SungkyunKwan Univ Communication Systems Chapter. 7 Baseband pulse Transmission by Cho Yeon Gon

Contents zChapter Introduction 7.2 Matched Filter 7.3 Error Rate Due to Noise 7.4 Intersymbol Interference 7.5 Nyquist’s Criterion for Distortionless Baseband Binary Transmission 7.6 Correlative-Level Coding 7.7 Baseband M-ary PAM Transmission 7.8 Tapped-Delay-Line Equalization 7.9 Adaptive Equalization 7.10 Eye Pattern

7.1 Introduction zCommunication transmission 1. Baseband transmission : not modulation 2. Passband transmission : modulation zWe study Baseband transmission in this chapter zSource of bit Error 1. ISI(Intersymbol Interference) - channel is dispersive (major) 2. Receiver noise(channel noise) zTwo sources of bit error arise in the system simultaneously. zWe proposed to consider them separately.

7.2 Matched Filter(1) zA basic problem that often arises in the study of communication systems is that of detecting a pulse transmitted over a channel that is corrupted by additive noise at the front end of the receiver. zFilter input - T : arbitrary observation interval - g(t) : binary symbol (1,0) - w(t) : sample function of a white noise process of zero mean and power spectral density *caution : It is assumed that the receiver has knowledge of the waveform of the pulse signal g(t)

7.2 Matched Filter(2) zSince filter is linear, the resulting output y(t) may be expressed as : signal n(t) : noise components zLinear Receiver

7.2 Matched Filter(3) zDesired Filter Output : output signal component be considerably greater than the output noise component n(t) is to have the filter make the instantaneous power in the output signal,measured at time t = T zPeak pulse signal-to-noise ratio : instantaneous power in output signal : average output noise power

7.2 Matched Filter(4) zFind to specify the impulse response h(t) of the filter such that the output signal-to-noise ratio is maximized. zFind G(f) : F.T of the Known signal g(t) H(f) : the transfer function of the filter

7.2 Matched Filter(5) zFind (7.7) zThus, substituting Eqs. (7.5) and (7.7) into (7.3), we may rewrite the expression for the peak pulse signal-to-noise ratio as –

7.2 Matched Filter(6) zOur problem is to find, for a given G(f), the particular form of the transfer function H(f) of the filter that makes a maximum zUsing schwarz’s inequality zUsing this relation in Eq. (7.8), we may redefine the peak pulse signal-to-noise ratio as

7.2 Matched Filter(7) zSo the maximum peak pulse signal-to-noise is zCorrespondingly, H(f) assumes its optimum value denoted by To find this optimum value we use Eq. (7.10), which, for the situation at hand, yeilds G*(f) : complex conjugate of the F.T of the input signal g(t) k : scaling factor of appropriate

7.2 Matched Filter(8) zBy Fourier Transform, we can obtain zAssumption - input noise w(t) is that it is stationary and white with zero mean and power spectral density zResult - impulse response of the optimum filter, except for the scaling factor k, is a time-reversed and delayed version of the input signal g(t)

7.2 Properties of Matched Filters zProperties : The peak pulse signal-to-noise ratio of a matched filter depends only on the ratio of the signal energy to the power spectral density of the white noise at the filter input zA filter, which is matched to a pulse signal g(t) of duration T, is characterized by an impulse response that is a time-reversed and delayed version of the input g(t), as shown by zIn frequency domain, the matched filter is characterized by a transfer function

7.3 Error Rate Due to Noise(1) zComponents of Receiver - matched filter - sampler - decision device

7.3 Error Rate Due to Noise(2) zTo proceed with the analysis, consider a binary PCM system based on nonreturn-to-zero(NRZ) signaling - x(t) = A + w(t) symbol 1 was sent = -A + w(t) symbol 0 was sent zDecision Step 1.Let y denote the sample value obtained at the end of a signal interval. 2.The sample value y is compared to a preset threshold 3. If then make a decision symbol 1, then symbol 0 4. If then make a decision random

7.3 Error Rate Due to Noise(3) zThere are two possible kinds of error to be considered: - symbol 1 is chosen when a 0 was actually transmitted; we refer to this error as an error of the first kind - symbol 0 is chosen when a 1 was actually transmitted; we refer to this error as an error of the second kind

7.4 Intersymbol Interference(1) zISI, which arises when the communication channel is dispersive. zTransmit filter of impulse response g(t), producing the transmitted signal zReceive filter output signal : scaling factor

7.4 Intersymbol Interference(2)

7.4 Intersymbol Interference(3) zReceiver filter output y(t), z- : the contribution of the ith transmitted bit - second term : represents the residual effect of all other transmitted bits on the decoding of the ith bit; this residual effect due to the occurrence of pulse before and after the sampling instant is called intersymbol interference(ISI)

7.5 Nyquist’s Criterion For Distortionless Baseband Binary Transmission(1) zCondition for eliminating ISI zIdeal Nyquist Channel The simplest way of satisfying Eq. (7.53) is to specify the frequency function P(f) to be in the form of a rectangular function, as shown by P(f) = 1/2W, -W<f<W 0, | f | > W the overall system bandwidth W : =

7.5 Nyquist’s Criterion For Distortionless Baseband Binary Transmission(2) zAccording to the solution described by Eqs.(7.54) and (7.55), no frequencies of absolute value exceeding half the bit rate are needed. Hence, one signal waveform that produces zero intersymbol interference is defined by the sinc function the special value of the bit rate is called the Nyquist rate and W is itself called the Nyquist bandwidth

7.5 Nyquist’s Criterion For Distortionless Baseband Binary Transmission(3) zRaised Cosine Spectrum