response signaling and Quadrature partial response modulation (QPR)
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Tutorial 16
By Charan Langton
Signal Processing and Simulation Newsletter
Partial Response signaling and Quadrature Partial Response (QPR) modulation
Nyquist limit states that the number of symbols you can safely transmit in a channel
of bandwidth 1 Hz that has intersymbol interference is 2 symbols per second. But to
achieve this bandwidth efficiency you need a brick wall filter, which is not build able.
Raised cosine signaling helps counter ISI but at the cost of increased bandwidth.
Fact 1
:
A channel with no ISI using a raised cosine
signaling with alpha = 0, allows us to successfully transmit a
symbol rate equal to twice the bandwidth.
Fact 2
:
Since practical alpha is around .2 to .3, the realistic
symbol rate possible is only (1 +
α
)W, with
W as the
excess bandwidth over the theoretical limit.
One of the main reasons we can not transmit 2 symbols per Hz is intersymbol
interference. Raised cosine signaling is one way to counter ISI. But it limits the
symbol rate that can be safely transmitted.
Is there some other way that also counters
ISI but allows us to achieve 2 symbols per Hz of bandwidth?
Partial Response signaling, also called Quadrature Partial Response (QPR) a concept
that is used both for pulse shaping and as a way to modulate information was
proposed by Adam Lender in 1964. The technique also goes by the general name of
correlative coding
.
There is an alphabet soup here that is often confusing.
Partial response, correlative
coding, duobinary, modified duobinary, Class I coding
, are all names for the same
thing.
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Intersymbol interference can be defined as spreading of symbol energy into adjacent
symbol. The result of which is that the adjacent symbol shape is corrupted. However,
with raised cosine signaling, the interference can be controlled such that if it is zero at
the slicer timing pulse, then its effect is negated. It does not matter how much ISI
distorts the signal as long as we know at the time of the sampling instant what the
amount of that interference is. This amount is zero for raised cosine signaling because
the signal shape (a sinc function) is forced to pass through zero as shown in Fig. 1.
Although the interference is present, it is zero just at the instant we sample the signal
to make decision about if it±s a 0 or a 1. This means that at the sampling instant, the
sampled voltage belongs only to the pertinent symbol, so the decision based on this
value is likely to be correct.
And that±s the concept of
controlled introduction of ISI
.
1
2
3
4
Interference into Symbol 4
from symbols 1, 2 and 3 are all zero.
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 Spring '11
 Tutorials
 Signal Processing, qpr, partial response

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