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Thermal noise in communication systems
- 1. Noise in communication systems • Thermal noise is described by a zero-mean white Gaussian random process • Its PSD is flat over all frequencies, hence, it is called white noise. • Thus, are also Gaussian distributed with flat PSD. • It is clear that the average power of this noise is infinite. • So what to do? Solution:Matched Filter Probability density function Power spectral density 176
- 2. © Dr. Aimal Khan Mapper Pulse Shaping X + Receive Filter Binary Decision Binary Data Sampler iV Binary Data ASKi nVV ~ 177 Modulator Channel Demodulator Detection of ASK
- 3. © Dr. Aimal Khan X + Detection of QAM Mapper Pulse Shaping X + Receive Filter Receive Filter Binary Decision Binary Data Binary Data Sampler XXiX nVV ~ XiV QiV QQiQ nVV ~ Pulse Shaping Modulator Channel Demodulator )( )( tn T tV Q Q 178
- 4. Optimum Receive Filter • Optimum receive filter in the sense of maximizing SNR is called matched filter. It will be discussed later, equalizing filter is skipped for the moment will be discussed later with ISI 179
- 5. Matched Filter for Baseband System and Maximum SNR ■ As done in the class 180
- 6. Matched Filter in case of ASK System ■ As done in the class 181
- 7. Matched Filter in case of PSK/QAM System ■ As done in the class 182
- 8. Binary Decision/Demapper Select the one with the Minimum Eucludian Distance Inphase axis Quadrature axis 183 Here V4 has the minimum distance The green dot is the received symbol 𝑉 𝑉4 𝑉3 𝑉2 𝑉1 𝑠 𝑣−𝑣1 𝑠 𝑣−𝑣2 𝑠 𝑣−𝑣3 𝑠 𝑣−𝑣4
- 9. Euclidian Distance between received Symbol V and the point 𝑉1 in the constellation Diagram 184 𝑠 𝑣−𝑣1 = (𝑉𝑥 − 𝑉1𝑥)2+(𝑉𝑄 − 𝑉1𝑄)2 𝑉1𝑥 is the inphase of symbol 𝑉1 𝑉1𝑄 is the quadrature of symbol 𝑉1 𝑉𝑄 is the quadrature of symbol received 𝑉 𝑉𝑋 is the inphse of symbol received 𝑉
- 10. Maximum likelihood Binary Decision/Demapping criteria for Binary schemes as done in the class ■ Calculate the euclidian distance from the received symbol to all of the constellation points. Select the one with the minimum distance. 185
- 11. Maximum likelihood Binary Decision/Demapping criteria for M-ary ASK as done in the class ■ As done in the class, Similar to the slide given in for the demapper of 4-QAM in the coming slide 186
- 12. Maximum likelihood Binary Decision/Demapping criteria for M-ary PSK /QAM as done in the class ■ Demonstrated in the next two slides 187
- 13. Mapper for Square 4-QAM Inphase axis Quadrature axis d d is mapped to is mapped to is mapped to is mapped to 188
- 14. Binary Decision/Demapper Select the one with the Minimum Eucludian Distance Inphase axis Quadrature axis 189 Here V4 has the minimum distance The green dot is the received symbol 𝑉 𝑉4 is demapped to 11 𝑉3 𝑉2 𝑉1
- 15. Euclidian Distance between received Symbol V and the point 𝑉1 in the constellation Diagram 190 = 𝑠 𝑣−𝑣1 = (𝑉𝑥 − 𝑉1𝑥)2+(𝑉𝑄 − 𝑉1𝑄)2 𝑉1𝑥 is the inphase of symbol 𝑉1 𝑉1𝑄 is the quadrature of symbol 𝑉1 𝑉𝑄 is the quadrature of symbol received 𝑉 𝑉𝑋 is the inphse of symbol received 𝑉
- 16. Intersymbol Interference ■ Convolution of Pulse with a low pass filter ■ Output of a matched filter calculation ■ Output of a matched filter in combination of additive noise and convolutive channel ■ The concept of Intersymbol interference ■ All these topics are covered on the board in the class 191
- 17. Course Outline Revisit ■ Digital Communications Basic Blocks, Introduction ■ Classification of signals ,Deterministic and Random, Periodic and Non-periodic (Signal, Energy and Power Signals, Analog and Discrete Signals) ■ Spectral Density, Auto-Correlation, ■ Bandwidth of Digital Signals, Baseband versus Band pass ■ Sampling Theorem, Aliasing, Over Sampling ■ Sampling and Quantizing effects, Channel effects, Signal to Noise Ratio ■ Pulse Code Modulation, PCM based Time division multiplexing 192
- 18. Course Outline Revisit ■ Uniform and Non Uniform Quantization, Companding ■ Waveform Representation of Binary Digits, M-ary Pulse Modulation waveforms ■ PCM waveform types, Line Coding ■ Correlative Coding, duo-binary coding and decoding, precoding ■ Error Performance, degradation in Digital Communication System, Demodulation and detection, SNR parameter in Digital Communication System ■ Detection of Binary Signals in Gaussian Noise, Matched Filter 193
- 19. Course Outline Revisit ■ Inter symbol Interference, Pulse shaping to reduce ISI, Error Performance ■ Eye Patterns, Digital Demodulation Techniques ■ Spread Spectrum, Frequency Hopping and Direct Sequence 194
- 20. What we discussed in the last lecture ■ Bandwidth Calculation ■ Inter Symbol Interference 195
- 21. Eye Diagram 196
- 22. How to combat ISI ■ Pulse shaping By using Nyquist Pulses ■ Using Equalization Zero Forcing Equalization Minimum Mean Squared Error Equalizer 197