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Point-to-Point Wireless Communication (I):Digital Basics, Modulation, Detection, Pulse Shaping

Point-to-Point Wireless Communication (I):Digital Basics, Modulation, Detection, Pulse Shaping 42
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Dr.ShivJindal,India,Teacher
Published Date:19-07-2017
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Point-to-Point Wireless Communication (I): Digital Basics, Modulation, Detection, Pulse Shaping Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 1The Basics Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 2Big Picture: Detection under AWGN Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 3Additive White Gaussian Noise (AWGN)  Thermal noise is described by a zero-mean Gaussian random process, n(t) that ADDS on to the signal = “additive”  Its PSD is flat, hence, it is called white noise.  Autocorrelation is a spike at 0: uncorrelated at any non-zero lag w/Hz Power spectral Density (flat = “white”) Autocorrelation Function Probability density function (uncorrelated) (gaussian) Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 4Effect of Noise in Signal Space  The cloud falls off exponentially (gaussian).  Vector viewpoint can be used in signal space, with a random noise vector w Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 5Maximum Likelihood (ML) Detection: Scalar Case “likelihoods” Assuming both symbols equally likely: u is chosen if A A simple distance criterion Log-Likelihood = Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 6AWGN Detection for Binary PAM p (z m ) z 2 p (z m ) z 1 s s 2 1  (t) 1 0  E E b b  s s / 2 1 2  P (m ) P (m ) Q e 1 e 2  N / 2 0   2E b  P P (2) Q B E  N 0  Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 7Bigger Picture General structure of a communication systems Noise Received Transmitted Received info. Info. signal signal SOURCE Transmitter Receiver Channel Source User Transmitter Source Channel Formatter Modulator encoder encoder Receiver Source Channel Formatter Demodulator decoder decoder Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 8Digital vs Analog Comm: Basics Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 9Digital versus analog  Advantages of digital communications:  Regenerator receiver Original Regenerated pulse pulse Propagation distance  Different kinds of digital signal are treated identically. Voice Data A bit is a bit Media Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 10Signal transmission through linear systems Input Output Linear system  Deterministic signals:  Random signals:  Ideal distortion less transmission: All the frequency components of the signal not only arrive with an identical time delay, but also are amplified or attenuated equally. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 11Signal transmission (cont’d)  Ideal filters: Non-causal Low-pass Band-pass High-pass Duality = similar problems occur w/ rectangular pulses in time domain.  Realizable filters: RC filters Butterworth filter Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 12Bandwidth of signal  Baseband versus bandpass: Baseband Bandpass signal signal Local oscillator  Bandwidth dilemma: Bandlimited signals are not realizable Realizable signals have infinite bandwidth Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 13Bandwidth of signal: Approximations  Different definition of bandwidth: a) Half-power bandwidth d) Fractional power containment bandwidth b) Noise equivalent bandwidth e) Bounded power spectral density c) Null-to-null bandwidth f) Absolute bandwidth (a) (b) (c) (d) Shivkumar Kalyanaraman Rensselaer Polytechnic Institute (e)50dB : “shiv rpi” 14Formatting and transmission of baseband signal Digital info. Format Textual source info. Pulse Transmit Analog Encode Sample Quantize modulate info. Pulse Channel Bit stream waveforms Format Analog info. Low-pass Decode Demodulate/ filter Receive Detect Textual sink info. Digital info. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 15Sampling of Analog Signals Time domain Frequency domain x (t) x (t) x(t) s X ( f ) X ( f ) X ( f ) s x(t) X ( f ) X ( f ) x (t)  x (t) s X ( f ) s Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 16Aliasing effect & Nyquist Rate LP filter Nyquist rate aliasing Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 17Undersampling &Aliasing in Time Domain Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 18Nyquist Sampling & Reconstruction: Time Domain Note: correct reconstruction does not draw straight lines between samples. Key: use sinc() pulses for reconstruction/interpolation Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 19Nyquist Reconstruction: Frequency Domain The impulse response of the reconstruction filter has a classic 'sin(x)/x shape. The stimulus fed to this filter is the series of discrete impulses which are the samples. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute : “shiv rpi” 20