ASK, FSK, PSK - Faculty of Computing, Engineering and Technology
Transcription
ASK, FSK, PSK - Faculty of Computing, Engineering and Technology
Faculty of Computing, Engineering & Technology Digital modulation: ASK, FSK, PSK Communications COMMS (CE700038-2) Alison L Carrington C203 [email protected] www.fcet.staffs.ac.uk/alg1 2008/9 Digital modulation: ASK, FSK, PSK 2 Overview Why is modulation is needed? What is modulation? Digital modulation & demodulation techniques Obtain SNR of system by: Signal Power Noise Power Determine the performance of different Digital Mod/Demod techniques with different amounts of noise COMMS (CE700038-2) 2008/9 3 Introduction Digital modulation: ASK, FSK, PSK Often send information in a digital form As binary words, bits represented by 1’s & 0’s Could be from a keyboard, characters encoded as 1’s & 0’s Or a microphone (speech) Or a temperature sensor converted to binary form by A/D converter. Why do we need to modulate? COMMS (CE700038-2) 2008/9 Digital modulation: ASK, FSK, PSK 4 Why modulate? The purpose of a communication system is to transfer information from a source to a destination Problems arise in baseband transmissions: Noise external & circuit noise reduces the signal-to-noise (S/N) ratio at the receiver, (Rx) reducing the quality of the output. Not able to fully utilise the available bandwidth: telephone quality speech has a bandwidth ≃ 3kHz co-axial cable has a bandwidth of 100's of Mhz. COMMS (CE700038-2) 2008/9 5 What is Modulation? #1 Digital modulation: ASK, FSK, PSK A message signal containing information is used to control parameters of a carrier signal i.e. the information is embedded onto the carrier The message can either be: Analogue – m(t) Digital – d(t), sequence of 1's and 0's When message is analogue = Analogue Modulation digital = Digital Modulation The carrier could either a 'sinusoidal wave' or a 'pulse train‘ At the destination the carrier+message must be demodulated so that the message can be Rx’d COMMS (CE700038-2) 2008/9 6 What is Modulation? #2 Digital modulation: ASK, FSK, PSK If the message d(t) controls amplitude = AMPLITUDE SHIFT KEYING ASK. Frequency = FREQUENCY SHIFT KEYING FSK Phase = PHASE SHIFT KEYING PSK. d(t) is a binary or 2 level signal representing 1's and 0's This is binary or 2 level, e.g. Binary FSK, BFSK, BPSK, etc. or 2 level FSK, 2ASK, 2PSK etc. COMMS (CE700038-2) 2008/9 7 What is Modulation? #3 Digital modulation: ASK, FSK, PSK Multiple Levels: A message signal could be multi-level or m levels each level represents a discrete pattern of 'information' bits. For example, m = 4 levels Why increase M? As the number of levels increase the amount of information transmitted increases – but the probability of receiving an error also increases COMMS (CE700038-2) 2008/9 Digital modulation: ASK, FSK, PSK 8 Baud Rate #1 The baud rate of a data communications system is the number of symbols per second transferred. As a symbol may have > 2 states, it may represent > 1 binary bit (a binary bit always represents exactly two states). Therefore the baud rate may not equal the bit rate COMMS (CE700038-2) 2008/9 9 Baud Rate #2 Digital modulation: ASK, FSK, PSK A Bell 212A modem uses QPSK modulation each symbol has one of four phase shifts (of 0(deg), 90(deg), 180(deg), or 270(deg)) two bits represent four states (00, 01, 10, and 11), the modem transmits 1,200 bits/s of information, using a symbol rate of 600 baud. Usually the baud rate of a modem will not equal the bit rate and is of no interest to the end user--only the data rate, in bits per second. As modems transfer signals over a telephone line the baud rate is limited to a maximum of 2400 baud. This is a physical restriction of telephone lines Higher data throughput achieved with 9600 or higher baud modems is accomplished by using sophisticated phase modulation, and data compression techniques COMMS (CE700038-2) 2008/9 10 Baud Rate #3 Digital modulation: ASK, FSK, PSK Asymmetric Digital Subscriber Line (ADSL) is used for Broadband Internet access Allows faster data transmission over copper telephone lines than a conventional voiceband modem By using the frequencies that are not used by a voice telephone call using Frequency Division Multiplexing (FDM). A splitter - or microfilter - allows a single telephone connection to be used for both ADSL service and voice calls simultaneously As phone lines vary in quality and were not originally engineered with DSL in mind, it can generally only be used over short distances, typically less than 4km. COMMS (CE700038-2) 2008/9 11 Baud Rate #4 Digital modulation: ASK, FSK, PSK Data +ve Bi polar NRZ -ve +ve Bi polar RZ -ve +ve Bi polar Bi Phase -ve Bit rate=1/τB Baud rate=1/τE ‘1’ τB ‘0’ ‘1’ ‘1’ ‘0’ ‘0’ Baud rate=1/τE=1000Baud τE Baud rate=1/0.5m=2000Baud τE Baud rate=1/0.5m=2000Baud τE Advantage of a transition in every bit – self checking e.g. if τB=1ms, Bit rate=1000bps COMMS (CE700038-2) 2008/9 12 System Block Diagram (S/N) Channel BW MOD Digital modulation: ASK, FSK, PSK d(t) MODULATOR ASK FSK PSK Noise vn(t) B Hz p0 CHANNEL EG. Txn line radio satellite Filter Bn DEMOD Noise bandwidth DEMODULATOR Decision Detector d(t) prob of error p DETECTOR/ DECISION COMMS (CE700038-2) 2008/9 Amplitude Shift Keying, ASK 13 Different amplitudes of carrier Usually, one amplitude is ‘0’ Digital modulation: ASK, FSK, PSK i.e. presence and absence of carrier is used Susceptible to sudden gain changes Inefficient, up to 1200bps on voice grade lines Used over optical fiber – due to low error source V1 V0 Amplitude Shift Keying ASK 1 T 0 destination 0 1 0 0 1 1 digital signal On off Keying, OOK COMMS (CE700038-2) 2008/9 14 ASK Modulation of data sequence d(t) Amplitude Shift Keying Digital modulation: ASK, FSK, PSK Analogue Multiplier d(t) V(t)=d(t).VCcos(ωCt) ASK/OOK d(t)=1 for ‘1’ d(t)=0 for ‘0’ Carrier VCcos(ωCt) Analogue Gate (4066) Carrier: VCcos(ωCt) V(t)=d(t).VCcos(ωCt) d(t)=1 for ‘1’ d(t)=0 for ‘0’ 0V COMMS (CE700038-2) 2008/9 Digital modulation: ASK, FSK, PSK 15 Phase Shift Keying, PSK Phase of carrier signal is shifted data Binary PSK: Two phases represent two binary digits Differential PSK: Phase shifted relative to previous transmission rather than some reference signal COMMS (CE700038-2) 2008/9 16 PSK Modulation of data sequence, d(t) d(t) Digital modulation: ASK, FSK, PSK Phase Shift Keying V(t)=d(t).VCcos(ωCt) d(t)= ‘1’ d(t)= ‘0’ Carrier VCcos(ωCt) (+1).VCcos(wCt) (-1).VCcos(wCt) d(t) ‘1’ or ‘0’ Osc ‘in-phase’ or ‘phase inverted’ VCcos(ωCt) +VCcos(ωCt) -1 or -VCcos(ωCt) COMMS (CE700038-2) 2008/9 Frequency Shift Keying, FSK Digital modulation: ASK, FSK, PSK 17 Two binary values represented by two different frequencies (near carrier) Less susceptible to error than ASK Applications: Up to 1200bps on voice grade lines, High frequency radio, even higher frequency on LANs using co-ax source V1 V0 Frequency Shift Keying FSK 1 T 0 destination 0 1 0 0 1 1 digital signal Various types: OFSK, FFSK COMMS (CE700038-2) 2008/9 18 FSK Modulation of d(t) Digital modulation: ASK, FSK, PSK Frequency Shift Keying VIN d(t) fOUT FSK V/F Osc f1 f1=fC+αV f0=fC fC ‘1’ t d(t) ‘1’ or ‘0’ ‘0’ V VIN f1 or f0 Osc f0 COMMS (CE700038-2) 2008/9 19 System Block Diagram – model for analysis (S/N) Channel BW MOD Digital modulation: ASK, FSK, PSK d(t) MODULATOR ASK FSK PSK Noise vn(t) B Hz p0 CHANNEL EG. Txn line radio satellite Filter Bn DEMOD Noise bandwidth DEMODULATOR Decision Detector d(t) prob of error p DETECTOR/ DECISION COMMS (CE700038-2) 2008/9 20 Channel - Impairments When signals are transmitted they are subject to noise Signal y = cos(x) Amplitude (V) 2 0 -2 -4 0 1 2 3 time (s) 4 5 6 0 1 2 3 time (s) 4 5 6 4 Amplitude (V) Digital modulation: ASK, FSK, PSK 4 2 0 -2 -4 Noise is assumed to be ADDITIVE, WHITE, GAUSSIAN, AWGN – mean of zero infinite bandwidth – hence a bandlimiting filter is required p0 is the noise power spectral density (Watts/Hertz) COMMS (CE700038-2) 2008/9 21 System Block Diagram – model for analysis (S/N) Channel BW MOD Digital modulation: ASK, FSK, PSK d(t) MODULATOR ASK FSK PSK Noise vn(t) B Hz p0 CHANNEL EG. Txn line radio satellite Filter Bn DEMOD Noise bandwidth DEMODULATOR Decision Detector d(t) prob of error p DETECTOR/ DECISION COMMS (CE700038-2) 2008/9 ASK & PSK Demodulator 22 Digital modulation: ASK, FSK, PSK Optimum Demodulator, based on ‘correlation’: Signal + Noise p0 i.e. how similar is the received signal to one of the possible transmitted signals: (S/N)IN VIN Bn cos(ωCt) carrier 1 T ∫ T 0 VINdt I&D ∆, ND + D VREF - Integrate & Dump, T is the bit duration ck Data Clock Q d(t) prob of error p COMMS (CE700038-2) 2008/9 23 Demodulator – FSK Digital modulation: ASK, FSK, PSK Optimum Demodulator, based on ‘correlation’: Signal + Noise p0 1 T (S/N)IN cos(ω1t) ∫ T 0 dt I&D + Bn - 1 T cos(ω0t) ∫ T 0 dt I&D ∆, ND + D VREF - ck Data Clock Q d(t) prob of error p A requirement to receive the carrier ωC or ω1 & ω0 & the 2008/9 ‘bit rate’ COMMS clock (CE700038-2) - DATA CLOCK 24 Demodulator – Circuit – A/P/FSK Digital modulation: ASK, FSK, PSK I&D pulse SIN S+N VIN Bn p0 NIN=p0Bn + R cos(ωCt) carrier VREF +V ∆, ND -V Input signal + bandlimited noise NIN=poBN multiplied by a carrier Cos(ωct) for ASK/PSK Cos(ω0t) & Cos(ω1t) for FSK COMMS (CE700038-2) 2008/9 25 PSK demodulation ex #1 Digital modulation: ASK, FSK, PSK If d(t) is a ‘1’, input is d(t)VCcos(ωCt) VIN=V1=d(t)VCcos(ωCt)*cos(ωCt)+Noise VIN=d(t)VCcos2(ωCt)+Noise d(t) d(t) VIN = VC + VC cos(2ϖ C t) + Noise 2 2 If d(t) is a ‘0’, input is -d(t)VCcos(ωCt) VIN=-d(t)VCcos2(ωCt)+Noise d(t) d(t) VIN = − VC − VC cos(2ϖ C t) + Noise 2 2 VIN COMMS (CE700038-2) 2008/9 26 PSK demodulation ex #2 The Integrate & Dump performs the ‘function’ Digital modulation: ASK, FSK, PSK where T is the duration of a bit 1 T ∫ T 0 T VIN dt 1 0 1 1 T The Integrator VOUT 1 RC =− VIN dt ∫ 0 RC Design RC=T VIN + R 0V +V VOUT -V (CE700038-2) 2008/9 COMMS PSK demodulation ex #3 Digital modulation: ASK, FSK, PSK 27 I&D pulse shown, allows the integrator to integrate for a time T, after which the integrator is cleared or ‘dumped’ by shorting out C & the integration recommences T 1 0 1 1 I&D ∆ Volts VREF VOUT Decision ‘1’ or ‘0’ ‘1’ ‘0’ COMMS (CE700038-2) ‘1’ ‘1’ 2008/9 28 PSK demodulation ex #4 Digital modulation: ASK, FSK, PSK Integrate & Dump Output: Input VIN 1 T ∫ T 0 VINdt VOUT= 1 T ∫ T 0 VINdt I&D cos(ωCt) Input = d(t)VCcos(ωCt) 1 T 2 d ( t ). V cos (ϖ C t)dt C ∫ 0 T V d(t) = C 2 VOUT = VOUT COMMS (CE700038-2) 2008/9 29 V0 VREF V1 Digital modulation: ASK, FSK, PSK - ∆ VREF D + ck Data Clock Q d(t) prob of error p V0 is the voltage when a ‘0’ was transmitted V1 is the voltage when a ‘1’ was transmitted The peak-to-peak input to the comparator is Change in Volts ∆ = V0-V1 This difference between a ‘1’ & a ‘0’ The reference VREF is set midway between V1 & V0. VREF ∆ ∆ V1 + V0 = V0 − = V1 + = 2 2 2 A HALF LEVEL THRESHOLD DETECTOR If V1=10V, V0=5V: ∆=2.5 & VREF=7.5VCOMMS (CE700038-2) 2008/9 PSK demodulation ex #6 30 Digital modulation: ASK, FSK, PSK Integration in presence of Noise i.e. Comp output which is clocked at the Data Clock Rate This makes a final decision if a ‘1’ or a ‘0’ is received 1 Noise 1 Noise 0 1 1 ∆ Volts VREF Noise causes this 0 1 0 1 0 1 Data CLK Q output 0, error Noise causes the integrator to fluctuate & causes errors COMMS (CE700038-2) 2008/9 31 Modulation & Demodulation FSK f f f f V1 1 0 Digital modulation: ASK, FSK, PSK V0 1 0 0 1 V1 1 d(t) fOUT f1 0 1 MOD V0 DEMOD V/F F/V VOUT gdt=α KHz/V V1 0 0 1 gdt=K V/KHz fC V0 f0 VIN VDC TB f0 f1 fIN ‘1’ ‘0’ V0 t V1 K is usually designed to be 1/α COMMS (CE700038-2) 2008/9 32 FSK Demodulation #2 gdt= α KHz/V fOUT Digital modulation: ASK, FSK, PSK fC f0 VDC TB ‘1’ ‘0’ t V1 V0 Bit rate=Baud rate f1=fC+αV1 Peak-to-peak deviation =f1-f0 fC=αVDC y=mx+c f0=fC-αV0 (V0 is –ve) fOUT=αVIN+f0 VIN VIN=VDC+d(t) VIN=VDC+V1 for 1’s VIN=VDC+V0 for 0’s f1=αVDC+αV1+f0 for 1’s fC=αVDC, TC=1/fC Normalised frequency Deviation ratio, h = f1 − f 0 Rb Rb=1/τB i.e. modulus of f1-f0 COMMS (CE700038-2) 2008/9 33 FSK Demodulation #3 Digital modulation: ASK, FSK, PSK The spectrum of the FSK signal depends on h. Waveforms V1 V0 1 0 0 1 0 0 1 Bit rate=Baud rate 1 Rb=1/τB VDC TB t Frequency Shift Keying FSK t f1 f0 f1 f0 f1 COMMS (CE700038-2) 2008/9 34 System Block Diagram – model for analysis (S/N) Channel BW MOD Digital modulation: ASK, FSK, PSK d(t) MODULATOR ASK FSK PSK Noise vn(t) B Hz p0 CHANNEL EG. Txn line radio satellite Filter Bn DEMOD Noise bandwidth DEMODULATOR Decision Detector d(t) prob of error p DETECTOR/ DECISION COMMS (CE700038-2) 2008/9 35 Performance of Digital Systems #1 Digital modulation: ASK, FSK, PSK Performance of Digital Data Systems is dependent on the bit error rate, b.e.r.* i.e. the probability of a bit being in error p= no. of errors, E as N → ∞ Total no. of bits N p depends on several factors The The The The modulation type: ASK, FSK or PSK demodulation method noise in the ‘system’ signal-to-noise ratio *p is a prediction of how the system will perform b.e.r. is a measure of how the system actually performs COMMS (CE700038-2) 2008/9 36 Performance #2 Digital modulation: ASK, FSK, PSK Obtain the received Signal Power Noise Power Calculate the SNR based on a particular modulation method Predict the theoretical performance using Error Function Tables COMMS (CE700038-2) 2008/9 37 Performance #3 Digital modulation: ASK, FSK, PSK (S/N)IN Filter Bn DEMOD ∆, ND VREF + D - ck Q d(t) prob of error p Data Clock Find ∆, ND in terms of SIN & NIN p as a function of (S/N)IN COMMS (CE700038-2) 2008/9 38 Performance #4 - Signal Power, SIN Digital modulation: ASK, FSK, PSK Usually assume an un-modulated carrier i.e. a signal=VCcos(ωCt) - ALWAYS VC Normalised Average Power=(VRMS)2 VC VRMS = Vpeak 2 = VC 2 2 2 Normalised Average Power=(VRMS)2= ⎛⎜ VC ⎞⎟ = VC = S IN 2 ⎝ 2⎠ 2 S IN VC = Watts 2 Similarly for FSK & PSK VC COMMS (CE700038-2) 2008/9 Digital modulation: ASK, FSK, PSK 39 Performance #4 - Noise Power, NIN Channel BW vn(t) Signal + Noise B Hz VIN Bn p0 ‘Peak’ value of noise, Normalised Average Noise Power, NIN=p0Bn vn(t)IN = 2p0 B ∴ N IN ∫ T 0 VINdt Dec Det I&D cos(ωCt) carrier ⎛ N pk = ⎜⎜ ⎝ 2 1 T Contrived to be equivalent to noise power ⎞ ⎟⎟ ⎠ 2 COMMS (CE700038-2) 2008/9 40 Performance #5 – SNR & p Digital modulation: ASK, FSK, PSK SIN/NIN 2 S IN 2 N pk S IN VC = / N IN 2 2 2 VC = Watts 2 N IN ⎛ N pk = ⎜⎜ ⎝ 2 ⎞ ⎟⎟ ⎠ 2 2 2 S IN VC = N IN N pk 2 VC = 2 N pk Substitute into the correct equation to obtain p B - ASK OOK B − FSK B − PSK PRK ⎞ ⎟ ⎟ ⎠ S IN ⎞⎟ 1 ⎛⎜ p = ⎜1 − erf 2⎝ 2 N IN ⎟⎠ S IN ⎞⎟ 1 ⎛⎜ p = ⎜1 − erf 2⎝ N IN ⎟⎠ COMMS (CE700038-2) 1 ⎛⎜ p = ⎜1 − erf 2⎝ S IN 4 N IN 2008/9 41 Performance #6 B - ASK OOK Digital modulation: ASK, FSK, PSK B − FSK B − PSK PRK 1 ⎛⎜ p = ⎜1 − erf 2⎝ ⎞ ⎟ ⎟ ⎠ S IN ⎞⎟ 1 ⎛⎜ p = ⎜1 − erf 2⎝ 2 N IN ⎟⎠ S IN ⎞⎟ 1 ⎛⎜ p = ⎜1 − erf 2⎝ N IN ⎟⎠ S IN 4 N IN 1 10-1 p PSK is ‘best performance’ FSK is next ASK is worst 10-2 10-4 10-5 PSK FSK ASK 5dB (S/N)IN dB COMMS (CE700038-2) 2008/9 Error Function 42 Digital modulation: ASK, FSK, PSK The "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by : erf ( z ) = 2 π ∫ z 0 e −t dt 2 erfc( z ) = 1 − erf ( z ) x erf(x) erfc(x) 0 0.000 1.000 0.1 0.112 0.888 0.2 0.223 0.777 0.3 0.329 0.671 0.4 0.428 0.572 0.5 0.520 0.480 0.6 0.604 0.396 0.7 0.678 0.322 0.8 0.742 0.258 0.9 0.797 0.203 1 0.843 0.157 1.1 0.880 0.120 1.2 0.910 0.090 1.3 0.934 0.066 x erf(x) erfc(x) 1.4 0.952 0.048 1.5 0.966 0.034 1.6 0.976 0.024 1.7 0.984 0.016 1.8 0.989 0.011 1.9 0.993 0.007 2 0.995 0.005 2.1 0.997 0.003 2.2 0.998 0.002 2.3 0.999 0.001 2.4 0.999 0.001 2.5 1.000 0.000 2.6 1.000 0.000 2.7 1.000 0.000 x erf(x) erfc(x) 2.8 1.000 7.50E-05 2.9 1.000 4.11E-05 3 1.000 2.21E-05 3.1 1.000 1.16E-05 3.2 1.000 6.03E-06 3.3 1.000 3.06E-06 3.4 1.000 1.52E-06 3.5 1.000 7.43E-07 COMMS (CE700038-2) 2008/9 43 Tutorial 1: find SNRdB for each case Case B Case A Signal y = cos(x) Signal + Noise: mean=0 & variance=0.1 Digital modulation: ASK, FSK, PSK 4 4 2 0 0 -2 -4 0 Case C -2 SNR = ? 1 2 3 4 5 6 -4 0 Case D Signal + Noise: mean=0 & variance=0.5 4 1 2 3 4 5 6 Signal + Noise: mean=0 & variance=1.0 4 Npk = 1.76V 2 0 -2 -2 1 2 3 4 Npk = 3.16V 2 0 -4 0 Npk = 0.302V 2 Npk = 0V 5 6 -4 0 1 2 3 4 5 6 COMMS (CE700038-2) 2008/9 44 Solution 1 SNR for case A: Digital modulation: ASK, FSK, PSK 2 S IN VC 1 = = =∞ 2 0 N IN N pk SNR for case B: S IN 1 = = 10.96 2 N IN (0.302 ) ⎛ Sin ⎞ ⎟⎟ SNRdB = 10 log10 ⎜⎜ ⎝ N in ⎠ SNRdB = ∞dB SNRdB = 10 log10 (10.96) SNRdB = 10.40dB SNR for case C: -4.91dB SNR for case D: -10.00dB COMMS (CE700038-2) 2008/9 Digital modulation: ASK, FSK, PSK 45 Tutorial 2 With Reference to the following equations and error function tables, what is the performance of Binary ASK, FSK & PSK at 0, 4 & 8dB? Plot your results on logarithmic / linear paper Comment on the performance at 4dB, rank the modulation schemes and comment COMMS (CE700038-2) 2008/9 Solution 2 SNR (dB) 0 1 2 3 4 5 6 7 8 9 10 1.E+00 probability of error, p Digital modulation: ASK, FSK, PSK 46 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 ASK FSK PSK COMMS (CE700038-2) 2008/9 47 Tutorial 3 Digital modulation: ASK, FSK, PSK Explain what is meant by ‘Baud Rate’ If data signal is represented as h(t) = +V for 1’s = -V for 0’s h(t) v(t) cos(ωCt) i) What modulation scheme is this? ii) Sketch the output waveform, v(t) iii)Obtain Vout(t) stating any assumptions h(t)[cos(ωCt)] LPF cos(ωCt) VOUT(t) COMMS (CE700038-2) 2008/9 48 Solution 3 Digital modulation: ASK, FSK, PSK i) Phase reversed keying ii) iii) Vout(t) : VOUT (t ) = h(t ) cos(ϖ C t ). cos(ϖ C t ) VOUT (t ) = h(t ) cos(0 ) + 2 h(t ) cos(2ϖ C t ) 1244244 3 use LPF to filter out this component VOUT (t ) = h(t ) 2 COMMS (CE700038-2) 2008/9