S-72.1140 Transmission Methods in Telecommunication Systems (5 cr)

1. S-72.1140 Transmission Methods in Telecommunication Systems (5 cr) Digital Transmission

2. I Baseband Digital Transmission • Why to Apply Digital Transmission? • Digital Transmission • Symbols and Bits • M-level Pulse Amplitude Modulation (PAM) • Line codes (Binary PAM Formats) • Baseband Digital Transmission Link • Baseband Unipolar Binary Error Probability • Determining Decision Threshold • Error rate and Q-function • Baseband Binary Error Rate in Terms of Pulse Shape and g • Pulse Shaping and Band-limited Transmission • Signaling With Cosine Roll-off Signals • Matched Filtering • Root-raised cos-filtering • Eye diagram

3. II Carrier Wave Digital Transmission • Waveforms of Digital Carrier Wave Communications • Detection of Digital CW • Coherent Detection • Error rate; General treatment • Non-coherent Detection • Example of error rate determination (OOK) • Timing and Synchronization • Error rate for M-PSK • Error rate for M-QAM • Comparison of digital CW methods

4. Why to Apply Digital Transmission? • Digital communication withstands channel noise, interference and distortion better than analog system. For instance in PSTN inter-exchange STP*-links NEXT (Near-End Cross-Talk) produces several interference. For analog systems interference must be below 50 dB whereas in digital system 20 dB is enough. With this respect digital systems can utilize lower quality cabling than analog systems • Regenerative repeaters are efficient. Note that cleaning of analog-signals by repeaters does not work as well • Digital HW/SW implementation is straightforward • Circuits can be easily configured and programmed by DSP techniques • Digital signals can be coded to yield very low error rates • Digital communication enables efficient exchange of SNR to BW-> easy adaptation into different channels • The cost of digital HW continues to halve every two or three years STP: Shielded twisted pair

5. Transmitted power; bandpass/baseband signal BW DigitalTransmission Information: - analog:BW & dynamic range - digital:bit rate Information source • ‘Baseband’ means that no carrier wave modulation is used for transmission Message estimate Message Information sink Source encoder Maximization of information transferred Source decoder In baseband systems these blocks are missing Channel Encoder Channel decoder Message protection & channel adaptation; convolution, block coding Interleaving Deinterleaving Modulator Demodulator Fights against burst errors Received signal(may contain errors) Transmitted signal Channel M-PSK/FSK/ASK..., depends on channel BW & characteristics wireline/wireless constant/variable linear/nonlinear Noise Interference

6. Symbols and Bits – M-ary PAM 1 1 0 1 1 0 0 0 1 1 1 1 Generally: (a PAM* signal) For M=2 (binary signalling): For non-Inter-Symbolic Interference (ISI), p(t) must satisfy: This means that at the instant of decision, received signal component is *Pulse Amplitude Modulation

7. Binary PAM Formats (1) Bit stream Unipolar RZ and NRZ Polar RZ and NRZ Bipolar NRZ or alternate mark inversion (AMI) Split-phase Manchester

8. Binary PAM Formats (2) • Unipolar RZ, NRZ: • DC component has no information, wastes power • Transformers and capacitors in route block DC • NRZ, more energy per bit, synchronization more difficult • Polar RZ, NRZ: • No DC term if ´0´and ´1´ are equally likely • Bipolar NRZ • No DC term • Split-phase Manchester • Zero DC term regardless of message sequence • Synchronization simpler • Requires larger bandwidth

9. Baseband Digital Transmission Link original message bits received wave y(t) Unipolar PAM decision instances message reconstruction at yields Gaussian bandpass noise message ISI

10. Baseband Unipolar Binary Error Probability Assume binary & unipolar x(t) The sample-and-hold circuit yields: Establish H0and H1 hypothesis: and pN(y): Noise probability density function (PDF) at the time instance of sampling

11. Determining Decision Threshold The comparator implements decision rule: Choose Ho (ak=0) if Y<V Choose H1 (ak=1) if Y>V Average error error probability: Transmitted ‘0’ but detected as ‘1’ Channel noise is Gaussian with the pfd:

12. Error rate and Q-function This can be expressed by using the Q-function by and also m: mean s2: variance

13. Assigment

14. Solution

15. Baseband Binary Error Rate in Terms of Pulse Shape setting V=A/2 yields then for unipolar, rectangular NRZ [0,A] bits probability of occurrence for bits ’0’ and ’1’ for polar, rectangular NRZ [-A/2,A/2] bits and hence

16. Assignment • Determine average power for the following signals T A -A A A/2 -A/2 -A T

17. Solution T A -A A A/2 -A/2 -A T

18. Pulse Shaping and Band-limited Transmission • In digital transmission signaling pulse shape is chosen to satisfy the following requirements: • yields maximum SNR at the time instance of decision (matched filtering) • accommodates signalto channel bandwidth: • rapid decrease of pulse energy outside the main lobe in frequency domain alleviates filter design • lowers cross-talk in multiplexed systems

19. Signaling With Cosine Roll-off Signals • Maximum transmission rate can be obtained with sinc-pulses • However, they are not time-limited. A more practical choice is the cosine roll-off signaling: for raised cos-pulsesb=r/2

20. Unipolar and Polar Error Rates in Terms of Eb/No • Eb/No is often indicated by • For sinc- pulse signalling the transmission BW is limited toand therefore noise before decision is limited toand therefore

21. H(f) + Matched Filtering Peak amplitude to be maximized Post filter noise Should be maximized Using Schwartz’s inequality

22. Assignment • What is the impulse response of the matched filter for the following signaling waveform? • How would you determine the respective output signal (after the matched filter)? A T

24. Monitoring Transmission Quality by Eye Diagram Required minimum bandwidth isNyqvist’s sampling theorem: Given an ideal LPF with the bandwidth B it is possible to transmit independent symbols at the rate:

25. Assignment • How many eye/openings you have in an M-level signaling?

26. S-72.1140 Transmission Methods in Telecommunication Systems (5 cr) Digital Bandpass Transmission

27. Binary Waveforms in Carrier Wave Communications ASK FSK PSK DSB

28. Carrier Wave Communications • Carrier wave modulation is used to transmit messages over a distance by radio waves (air, copper or coaxial cable), by optical signals (fiber), or by sound waves (air, water, ground) • CW transmission allocates bandwidtharound the applied carrier that depends on • message bandwidth and bit rate • number of encoded levels(word length) • source and channel encoding methods • Examples of transmission bandwidths for certain CW techniques: • MPSK, M-ASK • Binary FSK (fd=rb/2) • MSK (CPFSK fd=rb/4), QAM: FSK: Frequency shift keying CPFSK: Continuous phase FSK

29. Digital CW Detection • At the receiver, detection can be • coherent (carrier phase information used for detection) • non- coherent(no carrier phase used for detection) • differentially coherent(‘local oscillator’ synthesized from received bits) • CW systems characterized by bit or symbol error rate(number of decoded errors(symbols)/total number of bits(symbols)) • Number of allocated signaling levels determines constellation diagram (=lowpass equivalent of the applied digital modulation format)

30. Coherent Detection by Integrate and Dump / Matched Filter Receiver • Coherent detection utilizes carrier phase information and requires in-phase replica of the carrier at the receiver (explicitly or implicitly) • It is easy to show that these two techniques have the same performance:

31. 2-ASK 2-FSK Non-coherent Detection • Base on filtering signal energy on allocated spectra and using envelope detectors • Has performance degradation of about 1-3 dB when compared to coherent detection (depending on Eb/N0) • Examples:

32. Coherent (Optimum) Binary Detection • Received signal consists of bandpass filtered signal and noise that is sampled at the decision time instants tk yielding decision variable: • Quadrature presentation of the signaling waveform is • Assuming that the BPF has the impulse response h(t),signal component at the sampling instants is then expressed by

33. Optimum Binary Detection - Error Rate • Assuming ‘0’ and ‘1’ reception is equally likely, error happens when H0 (‘0’ transmitted) signal hits the dashed region or for H1 error hits the left-hand side of the decision threshold that is at For optimum performancewe have the maximized SNR that is obtained by matched filtering/ integrate and dump receiver Errors for ‘0’ or/and ‘1’ are equal alike, for instance for ‘0’:

34. Optimum Binary Detection (cont.) • Express energy / bit embedded in signaling waveforms by • Therefore, for coherent CW we have the SNR and error rate Note that the signaling waveform correlation greatly influences the SNR!

35. Example: Coherent Binary On-off Keying (OOK) • For on-off keying (OOK) the signaling waveforms areand the optimum coherent receiver can be sketched by

36. Timing and Synchronization • Performance of coherent detection is greatly dependent on how successful local carrier recovery is • Consider the bandpass signal s(t) with width Tbrectangular pulsespTb(t), that is applied to the matched filter h(t): yelding after filtering: nominal point of inspection at Tb

37. Therefore, due to phase mismatch at the receiver, the error rate is degraded to Analyzing phase error by Mathcad

38. Example • Assume data rate is 2 kbaud/s and carrier is 100 kHz for an BPSK system. Hence the symbol duration and carrier period aretherefore the symbol duration is in radians • Assume carrier phase error is 0.3 % of the symbol duration. Then the resulting carrier phase error isand the error rate for instance for isthat should be compared to the error rate without any phase errors or • Hence, phase synchronization is a very important point to remember in coherent detection (or carrier cycles)

39. decision region Error rate for M-PSK • In general,PSK error rate can be expressed bywhere d is the distance between constellation points (or a=d/2 is the distance from constellation point to the decision region border) and is theaverage number of constellation points in the immediate neighborhood. ThereforeNote that for matched filter reception

40. Error rate for M-QAM, example 16-QAM symbol error rate Constellation follows from 4-bit words and therefore

41. Non-coherent Detection

42. Example: Non-coherent On-off Keying (OOK) • Bandpass filter is matched to the signaling waveform (not to carrier phase), in addition fc>>fm, and therefore the energy for ‘1’ is simply • Envelopes follow Rice and Rayleigh distributions for ‘1’ and ‘0’ respectively: distribution for ”0”" distribution for "1"

43. Noncoherent OOK Error Rate • The optimum decision threshold is at the intersection of Rice and Rayleigh distributions (areas of error probability are the same on both sides of decision threshold) • Usually high SNR is assumed and hence the threshold is approximately at the half way and the error rate is the average of '0' and '1' reception probabilities • Therefore, error rate for noncoherent OOK equals probability to detect "0" in error probability to detect "1" in error

44. Comparison

45. Error Rate Comparison a: Coherent BPSK b: DPSK c:Coherent OOK d: Noncoherent FSK e: noncoherent OOK

46. Comparison of Quadrature Modulation Methods Note that still the performance is good, envelope is not constant. APK (or M-QASK) is used for instance in modems (pe=10-4) (pe=10-4) APK=MQASK M-APK: Amplitude Phase Shift Keying