Digital Communications

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Digital Communications

• EE549/449 FALL 2001
• Lecture 26
• Pulse Shaping
• Controlled Intersymbol Interference
• Wednesday October 24, 2001

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Root Raised Cosine (RC) rolloff Pulse Shaping

• We will see later in the semester that the noise
  is minimized at the receiver by using a matched
  filter
• If the transmit filter is H(f), then the receive
  filter should be H(f)
• The combination of transmit and receive filters
  must satisfy Nyquists first method for zero ISI
• Transmit filter with the above response is called
  the root raised cosine rolloff filter
• Root Raised Cosine rolloff pulse shapes are used
  in many applications such as US Digital Cellular,
  IS-54 and IS-136

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Practical Issues with Pulse Shaping

• Like the Sa(.) pulse, RC rolloff pulses extend
  infinitely in time
• However, a very good approximation can be
  obtained by truncating the pulse
• E.g., we can make h(t) extend from -3Tb to 3Tb
• RC rolloff pulses are less sensitive to timing
  errors than Sa(.) pulses
• Larger values of ? are more robust against timing
  errors
• US Digital Cellular (IS-54 IS-136) uses root RC
  rolloff pulse shaping with ? 0.35
• IS-95 uses pulse shape that is slightly different
  from RC rolloff shape
• European GSM uses Gaussian shaped pulses

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• Implementation of Raised Cosine Pulse
• Practical pulses must be truncated in time
• Truncation leads to sidelobes - even in RC pulses
• Can be digitally implemented with an FIR filter
• Analog filters such as Butterworth filters may
  approximate the tight shape of this spectrum
• Sometimes a square-root raised cosine spectrum
  is used when identical filters are implemented at
  transmitter and receiver
• This has to do with matched filtering

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Controlled ISI

• To achieve zero ISI, we have seen that it is
  necessary to transmit at below the Nyquist rate
• Is it possible to relax the condition on zero ISI
  and allow for some amount of ISI in order to
  achieve a rate gt 2B?
• Idea is to introduce some controlled amount of
  ISI instead of trying to eliminate it completely
• ISI that we introduce is deterministic (or
  controlled) and hence we can take care of it at
  the receiver
• How do we do this?
• Controlled amount of ISI is introduced by
  combining a number of successive binary pulses
  prior to transmission
• Since the combination is done in a known way, the
  receiver can be designed to correctly recover the
  signal
• We will now discuss different methods of
  controlled ISI

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Partial Response Signaling (PRS)

• Also known as Doubinary signaling, Correlative
  coding, Polybinary
• PRS is a technique that deliberately introduces
  some amounts of ISI into the transmitted signal
  in order to ease the burden on the pulse-shaping
  filters
• It removes the need to strive at achieving
  Nyquist filtering conditions, and high rolloff
  factors
• This strategy involves two key operations
• Correlative Filtering (CF)
• Digital Precoding (DP)
• CF purposely introduces some ISI, resulting in a
  pulse train with higher amplitude levels and
  correlated amplitude sequences
• Nyquist rate no longer applies since the
  correlated symbols are no longer independent
• Hence higher signaling rate can be used

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• The transfer function H(f) is equivalent to the
  Tap Delay Line model

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• Since h(t) sinc(t/T) and R1/T, the overall
  impulse response is
• and
• where
• PRS changes the amplitude sequence ak ? ak
• ak has a correlated amplitude span of N symbols
  since each ak depends on the previous N values
  of ak
• Also, when ak has M levels, ak sequence has M gt
  M levels
• A whole family of PRS methods exists
• Lets look at a few specific cases of PRS

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Duobinary Signaling

• Also called class 1 signaling
• Simplest form of PRS with M 2, N 1, Co C1
  1
• The input data sequence is combined with a 1-bit
  delayed version of the same sequence (the
  controlled ISI) and then passed through the
  pulse-shaping filter
• Duobinary Encoder

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• Each incoming pulse is added to the previous
  pulse
• The bit or data sequence yk are not independent
• Each yk digit caries with it the memory of the
  prior digit
• It is this correlation between digit that is
  considered the controlled ISI which can be easily
  removed at the receiver
• Impulse Response of Duobinary Signal

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• From
• it can be shown that (exercise - show this)
• Impulse response h(t) for the duobinary scheme is
  simply the sum of two sinc waveforms, delayed by
  one bit period w.r.t each other

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• Duobinary signaling can be interpreted as
  adjacent pulse summation followed by rectangular
  low pass filtering
• Encoder takes a 2 level waveform and produces a 3
  level waveform
• Duobinary Decoding
• The role of the receiver is to recover xk from yk
• Transmitted signal (assuming no noise) is
• xk can assume one of 2 values ?A, depending on
  whether the k-th bit is 1 or 0
• Since yk depends on xk and xk-1, yk can have 3
  values (no noise)

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• In general, (M-ary transmission), PRS results in
  2M-1 output levels
• Detection involves subtracting xk-1 decisions
  from yk digits such that
• The detection process is the reverse operation at
  the transmitter
• Decision rules is
• A major drawback to this technique is that once
  errors are made, they tend to propagate through
  the system

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• A Duo-binary Baseband System
• Advantage
• It permits transmission at the Nyquist rate
  without the need for linear phase rectangular
  pulse shaping
• Disadvantages
• There is no one to one mapping between detected
  ternary symbol and the original binary digits (2
  ? 3)

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• Require more power
• Ternary nature of duobinary signal requires about
  3 dB greater SNR compared to ideal signaling
  (i.e, binary) for a given PB
• The decoding process results in propagation of
  errors
• Because output data bits are decoded using
  previous data bit, if it is in error then the new
  output will be in error, and so on
• In other words, errors will propagate through the
  system
• It is ineffective for AC coupled signal
• PSD has substantial values at zero making it
  unsuitable for use with AC coupled transmission
• Note
• Problem 3 can be solved by a technique known as
  precoding
• Problem 4 is solved by a technique known as
  modified duobinary

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Summary of Duobinary Baseband System

• In general, (M-ary transmission), PRS results in
  2M-1 output levels
• Detection involves subtracting xk-1 decisions
  from yk digits such that
• Decision rules is

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• Composite pulses arising from like and unlike
• combinations of input impulse pair

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• Duobinary waveform arising from an example binary
  sequence

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Example 30 (Duobinary Coding)

• (See example 2.4)
• Binary sequences xk 0 0 1 0
  1 1 0
• Amplitude ak 1 -1 -1 1 -1
  1 1 -1
• Coding Rule
• Decoding Rule
• Output sequence