Lecture Notes: EEEC6440315 Communication Systems - Inter Symbol Interference and Pulse Shaping

Course: BEng (Hons) in Electrical and Electronic Engineering

1. EEEC6440315 COMMUNICATION SYSTEMS Inter Symbol Interference And Pulse Shaping FACULTY OF ENGINEERING AND COMPUTER TECHNOLOGY BENG (HONS) IN ELECTRICAL AND ELECTRONIC ENGINEERING Ravandran Muttiah BEng (Hons) MSc MIET

2. Band Limited Channel And Inter Symbol Interference Rectangular pulses are suitable for infinite bandwidth channels (practically - wideband). Practical channels are band limited ⇒ Pulses spread in time and are smeared into adjacent slots. This is Inter S ymbol I nterference (ISI) 1

3. 2 1 0 0 0 1 0 1 1 t t t t t t Intersymbol Interference Sampling Points (Transmitter Clock) Sampling Points (Receiver Clock) Sampling Points (Receiver Clock) Input Binary Waveform Individual Pulse Response Received Waveform Figure 1: Inter Symbol Interference.      

4. 3 Figure 2 : Channel noise. Eye Diagram Convenient way to observe the effect of ISI and channel noise on an oscilloscope. Best Sampling Time 0 1 1 0 0 1 Eye Pattern Waveform Ideal Filtering Filtering With ISI N oise Plus ISI     Maximum Distortion Noise Margin t t t

5. 4 Peak distortion Noise Margin Distortion of Zero Crossings Sensitivity to Timing Error Optimum Sampling Time Figure 3: Eye diagram. Oscilloscope presentations of a signal with multiple sweeps (triggered by a clock signal), each is slightly larger than symbol interval. Quality of a received signal may be estimated. Normal operating conditions (no ISI, no noise) ⇒ Eye is open. Large ISI or noise ⇒ Eye is closed.

6. 5 Timing error allowed ⇒ width of the eye, called eye opening (preferred sampling time – at the largest vertical eye opening). Sensitivity to timing error ⇒ Slope of the open eye evaluated at the zero crossing point. Noise margin ⇒ The height of the eye opening.

7. 6 Transmitting Filter   Channel (Filter) Characteristics   Receiver Filter   Transmission Over A Band - Limited Channel Flat Top Pulses Recovered Rounded Pulse (to sampling and decoding circuits)     Figure 4 : Baseband transmission system. Input PAM signal, Output signal, , Sampled output at , transmitted symbol inter symbol interference  

8. 7 Pulse Shaping To Eliminate ISI In 1928 Nyquist discovered 3 methods to eliminate ISI: Zero ISI pulse shaping. Controlled ISI (Eliminated later on by an Equalizer). Zero average ISI (negative and positive areas under the pulse in an adjacent interval are equal). Zero ISI pulse shaping, ⇒  

9. 8 Example 1: , Hence, pulses allows to eliminate ISI at sampling instants.   Figure 5: Zero ISI pulse.   -3 -2 -1 -0 1 2 3 -0.3 0.3 0.6 0.9

10. 9 Nyquist Criterion For Zero ISI Provides a generic solution to the zero ISI problem. A necessary and sufficient condition for to satisfy, Consider a channel band-limited to for 3 cases. ⇒ No way to eliminate ISI. ⇒ Only eliminates ISI. The highest possible transmission rate for transmission with zero ISI is , not . ⇒ Many signals may eliminated ISI in this case. Note: is the transmission rate (symbols/second)  

11. 10 Figure 6 : , and .                                                     Case 1: Case 2: Case 3:        

12. 11 Raised Cosine Pulse When , raised cosine pulse is widely used. The raised cosine pulse has Fourier transform, which its spectrum is, w here is roll-off factor, . The bandwidth above the Nyquist frequency is called excess bandwidth. Where, Time-domain waveform of the raised cosine pulse,  

13. 12 When , pulse reduces to and . , symbol rate . Tails decay as , mistiming is not a big problem. Smooth shape of the spectrum, easier to design filters.   1 0.5 0.5 1 1 -1 -2 -3 Figure 7: Raised Cosine Spectrum. Figure 8: Time Domain Pulse.   -0.5 -1 0.5 1 2 3

14. 13 Example 2: Wideband Code-Division Multiple-Access (WCDMA) is the main technology behind 3 rd Generation (3G) cellular systems implements a Square-Root Raised Cosine pulse shape with excess bandwidth , which translates the signaling rate of   MHz to a bandwidth of      MHz (the factor 2 arises for the RF bandwidth). Accounting for the guard-bands to minimise interference between neighboring channels, the signal bandwidth in WCDMA systems is MHz.  

15. Leon W. Couch II, Digital and Analogue Communication Systems, Prentice Hall, 1999. References 14