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Digital Communication I: Modulation and Coding Course-Lecture 6

Signal detection in AWGN channels Minimum distance detector. Maximum likelihood. Average probability of symbol error. Union bound on error probability. Upper bound on error probability based on the minimum distance.ISI in the detection process due to the filtering effects of the system Overall equivalent system transfer function | Digital communications I: Modulation and Coding Course Period 3 - 2007 Catharina Logothetis Lecture 6 Lecture 6 Last time we talked about: Signal detection in AWGN channels Minimum distance detector Maximum likelihood Average probability of symbol error Union bound on error probability Upper bound on error probability based on the minimum distance Lecture 6 Today we are going to talk about: Another source of error: Inter-symbol interference (ISI) Nyquist theorem The techniques to reduce ISI Pulse shaping Equalization Lecture 6 Inter-Symbol Interference (ISI) ISI in the detection process due to the filtering effects of the system Overall equivalent system transfer function creates echoes and hence time dispersion causes ISI at sampling time Lecture 6 Inter-symbol interference Baseband system model Equivalent model Tx filter Channel Rx. filter Detector Equivalent system Detector filtered noise Lecture 6 Nyquist bandwidth constraint Nyquist bandwidth constraint: The theoretical minimum . | Digital communications I: Modulation and Coding Course Period 3 - 2007 Catharina Logothetis Lecture 6 Lecture 6 Last time we talked about: Signal detection in AWGN channels Minimum distance detector Maximum likelihood Average probability of symbol error Union bound on error probability Upper bound on error probability based on the minimum distance Lecture 6 Today we are going to talk about: Another source of error: Inter-symbol interference (ISI) Nyquist theorem The techniques to reduce ISI Pulse shaping Equalization Lecture 6 Inter-Symbol Interference (ISI) ISI in the detection process due to the filtering effects of the system Overall equivalent system transfer function creates echoes and hence time dispersion causes ISI at sampling time Lecture 6 Inter-symbol interference Baseband system model Equivalent model Tx filter Channel Rx. filter Detector Equivalent system Detector filtered noise Lecture 6 Nyquist bandwidth constraint Nyquist bandwidth constraint: The theoretical minimum required system bandwidth to detect Rs [symbols/s] without ISI is Rs/2 [Hz]. Equivalently, a system with bandwidth W=1/2T=Rs/2 [Hz] can support a maximum transmission rate of 2W=1/T=Rs [symbols/s] without ISI. Bandwidth efficiency, R/W [bits/s/Hz] : An important measure in DCs representing data throughput per hertz of bandwidth. Showing how efficiently the bandwidth resources are used by signaling techniques. Lecture 6 Ideal Nyquist pulse (filter) Ideal Nyquist filter Ideal Nyquist pulse Lecture 6 Nyquist pulses (filters) Nyquist pulses (filters): Pulses (filters) which results in no ISI at the sampling time. Nyquist filter: Its transfer function in frequency domain is obtained by convolving a rectangular function with any real even-symmetric frequency function Nyquist pulse: Its shape can be represented by a sinc(t/T) function multiply by another time function. Example of Nyquist filters: Raised-Cosine filter Lecture 6 Pulse shaping to reduce ISI Goals and trade-off in pulse-shaping .