131B_1_AMnoise

131B_1_AMnoise - signal power A 2 I 1 + a 2 R m H LM The...

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NOISE ANALYSIS FOR AMPLITUDE MODULATION We study the effect of Noise in A M systems We have seen that the signal transmiited over the channel can be expressed : s H t L = A H 1 + a m H t LL Sin @ 2 Π f c t + Φ D The channel is modelled as an additive Gaussian noise channel so that the signal received can be expressed : r H t L = s H t L + n H t, Ω L where n H . L is white Gaussian with spectral density N. Hence using the narrow band noise representation we have r H t L = H A H 1 + a m H t LL Cos @ Φ D + n I H t, Ω L L Sin @ 2 Π f c t D + I A H 1 + a m H t LL Sin @ Φ D + n q H t, Ω LM Cos @ 2 Π f c t D where we model the unknown carrier phase Φ a random variable uniform @ 0, 2 Π D , independent of the noise. Then Sin @ Φ D and Cos @ Φ D are uncorrelated so that each term is uncorrelated with the other and the covariance function of r H t L is R r H t L = A 2 I 1 + a 2 R m H t LM Cos @ 2 Π f c t D + R n H t L Cos @ 2 Π f c t D where A is the received carrier amplitude, R n H t L = 2 W N Sin @ Π 2 Wt D±H Π 2 W t L and hence Noise power R n H 0 L = 2 W N where N is the spectral density of the channel noise, and
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Unformatted text preview: signal power A 2 I 1 + a 2 R m H LM The ratio of received signal power to noise power H SNR L is : H S N L b = A 2 I 1 + a 2 R m H LM H 2 W N L If we demodulate with a phase coherent demodulator and low pass filter we would get A H 1 + a m H t LL + n 1 H t, L and we remove the DC component with a DC block, we get Aa m H t L + n 1 H t, L and the output SNR is A 2 a 2 R m H L 2 W N = I A 2 a 2 R m H L A 2 I 1 + a 2 R m H LMM H S N L b = H S N L b where < 1, is the modulation efficiency Example : For speech signals R H L ~ 0.1 And a ~ 0.8-0.9, so that ~ .075 or a loss of 11 db because of the power needed to transmit the carrier. 2 AMnoise.nb...
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131B_1_AMnoise - signal power A 2 I 1 + a 2 R m H LM The...

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