6. Modulation and Multiplexing Techniques

Size: px

Start display at page:

Download "6. Modulation and Multiplexing Techniques"

Eugenia Elliott
6 years ago
Views:

1 6. Modulation and Multiplexing Techniques The quality of analog transmission is S/N (signal to noise ratio). signal power S/N = baseband noise power S/N can be greater than C/N. For instance for FM (frequency modulation) TV transmission: [S/N] can be up to 35 db larger than [C/N]. The quality of digital transmission is BER (bit error rate). number of improperly detected bits during time t BER = total number of bits detected during time t e.g. BER = 10-5 è on average 1 bit in 100,000 is wrong. S/N and BER depend on C/N and on the modulation technique. Analogue modulation Amplitude modulation (AM) Frequency modulation (FM) Phase modulation (PM Digital modulation Amplitude shift keying (ASK) Frequency shift keying (FSK) Phase shift keying (PSK) o Binary PSK (BPSK) o Quadrature PSK (QPSK)

2 Analogue modulation carrier carrier modulator modulated carrier A 0 cos(w c t+y) C(t)=A(t)cos[w c t+f(t)] modulating signal or baseband signal m(t) (from data, TV ) AM: message is carried in A(t): C(t)= A(t)cos[w c t+f 0 ] FM: message is carried in w(t): C(t)=A 0 cos[w(t)+f 0 ] PM: message is carried in f(t) : C(t)=A 0 cos[w c t+f(t)] Demodulation Modulated carrier C(t) Carrier demodulator recovered baseband signal m(t) A 0 cos[w c t+y ] Amplitude modulation (AM) c(t) = A(t) cos (w c t + f 0 ) w c : carrier angular frequency = A 0 [1+D a m(t)] cos (w c t + f 0 )

3 D a : 0 D a 1 : amplitude modulation index m(t) : m(t) 1 : baseband signal Graphical example for a special case: m(t) = cos w m t A 0 w m : modulating frequency D a =0 A 0 cos[w c t+f 0 ] m(t) 1 m(t) = cos w m t -1 c(t) A 0 D a =0.5 C(t)=A 0 [1+ 0.5cosw m t]cos(w c t + f 0 ) -A 0 AM spectrum Amplitude baseband spectrum f=w/2p 0 f m f c - f m f c f c +f m

4 General case: baseband signal m(t) consists of sine waves with continuous range of frequencies. C(t) A 0 0 AM spectrum for general case Amplitude triangular baseband spectrum lower sideband upper sideband f max f c - f max f c f c +f max Here, the spectrum of m(t) is just plotted as a triangularly shaped spectrum. S/N» C/N at detector output 1. AM does not provide improvement of S/N over C/N. 2. AM is very susceptible to non-linear distortions as produced in satellite transponders, and is easily disturbed by link noise and interference. è AM is essentially never used in satellite communications. Frequency modulation (FM) c(t) = A 0 cos (w(t) + f 0 ) w c : carrier angular frequency

5 = A 0 cos[(w c t) +D ò m(t) dt + f 0 ] D: constant For special case : m(t) = cos w m t c(t) = A 0 cos[(w c t) + b sin w m t + f 0 ] b = ad/w m = Dw/w m = Df/f m : modulation index Graphical example: w m = 2p f m Dw = 2p Df : modulation frequency : max. frequency deviation, i.e. the frequency of the modulated carrier varies between w c =-Dw and w c =+Dw. b=0 c(t)=a 0 cos[w c t+y] m(t)=a cos w m t b>0 c(t)=a 0 [(w c t)+bsin w m t+f 0 ] How does the spectrum look? Complicated since the FM waveform takes the form of cos of sin! è Spectrum can be represented by Bessel functions.

n ³ 0 FM spectrum f m f c f c +f m There is an infinite number of side frequencies. However, the amplitudes of the side spectral components decrease very rapidly for those components larger than b.

6 n ³ 0 FM spectrum f m f c f c +f m There is an infinite number of side frequencies. However, the amplitudes of the side spectral components decrease very rapidly for those components larger than b. è We do not need an infinitely wide filter bandwidth. Most of the information of a FM signal is in fact passed through a filter with a finite bandwidth, B, that depends on the modulation index b. The bandwidth, B, is essentially the range in frequencies from f c (b + 1) f m to f c + (b + 1) f m. B=2 (b + 1) f m B=2 (Df + f m ) : Carson s rule If m(t) is not just a cosine wave but a signal with a continuous range of spectral components, then we characterize such a spectrum as before as follows:

7 Amplitude f max Then: b= DF/f max B= 2 (DF+ f max ) f max : modulation index for highest frequency in baseband spectrum. b is also sometimes called the deviation ratio, D. DF is similar to Df, that is, it is the frequency range over which the carrier frequency is modulated. Examples: 1) A 100 MHz carrier is frequency modulated by a 1 khz tone which produces frequency deviations of up to 75 khz. b = Df/f m = 75/1 = 75 B= 2 (Df+ f m ) = 2 (75 + 1) = 152 khz 2) A video signal of bandwidth 4.2 MHz is used to frequencymodulate a carrier with DF = MHz. D = b= DF/f max = 10.75/4.2 = 2.56

8 B= 2 (DF+ f max ) = 2 ( ) = 29.9 MHz Signal-to-noise ratio For FM, the S/N is not equal to C/N. There are three factors that cause an improvement of S/N over C/N. 1. The processing gain K R of the detector as a function of b. S/N = K R C/N K R = 3 (b + 1) b 2 (This is valid only if [C/N] ³ 10 db) Example: For a video signal with b =2.56 è K R = 70 or 18.5 db 2. Preemphasis and Deemphasis The noise at the output of an FM demodulator where conversion back to baseband takes place, increases with increasing frequency. Receiver Amplitude Baseband spectrum of modulating signal m(t) without preemphasis Noise spectrum S/N is lower for higher f f Transmitter modulating signal spectrum before and after preemphasis

9 Receiver before de-emphasis after de-emphasis è Increase of S/N by P: P = emphasis improvement factor [P] 4 db for telephony [P] 13 db for TV 3. Noise weighting By modifying the noise spectrum and adjusting it to the response of the output device and /or the response to the human ear, S/N can be further improved, by [W]. [W] 2.5 db for telephony [W] 12 db for TV Multiplexing Mixed upward to modulate carrier at 6 GHz 70 MHz LO FM modulators 70 MHz LO FM demodulators Frequency division multiplexer Frequency division demultiplexer Baseband channels, terrestrial link

10 The most common analogue multiplexing technique is frequency division multiplexing (FDM). The most common digital multiplexing technique is time division multiplexing (TDM). FDM and TDM are transmission features. FDM and TDM should not be confused with frequency division multiple access (FDMA) and time division multiple access (TDMA). FDMA and TDMA are traffic features. Hirarchical structure of FDM according to CCITT (CCITT Comité Consultatif Internationale de Télégraphique et Téléphonique (International Telegraph and Telephone Consultative Committee) is an agency of the International Telecommunications Union (ITU). The ITU is an agency of the UN. The CCITT is an agency coordinating telephone and data communications systems on a worldwide basis and dealing with regulatory matters and with technical standards.)

11 12 baseband (voice channels) (1) khz khz khz (2) 108 khz khz khz khz (12) khz khz khz 64 khz khz Multiplexed signal ( 1 group) khz

12 Spectra are separated by 4 khz to allow for guardband for filtering purposes so that distortions from neighbouring channels are limited. 5 groups (1) khz khz khz (2) 420 khz khz khz khz (5) khz khz khz 612 khz khz Multiplexed signal (1 supergroup) khz

13 5 supergroups 1 basic mastergroup 3 basic mastergroups 1 super mastergroup 900 voice channels multiplexed! ,380 khz 12 (voice) channels è 1 group 5 groups è 1 supergroup 5 supergroups è 1 basic mastergroup 3 mastergroups è 1 super mastergroup The super mastergroup is the highest baseband unit voice channels are frequency division multiplexed. However, lots of other schemes are in use.

14 Transmitting and receiving ends of a typical FDM system Incoming voice channels composite FDM signal 70 MHz FM signal bandwidth: B IF =2(DF+f max ) 0 -- f max to converters and Multi- Frequency Modulator b=df/f max or transmitters plexer 0 f max b=df rms /f max khz b (bandwidth)=3.1 khz f c =70 MHz DF rms : rms frequency deviation per channel DF : peak frequency deviation w.r.t. all channels : center frequency of individual channel f m from IF amplifier, composite FDM signal outgoing voice channels 70 MHz FM signal Frequency Demultiplexer Demodulator C/N (overall C/N of link) S/N S/N=C/N 3(b+1)b 2 PW F LO 70 MHz

15 Example for S/N of a typical FDM system: [C/N] = 25 db [P] = 4 db [W] = 2.5 db DF = 281 khz DF rms = 35 khz f max = 108 khz b = 3.1 khz [S/N] = [C/N] + [3 ( b + 1) b 2 ] + [P] + [W] = = db

16 The baseband signal Here are 4 different kinds Wikipedia

17 Digital modulation carrier carrier modulator modulated carrier m(t) ASK (amplitude shift keying) OOK (on-off keying) FSK (frequency shift keying) PSK (phase shift keying) BPSK (binary PSK) QPSK (quadrature PSK) Digital de-modulation Modulated carrier Carrier demodulator recovered baseband signal

18 ASK FSK (Binary) PSK

QPSK: four distinct phases are utilized. That Means that essentially two BPSK signals are transmitted at once è rate of transmission is doubled.

19 QPSK: four distinct phases are utilized. That Means that essentially two BPSK signals are transmitted at once è rate of transmission is doubled. Baseband bandwidth: The baseband bandwidth, B, of the digital modulating signal depends on the bit rate, R b, and the type of modulation and the filters involved For BPSK : B IF [Hz] = R b [bits per second] For FSK, the bandwidth is larger. Bit error rate (BER) BER characterizes quality of digital transmission. erfc is the complementary error function E b Energy per bit = db [E b /N 0 ] 10 db N 0 Noise power spectral density P R received power (W:J/s) E b = = R b bit rate (bits/s)

By encoding extra bits (redundant bits) it is possible to detect and correct certain errors in the decoding

20 If B N = R B Example: [C/N] = [E b / N 0 ] = 1.56 db è BER = = 6 db è BER = improvement of BER is possible through coding. By encoding extra bits (redundant bits) it is possible to detect and correct certain errors in the decoding process. However, transmission rate is reduced è E b is reduced. But error rate is also reduced. For E b / N 0 ³ 5 db, coding gain can be achieved. Example: E b / N 0 = 6 db è BER 10-7 can be achieved!

Chapter 7 Multiple Division Techniques for Traffic Channels

Introduction to Wireless & Mobile Systems Chapter 7 Multiple Division Techniques for Traffic Channels Outline Introduction Concepts and Models for Multiple Divisions Frequency Division Multiple Access