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Digital Communications. EE549/449 FALL 2001 Lecture #26 Pulse Shaping Controlled Intersymbol Interference Wednesday October 24, 2001. Root Raised Cosine (RC) rolloff Pulse Shaping.

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digital communications
Digital Communications

EE549/449 FALL 2001

Lecture #26

Pulse Shaping

Controlled Intersymbol Interference

Wednesday October 24, 2001

root raised cosine rc rolloff pulse shaping
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 Nyquist’s 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
practical issues with pulse shaping
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
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
controlled isi
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 > 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
partial response signaling prs
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
Since h(t) = sinc(t/T) and R=1/T, the overall impulse response is



  • PRS changes the amplitude sequence ak a+k
  • a+k has a correlated amplitude span of N symbols since each a+k depends on the previous N values of ak
  • Also, when ak has M levels, a+k sequence has M+ > M levels
  • A whole family of PRS methods exists
  • Lets look at a few specific cases of PRS
duobinary signaling
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
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:

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:
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)
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
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)
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


    • Problem 3 can be solved by a technique known as precoding
    • Problem 4 is solved by a technique known as modified duobinary
summary of duobinary baseband system
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
Composite pulses arising from like and unlike

combinations of input impulse pair

example 30 duobinary coding
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