Bandpass Modulation and Demodulation 1. Why Modulate? 2. Signals and Noise 3. Digital Bandpass Modulation Techniques, 4. Detection of Signals in Gaussian Noise 5. Coherent Detection 6. Noncoherent Detection 7. Error Perforance for Binary Systems 8. M-ary Signaling and Performance 9. Symbol Error Performance for M-ary Systems(M>2) 10.Conclusion [1] Ch3. Modulation and Demodulation

3.1 Modulation  Digital symbol ==> Waveform  Frequency translating (Carrier Modulation) [2] Ch3. Modulation and Demodulation

3.2 Signals and Noise  Noise : Intersymbol Interference , Distortion  r(t) => Receive signal s(t) => Sum of the transmitted signal n(t) => Thermal noise  The probability density function(pdf), p(n),of the zero-mean noise voltage is exressed as p(n) = [ 1/ (2)1/2 ] exp [-1/2 (n/ )2] 2 => noise variance The normalized or standardized Gaussian density function of a zero-mean process is obtained by assuming that =1. The normalized pdf is shown sketched in Figure 1.7 [3] Ch3. Modulation and Demodulation

[4] Ch3. Modulation and Demodulation

 A Geometric View of Signals and Noise [5] Ch3. Modulation and Demodulation

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 Waveform Energy [8] Ch3. Modulation and Demodulation

 Generalized Fourier Transforms Solution [9] Ch3. Modulation and Demodulation

 Representing White Noise with Orthogonal Waveforms [10] Ch3. Modulation and Demodulation

 Variance of White Noise White Noise : 광의의 정상적 확률과정 N(t)의 전력스펙트럼 밀도가 전주파수에 걸쳐 일정한 경우 [11] Ch3. Modulation and Demodulation

3.3 Digital Bandpass Modulation Techniques  Carrier wave s(t) = A(t) cos (t) (3.23) (t) = w0t + (t) (3.24) s(t) = A(t) cos [ w0t + (t) ] (3.25) 정보내용이 A(t)에 실리면 진폭변조 (t) =  0 = 정수 정보내용이 (t) = w0t + (t) 에 포함되면 각변조 s(t) = 정수 정보내용이 (t) 에 포함되면 위상변조 정보내용이 d(t)/dt = '(t) 에 포함되면 주파수변조 (t) = 2πfct + (t) '(t) = 2πfct + '(t) [12] Ch3. Modulation and Demodulation

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 Phase Shift Keying  Frequency Shift Keying [15] Ch3. Modulation and Demodulation

S(t) = A cos wt (3.30)  Amplitude Shift Keying  Amplitude Phase Keying S(t) = A cos wt (3.30) [16] Ch3. Modulation and Demodulation

3.4 Detection of Signal in Gaussian noise  Decision Regions [17] Ch3. Modulation and Demodulation

Choose the si(t) whose index (3.35) corresponds to the max zi(t)  Correlation Receiver 0 <= t <= T i = 1, . . . , M r(t) = si(t) + n(t) (3.33) Choose the si(t) whose index (3.35) corresponds to the max zi(t) z(T) = z1(T) - z2(T) (3.36) z(T) =ai(T) + n0(T) i = 1, 2 [18] Ch3. Modulation and Demodulation

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Decision line  Binary Decision Threshold [20] Ch3. Modulation and Demodulation

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3.5 Coherent Detection  Coherent Detection of PSK [22] Ch3. Modulation and Demodulation

[23] Ch3. Modulation and Demodulation

 Sampled Matched Filter r(k) = s(k) + n(k) k = 0, 1, . . . [24] Ch3. Modulation and Demodulation

 Coherent Detection of Multiple Phase Shift keying [25] Ch3. Modulation and Demodulation

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 Coherent Detection on FSK [28] Ch3. Modulation and Demodulation

[29] Ch3. Modulation and Demodulation