Communication Systems, 5e Chapter 11: Baseband Digital Transmission Chapter 14: Bandpass Digital Transmission A. Bruce Carlson Paul B. Crilly © 2010 The McGraw-Hill Companies Chapter 11 & 14 • Chapter 11: Baseband Digital Transmission – Digital signals and systems – Noise and errors – Bandlimited digital PAM systems – Synchronization Techniques • Chapter 14: Bandpass Digital Transmission – Digital CW modulation – Coherent binary systems – Noncoherent binary systems – Quadrature-carrier and M-ary systems – Orthogonal frequency division multiplexing – Trellis-coded modulation © 2010 The McGraw-Hill Companies Why go digital? • Stability – Inherently invariant of performance. Identical clock rates result in identical results. No temperature variance or component aging effects. • Flexibility – Reprogramming allows for changes and upgrades – Apply digital signal processing to meet different needs encryption, compression, encoding • Reliable Reproduction – All circuits perform identically with identical results. 3 Digital Formatting and Transmission 4 Digital Signals and Systems • An ordered sequence of symbols – Produced by a discrete information source – With symbols drawn from a defined alphabet • Binary symbols are one subset of symbols – Represent binary digits, 0 and 1 known as bits – Symbols may be represented by multiple bits (M-ary) • Interested in: – Symbol rate, symbols per second and bits per second (bps) – Symbol error probability or rate (bit-error-rate or BER measures) 5 Digital Pulse-Amplitude Modulation (PAM) • Also referred to as pulse-code modulation (PCM) • The amplitude of pulse take on discrete number of waveforms and/or levels within a pulse period T. xt a k p t kT k • p(t) takes on many different forms, a rect for example 1 0 t T pt 0 else xmT a k p mT kT a m p a m , for 0 T k 6 Digital Signaling Rate • For symbols of period T, the symbol rate is R=1/T • The rate may be in bits-per-second when bits are sent. A bps rate is usually computed and defined. • The rate may be in symbols-per-second when symbols are sent. When there are a defined number of bits-per-symbol, the rate may be defined in bits-per-second as well. – If parity or other non-data bits are sent, the messaging rate and the signaling rate may differ. 7 PAM/PCM Types NRZ RZ Manchester AMI-Bipolar Encoding Biphase Mark Code (Alternate Mark Inversion) 8 PAM/PCM Transmission • Pulse code modulation (PCM) is used when a binary data stream is to be sent • In PCM the binary sequence is used to define logical signal levels for transmission. – A logical level may map to bits (e.g. 0-High, 1-Low) – A bit value may define whether a level changes or not, i.e. Mark : change whenever the bit is a one Space: change whenever the bit is a zero – Period half-cycles can take on various structures based on a bit value or the sequence of bits 9 PCM Common Waveform Types • Marks (1’s) and Spaces (0’s) • Non-return-to-zero (NRZ) – Level, Mark, Space • Return-to-zero (RZ) – unipolar, bipolar, AMI (alternate mark inversion) • Manchester – biphase level, biphase mark, biphase space 10 PCM Types Again NRZ RZ Manchester AMI-Bipolar Encoding Biphase Mark Code (Alternate Mark Inversion) 11 PCM Type Selection • Spectral characteristics (power spectral density and bandwidth efficiency) • Bit synchronization capability • Error detection capability • Interference and noise immunity • Implementation cost and complexity – Simple to modulate and demodulate 12 Spectral Attributes of PCM If Bandwidth W=1/T, then WT=1 Note that WT=0.5 or a bandwidth equal to ½ the symbol rate can be used! 13 ABC Binary PAM formats (a) unipolar RZ & NRZ (b) polar RZ & NRZ (c) bipolar NRZ (d) split-phase Manchester (e) polar quaternary NRZ Figure 11.1-1 14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. M-ary Coded Symbols • When multiple bits per symbol are sent M 2n – The symbol rate is R Bit R Bit R Symbol log2 M n – “Quaternary NRZ” is a 4-ary symbol providing 2 bits- per-symbol based on 4 amplitude levels • Digital mapping of the symbols is performed • Gray Codes typically used so that the nearest neighbor only has one-bit different (improves the bit-error rate of the symbol type being used) 15 Transmission Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. (a) Baseband transmission system (b) signal-plus-noise waveform: Figure 11.1-2 ~ yt a k p t t d kT n t k 16 Transmission ~ yt a k p t t d kT n t k • The digital signal is time delayed t d • The pulse is “filtered” and/or distorted by the channel ~ pt fnp t hc t • Recovering or Regenerating the signal may not be trivial ˆ ~ ymT td am ak p mT kT n mT td km – Signal plus inter-symbol interference (ISI) plus noise 17 Distorted Binary Baseband Signal Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. (a) Distorted polar binary signal (b) eye pattern: Figure 11.1-3 • The eye pattern results after signal demodulation and filtering. The “optimal” sampling time and other measurement of signal/receiver performance can be measured (noise margin, timing jitter, timing sensitivity, etc) 18 Symbol Periods and ISI • For a signal with the maximum number of level transitions (typically, 01010101) • The binary signal would form a square wave of period 2T. – Fourier Series of fundamental plus odd harmonics • To minimally pass this signal, a low pass filter with cutoff frequency of B 1/2T = R/2 may be used … – This concept also comes from Nyquist – Therefore the previous comments about BT = ½ 19 Symbol Periods and ISI (2) • To minimally pass this signal, a low pass filter with cutoff frequency of R/2 may be used … • The optimal binary symbol pulse shape would then have a band-limited spectrum … 1 f t Pf rect pt sinc t R sinc R R T • Note that the value of other symbols that could cause ISI is equal to zero at the “optimal” symbol sampling time … the center of the eye diagram. – A way to minimize ISI using the optimal filter! 20 Matlab Bipolar NRZ • Sinc Function Waveform Sum (SincEyev2.m) • Eye Diagram Eye Diagram For Square Wave 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 -0.2 -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 -1 -1 -4 -3 -2 -1 0 1 2 3 4 -8 -6 -4 -2 0 2 4 6 8 21 Matlab Bipolar NRZ (2) • Sinc Function Waveform Sum • Power Spectral Density Power Spectral Density 20 1 0.8 10 0.6 0 0.4 -10 0.2 0 -20 -0.2 -30 -0.4 -40 -0.6 -0.8 -50 -1 -60 -4 -3 -2 -1 0 1 2 3 4 0 1 2 3 4 5 6 7 8 22 Baseband Binary Receiver Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 11.2-1 yt a k p t kT ht nin t h t k yt k a k n t k • Synchronous Time sampling of maximum filter output 23 Regeneration of a unipolar signal Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. (a) signal plus noise (b) S/H output (c) comparator output: Figure 11.2-2 24 Unipolar Binary Error Probability • Hypothesis Testing using a voltage threshold – Hypothesis 0 • The conditional probability distribution expected if a 0 was sent pY yk | H0 pY a k n t k | a k 0 pY n t k pY yk | H0 pN yk – Hypothesis 1 • The conditional probability distribution expected if a 1 was sent pY yk | H1 pY a k n t k | a k A pY A n t k pY yk | H1 pN yk - A 25 Decision Threshold and Error Probabilities Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Conditional PDFs Figure 11.2-3 V P P Y V p y | H dy e1 Y 1 P P Y V p y | H dy e0 Y 0 V • Use Hypothesis to establish a decision rule – Use threshold to determine the probability of correctly and incorrectly detecting the input binary value 26 Average Error Probability • Using the two error conditions: – Detect 1 when 0 sent – Detect 0 when 1 sent Perror PH0 Pe0 P H1 Pe1 • For equally likely binary values 1 PH P H 0 1 2 1 P P P error 2 e0 e1 • Optimal Threshold PH0 pY Vopt | H0 PH1 pY Vopt | H1 27 Threshold regions for conditional PDFs Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 11.2-4 A V opt 2 28 For AWGN • The pdf is Gaussian 1 y2 p y | H p y exp Y 0 N 2 22 2 1 2 for Qx exp d 2 x 2 V A P P Y V p y dy Q Q e0 N V 2 V A V A P P Y V p y A dy Q Q e1 N 2 29 Modification for Bipolar Signals • Hypothesis Testing using a voltage threshold – Hypothesis 0 • The conditional probability distribution expected if a 0 was sent pY yk | H0 pY a k n t k | a k A pY - A n t k pY yk | H0 pN yk A – Hypothesis 1 • The conditional probability distribution expected if a 1 was sent pY yk | H1 pY a k n t k | a k A pY A n t k pY yk | H1 pN yk - A A A V 0 30 opt 2 2 Modification for Bipolar Signals (2) • Determining the error probability A V A P P Y V p y A dy Q Q e0 N V V A V A P P Y V p y A dy Q Q e1 N • Notice that the error has been reduced – The distance between the expected signal values may be twice as large as the unipolar case (using +/- A) 31.