chapter 5dfgd

Equalization chapter 5 digital communication

©® A.Sarkar ECE, JGEC



Signaling with controlled ISI: Partial Response signaling The Nyquist criterion pulse results in a bandwidth larger than the theoretical minimum. If we wish to reduce the pulse bandwidth further, we may widen the pulse p(t).Widening the pulse may result in ISI with the neighboring pulses. However as in the binary case with jus two symbols a known amount of ISI is permissible because of their few interference patterns. Consider a pulse specified by P(nTb)=1 n=0,1 =0 for all other n we use polar signaling using this pulse that is 1 is transmitted by p(t) and 0 is transmitted using –p(t).The Received signal is sampled at t=nTb and the pulse has zero value at all n except n=0,1 where the value is 1.Clearly such a pulse causes zero ISI with all the pulses except succeeding pulse. Therefore we need to worry about ISI with succeeding pulse only. Consider two succeeding pulses located at 0 and Tb respectively. If both the pulses are +ve the sample value will be 2.If both the pulses are –ve the sample value would be –2.But if both pulses are of opposite polarity the sample value would be 0.This clearly allows us to make correct decisions at the sampling instants. The decision rule is as follows If the sample value is +ve the present bit is 1 and the previous bit is 1 If the sample value is -ve the present bit is 0 and the previous bit is 0 If the sample value is 0 the present bit is complement of the previous bit Transmitted sequence 1 1 0 1 1 0 0 0 1 0 1 1 1 samples of x(t) 1 2 0 0 2 0 -2 -2 0 0 0 2 2 detected sequence 1 1 0 1 1 0 0 0 1 0 1 1 1 This example also shows the error detecting capability of this scheme. Examination of the samples of the waveform x(t) shows that there are always an even no of zero valued b/n two full valued samples of same polarity and an odd no. of zero valued samples b/n two full valued samples of opposite polarity. Thus the 2nd sample value of x(t) is 2 and the next full value d sample(5th sample) is 2.Between these two full valued samples of the same polarity there are an even no(i.e 2) zero valued samples. If one of the sample values is detected wrong ,the rule is violated and the error is detected. The pulse goes to zero at t= -Tb and t=2Tb, resulting a pulse width of the primary lobe 50% higher than Nyquist criterion pulse. this leads to a reduction in bandwidth. This is the 2nd method proposed by Nyquist. This scheme is also known as correlative or partial-response signaling. A pulse satisfying the above criterion is called duo binary pulse. *****



**** digit interpretation is based on previous digit. If a digit was detected wrong ,the error would tend to propagate. in differential coding which eliminates this problem a 1 is transmitted by a pulse identical to that of previous bit and a 0 is transmitted by a pulse negative of that used for previous bit. If we use a duo binary pulse p(t) instead of a rectangular pulse in the differential coding, something interesting happens. suppose the kth data bit is 1.Because of differential coding ,this bit is transmitted by a pulse identical to the previous pulse)two pulses of same polarity).Hence the kth sample of the received signal is either 2 or –2.On the other hand if the kth bit is 0,the present pulse is the –ve of the previous pulse(transition) and the kth sample of the received signal is 0.Thus if we use differential coding in conjugation with duo binary pulse our detection technique is simplified. If the sample value is 0,the incoming data bit is 0 and if the sample value is +/-2, the incoming data bit is 1.This scheme not only simplifies the decision rule but also makes the decision independent of the previous digit and thus eliminates error propagation.



The ISI and other signal degradations can be studied on an oscilloscope through eye diagram. The channel o/p is applied to the vertical i/p of an oscilloscope. The time base of the scope is triggered at the same rate as that of incoming pulses and it yields a sweep lasting exactly Tb, the interval of one pulse. The oscilloscope shows the superposition of several traces, which is nothing but the i/p signal (vertical i/p) cut up every Tb and then superimposed. The oscilloscope pattern thus found looks like a human eye and hence the name eye diagram. As an example, consider the transmission of a binary signal by polar rectangular pulses. If the channel is ideal with infinite bandwidth, pulses will be received without distortion. When the signal is cut up, every pulse interval or each piece will be either a +ve or a –ve rectangular pulse. When those are superimposed, the resulting eye diagram will be as shown in figure a. If the channel is not distortion less or has finite bandwidth, or both, received pulses will be no longer be rectangular but will be rounded and spread out. If the equalizer is adjusted properly to eliminate ISI at the pulse sampling instants, the resulting eye diagram will be rounded shown in fig b., but will still have full opening at the midpoint of the eye .This is because the midpoint of the eye represents the sampling instant of each pulse, where the pulse amplitude is maximum without interference from any other pulse(because of zero ISI).If ISI is not zero, pulse values at their respective sampling instants will deviate from the full scale values by varying amounts in each trace, causing a blur and thus closing the eye partially at the midpoint as shown in fig c. In the presence of channel noise, the eye will tend to close in all cases. Smaller noise will cause less closing. The decision threshold as to which symbol (1 or 0) is transmitted is the midpoint of the eye. Observe that for zero ISI, the system can tolerate noise of up to one-half the vertical opening of the eye. Because the ISI reduces the eye opening, it clearly reduces noise tolerance. The eye diagram is also used to determine optimum tap settings of the equalizer. Taps are adjusted to obtain the maximum vertical and horizontal eye openings. Use of eye diagrams

• To decide the optimum sampling or decision making instant (the instant where the eye opening is maximum)

• Amount of noise can be tolerated • The width of the eye opening indicates the time interval over which the decision can be made • It is desirable to have an eye with the maximum horizontal opening • If the decision making instant deviates from the instant where the eye has a maximum vertical opening , the

margin to noise tolerance is reduced. This causes higher error probability in pulse detection

chapter 5dfgd

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