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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

EE549/449 FALL 2001

Lecture #26

Pulse Shaping

Controlled Intersymbol Interference

Wednesday October 24, 2001


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

  • 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

  • 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)

  • 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


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


  • Since h(t) = sinc(t/T) and R=1/T, the overall impulse response is

    and

    where

  • 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

  • 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:


  • 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:


  • 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

        Note:

      • 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

    • 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


    Duobinary waveform arising from an example binary sequence


    Example 30: (Duobinary Coding)

    (See example 2.4)

    • Binary sequencesxk 0 0 1 0 1 1 0

    • Amplitude: ak1 -1 -1 1 -1 1 1 -1

    • Coding Rule:

    • Decoding Rule:

    • Output sequence


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