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,Modulation Techniques,Microwave and RF Design of Wireless Systems,Chapter 9,Dr. Zhang Yonghong,Comparing with transmitting,baseband,signal directly,to transmit data by modulating a higher frequency,carrier wave has the effect on:,controlling the radiated frequency spectrum.,more efficient use of the allocated RF bandwidth.,flexibility in accommodating different,baseband,signal formats.,Amplitude Frequency Phase,AM FM PM,Analog modulation (vary continuously),Digital modulation (change in discrete steps),more efficient use of the radio spectrum.,usually requires less power. CDMA,over a fading communications channel.,more compatible with the use of error correcting codes.,In contrast to analog modulation,digital modulation has:,9.1 Analog Modulation,9.2 Binary Digital,Modulation,9.3 Error Probabilities for Binary,Modulation,9.4 Effect of,Rayleigh,Fading on Bit Error,Rats,9.5 M-,ary,Digital,Modulation,9.1 Analog Modulation,Basic analog modulation:,AM (SSB, DSB), FM, PM,PPM (Pulse Position Modulation),is used in UWB (ultra wideband) system.,1. Signal-Sideband Modulation,2. DSB-SC,Modulation,3. DSB-LC,Modulation,4. Envelope Detection of DSB-LC,Modulation,5. Frequency Modulation (,FM,),1. Signal-Sideband Modulation,m(t):,bandlimited,modulating waveform,f,M,: the maximum frequency of m(t),n,0,/2: two-sided power spectral density of,Gaussian,white noise.,Contributed by the transmitter channel and noise generated by the input stages of the receiver.,The demodulator LO is identical in frequency and phase,with the modulator LO-synchronous or coherent demodulator.,Input signal power:,Output signal power:,Input narrowband noise power:,Output noise power:,The output SNR:,Conclusion:,SSB demodulator does not degrade the input,SNR,.,2. DSB-SC Modulation,Double-sideband suppressed carrier (DSB-SC),Conclusion:,the DSB-SC demodulator improves the input signal-to-noise ratio by a factor of two.,F,SSB,=2F,DSB,But,Conclusion:,The coherent SSB and DSB-SC demodulators have the same SNR,performance,.,3. DSB-LC Modulation,Advantage:,the carrier signal can be used as a reference signal to phase-look the local oscillator to synchronization with the incoming signal.,Double-Sideband Large-Carrier (DSB-LC),Disadvantage:,the carrier power increases the total input power but does not contain any modulation information.,m: modulation index,IF m1, DSB-LC,DSB-SC,m=1 implies a reduction in SNR of 4.8dB.,4. Envelope Detection of DSB-LC Modulation,Advantage of DSB-LC,: can be detected by using an envelope detector, without a LO and mixer, results in a much simple receiver circuit, such as broadcast AM radio.,noncoherent,demodulation,Serious distortion for small,S,i,/N,i,SNR,If |m|1 over modulation, it will not correctly recover the modulating,waveform,.,5. Frequency Modulation (FM),Application:,Broadcast radio, television sound, two-way voice radio,AMPS cellular telephone system.,An FM waveform:,Where, modulating signal,Modulation index:,: Maximum frequency deviation.,Spectrum:,sidebands are spaced at,f,m,on either side of the carrier at ,IF.,amplitudes, given by,AJ,n,(,), decrease for large n.,Carsons rule, B,IF bandwidth,Through differentiator and envelope detection,the output voltage:,For the equal transmit power,Improving factor:,Conclusion:,FM allows an improvement in SNR at the expense of increased bandwidth, while AM does not., S/N, B,=4 SNR,FM,=72SNR,DSB-LC (m=1),B,FM,=5,B,DSB,9.2 Binary Digital Modulation,Amplitude shift keying (ASK),Frequency shift keying (FSK),Phase shift keying (PSK),1. Binary Signals,2. Amplitude Shift,Keying,3. Frequency Shift Keying,(,FSK,),4.,PSK,5. Carrier,Synchroniza,tion,1. Binary Signals,Return-to-Zero code,Non-Return-to-Zero code,Polar NRZ code DC=0,2. Amplitude Shift Keying,where m(t) =0 or 1,(a) Modulator,Identical to the,DSB-SC modulator,Synchronous demodulation,:,After low-pass filtering,(b) Synchronous demodulation,Notice,: LO has precisely the same phase and frequency as the incoming signal, or distortion may be introduced.,Envelope detection,noncoherent, no,LO,(c) Envelope detection,3. Frequency Shift Keying (FSK), -frequency deviation,IF =,1, the up branch output: 1/2,The down branch output: 0,IF =,2, the up branch output: 0,The down branch output: 1/2 reverse phase,It requires two coherent LO operating at,1, and ,2,.,(PLL detector, the control voltage of V,CO,in,PLL,),Envelope detector,4. PSK,The phase of the carrier wave is “0,” or“180,”.,m (t) =1 or -1,Due to the sharp transitions caused by phase reversal, the spectrum of the PSK waveform is relatively wide in bandwidth, resulting that PSK is impractical for,multichannel,wireless systems.,PSK modulator,ASK,:,Non-constant envelope modulation,Coherent demodulation,Noncoherent,demodulation,(envelope detection),FSK:,Constant envelope modulation,Coherent demodulation,Noncoherent,demodulation,(after conversion),PSK:,Constant envelope modulation,Coherent,demodula,tion,5. Carrier Synchronization,The effect of a phase error,is that the output signal is reduced in amplitude by,cos,while an error,in frequency introduces a factor of,cos,t.,The bit error rates of envelope detection are not as good as those obtained with coherent detection.,Two ways to realize synchronization:, transmit a pilot carrier, used to phase-lock the LO., use a carrier-recovery circuit.,Use a phase-locked loop or by frequency multiplier and divider.,In fact, employing digital signal processing (DSP) circuits to perform all function of signal,conditioning, carrier recovery and synchronization demodulation, and signal format,ting,.,9.3 Error Probabilities for Binary Modulation,The presence of noise in a communication channel introduces the possibility that errors will be made during the detection process.,1. PCM Signal and,Detectors,2. Synchronous,ASK,3. Synchronous,PSK,4. Synchronous,FSK,5. Bit rate and Bandwidth Effici,ent,6. Comparison of ASK FSK and PSK,Systems,1. PCM Signal and Detectors,Pulse coded modulation (PCM),where,Define,: bit energy,The output noise power,The variance of the,gaussian,probability distribution,func,tion,2. Synchronous ASK,Ideal if s(t)=s,2,(t) =0, s,0,(T) =0,if s(t)=s,1,(t)=V, s,0,(T)=VT,Practical if s,0,(T)+n,0,(T)VT/2, m(t)=1 ,Let,3. Synchronous PSK,If,Threshold level: 0,ASK: VT/2,For the same probability of error, PSK requires only one-fourth the power of an ASK system. Since an ASK signal is off half the time, in terms of average transmit power, the PSK result is better by a factor of two (3,dB,).,Due to symmetry of the PSK signal and the demodulator.,4. Synchronous FSK,Threshold: 0 the signal levels are similar to the PSK case.,For the noise voltages:,n,1,and n,2,are uncorrelated.,Conclusion:,The total noise power of the FSK demodulator is doubled relative to the synchronous ASK or PSK demodulator.,Conclusion:,synchronous FSK requires 3 dB more signal power than equivalent PSK system for the same probability of error.,synchronous FSK requires 3 dB less power than an ASK system on a peak power basis.,FSK and ASK have equal error rates when compared in terms of average transmit,power,.,5. Bit Rate and Bandwidth Efficient,Define,R,b,:,dimension of,E,b,: W,S,dimension of n,0,: W,/Hz,E,b,/n,0,: dimensionless,the bit rate of the binary message signal,dimension of,R,b,: bps (bit per second),The signal power:,It means the error rate will increase with an increase in bit rate, for a fixed noise power spectrum density, and is independent of the receiver bandwidth.,IF bandwidth f,RF bandwidth,R,b,: depend on the type of modulation,f may range from one to several times the bit rate,R,b,.,S/N before demodulation = S/N after demodulation.,Reference to equation (9.2), (9.3), (9.4) and (9.64, (9.65).,bandwidth efficiency (bps/Hz) of 1 bps/Hz.,For a binary modulation method, transmitting one bit each bit,period,.,means that,This is for the,baseband, not for the IF or,RF,.,6. Comparison of ASK FSK and PSK Systems,Coherent PSK,:,The lowest error rate, 9.6 dB for 10,-5, high price for LO and wide signal bandwidth (2R,b,4R,b,). Best in fading environments. Used in space and satellite communications.,Coherent FSK,:,Requires 34 dB more power than PSK. 12. 6 dB for 10,-5,.,Noncoherent,FSK,:,13.4 dB for 10,-5, widespread historical application in a wide variety of systems, such as date modems, teletype, fax.,Coherent ASK:,Transmitter is simple. 15.6dB for 10,-5, very poor in a fading environment, low data rates limited to short-range, low-lost, used in telemetry and RFID.,Noncoherent,ASK:,Transmitter and receiver are simple, 16.5 dB for 10,-5, very poor in a fading environment, low data rates, short-range, low-cost, used in telemetry and RFID.,EXAMPLE 9.3,page,319.,ASK,FSK,PSK,4,E,b,/n,0,2,E,b,/n,0,E,b,/n,0,15.6dB,12.6dB,9.6dB,E,b,/n,0,for,P,e,=10,-5,9.4 Effect of,Rayleigh,Fading on Bit Error Rats,PDF of a,Rayleigh,fading is,where,is the,rms,value of the distribution of r(t).,1. Effect of,Rayleigh,Fading on Coherent PSK,Where,is the average received bit energy-to-noise,power spectral density ratio of the faded received signal.,2.,Effect of,Rayleigh,Fading on,Noncoherent,FSK,For envelope detection of FSK,3. Comparison of Faded and,Nonfaded,Error Rates,Conclusion:,Fading has the effect of dramatic increasing the required bit energy-to-noise ratio., Error-correcting codes can be used very effectively to improve the error rate for channel fading occurring in short bursts.,Nonfaded,case:,Eye diagram,EXAMPLE 9.4,p,.,323.,9.5 M-,ary,Digital Modulation,Binary modulation methods (ASK, FSK and PSK) transmit one bit per signaling interval, with a bandwidth efficiency of 1bps/Hz.,The data can be divided into groups.,Each group have n binary codes.,One symbol in M=2,n,is transmitted in each signaling interval.,Thus a bandwidth efficiency of n bps/Hz is achieved.,1.,Quadrature,Phase Shift,Keying,2. Probability of Error for,QPSK,3. M-,ary,Phase Shift,Keying,4.,Quadrature,Amplitude Modula,tion,(QAM),5. Channel,Capacity,1.,Quadrature,Phase Shift Keying,n=2, M=4,+,=,The carrier of QPSK:,Note:,Each QPSK phase state can be used to represent two bits of data.,The bandwidth of the QPSK spectrum is narrower than the spectrum of a BPSK signal, because of the average transition between phase states is 90,0,.,The output of the QPSK modulator is a double sideband suppressed carrier signal.,The QPSK output is a constant envelope signal.,The channel should be constant group delay.,Block diagram of a QPSK modulator,Gray Coding,Advantage:,When an error occurs, it is most likely that only one of the bits will be in error, rather than both,bits,.,S,0,45,0,1,1,S,1,135,0,0,1,S,2,-135,0,0,0,S,3,-45,0,1,0,2. Probability of Error for QPSK,The overall probability of error for a symbol is:,A symbol error is most likely to cause only a single bit error for Gray coding. Since each symbol contains two bits, the bit error rate for QPSK will be one-half the symbol error rate:,for BPSK,Led to the extensive use of QPSK modulation in a wide variety of applications, such as CDMA-PCS telephone systems, The Iridium LEO satellite telephone system, and the DBS.,Conclusion,:,with QPSK it is possible to achieve twice the data rate as for BPSK, with less bandwidth and the same error rate.,Bandwidth efficiency is 2 bps/Hz.,EXAMPLE 9.5,page,329.,3. M-,ary,Phase Shift Keying,for i=0, 1, 2 M-1, M=2,n,M=2 for BPSK M=4 for QPSK,bandwidth efficiency n bps/,Hz,4.,Quadrature,Amplitude Modulation (QAM),QPSK:,Generally If,4-QAM is QPSK.,It encompasses ASK and M-PSK.,A symbol includes four bit.,High bandwidth efficiency,Increasingly being used.,M-,QAM, the maximum of M is 256.,5. Channel Capacity,To achieve as low an error as is desired once,E,b,/n,0,is above a critical value.,C is the maximum data rate capacity of the channel (bps).,B is the bandwidth (Hz).,S is the signal power (W).,n,0,/2 is the two-sided power spectral density of the,gaussian,noise (W/Hz).,For a given channel in the presence of additive,gaussian,noise and bandwidth, the maximum data rata C can be achieved.,In practical, only a fraction of C can be achieved.,The use of error correcting codes can provide performance close to the,limit.,QPSK:,constant envelope modulation,nonconstant,envelope modulation,
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