EE3008_Lecture8 - 1 Lecture 8 Digital Communications Part...

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1 Lecture 8. Digital Communications Part III. Digital Demodulation • Binary Detection • M-ary Detection Department of Electronic Engineering EE3008 Principles of Communications Lecture 8
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2 Digital Communications SOURCE User Analog Signal A-D Conversion Bit sequence 0001101110…… Digital Bandpass Modulation Digital Baseband Modulation Digital Baseband Demodulation Digital Bandpass Demodulation Source t t D-A Conversion t Channel Baseband Channel Bandpass Department of Electronic Engineering EE3008 Principles of Communications Lecture 8
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3 Digital Demodulation Corrupted Digital waveform Channel Baseband/Bandpass Bit sequence Digital Baseband/ Bandpass Demodulation Bit sequence Digital Baseband/ Bandpass Modulation ˆ { } i b { } i b Transmitted Digital waveform What are the sources of signal corruption? How to detect the signal (to obtain the bit sequence )? ˆ { } i b How to evaluate the fidelity performance? Department of Electronic Engineering EE3008 Principles of Communications Lecture 8
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Sources of Signal Corruption Channel 1 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 Suppose that channel bandwidth is properly chosen such that most frequency components of the transmitted signal can pass through the channel. Transmitted signal s ( t ) Received signal y ( t ) t Thermal Noise: caused by the random motion of electrons within electronic devices. Department of Electronic Engineering EE3008 Principles of Communications Lecture 8 4
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5 Modeling of Thermal Noise ü At each time slot t 0 , n ( t 0 ) ( i.e., zero-mean Gaussian random variable with variance ): 2 2 0 0 1 ( ) exp 2 2 n x f x σ πσ = ü The thermal noise is superimposed ( added ) to the signal: y ( t )= s ( t )+ n ( t ) x 0 f n ( x ) Pr{ X > a } = f n ( x ) dx a = Q a σ 0 a -a Pr{ X < a } = f n ( x ) dx −∞ a = y = x f n ( y ) dy a = f n ( y ) dy a = Pr{ X > a } The thermal noise is modeled as a WSS process n ( t ) . N (0, σ 0 2 ) 2 0 σ Department of Electronic Engineering EE3008 Principles of Communications Lecture 8
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6 Modeling of Thermal Noise ü The thermal noise has a power spectrum that is constant from dc to approximately 10 12 Hz: n ( t ) can be approximately regarded as a white process. f (Hz) 10 12 G n ( f ) -10 12 N 0 /2 Two-sided Power Spectral Density N 0 /2 The thermal noise is also referred to as additive white Gaussian Noise (AWGN) , because it is modeled as a white Gaussian WSS process which is added to the signal. Department of Electronic Engineering EE3008 Principles of Communications Lecture 8
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