Chapter 6 Passband Data Transmission

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1 Chapter 6 Passband Data Transmission Passband Data Transmission concerns the Transmission of the Digital Data over the real Passband channel. 6.1 Introduction Categories of digital communications (ASK/PSK/FSK) o Three basic signaling schemes in digital communications Amplitude-shift keying (ASK) Phase-shift keying (PSK) Frequency-shift keying (FSK) Po-Ning Chen@cm.nctu Chapter 6-2 1

2 6.1 Introduction Categories of M-ary digital communications (ASK/PSK/FSK) o Three basic signaling schemes in M-ary digital communications ary Amplitude-shift keying (ASK) T T b 4-ary Phase-shift keying (PSK) 4-ary Frequency-shift keying (FSK) Po-Ning Chen@cm.nctu Chapter Introduction Categories of M-ary digital communications (Constant Envelope versus Non-Constant Envelope) o Constant envelope: A necessity for non-linear channels Non-constant envelope (ASK) T T b Constant envelope (PSK) Constant evnelope (FSK) Po-Ning Chen@cm.nctu Chapter 6-4 2

3 6.1 Introduction Categories of digital communications (Coherent versus Non-Coherent) o Coherent technique n The transmitter and receiver are required to be synchronized in both carrier phase and bit timing. o Non-Coherent technique n The transmitter and receiver are not required to be synchronized in both carrier phase and bit timing. Po-Ning Chen@cm.nctu Chapter Introduction Roadmap o In this chapter, we will focus on n Power : A resource in communication o Power Spectra n The relation between passband signal and baseband signal is easier to identify in spectra view n Bandwidth: Another resource in communication o Bandwidth efficiency : The ratio of data rate in bits per second to the effectively utilized bandwidth. (Bits/Second/Hz) n Probability of M-ary symbol error (Union bound) Po-Ning Chen@cm.nctu Chapter 6-6 3

4 6.1 Introduction Relation between passband and baseband signals o Math relation between passband and baseband signals (spectrum view) Po-Ning Chen@cm.nctu Chapter Introduction Relation between passband and baseband signals Po-Ning Chen@cm.nctu Chapter 6-8 4

5 6.1 Introduction Relation between passband and baseband signals Signal Spectrum Po-Ning Chapter Introduction Relation between passband and baseband signals o Math relation between passband and baseband signals (power spectrum view subject to wise-sense stationarity) Po-Ning Chen@cm.nctu Chapter

6 6.1 Introduction Relation between passband and baseband signals o Let o Po-Ning Chen@cm.nctu Chapter Introduction Relation between passband and baseband signals Po-Ning Chen@cm.nctu Chapter

7 6.1 Introduction Relation between passband signal and baseband signal Po-Ning Chapter Introduction Relation between passband signal and baseband signal Po-Ning Chapter

8 6.1 Introduction Relation between passband signal and baseband signal Power Spectral Density Po-Ning Chapter Introduction Relation between passband signal and baseband signal o Integration of the Power Spectral Density gives the Power. n Integration of the Prabability Density gives the Prabability. Po-Ning Chen@cm.nctu Chapter

6.2 Passband transmission model Message source Po-Ning Chen@cm.nctu Chapter 6-17 6.

9 6.2 Passband transmission model Message source Po-Ning Chapter Passband transmission model Signal space analysis Recall Chapter 5: Signal Space Analysis 2-dimensional vector codeword (N=2) N-dimensional vector codeword Po-Ning Chapter

6.2 Passband transmission model Signal space analysis Recall Chapter 5: Signal Space Analysis Po-Ning Chen@cm.

10 6.2 Passband transmission model Signal space analysis Recall Chapter 5: Signal Space Analysis Po-Ning Chapter Passband transmission model Signal space analysis o n What is an energy signal? Po-Ning Chen@cm.nctu Chapter

11 6.2 Passband transmission model Signal space analysis Po-Ning Chapter Passband transmission model Signal space analysis o Po-Ning Chen@cm.nctu Chapter

12 6.2 Passband transmission model Signal space analysis o Po-Ning Chen@cm.nctu Chapter Passband transmission model Communication channel o Communication channel n Linear: Principle of superposition n n Sufficient bandwidth AWGN Po-Ning Chen@cm.nctu Chapter

13 6.2 Passband transmission model Signal space analysis o Detector Po-Ning Chen@cm.nctu Chapter Passband transmission model Decoder o Signal transmission decoder Po-Ning Chen@cm.nctu Chapter

14 6.3 Coherent phase-shift keying o Binary PSK Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Antipodal signal o Vector space analysis of binary PSK n Antipodal signal Po-Ning Chen@cm.nctu Chapter

6.3 Coherent phase-shift keying Signal space analysis Signal-space diagram Po-Ning Chen@cm.nctu Chapter 6-29 6.

15 6.3 Coherent phase-shift keying Signal space analysis Signal-space diagram Po-Ning Chapter Coherent phase-shift keying Optimal decision region o Error probability of binary PSK Po-Ning Chen@cm.nctu Chapter

Recall: Po-Ning Chen@cm.nctu Chapter 6-31 6.

16 Recall: Po-Ning Chapter Coherent phase-shift keying Error probability o Error probability of binary PSK n Based on the decision rule Po-Ning Chen@cm.nctu Chapter

17 6.3 Coherent phase-shift keying Block diagram o Block diagram for PSK transmitter and (coherent) receiver (coherent) Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Baseband signal o (Complex) Baseband signal of binary PSK passband signal Po-Ning Chen@cm.nctu Chapter

6.3 Coherent phase-shift keying Sequential baseband signal o Sequence of complex baseband signals n No autocorrelation function for one-shot single random variable n Calculation

18 6.3 Coherent phase-shift keying Sequential baseband signal o Sequence of complex baseband signals n No autocorrelation function for one-shot single random variable n Calculation of autocorrelation function requires a random process. Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Autocorrelation function Po-Ning Chen@cm.nctu Chapter

19 Po-Ning Chapter Coherent phase-shift keying Autocorrelation function o Power spectrum of binary PSK Po-Ning Chen@cm.nctu Chapter

20 6.3 Coherent phase-shift keying Autocorrelation function o Power spectrum of binary PSK Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Quadriphaseshift keying o QPSK E is the transmitted energy per QPSK symbol, and T is the symbol duration. o Vector space analysis of QPSK Po-Ning Chen@cm.nctu Chapter

21 6.3 Coherent phase-shift keying Quadriphaseshift keying o Two-dimensional signal space diagram of QPSK Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Quadriphaseshift keying o Example 6.1 Po-Ning Chen@cm.nctu Chapter

22 o Error probability of QPSK Po-Ning Chapter Coherent phase-shift keying Error probability of QPSK o Following the same derivation as that in Slide 6-32 Po-Ning Chen@cm.nctu Chapter

23 6.3 Coherent phase-shift keying Error probability of QPSK o Symbol error rate of QPSK Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Error probability of QPSK o Alternative approach to derive the symbol error rate of QPSK Po-Ning Chen@cm.nctu Chapter

24 6.3 Coherent phase-shift keying Summary o Partial summary n QPSK (with Gray code mapping) and BPSK have the same BER under the same E b /N 0. n QPSK however doubles the transmission bit rate per second (or uses half the bandwidth under the same bit rate) by introducing another quadrature. n In its implementation, QPSK is more complex since it involves two quadratures. Po-Ning Chen@cm.nctu Chapter Coherent phaseshift keying QPSK diagram o Block diagram of QPSK transmitter and receiver coherent Po-Ning Chen@cm.nctu Chapter

25 6.3 Coherent phase-shift keying Sequential baseband signal o Sequence of complex baseband signals n No autocorrelation function of one-shot (namely, single) random variable. n Calculation of autocorrelation function requires a random process. Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Sequential baseband signal Po-Ning Chen@cm.nctu Chapter

26 6.3 Coherent phase-shift keying Autocorrelation function o Power spectrum of BPSK and QPSK under the same E b and T b QPSK BPSK Po-Ning Chen@cm.nctu Chapter 6-51 Single sign change = 90 degree shift Double sign change = 180 degree shift 6.3 Coherent phase-shift keying Offset QPSK o Example 6.1: n QPSK 90 degree 0 degree 90 degree 90 degree 90+90=180 degree phase shift 90+0=90 degree phase shift Po-Ning Chen@cm.nctu Chapter

27 6.3 Coherent phase-shift keying Offset QPSK o Example 6.1: n Offset QPSK Po-Ning Chen@cm.nctu 90 degree phase shift 90 degree phase shift 90 degree phase shift Chapter Coherent phase-shift keying Offset QPSK o Offset QPSK n By offseting the quadrature component by half a symbol interval with respect to the in-phase component, Offset QPSK limits the amplitude fluctuation to 90 degree. n The 90 degree phase transition in OQPSK occurs twice as frequently encountered in QPSK. n o Personal comment: One 180 degree phase transition in QPSK becomes two 90 degree phase transitions in OQPSK. Hence, twice is an over-estimate. Under AWGN and coherent receiver, the error rate of OQPSK is exactly the same as that of QPSK. Po-Ning Chen@cm.nctu Chapter

28 6.3 Coherent phase-shift keying p/4-shifted DQPSK o p/4-shifted DQPSK (D=Differential) n The input dibit does not determine the absolute phase, but the phase change. Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying p/4-shifted DQPSK o p/4-shifted DQPSK n The phase transition is restricted to either 45 or 135 degree. o No 0 degree phase transition occurs now! n Noncoherent receiver is feasible. Po-Ning Chen@cm.nctu Chapter

6.3 Coherent phase-shift keying Detection of p/4-shifted DQPSK o Noncoherent receiver n Differential detector Po-Ning Chen@cm.nctu Chapter 6-57 6.

29 6.3 Coherent phase-shift keying Detection of p/4-shifted DQPSK o Noncoherent receiver n Differential detector Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying M-ary PSK o M-ary PSK E is the transmitted energy per M-ary PSK symbol, and T is the symbol duration. o Vector space analysis of M-ary PSK Po-Ning Chen@cm.nctu Chapter

30 6.3 Coherent phase-shift keying M-ary PSK o Example 8PSK (Octaphase-shift keying) Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Union bound of M-ary PSK error Po-Ning Chen@cm.nctu Chapter

31 6.3 Coherent phase-shift keying Union bound of M-ary PSK error o If the signal constellation is symmetric in the sense that then Po-Ning Chen@cm.nctu Chapter Coherent phase-shift keying Union bound of M-ary PSK error o Example 8PSK Po-Ning Chen@cm.nctu Chapter

32 6.3 Coherent phase-shift keying Union bound of M-ary PSK error This is the lower bound of the upper bound. So it is not really an upper bound! Po-Ning Chapter Coherent phase-shift keying Power spectra of M-ary PSK signals o Same as Slide 6-50 Po-Ning Chen@cm.nctu Chapter

33 6.3 Coherent phase-shift keying Power spectra of M-ary PSK signals Po-Ning Chapter Coherent phase-shift keying Bandwidth efficiency o Bandwidth efficiency of M-ary PSK signals n Null-to-null bandwidth n Bandwidth efficiency Po-Ning Chen@cm.nctu Chapter

34 6.3 Coherent phase-shift keying Bandwidth efficiency o Final note n There is a trade-off between symbol error rate and bandwidth efficiency for M-ary PSK signals. Po-Ning Chen@cm.nctu Chapter Hybrid amplitude/phase modulation schemes o For M-ary PSK signals, the in-phase and quadrature components are dependent. n How about making them independent (to increase the data rate)? n Answer: M-ary quadrature amplitude modulation (QAM) Po-Ning Chen@cm.nctu Chapter

35 6.4 Hybrid amplitude/phase modulation schemes o Square constellation PSK n Gray-encoded quadbits o Gray-encode the first two bits by quadrants (PSK) o Gray-encode the remaining two bits within quadrants (ASK) Po-Ning Chen@cm.nctu Chapter Hybrid amplitude/phase modulation schemes o Symbol error rate of square QAM o Symbol error rate of equal-prior L-ary ASK Po-Ning Chen@cm.nctu Chapter

o Symbol error rate of equal-prior L-ary ASK Po-Ning Chen@cm.nctu Chapter 6-71 6.

36 o Symbol error rate of equal-prior L-ary ASK Po-Ning Chapter Hybrid amplitude/phase modulation schemes o Average transmitted energy of M-ary QAM Po-Ning Chen@cm.nctu Chapter

37 6.4 Hybrid amplitude/phase modulation schemes o Square constellation QAM n M is usually even power of two. n For example, M = 2 2, 2 4, 2 6, 2 8, (in such case L = 2, 2 2, 2 3, 2 4, ) o Question: How about M = 2 3, 2 5, 2 7, n Answer: Cross constellation QAM Po-Ning Chen@cm.nctu Chapter Hybrid amplitude/phase modulation schemes o Symbol error rate of cross-constellation QAM Po-Ning Chen@cm.nctu Chapter

38 6.4 Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) o QAM can be viewed as one of the family members in carrierless amplitude/phase modulation (CAP) Po-Ning Chen@cm.nctu Chapter 6-75 o Re-express QAM into CAP form Carrierless since no carrier f c appears in this formula. Po-Ning Chen@cm.nctu Chapter

39 6.4 Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) o Properties of the passband in-phase and quadrature pulses in CAP n Property 1: Po-Ning Chen@cm.nctu Chapter Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) Po-Ning Chen@cm.nctu Chapter

40 A2.3 Hilbert transform o Let P(f) be the spectrum of a real function p(t). n By convention, denote by u(f) the unit step function, i.e., Multiply by 2 to unchange the area. o Put g + (t) to be the function corresponding to 2u(f)P(f). Po-Ning Chen@cm.nctu Chapter A2.3 Hilbert transform o How to obtain g + (t)? o Answer: Hilbert Transformer. Proof: Observe that Then by the next slide, we learn that Po-Ning Chen@cm.nctu Chapter

41 By extended Fourier transform, Po-Ning Chapter A2.3 Hilbert transform Po-Ning Chapter

42 A2.3 Hilbert transform 1 h( t ) = pt Po-Ning Chen@cm.nctu Chapter Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) Po-Ning Chen@cm.nctu Chapter

43 A2.3 Hilbert transform n Hence, Hilbert transform is basically a 90 degree phase shifter. Po-Ning Chen@cm.nctu Chapter A2.3 Hilbert transform 1 h( t ) = pt 1 h( t ) = pt Ä -1 Po-Ning Chen@cm.nctu Chapter

44 A2.3 Hilbert Transform o An important property of Hilbert transform is that: (Examples of Hilbert transform pairs can be found in Table A6.4.) Po-Ning Chen@cm.nctu Chapter Po-Ning Chen@cm.nctu Chapter

45 6.4 Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) o Properties of the passband in-phase and quadrature pulses in CAP n Property 2: n Property 3: o This is similar to use another pulse shaping function as g(t)*l(t). o One is thus free to choose the pulse shaping function (to, e.g., improve the bandwidth efficiency) without affecting the orthogonality of two quadratures. Po-Ning Chen@cm.nctu Chapter 6-89 o Example 6.4: Bandwidthefficient spectral shaping n a = 0.2 Po-Ning Chen@cm.nctu Chapter

46 6.4 Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) o Block diagram of CAP transmitter (See Slide 6-76) Po-Ning Chen@cm.nctu Chapter Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) o Block diagram of CAP receiver Po-Ning Chen@cm.nctu Chapter

47 6.4 Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) o How about channels with intersymbol interferences, in addition to AWGN? s(t) Linear time-variant filter h(t) + x(t) Channel w(t) Po-Ning Chen@cm.nctu Chapter 6-93 o Recall in Section 4.9: Optimum linear receiver. Recall the below terms: 1. Zero-forcing equalizer 2. Nyquist criterion/isi 3. Noise enhancement 4. MMSE equalizer n Design of receiver c(t) as an MMSE equalizer Po-Ning Chen@cm.nctu Chapter

48 6.4 Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) o This leads to Fig in text. o Can we implement the above structure in digital form? Po-Ning Chen@cm.nctu Chapter Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) Combine into one FIR filter May be adaptive when required Po-Ning Chen@cm.nctu Chapter

49 6.4 Hybrid amplitude/phase modulation schemes Carrierless amplitude/phase modulation (CAP) o Applications of CAP n Passband transmission of digital data over twisted-pair wiring of lengths less than 100m. n Data rates may range from 51 upto 155 Mbps with bandwidth being strictly limited to 30 MHz. Po-Ning Chen@cm.nctu Chapter Coherent frequency-shift keying o (M-ary) ASK, (M-ary) PSK and (M-ary) FSK are three major categories of digital modulations, in which QAM can be viewed/analyzed similarly to (M-ary) PSK. o In this section, the last one, i.e., (M-ary) FSK, will be introduced and discussed. Po-Ning Chen@cm.nctu Chapter

6.5 Coherent frequency-shift keying o Binary FSK E b is the transmitted energy per bit, and T b is the bit duration. o Vector space analysis of binary FSK Po-Ning Chen@cm.nctu Chapter 6-99 E. D.

50 6.5 Coherent frequency-shift keying o Binary FSK E b is the transmitted energy per bit, and T b is the bit duration. o Vector space analysis of binary FSK Po-Ning Chen@cm.nctu Chapter 6-99 E. D. Sunde, "Ideal binary pulse transmission by AM and FM," Bell Labs Technical Journal, 38, pp , November With this multiple-(1/t b ) restriction, it becomes continuous-phase in every inter-bit transition. Such kind of forced continuous-phase signals, known as Sunde s FSK, surely belongs to the general continuous-phase FSK (CPFSK) family. Po-Ning Chen@cm.nctu Chapter

Thus there are three basic modulation techniques: 1) AMPLITUDE SHIFT KEYING 2) FREQUENCY SHIFT KEYING 3) PHASE SHIFT KEYING

Thus there are three basic modulation techniques: 1) AMPLITUDE SHIFT KEYING 2) FREQUENCY SHIFT KEYING 3) PHASE SHIFT KEYING CHAPTER 5 Syllabus 1) Digital modulation formats 2) Coherent binary modulation techniques 3) Coherent Quadrature modulation techniques 4) Non coherent binary modulation techniques. Digital modulation formats: