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Chapter 3

Chapter 3. Baseband Pulse and Digital Signaling. Based on the fundamentals learned in Chapters 1-2, we now consider specific communication issues. Pulse code modulation and delta modulation N-ary digital signals Intersymbol interference Multiplexing Transmission.

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Chapter 3

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  1. Chapter 3 Baseband Pulse and Digital Signaling

  2. Based on the fundamentals learned in Chapters 1-2, we now consider specific communication issues. • Pulse code modulation and delta modulation • N-ary digital signals • Intersymbol interference • Multiplexing • Transmission

  3. Basic Model of Communication Digital Source Transmitter Channel Receiver Destination Source generates from a finite set of symbols.

  4. Transmitter Source Encoder Channel Encoder Baseband Signaling • Source Encoder translates the out put of the source in an • efficient manner for communication (e.g., compression). • Channel Encoder transforms the coded source to enable • error detection and correction at the receiver (e.g., add • redundancy). • Baseband signaling encodes digital information in a • sequence of analog pulses.

  5. Practical consideration of Channel Modulation Physical Transmission Physical Medium Physical Reception Demodulation Noise Channel model used in this class (simplified) H(f)

  6. Receiver Optimal Filter Channel Decoder Source Decoder Optimal filter makes “best guess” of transmitted analog pulses. Channel decoder inverses operation of channel encoder (i.e., error detection and correction). Source decoder inverses operation of source encoder.

  7. Pulse Amplitude Modulation (PAM) • Baseband operation • Transforming continuous time analog signals into discrete time analog pulses • Information carried in amplitude of pulses. • First step in the analog to digital conversion (A/D) • Pre-cursor to Pulse Code Modulation (PCM) • Sometimes, PAM signals are used directly for transmission without making it into PCM • Two types of PAM • Gating • Sample and hold

  8. Analog Source over Digital Communication Digital Communication System Analog Source A/D Conversion D/A Conversion Analog Output • PAM can be thought of as - Hybrid analog / digital communication system - Part of analog-to-digital conversion process

  9. Any one of these has the same shape as the original W(f). Thus gated PAM is a linear operation.

  10. Demodulation of Gated PAM signal Oscillator multiplies cos(nwst) to the received PAM signal.This operation is equivalent to bringing down the frequency of thereceived signal by nws.

  11. They do not have the same shape as the original W(f). Thus S/H PAM is a non linear operation.

  12. Pulse Code Modulation (PCM) is a special form of A/D conversion. It consists of sampling, quantizing, and encoding steps. It is widely popular because: - Used for long time in telephone systems - Inexpensive electronics exists - Errors can be corrected during long haul transmission - Can use time division multiplexing PCM signal

  13. Signals in PCM Process

  14. Design Issues for PCM- Analog to Digital Conversion Aliasing Sample timing accuracy Quantization noise D/A accuracy Reconstruction filter- Digital Communication Technique Encoding and decoding Signal format Transmit and receive filters Channel effects Statistical decision making error

  15. Bandwidth of PCM • Assume w(t) is bandlimited to B hertz. • Minimum sampling rate = 2B samples / second • A/D output = n bits per sample (quantization level M=2n) • Assume a simple PCM without redundancy. • Minimum channel bandwidth = bit rate /2 • Bandwidth of PCM signals: BPCM nB (with sinc functions as orthogonal basis) BPCM 2nB (with rectangular pulses as orthogonal basis) • For any reasonable quantization level M, PCM requires much higher bandwidth than the original w(t).

  16. Effects of Noise • Types of Noise • Quantizing noise (during A/D conversion) • Environment noise (e.g., EM interference) • Filtering noise (low pass filtering at decoder) • Types of Quantization Noise • Overload noise (input too large) • Random noise (input too small) • Granular noise (non uniform error jump) • Hunting noise (too long of quite time) •  Special quantizers are used (µ-law, A-law quantizers)

  17. Performance of PCM (Pe  0, uniform quantization steps)

  18. Quantization Quantization is a non linear transformation which maps elements from a continuous set to a finite set. It is also the second step required by A/D conversion. Sample Quantize Analog Signal - Continuous time - Continuous value Digital Signal - Discrete time - Discrete value - Discrete time - Continuous value

  19. Uniform Quantization output w2(t) V -V V input w1(t) -V Region of operation For M=2n levels, step size :  = 2V /2n = V(2-n+1)

  20. Quantization Error, e output w2(t) V -V V input w1(t) -V Error, e /2 -/2 input w1(t)

  21.  Error is symmetric around zero. 0

  22. Definition. The dynamic range of an input signal is the ratio of the largest to the smallest power levels which the input signal can take on and be reproduced with the acceptable signal distortion. The dynamic range of the quantizer input in the PCM system is 6n dB.

  23. Nonuniform Quantizer Used to reduce quantization error and increase the dynamic range when input signal is not uniformly distributed over its allowed range of values. allowed values input values for most of time time

  24. “Compressing-and-expanding” is called “companding.” Nonuniform quantizer Discrete samples Uniform Quantizer digital signals Compressor • • • • Channel • • • • output Decoder Expander received digital signals

  25. Compression Techniques

  26. Practical Implementation of µ-law compressor

  27. Output SNR of 8-bit PCM systems with and without companding.

  28. Baseband Signaling Transmitter Receiver w#(t) w(t) Baseband Signaling Channel H(f) Optimal Filter • Once the sending end prepared digital signals (e.g., • PCM) to send, now it is the job of Baseband Signaling to • prepare the signals suited for the channel. • What should w(t) be? •  Orthogonal set of signals {k (t), k=1,2,3, ..., N}

  29. Note • For practical implementation, we can only use a finite • number, N, of the orthogonal set of signals {k (t), k=1,2,3, ..., N}. • Again, for practical implementation, the time duration must be • finite, To < . • The goal is to find a set {k (t), k=1,2,3, ..., N} such that • w(t) represents the digital signals prepared (e.g., PCM) and • a small amount of distortion in the channel does not • affect the recovery of w(t) from the received signal, w#(t).

  30. Example. In ASCII character, “X” is 0001101. Then, using a certain {k (t), k=1,2,3, ..., 7}, “X” is represented (for 0 < t < To) as

  31. Definition. Baud (symbol) rate D = N / To.Definition. Bit rate R = n / Towhere n is the number of data bit sent in To seconds.If wk is binary, n = N and w(t) is a binary signal. If wk is not binary, n  N and w(t) is a multilevel signal.

  32. Binary InputOutput Voltage 11 +3 10 +1 00 -1 01 -3

  33. Example. 01001110 -3 -1 +3 +1 w1= -3, w2= -1, w3 = +3, w4= +1 Note that 2ms is allowed for sending each symbol.

  34. Line Code • On the channel, we might want to send binary numbers directly. • The resulting bit patterns on the channel might create a static voltage, which is not desired. • Use line code to eliminate the average static voltage. • - Save power • - Save bandwidth (possibly) 1 1 1 1 1 5 volt average static voltage 0 volt 0 0 0 0 0 0

  35. Types of Line Code • Unipolar signaling: 1 = +A volt, 0 = 0 volt • Polar signaling: 1 = +A volt, 0 = -A volt • Biopolar signaling: 1 = +A or –A, 0 = 0 volt • (Also called the alternate mark inversion – AMI) • Machester signaling: • 1 = +A (half duration) followed by –A (half duration) • 0 = -A (half duration) followed by +A (half duration) • Additional combinations can be made along with RZ (return to zero) and NRZ (non return to zero).

  36. Desired Properties of Line Code • Self synchronization • Low probability of bit error • Spectral efficiency • Low transmission speed • Error detection capability • Transparency

  37. Power Spectral Density for Line Code(We will not follow the details in the book.)

  38. Eye Pattern Seen in oscilloscopeThe Cleaner, the betterGood indication of transmission quality

  39. Regenerative Repeater

  40. Bit Synchronization To accurately detect received signals, synchronization timing is needed. - derived from received data - separate signal sent from source Synchronization - bit level - frame level - carrier level

  41. Binary-to-Multilevel Conversion

  42. Spectral Efficiency Line Code First Null Bandwidth Spectral Efficiency (Hz) =R/B bits/s Unipolar NRZ R 1 Polar NRZ R 1 Unipolar RZ 2R 0.5 Bipolar RZ R 1 Manchester NRZ 2R 0.5 Multilevel polar NRZ R/l l

  43. Intersymbol Interference • No channel has infinite bandwidth • Most transmission schemes require higher bandwidth than available in the channel. • Square wave requires infinite bandwidth. • Synch function is not possible due to causality violation. • Modified synch function to satisfy the causality requires higher bandwidth. • Each symbol may be smeared into adjacent time slots. • Intersymbol Interference (ISI) is the spreading of symbol pulses from • one slot into adjacent slots.

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