S. Mandayam/ECE Dept./Rowan University Digital Communications / Fall 2002 Shreekanth Mandayam ECE Department Rowan University Lecture 5 October 7, 2002

S. Mandayam/ECE Dept./Rowan University Plan Baseband Data Transmission Recall: Binary Symmetric Channel Joint and Conditional Probabilities Baye’s Theorem BER Optimum Receiver Detection in the presence of AWGN Receiver Model Noise Model Single Sample Detector Matched Filter Detector Unipolar and Bipolar Signaling

S. Mandayam/ECE Dept./Rowan University Digital Communications Transceiver Anti- aliasing Filter SamplingQuantization Data Encryption Encoder Source Encoder Error Control Encoder Channel/ Line Encoder Modulator MUX Audio Amp Source Decoder Data Encryption Decoder Error Control Decoder Equalization / Decision Circuits Demod- ulator DEMUX Reconstruction/ DAC ADC CODEC MODEM Analog o/p Multiple access channel Analog i/p

S. Mandayam/ECE Dept./Rowan University Recall: Binary Symmetric Channel Digital Modulation System Digital Demodulation System Discrete Memoryless Channel 0/1 r 0 /r 1 0/1 Noise Channel Transition Diagram m1m1 m0m0 r1r1 r0r0 m 0 /m 1

S. Mandayam/ECE Dept./Rowan University Receiver Model m TX  s(t) n(t) LPF Comparator r(t) t=t 0 VTVT m ~ r 0 (t) r 0 (t 0 )

S. Mandayam/ECE Dept./Rowan University Thermal (Johnson) Noise x x PSD of thermal noise frequency, Hz PSD, W/Hz

S. Mandayam/ECE Dept./Rowan University All White Gaussian Noise (AWGN) x f(x) m

S. Mandayam/ECE Dept./Rowan University Computing Probability of Error r0r0 Condtional PDFs f(r 0 \s 1 sent) f(r 0 \s 2 sent) VTVT P(error\s 1 sent) P(error\s 2 sent)

S. Mandayam/ECE Dept./Rowan University Matched Filter Matched Filter h(t) r 0 (t) = s 0 (t) + n 0 (t) r(t) = s(t) + n(t) demos/matched_filter

S. Mandayam/ECE Dept./Rowan University Lab Project 1: Monte Carlo Simulation of a Baseband Binary Communications System Random Binary Source Line Encoder  m Error Counter Detector m ~ AWGN Comparator 0/1 0/A or -A/+A

S. Mandayam/ECE Dept./Rowan University Summary