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

2. 2 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen I Baseband Digital Transmission n Why to Apply Digital Transmission? n Digital Transmission n Symbols and Bits –M-level Pulse Amplitude Modulation (PAM) –Line codes (Binary PAM Formats) n 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  n Pulse Shaping and Band-limited Transmission –Signaling With Cosine Roll-off Signals –Matched Filtering –Root-raised cos-filtering n Eye diagram

3. 3 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen II Carrier Wave Digital Transmission n Waveforms of Digital Carrier Wave Communications n Detection of Digital CW –Coherent Detection Error rate; General treatment –Non-coherent Detection Example of error rate determination (OOK) n Timing and Synchronization n Error rate for M-PSK n Error rate for M-QAM n Comparison of digital CW methods

4. 4 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Why to Apply Digital Transmission? n 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 n Regenerative repeaters are efficient. Note that cleaning of analog-signals by repeaters does not work as well n Digital HW/SW implementation is straightforward n Circuits can be easily configured and programmed by DSP techniques n Digital signals can be coded to yield very low error rates n Digital communication enables efficient exchange of SNR to BW-> easy adaptation into different channels n The cost of digital HW continues to halve every two or three years STP: Shielded twisted pair

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

6. 6 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Symbols and Bits – M-ary PAM 110011111010 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 Generally: (a PAM* signal) *Pulse Amplitude Modulation

7. 7 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Binary PAM Formats (1) Unipolar RZ and NRZ Polar RZ and NRZ Bipolar NRZ or alternate mark inversion (AMI) Bit stream Split-phase Manchester

8. 8 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Binary PAM Formats (2) n 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 n Polar RZ, NRZ: –No DC term if ´0´and ´1´ are equally likely n Bipolar NRZ –No DC term n Split-phase Manchester –Zero DC term regardless of message sequence –Synchronization simpler –Requires larger bandwidth

9. 9 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Baseband Digital Transmission Link message reconstruction at yields messageISI Gaussian bandpass noise Unipolar PAM original message bits decision instances received wave y(t)

10. 10 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Baseband Unipolar Binary Error Probability The sample-and-hold circuit yields: Establish H 0 and H 1 hypothesis: and p N (y): Noise probability density function (PDF) at the time instance of sampling Assume binary & unipolar x(t)

11. 11 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Determining Decision Threshold Choose Ho (a k =0) if Y<V Choose H1 (a k =1) if Y>V The comparator implements decision rule: Average error error probability: Channel noise is Gaussian with the pfd: Transmitted ‘0’ but detected as ‘1’

12. 12 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Error rate and Q-function This can be expressed by using the Q-function by and also m: mean  2 : variance

13. 13 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Assigment

14. 14 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Solution

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

16. 16 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Assignment n Determine average power for the following signals T T A -A A A/2 -A/2

17. 17 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Solution T A -A A A/2 -A/2 T

18. 18 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Pulse Shaping and Band-limited Transmission n 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 signal to channel bandwidth: rapid decrease of pulse energy outside the main lobe in frequency domain alleviates filter design lowers cross-talk in multiplexed systems

19. 19 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Signaling With Cosine Roll-off Signals n Maximum transmission rate can be obtained with sinc-pulses n However, they are not time-limited. A more practical choice is the cosine roll-off signaling: for raised cos-pulses  =r/2

20. 20 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Unipolar and Polar Error Rates in Terms of Eb/No n Eb/No is often indicated by n For sinc- pulse signalling the transmission BW is limited to and therefore noise before decision is limited to and therefore

21. 21 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Matched Filtering H(f) + + Should be maximized Post filter noise Peak amplitude to be maximized Using Schwartz’s inequality

22. 22 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Assignment n What is the impulse response of the matched filter for the following signaling waveform? n How would you determine the respective output signal (after the matched filter)? T A

23. 23 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

24. 24 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Monitoring Transmission Quality by Eye Diagram Required minimum bandwidth is Nyqvist’s sampling theorem: Given an ideal LPF with the bandwidth B it is possible to transmit independent symbols at the rate:

25. 25 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Assignment n 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. 27 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Binary Waveforms in Carrier Wave Communications ASK FSK PSK DSB

28. 28 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Carrier Wave Communications n 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) n CW transmission allocates bandwidth around 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: n MPSK, M-ASK n Binary FSK (f d =r b /2) n MSK (CPFSK f d =r b /4), QAM: FSK: Frequency shift keying CPFSK: Continuous phase FSK

29. 29 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Digital CW Detection n 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) n CW systems characterized by bit or symbol error rate (number of decoded errors(symbols)/total number of bits(symbols)) n Number of allocated signaling levels determines constellation diagram (=lowpass equivalent of the applied digital modulation format)

30. 30 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Coherent Detection by Integrate and Dump / Matched Filter Receiver n Coherent detection utilizes carrier phase information and requires in- phase replica of the carrier at the receiver (explicitly or implicitly) n It is easy to show that these two techniques have the same performance:

31. 31 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Non-coherent Detection 2-ASK 2-FSK n Base on filtering signal energy on allocated spectra and using envelope detectors n Has performance degradation of about 1-3 dB when compared to coherent detection (depending on E b /N 0 ) n Examples:

32. 32 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Coherent (Optimum) Binary Detection n Received signal consists of bandpass filtered signal and noise that is sampled at the decision time instants t k yielding decision variable: n Quadrature presentation of the signaling waveform is n Assuming that the BPF has the impulse response h(t), signal component at the sampling instants is then expressed by

33. 33 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Optimum Binary Detection - Error Rate n Assuming ‘0’ and ‘1’ reception is equally likely, error happens when H 0 (‘0’ transmitted) signal hits the dashed region or for H 1 error hits the left-hand side of the decision threshold that is at Errors for ‘0’ or/and ‘1’ are equal alike, for instance for ‘0’: For optimum performance we have the maximized SNR that is obtained by matched filtering/ integrate and dump receiver

34. 34 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Optimum Binary Detection (cont.) n Express energy / bit embedded in signaling waveforms by n Therefore, for coherent CW we have the SNR and error rate Note that the signaling waveform correlation greatly influences the SNR!

35. 35 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Example: Coherent Binary On-off Keying (OOK) n For on-off keying (OOK) the signaling waveforms are and the optimum coherent receiver can be sketched by

36. 36 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Timing and Synchronization n Performance of coherent detection is greatly dependent on how successful local carrier recovery is n Consider the bandpass signal s(t) with width T b rectangular pulses p Tb (t), that is applied to the matched filter h(t): yelding after filtering: nominal point of inspection at T b

37. 37 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Analyzing phase error by Mathcad n Therefore, due to phase mismatch at the receiver, the error rate is degraded to

38. 38 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Example n Assume data rate is 2 kbaud/s and carrier is 100 kHz for an BPSK system. Hence the symbol duration and carrier period are therefore the symbol duration is in radians n Assume carrier phase error is 0.3 % of the symbol duration. Then the resulting carrier phase error is and the error rate for instance for is that should be compared to the error rate without any phase errors or n Hence, phase synchronization is a very important point to remember in coherent detection (or carrier cycles)

39. 39 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Error rate for M-PSK n In general,PSK error rate can be expressed by where d is the distance between constellation points (or a=d/2 is the distance from constellation point to the decision region border) and is the average number of constellation points in the immediate neighborhood. Therefore Note that for matched filter reception decision region

40. 40 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Error rate for M-QAM, example 16-QAM symbol error rate Constellation follows from 4-bit words and therefore

41. 41 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Non-coherent Detection

42. 42 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Example: Non-coherent On-off Keying (OOK) n Bandpass filter is matched to the signaling waveform (not to carrier phase), in addition f c >>f m, and therefore the energy for ‘1’ is simply n Envelopes follow Rice and Rayleigh distributions for ‘1’ and ‘0’ respectively: distribution for "1" distribution for ”0”"

43. 43 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Noncoherent OOK Error Rate n 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) n 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 n Therefore, error rate for noncoherent OOK equals probability to detect "0" in error probability to detect "1" in error

44. 44 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Comparison

45. 45 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Error Rate Comparison a: Coherent BPSK b: DPSK c:Coherent OOK d: Noncoherent FSK e: noncoherent OOK a: Coherent BPSK b: DPSK c:Coherent OOK d: Noncoherent FSK e: noncoherent OOK

46. 46 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen 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 APK=MQASK (p e =10 -4 ) M-APK: Amplitude Phase Shift Keying (p e =10 -4 )