Fundamentals of Digital Communication

Fundamentals of Digital Communication Network Infrastructures A.A. 2017/18 Digital communication system Analog Digital Input Signal Analog/ Digital Low Pass Filter Sampler Quantizer Source Encoder Channel Encoder Multiplexer Carrier Twisted Pair Co-axial Cable Optical Fiber Wireless Space To Channel From Channel Modulator De- Modulator Pulse Shaping Filters Receiver Filter Line Encoder Detector Carrier Recovery Symbol timing Recovery Signal at the user end Digital-to-Analog Converter Channel Decoder De- Multiplexer Analog Digital 2 1

Digital Modulation cost effective because of advances in digital technology (VHDL, DSP, FPGA ) advantages/disadvantages vs analog - better noise immunity - robustness to channel impairments - ability to multiplex information - error control: detect & correct corrupt bits - able to encrypt data - flexible software modulation & demodulation - requires complex signal conditioning modulating signal (message) represented as pulses n bits represented by m finite states n = log 2 m 3 Factors in Digital Modulation efficiency: low BER at low SNR channel: multipath & fading conditions minimize bandwidth required cost-effective & easy implementation Performance Measures for Modulation Schemes (i) p = power efficiency (ii) B = bandwidth efficiency 4 2

(i) Power Efficiency, p Ability to preserve signal fidelity at low power increasing signal power increases noise immunity specifics depend on modulation technique measures trade-off between fidelity & signal power p often expressed as ratio of E b to N 0 at receiver input to achieve specified BER p =E b / N 0 E b = bit energy N 0 = noise power spectral density 5 (ii) Bandwidth Efficiency, B Ability to accommodate data in limited bandwidth increasing data rate requires increased bandwidth direct relationship to system capacity measured in terms of bit rate, R b & RF bandwidth, B B =R b /B 6.36 Fundamental Upper Bound on achievable Bit Rate per given Bandwidth (aka Shannon Bound) Bmax = C/B S Bmax = log 2 1 6.37 N C = maximum channel capacity (bps) 6 3

typically there is a tradeoff between B & p e.g addition of error control codes increases p and decreases B - increases bandwidth for given data rate - reduces required received power for specified BER use of M-ary keying increases B and decreases p - decreases bandwidth for given data rate - requires increased receive power for specified BER 7 Additional factors in digital modulation cost & complexity simplicity is better channel impairments (Rayleigh, Ricean fading) - multipath dispersion - interference detection sensitivity to timing jitter time varying channel typically system is simulated & all factors are analyzed prior to selection of methods and specification of parameters 8 4

Analog vs. Digital Analog signals Value varies continuously Digital signals Value limited to a finite set x(t) x(t) t Binary signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1/T bits per second x(t) 1 0 T 0 0 1 1 0 t t 9 Performance Metrics In analog communications we want, mˆ ( t) m( t) Digital communication systems: Data rate (R bps) Limited by Channel Capacity Probability of error Without noise, there are no bit errors Bit Error Rate (BER): Number of bit errors that occur for a given number of bits transmitted. What s BER if P e =10-6 and 10 7 bits are transmitted? 10 5

Analog versus Digital Harder to separate noise from an analog signal than from a digital signal If there is too much noise cannot discern a high voltage from a low voltage 11 Analog versus Digital Regenerator receiver Original pulse Regenerated pulse Propagation distance Different kinds of digital signal are treated identically. Data Voice Media A bit is a bit! 12 6

Analog versus Digital Stability of components: Analog hardware change due to component aging, heat, etc. Flexibility: Perform encryption Compression Error correction/detection Reliable reproduction 13 Bandwidth of signal Baseband versus bandpass: Baseband signal Local oscillator Bandpass signal Bandwidth dilemma: Bandlimited signals are not realizable! Realizable signals have infinite bandwidth! 14 7

Different definition of bandwidth: a) Half-power bandwidth b) Noise equivalent bandwidth c) Null-to-null bandwidth d) Fractional power containment bandwidth e) Bounded power spectral density f) Absolute bandwidth (a) (b) (c) (d) (e)50db 15 Sampling Time domain Frequency domain x s X s x(t) X ( f ) ( t) x ( t) x( t) ( f ) X ( f ) X ( f ) (t) x ( f ) X (t) x s ( f ) X s 16 8

Aliasing effect LP filter Nyquist rate aliasing 17 Sampling theorem Analog signal Sampling process Pulse amplitude modulated (PAM) signal Sampling theorem: A bandlimited signal with no spectral components beyond, can be uniquely determined by values sampled at uniform intervals of The sampling rate, is called Nyquist rate. 18 9

Quantization Amplitude quantizing: Mapping samples of a continuous amplitude waveform to a finite set of amplitudes. Out In Average quantization noise power Quantized values Signal peak power Signal power to average quantization noise power 19 Encoding (PCM) Pulse code modulation (PCM): Encoding the quantized signals into a digital word (PCM word or codeword). Each quantized sample is digitally encoded into an l bits codeword where L in the number of quantization levels and 20 10

amplitude x(t) 111 3.1867 Quantization example 110 2.2762 Quant. levels 101 1.3657 100 0.4552 011-0.4552 boundaries 010-1.3657 001-2.2762 000-3.1867 PCM codeword xq(nts): quantized values x(nts): sampled values Ts: sampling time t 110 110 111 110 100 010 011 100 100 011 PCM sequence 21 Quantization error Quantizing error: The difference between the input and output of a quantizer e( t) xˆ( t) x( t) Process of quantizing noise Qauntizer y q(x) Model of quantizing noise AGC x (t) xˆ ( t) x x (t) xˆ ( t) e(t) + e( t) xˆ( t) x( t) 22 11

Quantization error Quantizing error: Granular or linear errors happen for inputs within the dynamic range of quantizer Saturation errors happen for inputs outside the dynamic range of quantizer Saturation errors are larger than linear errors Saturation errors can be avoided by proper tuning of AGC Quantization noise variance: 2 q E 2 2 2 2 {[ x q( x)] } e ( x) p( x) dx Lin Sat 2 2 ql Lin 2 p( xl ) ql Uniform q. 12 L / 2 1 l0 2 Lin 2 q 12 23 Uniform and non-uniform quant. Uniform (linear) quantizing: No assumption about amplitude statistics and correlation properties of the input. Not using the user-related specifications Robust to small changes in input statistic by not finely tuned to a specific set of input parameters Simply implemented Application of linear quantizer: Signal processing, graphic and display applications, process control applications Non-uniform quantizing: Using the input statistics to tune quantizer parameters Larger SNR than uniform quantizing with same number of levels Non-uniform intervals in the dynamic range with same quantization noise variance Application of non-uniform quantizer: Commonly used for speech 24 12

Non-uniform quantization It is done by uniformly quantizing the compressed signal. At the receiver, an inverse compression characteristic, called expansion is employed to avoid signal distortion. compression+expansion companding y C(x) x xˆ (t) y(t) y ˆ( t ) xˆ ( t) Compress x Transmitter Quantize Channel Expand Receiver ŷ 25 Pulse Code Modulation (continued) Binary values are later converted to an analog signal Waveform similar to original results 26 13

Pulse Code Modulation (continued) The more snapshots taken in the same amount of time, or the more quantization levels, the better the resolution 27 Pulse Code Modulation (continued) Because the human voice has a fairly narrow bandwidth Telephone systems digitize voice into either 128 levels or 256 levels Called quantization levels If 128 levels, then each sample is 7 bits (2 ^ 7 = 128) If 256 levels, then each sample is 8 bits (2 ^ 8 = 256) 28 14

Pulse Code Modulation (continued) How fast do you have to sample an input source to get a fairly accurate representation? Nyquist says 2 times the bandwidth Thus, if you want to digitize voice (4000 Hz), you need to sample at 8000 samples per second 29 Delta Modulation An analog waveform is tracked using a binary 1 to represent a rise in voltage and a 0 to represent a drop 30 15

Source Coding To eliminate redundancy Huffman Coding Shannon-Fano Coding To maximize information rate in a transmission What is Information Rate? Information per bit Entropy 31 Channel Coding Error Control Coding To reduce the impact of channel errors by controlled introduction of redundancy Decrease in effective data rate Increased coding gain Forward Error Correcting Codes Linear Block Codes Convolutional Codes ARQ methods 32 16

Line Coding Formats (Converting Data into Signals) Numerous techniques NRZ-L NRZ-I Manchester Differential Manchester Bipolar AMI 33 Converting Data into Signals (continued) 34 17

Pulse Shaping Filters Bandlimiting signals in frequency domain spreads signal in time domain Inter-Symbol Interference ISI Nyquist Criterian to overcome ISI Pulse Shaping Filters Raised Cosine Filters Gaussian shaping filters 35 Consider: sin( t / Ts ) h eff (t) = 6.44 t / T s Assume that for n > 0 h eff (nt s ) = 0 1 0.8 0.6 0.4 0.2 0-0.2 x NYQ (t) sin( t / T s ) t / T s -6T -4T -2T 0 2T 4T 6T h eff (nt s ) = 0 18

Transfer function of Nyquist Pulse Shaping Filter H NYQ (f) 1 1 2T 1 1 2T 2T 1 2T 1 2T 1 2T scaling factor, 0 1 = 0 Guassian filter has narrow absolute bandwidth not as narrow as RC filter sharp cut-off frequency & low overshoot smooth transfer function & no zero crossings good design choice when cost & power efficiency are most important BER from ISI is less critical issue Nyquist (RRC) filters have zero crossings at adjacent symbol peaks truncated transfer function assume flat channel response (equalized) 19

Baseband RC Filter impulse response plotted for 0 1 Baseband Gaussian Filter impulse response plotted for different B 3dB T s = 0 = 0.5 = 1 h RC (t) 1/T s h G (t) = 0.5 = 0.75 = 1.0 = 2.0-4T -3T -2T -T 0 T 2T 3T 4T 3 T s 2 T s 2 T s 2 3 s T 2 t 39 What is modulation Modulation is the process of encoding information from a message source in a manner suitable for transmission It involves translating a baseband message signal to a bandpass signal at frequencies that are very high compared to the baseband frequency. Baseband signal is called modulating signal Bandpass signal is called modulated signal 40 20

Modulation Techniques Modulation can be done by varying the Amplitude Phase, or Frequency of a high frequency carrier in accordance with the amplitude of the message signal. Demodulation is the inverse operation: extracting the baseband message from the carrier so that it may be processed at the receiver. 41 Fundamentals of Signals Amplitude Height of the wave above or below a given reference point Frequency Number of times a signal makes complete cycle within a given time frame Spectrum - Range of frequencies that a signal spans from minimum to maximum Bandwidth - The absolute value of the difference between the lowest and highest frequencies of a signal For example, voice spectrum 300-3100 Hz 42 21

Fundamentals of Signals (continued) Phase Position of the waveform relative to a given moment of time or relative to time zero A change in phase can be any number of angles between 0 and 360 degrees Phase changes often occur on common angles, such as 45, 90, 135, etc. 43 Where do you need modulation? Orthogonal Frequency Division Multiplexing ADSL 44 22

Formatting and transmission of baseband signal Digital info. source Textual info. Analog info. Sample Format Quantize Encode Pulse modulate Transmit sink Analog info. Textual info. Low-pass filter Format Decode Bit stream Pulse waveforms Demodulate/ Detect Channel Receive Digital info. 45 Modulation -Transmitting Digital Data with Analog Signals Three basic techniques: Amplitude shift keying Frequency shift keying Phase shift keying 46 23

Amplitude Shift Keying One amplitude encodes a 0 while another amplitude encodes a 1 (a form of amplitude modulation) 47 Amplitude Shift Keying (continued) Some systems use multiple amplitudes 48 24

Amplitude Shift Keying (continued) Multiple Signal Levels Why use multiple signal levels? We can represent two levels with a single bit, 0 or 1 We can represent four levels with two bits: 00, 01, 10, 11 We can represent eight levels with three bits: 000, 001, 010, 011, 100, 101, 110, 111 Note that the number of levels is always a power of 2 49 Frequency Shift Keying One frequency encodes a 0 while another frequency encodes a 1 (a form of frequency modulation) 50 25

Phase Shift Keying One phase change encodes a 0 while another phase change encodes a 1 (a form of phase modulation) 51 Goal of Advanced Modulation and Coding Techniques Modulation is difficult task in hostile channels like the mobile radio channels Small-scale fading and multi-path conditions. The goal of a modulation scheme is: To transport the message signal through the radio channel with best possible quality. To occupy least amount of radio (RF) spectrum. 52 26

Multipath Propagation LOS pulses multipath pulses signal at sender signal at receiver power long term fading short term fading t 53 Wireless channel Effective channel depends on both physical environment and bandwidth! 54 27

Channel Classification Flat Fading Channel Slow Fading Channel Channel Coherence bandwidth >> Signal bandwidth Channel Coherence time >> Symbol duration Frequency Selective Fading Channel Fast Fading Channel Channel Coherence bandwidth << Signal bandwidth Channel Coherence time >> Symbol duration 55 Phase Shift Keying (continued) Quadrature Phase Shift Keying Four different phase angles are used: 45 degrees 135 degrees 225 degrees 315 degrees 56 28

Phase Shift Keying (continued) 57 Phase Shift Keying (continued) Quadrature Amplitude Modulation 12 different phases are combined with two different amplitudes Since only 4 phase angles have 2 different amplitudes, there are a total of 16 combinations. With 16 signal combinations, each baud equals 4 bits of information (2 ^ 4 = 16) 58 29

Phase Shift Keying (continued) 59 Spread Spectrum Technology A secure encoding technique that uses multiple frequencies or codes to transmit data Two basic spread spectrum technologies: Frequency hopping spread spectrum Direct sequence spread spectrum 60 30

Spread Spectrum Technology (continued) 61 Spread Spectrum Technology (continued) Direct Sequence Spread Spectrum This technology replaces each binary 0 and binary 1 with a unique pattern, or sequence, of 1s and 0s For example, one transmitter may transmit the sequence 10010100 for each binary 1, and 11001010 for each binary 0 Another transmitter may transmit the sequence 11110000 for each binary 1, and 10101010 for each binary 0 62 31

OFDM OFDM = Orthogonal FDM Carrier centers are put on orthogonal frequencies ORTHOGONALITY - The peak of each signal coincides with trough of other signals Subcarriers are spaced by 1/Ts 63 Thank you 64 32