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Baseband Data Transmission IIReference – Chapter 4.4-4.5, S. Haykin, Communication Systems, Wiley. E.1
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IntroductionIntroduction – Intersymbol interference (ISI) is different from noise in that it is a signal-dependent form of interference that arises because of deviations in the frequency response of a channel from the ideal channel. • This non-ideal communication channel is also called dispersive – The result of these deviation is that the received pulse corresponding to a particular data symbol is affected by the tail ends of the pulses representing the previous symbols and the front ends of the pulses representing the subsequent symbols. E.2
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Introduction– Example, for a binary PAM system without matched filter 1 0 1 t Sample points E.3
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Introduction– Two scenarios • The effect of ISI is negligible in comparison to that of channel noise. use a matched filter, which is the optimum linear time-invariant filter for maximizing the peak pulse signal-to-noise ratio. • The received signal-to-noise ratio is high enough to ignore the effect of channel noise (For example, a telephone system) control the shape of the received pulse. E.4
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Intersymbol Interference Consider a binary system, the incoming binary sequence {bk } consists of symbols 1 and 0, each of duration Tb . The pulse amplitude modulator modifies this binary sequence into a new sequence of short pulses (approximating a unit impulse), whose amplitude ak is + 1 if bk = 1 represented in the polar form ak = − 1 if bk = 0{bk } Pulse- {ak } s (t ) xo (t ) x(t ) Transmit amplitude Channel filter g (t ) h(t ) modulator w(t ) White noise E.5
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Intersymbol InterferenceThe short pulses are applied to a transmit filter ofimpulse response g(t), producing the transmitted signal s (t ) = ∑ ak g (t − kTb ) k The signal s (t ) is modified as a result of transmission through the channel of impulse response h(t ) . In addition, the channel adds random noise to the signal.{bk } Pulse- {ak } s (t ) xo (t ) x(t ) Transmit amplitude Channel filter g (t ) h(t ) modulator w(t ) White noise E.6
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Intersymbol InterferenceThe noisy signal x(t ) is then passed through a receivefilter of impulse response c(t ) .The resulting output y (t )is sampled and reconstruced by means of a decisiondevice. x(t ) y(t) 1 if y > λ Receive Decision filter c(t ) device 0 if y < λ Sample at ti = iTb λThe receiver output is ∑ y (t ) = µ a k p (t − kTb ) + n(t ) kwhere µp (t ) = g (t ) ⊗ h(t ) ⊗ c(t ) and µ is a constant. E.7
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Intersymbol InterferenceThe sampled output is ∑ y (t i ) = µ ak p[(i − k )Tb ] + n(t i ) k ----- (1) = µa i + µ ∑a k k p[(i − k )Tb ] + n(t i ) k ≠i µai : contribution of the ith transmitted bit. µ ∑ ak p[(i − k )Tb ] : k k ≠i the residual effect of all other transmitted bits. (This effect is called intersymbol interference) E.8
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Distortionless TransmissionIn a digital transmission system, the frequencyresponse of the channel h(t ) is specified.We need to determine the frequency responses of thetransmit g (t ) and receive filter c(t ) so as to reconstructthe original binary data sequence {bk } Pulse- {ak } s (t ) xo (t ) x(t ) Transmit amplitude Channel filter g (t ) h(t ) modulator w(t ) White noise x(t ) y(t) 1 if y > λ Receive Decision filter c(t ) device 0 if y < λ Sample at ti = iTb λ E.9
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Distortionless TransmissionThe decoding requires that 1 i = k p (iTb − kTb ) = …..(2) 0 i ≠ k(If this equation is satisfied and S/N is large, equation (1) becomes y (ti ) = µai )It can be shown that equation (2) is equivalent to ∞ ∑ P( f − n / T ) = T n = −∞ b b ….. (3) E.10
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Distortionless Transmission– Example 1 0 1 t p (t ) Sample points E.11
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Distortionless Transmission– Example p( f ) Tb 1 / Tb f ∞ p ( f − 1 / Tb ) p ( f − 2 / Tb ) ∑ p( f − n / T ) = T b b n = −∞ f E.12
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