1. Chapter 4_ part 1b Baseband Data Transmission EKT 357 Digital Communications

2. Chapter Overview Intersymbol Interference (ISI) Intersymbol Interference (ISI) Raised-Cosine Filter Raised-Cosine Filter Eye Pattern Eye Pattern

3. Intersymbol Interference (ISI) During transmission of signal, it was noticed that received signals tended to get elongated and smeared into each other. During transmission of signal, it was noticed that received signals tended to get elongated and smeared into each other. How does this actually affect the communication transmission? How does this actually affect the communication transmission?

4. Intersymbol Interference  If the rectangular multilevel pulses are filtered improperly as they pass through a communications system, they will spread in time, and the pulse for each symbol may be smeared into adjacent time slots and cause Intersymbol Interference.

5. Intersymbol Interference (ISI) Due to effect of system filtering, the received pulses can overlap one another. Due to effect of system filtering, the received pulses can overlap one another. Tail of pulse can smear into adjacent symbol intervals, and degrading the error performance - Intersymbol interference (ISI) Tail of pulse can smear into adjacent symbol intervals, and degrading the error performance - Intersymbol interference (ISI) effects of filtering effects of filtering

6. Intersymbol Interference (ISI) Equivalent system transfer function Equivalent system transfer function H(f) = H t (f) H c (f) H r (f) H(f) = H t (f) H c (f) H r (f)Where H t (f) – transmitting filter H c (f) – filtering within the channel H r (f) – equalizing filter

7. Intersymbol Interference (ISI) Equivalent model with transfer function system Typical baseband digital system (Ideal)

8. Nyquist showed that the theoretical minimum system bandwidth needed in order to detect Rs symbols/s, without ISI is (Rs/2) symbol/s/hertz Nyquist showed that the theoretical minimum system bandwidth needed in order to detect Rs symbols/s, without ISI is (Rs/2) symbol/s/hertz Bandwidth efficiency Bandwidth efficiency How much date rate can be supported by the system with each unit frequency band How much date rate can be supported by the system with each unit frequency band The higher bandwidth efficiency, the better the system is. The higher bandwidth efficiency, the better the system is. Intersymbol Interference (ISI)

9. Example 1 Theoretical maximum symbol rate packing without ISI is Rs= 2 symbols/s/Hz. For a given symbol set size of M = 64, calculate what is the maximum bandwidth efficiency without ISI? Theoretical maximum symbol rate packing without ISI is Rs= 2 symbols/s/Hz. For a given symbol set size of M = 64, calculate what is the maximum bandwidth efficiency without ISI?

10. Raised-cosine filter Pulse Shaping to reduce ISI Pulse Shaping to reduce ISI Pulse that spread in time will degrade the system’s error performance due to increase ISI. Pulse that spread in time will degrade the system’s error performance due to increase ISI. Reduce the required system bandwidth. Reduce the required system bandwidth. Compress the bandwidth of the data impulse to some reasonably small bandwidth greater than the Nyquist minimum – pulse shaping with Nyquist filter. Compress the bandwidth of the data impulse to some reasonably small bandwidth greater than the Nyquist minimum – pulse shaping with Nyquist filter. Most popular of Nyquist filter Most popular of Nyquist filter Raised-cosine filter Zero ISI is only when the sampling is performed at exactly the correct sampling time when the tails of pulses are large. Zero ISI is only when the sampling is performed at exactly the correct sampling time when the tails of pulses are large.

11. Raised-cosine filter Transfer function response of raised-cosine filter with various roll-off factors Transfer function response of raised-cosine filter with various roll-off factors

12. Raised-cosine filter Impulse response of raised-cosine filter with various roll-off factors Impulse response of raised-cosine filter with various roll-off factors Comprise main lobe and side lobes called pre- and post- lobe tails that are infinitely long. Comprise main lobe and side lobes called pre- and post- lobe tails that are infinitely long.

13. Raised-cosine filter Raised-cosine filter Raised-cosine filter One frequently used H(f) transfer function belonging to the Nyquist class (zero ISI at the sampling time). One frequently used H(f) transfer function belonging to the Nyquist class (zero ISI at the sampling time). The roll-off factor is defined to be r = (W-W)/W, where 0<r< 1. The roll-off factor is defined to be r = (W-W)/W, where 0<r< 1. W= absolute bandwidth, W = minimum nyquist bandwidth. W= absolute bandwidth, W = minimum nyquist bandwidth. 0 0 \ \ 0

14. Raised-cosine filter Minimum required bandwidth Minimum required bandwidth DSB bandwidth DSB bandwidth R = symbol rate R = symbol rate s

15. Example 2 Find the minimum required bandwidth for the baseband transmission of a four-level PAM pulse sequence having a data rate of R = 2400 bits/s if r = 1. Find the minimum required bandwidth for the baseband transmission of a four-level PAM pulse sequence having a data rate of R = 2400 bits/s if r = 1. The same 4-ary PAM sequence is modulated onto a carrier wave, so that the baseband spectrum is shifted and centered at frequency, f. Find the minimum required DSB bandwidth for transmitting the modulated PAM sequence. Assume that the system transfer characteristic is the same as above question The same 4-ary PAM sequence is modulated onto a carrier wave, so that the baseband spectrum is shifted and centered at frequency, f. Find the minimum required DSB bandwidth for transmitting the modulated PAM sequence. Assume that the system transfer characteristic is the same as above question

16. Example 3 A voice signal is sampled at 8000 samples/s. What is the minimum system bandwidth required for the detection of PAM with no ISI and with a filter roll – off characteristic of r=1?

17. Example 4 Consider that you desire a digital transmission system, such that the quantization distortion of any audio source does not exceed 2% of the peak to peak analog signal voltage. If the audio signal bandwidth and the allowable transmission bandwidth is taken at the Nyquist rate of 4000 sample/s, conclude the value of bandwidth efficiency (bits/s/Hz).

18. Eye Pattern Is the display that results from measuring a system’s response to baseband signals. Is the display that results from measuring a system’s response to baseband signals. The optimum sampling time corresponds to the maximum eye opening, yielding the greatest protection against noise. The optimum sampling time corresponds to the maximum eye opening, yielding the greatest protection against noise. Qualitatively assessing the extent of the ISI. Qualitatively assessing the extent of the ISI. As the eye closes, ISI is increasing; as the eye opens, ISI is decreasing. As the eye closes, ISI is increasing; as the eye opens, ISI is decreasing.

19. ISI on Eye Patterns The amount of ISI can be seen on an oscilloscope using an Eye Diagram or Eye pattern. The amount of ISI can be seen on an oscilloscope using an Eye Diagram or Eye pattern. Time (T b ) Amplitude Noise Margin Distortion Extension Beyond T b is ISI

20. Eye Pattern ISI measured by eye pattern ISI measured by eye pattern D is a measure of distortion caused by ISI. D is a measure of distortion caused by ISI. M is a measure of noise margin. M is a measure of noise margin. J is a measure of the timing jitter. J is a measure of the timing jitter. S is a measure of the sensitivity-to-timing error. S is a measure of the sensitivity-to-timing error. A N T T

21. Performance Degradation Two types of error Two types of error 1. Due to a decrease in received signal power or an increase in noise or interference power, giving rise to a loss in signal-to-noise ratio, E b /N o 2. Due to signal distortion such as ISI