EE5713 : Advanced Digital Communications

Week 4, 5:  Inter Symbol Interference (ISI)  Nyquist Criteria for ISI  and Raised-Cosine Filter   Error Performance Degradation (On Board)  Demodulation and Detection (On Board)

 Eb/No and Error Probability (On Board)  Matched Filter and Correlator Receiver (On Board)  Equalization (On Board)

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 1 Baseband Communication System . We have been considering the following baseband system

 The transmitted signal is created by the line coder according

to  s(t)  an g(t  nTb ) n where an is the symbol mapping and g(t) is the pulse shape Problems with Line Codes  One big problem with the line codes is that they are not bandlimited  The absolute bandwidth is infinite  The power outside the 1st null bandwidth is not negligible. That is, the power in the sidelobes can be quite high 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 2 (ISI)

. If the transmission channel is bandlimited, then high frequency components will be cut off – Hence, the pulses will spread out – If the pulse spread out into the adjacent symbol periods, then it is said that intersymbol interference (ISI) has occurred Intersymbol Interference (ISI) . Intersymbol interference (ISI) occurs when a pulse spreads out in such a way that it interferes with adjacent pulses at the sample instant . Causes – Channel induced which spreads or disperses the pulses – Multipath effects (echo)

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 3 Pulse spreading

– Due to improper filtering (@ Tx and/or Rx), the received pulses overlap one another thus making detection difficult . Example of ISI – Assume polar NRZ

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 4 Inter Symbol Interference

– Input data stream and bit superposition

. The channel output is the sum of the contributions from each bit

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 5 ISI

Note: . ISI can occur whenever a non-bandlimited line code is used over a bandlimited channel . ISI can occur only at the sampling instants . Overlapping pulses will not cause ISI if they have zero amplitude at the time the signal is sampled

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 6 ISI Baseband Communication System Model

where hT (t)  Impulseresponseof the transmitter,

hC (t)  Impulseresponseof the channel,

hR (t)  Impulseresponseof the receiver 

s(t)  anhT (t  nT), n  r(t)  an gT (t  nT)  n(t), where g(t)  hT (t)*hC (t), T 1/ fs n  y(t)  anhe (t  nT)  ne (t) where he (t)  hT (t)*hC (t)*hR (t), n ne (t)  n(t)*hC (t)*hR (t)

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 7 ISI Baseband Communication System Model

. Note that he(t) is the equivalent impulse response of the receiving filter

. To recover the information sequence {an}, the output y(t) is sampled at t = kT, k = 0, 1, 2, … . The sampled sequence is 

y(kT)  anhe (kT  nT)  ne (kT) n or equivalently AWGN term

 

yk   anhkn  nk  h0ak  anhkn  nk n n,nk Desired symbol scaled by gain parameters h0 Effect of other symbols at the sampling instants t=kT where hk  he (kT), nk  ne (kT), k  0,1,2,..

– h0 is an arbitrary constant

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 8 Signal Design for Bandlimited Channel

Zero ISI  y(kT)  h0ak  anhe (kT  nT)  ne (kT) n,nk . To remove ISI, it is necessary and sufficient to make the term

he (kT  nT)  0, for n  k and h0  0 . Nyquist Criterion – Pulse amplitudes can be detected correctly despite pulse spreading or overlapping, if there is no ISI at the decision- making instants

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 9 Nyquist Criterion: Time domain

p(t): impulse response of a transmission system (infinite length) Suppose 1/T is the sample rate The necessary and sufficient condition for p(t) to satisfy Nyquist Criterion is

1,n  0 pnT    0,n  0

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 10 1st Nyquist Criterion: Time domain . Pulse shape that satisfy this criteria is Sinc(.) function, e.g.,

 t  he (t) or p(t)  sin c   sin c(2Wt)  T  . The smallest value of T for which transmission with zero ISI is possible is 1 T  . Problems with Sinc(.) function 2W – It is not possible to create Sinc pulses due to – Infinite time duration – Sharp transition band in the frequency domain – Sinc(.) pulse shape can cause ISI in the presence of timing errors • If the received signal is not sampled at exactly the bit instant, then ISI will occur 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 11 1st Nyquist Criterion: Time domain

p(t) 1  shaping function

0 no ISI ! t 1  T 2 fs t0 2t0

Equally spaced zeros, 1 -1 interval  T 2 fs

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 12 Sample rate vs. bandwidth

. W is the channel bandwidth for P(f) . When 1/T > 2W, there is no way, we can design a system with no ISI

P(f)

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 13 Sample rate vs. bandwidth

. When 1/T = 2W (The Nyquist Rate), rectangular function satisfy Nyquist condition sin t T t  T, f W  p t   sinc ; P f    , t  T  0,otherwise 1  f  P f   rect   T rect fT ; 2W 2W  

T

W

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 14 Sample rate vs. bandwidth

. When 1/T < 2W, numbers of choices to satisfy Nyquist condition – Raised Cosine Filter – Duobinary Signaling (Partial Response Signals) – Gaussian Filter Approximation

. The most typical one is the raised cosine function

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 15 Raised Cosine Pulse

. The following pulse shape satisfies Nyquist’s method for zero ISI

 rt   rt   rt  sin  cos  cos   T   T   t   T  p(t)   sinc  rt 4r 2t 2 T 4r 2t 2 1   1 T T 2 T 2 . The Fourier Transform of this pulse shape is  1 r T , 0 | f |  2T   T  1 r  1 r 1 r P( f )  T / 21 cos | f |  ,  | f |    r  2T  2T 2T  1 r 0, | f |   2T . where r is the roll-off factor that determines the bandwidth

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 16 Raised cosine shaping

. Tradeoff: higher r, higher bandwidth, but smoother in time. P(ω)  W r=0 r = 0.25 r = 0.50 r = 0.75 r = 1.00 2w p(t) W ω

π π   W 0 W

0 t 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 17 Rolloff and bandwidth

. Bandwidth occupied beyond 1/2T is called the excess bandwidth (EB) . EB is usually expressed as a %tage of the Nyquist frequency, e.g., – Rolloff factor, r = 1/2 ===> excess bandwidth is 50 % – Rolloff factor, r = 1 ===> excess bandwidth is 100 % . RC filter is used to realized Nyquist filter since the transition band can be changed using the roll-off factor . The sharpness of the filter is controlled by the parameter r . When r = 0 this corresponds to an ideal rectangular function . Bandwidth B occupied by a RC filtered signal is increased from its minimum value 1 Bmin  2Ts . So the bandwidth becomes: B  Bmin 1 r 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 18 Rolloff and bandwidth

. Benefits of large roll off factor – Simpler filter – fewer stages (taps) hence easier to implement with less processing delay – Less signal overshoot, resulting in lower peak to mean excursions of the transmitted signal – Less sensitivity to symbol timing accuracy – wider eye opening . r = 0 corresponds to Sinc(.) function

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 19 Partial Response Signals

. To improve the bandwidth efficiency – Widen the pulse, the smaller the bandwidth. – But there is ISI. For binary case with two symbols, there is only few possible interference patterns. – By adding ISI in a controlled manner, it is possible to achieve a signaling rate equal to the Nyquist rate i.e. Duobinary and Polibinary Signaling (Covered in the previous lectures)

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 20 Eye Patterns

. An eye pattern is obtained by superimposing the actual waveforms for large numbers of transmitted or received symbols – Perfect eye pattern for -free, bandwidth-limited transmission of an alphabet of two digital waveforms encoding a binary signal (1’s and 0’s)

– Actual eye patterns are used to estimate the bit error rate and the signal to- noise ratio

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 21 Eye Patterns

Concept of the eye pattern

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 22 Eye Patterns

Concept of Eye diagram Mask. Waveform must not intrude into the shaded regions.

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 23 Cosine rolloff filter: Eye pattern

2nd Nyquist 1st Nyquist: 1st Nyquist: 2nd Nyquist: 2nd Nyquist:

1st Nyquist

1st Nyquist: 1st Nyquist:  2nd Nyquist: 2nd Nyquist:

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 24 Eye Diagram Examples

EYE DIAGRAM 1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec)

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 25 Eye Diagram Examples

EYE DIAGRAM WITH NOISE (Variance =0.1) 1.5

1

0.5

0

-0.5

-1

-1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec)

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 26 Eye Diagram Examples

EYE DIAGRAM WITH NOISE (Variance =0.5) 3

2

1

0

-1

-2

-3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec)

3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 27