ANALOG COMMUNICATION (9)

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1 11/5/013 DEARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING ANALOG COMMUNICATION (9) Fall 013 Original slides by Yrd. Doç. Dr. Burak Kellei Modified by Yrd. Doç. Dr. Didem Kivan Tureli OUTLINE Noise in Analog Modulation Reeiver Model Noise in DSB-SC Reeivers Noise in AM Reeivers Threshold Effets 1

2 11/5/013 RECEIVER MODEL The noise at the input of reeiver additive, white and Gaussian This enables a method to understand the effet of the noise a framework for the omparison of the noise performane of different CW modulations The reeiver model must provide an adequate desription of the reeiver noise must aount for the inherent filtering and modulation harateristis of the system must be simple enough for statistial analysis RECEIVER MODEL The power spetral density of the noise w(t) is N 0 / defined for both positive and negative frequenies. N 0 is the average noise power per unit bandwidth measured at the front-end of the reeiver. The band-pass filter s bandwidth is equal to the transmission bandwidth of the modulated signal s(t) and mid-frequeny is equal to the arrier frequeny f

3 11/5/013 RECEIVER MODEL The arrier frequeny f is large ompared to the transmission bandwidth B T. The filtered noise n(t) as narrowband noise is represented as n where n I (t) is the in-phase noise omponent and n Q (t) is the quadrature noise omponent. The filtered signal x(t) t n t os f t n t sin f t I x Q t st nt RECEIVER MODEL The average noise power at the demodulator input is equal to the total area under the urve of the power spetral density S N (f). The average noise power is equal to N 0 B T 3

4 11/5/013 RECEIVER MODEL Sine the noise is additive, we an define the signal to noise ratio (), whih is defined as the ratio of average power of the modulated signal s(t) to the average power of the filtered noise. The defined at the hannel output or demodulator input is alled as C The defined at the demodulator or reeiver output is alled O RECEIVER MODEL We an define a figure of merit to ompare different CW modulation shemes. Depending on the modulation sheme the figure of merit an be less than one equal to one greater than one Figure of Merit O C 4

5 11/5/013 NOISE IN DSB-SC RECEIVERS The DSB-SC signal is demodulated using oherent detetion. The loally generated sinusoidal signals phase perfetly mathes with the transmitter s loal osillators phase. This synhronization is usually performed using a phase loked loop (LL) NOISE IN DSB-SC RECEIVERS The DSB-SC omponent of the filtered signal x(t) is s t CA os f t m t where C is the system dependent saling fator in order to ensure that the signal omponent s(t) is measured in the same units as the additive noise omponent n(t). The average power of the message signal is W W S M f df 5

6 11/5/013 NOISE IN DSB-SC RECEIVERS The signal power in DSB-SC signal is S C A With a noise spetral density of N 0 /, the average noise power in the message bandwidth W is equal to WN 0. The hannel signal-to-noise ratio is C, DSB C A WN where C ensures that this ratio is dimensionless. 0 NOISE IN DSB-SC RECEIVERS Let s determine the output signal-to-noise ratio at the oherent demodulator output x t st nt CA os f tmt n t os f t n t sinf t The output of the produt-modulator omponent of the oherent detetor is v t xt osf t 1 1 CA mt ni 1 I I t CA mt n t os 4f t n t sin4f t 1 Q Q 6

7 11/5/013 NOISE IN DSB-SC RECEIVERS The low-pass filter removes the high frequeny omponents of v(t) and the reeiver output is y 1 t CA mt n t The message signal m(t) and in-phase noise omponent n I (t) appear additively at the reeiver output. The quadrature omponent n Q (t) is ompletely rejeted by the oherent detetor. Coherent demodulator guarantees that the signal and noise omponent are additive irrespetive of signal-to-noise ratio. 1 I NOISE IN DSB-SC RECEIVERS The signal power at the detetor output is C A 4 The noise power at the detetor output is N The signal-to-noise ratio at the output is 1 O s WN WN C A / 4 C A WN / WN 0 0 7

8 11/5/013 NOISE IN DSB-SC RECEIVERS The figure of merit of DSB-SC system is O C 1 Note that C fator is ommon and anels out in evaluating the figure of merit. In an AM signal the transmitted signal is s t A 1 k mt os f t k a is small enough not to reate any phase reversal a For reeiver simpliity envelope detetor is used to demodulate the AM signal. The average arrier power is A 8

9 11/5/013 The average message signal omponent of AM signal is A k a where is the average power of the message signal. Total average power of the full AM signal is A 1 ka The average noise power in the message bandwidth is similar to DSB-SC and equal to WN 0 The hannel signal-to-noise ratio for AM is C, AM The AM reeiver with noise model is A 1 ka WN 0 9

10 11/5/013 To evaluate the output signal-to-noise ratio, we need to write the filtered noise in terms of its inphase and quadrature omponents. x t s t n t A A k mt n t os f t n t sinf t a The envelope of the AM signal arries the message signal. Therefore, the envelope of x(t) needs to be determined from its phasor diagram. I Q hasor diagram for AM wave plus narrowband noise for the ase of high arrier-to-noise ratio From this phasor diagram the reeiver output is obtained as y t xt A A k mt n t n t envelope of a I Q 10

11 11/5/013 The signal y(t) is the output of an ideal envelope detetor. The envelope detetor output is omplex and hard to analyze. It needs to be simplified in order to ahieve some meaningful results. The first assumption is the average arrier power is large ompared to noise so that the signal term is larger then the noise term. y(t) an be approximated as y t A A k mt n t a I The d term A in the envelope detetor output y(t) is due to the demodulation of the arrier wave. If we neglet this d term, the output signal-tonoise ratio at the envelope detetor output is O, AM A ka WN The Figure of Merit of the AM system is O C ka 1 k a 0 11

12 11/5/013 Although the noise performane of DSB-SC or SSB is one, the noise performane of an AM system is always less than unity. This is due to the waste of the transmitted arrier power, whih does not arry any information. EXAMLE Compare the DSB-SC noise performane to the AM noise performane (100 perent modulation) of the following sinusoidal wave. m t A os f t m m 1

13 11/5/013 EXAMLE - SOLUTION The average power of the message signal is 1 A m Therefore, the figure of merit of AM system is 1 ka A m O ka Am 1 C 1 k ka Am a A m For 100 perent modulation k a A m = 1. Therefore the AM systems figure of merit is 1/3, on the other hand DSB-SC FOM is 1. This means we need to transmit 3x power in AM to ahieve the same noise performane as DSB-SC THRESHOLD EFFECT When the arrier-to-noise ratio is small ompared with unity, the noise term dominates and the performane of the envelope detetor hanges ompletely. In this ase it is more onvenient to represent the noise n(t) in terms of its envelope r(t) and phase (t) n t r t os f t t 13

14 11/5/013 THRESHOLD EFFECT The orresponding phase diagram is Assuming that the arrier-to-noise ratio is so low that the arrier amplitude A is small ompared with the noise envelope r(t) the envelope detetor output is approximately y t rt A os t A k mt os t a THRESHOLD EFFECT This relation shows that when arrier-to-noise ratio is low, the detetor output has no omponent stritly proportional to message signal m(t). Note that the envelope detetor is not sensitive to the phase (t), whih is multiplied by the message signal. This means total loss of the message signal and referred as the threshold effet. Every nonlinear detetor shows this threshold effet. On the other hand this effet does not arise in a oherent detetor. 14

ENSC327 Communications Systems 4. Double Sideband Modulation. Jie Liang School of Engineering Science Simon Fraser University

ENSC327 Communications Systems 4. Double Sideband Modulation. Jie Liang School of Engineering Science Simon Fraser University ENSC327 Communiations Systems 4. Double Sideband Modulation Jie Liang Shool of Engineering Siene Simon Fraser University 1 Outline DSB: Modulator Spetrum Coherent Demodulator: Three methods Quadrature-arrier