Communications I (ELCN 306)

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1 Communications I (ELCN 306) c Samy S. Soliman Electronics and Electrical Communications Engineering Department Cairo University, Egypt samy.soliman@cu.edu.eg Website: c Samy S. Soliman (Cairo University) ELCN / 58

2 Outline 1 Introduction to Digital Communications 2 Pulse Modulation 3 Pulse Amplitude Modulation 4 Time Division Multiplexing 5 Pulse Code Modulation Quantization Encoding - Line Codes Regeneration Decoding Filtering c Samy S. Soliman (Cairo University) ELCN / 58

3 Introduction to Digital Communications c Samy S. Soliman (Cairo University) ELCN / 58

4 Introduction Communication Process It is a process that involves the transfer of information from one point to another Basic Modes of Communication 1 Broadcasting 2 Point-to-Point Communication Activity: Think (Give examples of each mode of communication) Activity: Analyze (What are the differences between the modes of communication) c Samy S. Soliman (Cairo University) ELCN / 58

5 Introduction Communication Resources 1 Transmitted Power 2 Channel Bandwidth Activity: Think (Give examples of communication channels and their classification) This gives rise to the need of modulation: 1 Ease of Radiation 2 Simultaneous transmission of several signals SNR Signal-to-noise ratio: Ratio of the average signal power to the average noise power. c Samy S. Soliman (Cairo University) ELCN / 58

6 Introduction Classification of Modulation Process 1 Continuous-Wave Modulation 2 Pulse Modulation 3 Digital Modulation Note In the following, we will focus on Pulse Modulation (PM), which refers to the Discretization of the signal. It is further classified to 1 Analog PM 2 Digital PM c Samy S. Soliman (Cairo University) ELCN / 58

7 Introduction c Samy S. Soliman (Cairo University) ELCN / 58

8 Basics of Communication: Introduction c Samy S. Soliman (Cairo University) ELCN / 58

9 Why Digital Communication Systems? Features of Digital Communication Systems Transmitter sends a waveform from a finite set of possible waveforms during a limited time Channel distorts, attenuates and adds noise to the transmitted signal Receiver decides which waveform was transmitted from the noisy received signal Probability of erroneous decision is an important measure for the system performance Advantages of Digital Communication Systems The ability to use regenerative repeaters Different kinds of digital signals are treated identically Immunity to noise c Samy S. Soliman (Cairo University) ELCN / 58

10 Designing Digital Communication Systems Necessary Knowledge/Tools for the Design of DCS 1 Classification of signals 2 Random processes 3 Noise in communication systems 4 Signal transmission through linear systems 5 Bandwidth of signal c Samy S. Soliman (Cairo University) ELCN / 58

11 Pulse Modulation c Samy S. Soliman (Cairo University) ELCN / 58

12 Pulse Modulation c Samy S. Soliman (Cairo University) ELCN / 58

13 Pulse Amplitude Modulation c Samy S. Soliman (Cairo University) ELCN / 58

14 Pulse Amplitude Modulation (PAM) Definition PAM is the simplest and most basic form of analog pulse modulation The amplitudes of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous message signal The message is instantaneously sampled every T s seconds The duration of each sample is lengthened to a constant value for T seconds (Sample and Hold) Train of Pulses The pulses can be rectangular or any appropriate shape s(t) = n m(nt s )h(t nt s ) c Samy S. Soliman (Cairo University) ELCN / 58

15 PAM: Sampling The instantaneously sampled version of m(t) is given as m s (t) = n m(nt s )δ(t nt s ) After some mathematical manipulation, the PAM signal can be expressed as s(t) = m s (t) h(t) PAM Signal s(t) = m s (t) h(t) S(f ) = M s (f ).H(f ) c Samy S. Soliman (Cairo University) ELCN / 58

16 PAM: Flat-Top Rectangular Pulse For rectangular pulses h(t) = { 1, 0 < t < T 0, elsewhere H(f ) = Tsinc(fT )e jπft Recall that M s (f ) = f s M(f kf s ) k c Samy S. Soliman (Cairo University) ELCN / 58

17 PAM: Time Domain c Samy S. Soliman (Cairo University) ELCN / 58

18 PAM: Demodulation Message Recovery: LPF The first step in the recovery of the original signal is through using a Low-Pass Reconstruction Filter The spectrum of the filter output is LPF {M s (f ).H(f )} = M(f )LPF {sinc(ft )e jπft } This is an amplitude distorted and T /2 delayed version of the message Message Recovery: Equalizer An equalizer is connected in cascade with the LPF and it is used to correct the amplitude distortion The magnitude response of the equalizer is given as 1 Tsinc(fT ) = πf sin(πft ) c Samy S. Soliman (Cairo University) ELCN / 58

19 PAM: Duty Cycle of Pulses Duty Cycle = T T s The presence of T causes the presence of amplitude distortion As T, distortion For duty cycle T T s 0.1, the amplitude distortion is less than 0.5% and the use of equalization can be ignored. c Samy S. Soliman (Cairo University) ELCN / 58

20 Time Division Multiplexing c Samy S. Soliman (Cairo University) ELCN / 58

21 Time Division Multiplexing Purpose: To enable the joint utilization of the communication resources by a plurality of independent message sources, without creating mutual interference among them. Resources: Physical channel, Time, Bandwidth, etc. c Samy S. Soliman (Cairo University) ELCN / 58

22 Time Division Multiplexing LPF Low-pass anti-aliasing filters. Commutator Takes a narrow sample of each of the N input messages at a rate f s 2W Sequentially interleaves these N samples inside a sampling interval T s This expands the bandwidth by a factor of N c Samy S. Soliman (Cairo University) ELCN / 58

23 Time Division Multiplexing Pulse Modulator Transforms the multiplexed signal into a form suitable for transmission over the channel Pulse Demodulator Makes decisions to transform the received pulses into their corresponding samples. c Samy S. Soliman (Cairo University) ELCN / 58

24 Time Division Multiplexing Decommutator Demultiplex the samples to their corresponding destination Operates in synchronism with the commutator at the transmitter. Such synchronization is essential for proper operation LPF Low-Pass reconstruction filter c Samy S. Soliman (Cairo University) ELCN / 58

25 Pulse Code Modulation c Samy S. Soliman (Cairo University) ELCN / 58

26 Pulse Code Modulation: Basic Elements c Samy S. Soliman (Cairo University) ELCN / 58

27 PCM: Introduction Definition A message signal is represented by a sequence of coded pulses Accomplished by representing the signal in discrete form in both time and amplitude c Samy S. Soliman (Cairo University) ELCN / 58

28 PCM Transmitter: Sampling Definition It is the process of transforming a message signal m(t) into an analog discrete signal m(nt s ) with a sampling frequency f s which is higher than twice the highest frequency component W of the message signal Ensure perfect reconstruction at the Receiver Narrow rectangular pulses instantaneous sampling Proceeded by an anti-aliasing filter Reduces the continuously varying message signal to a limited number of discrete values per second c Samy S. Soliman (Cairo University) ELCN / 58

29 Quantization c Samy S. Soliman (Cairo University) ELCN / 58

30 PCM Transmitter: Quantization Definition It is the process of transforming the sample amplitude m(nt s ) into a discrete amplitude ν(nt s ) taken from a finite set of possible amplitudes c Samy S. Soliman (Cairo University) ELCN / 58

31 PCM Transmitter: Quantization c Samy S. Soliman (Cairo University) ELCN / 58

32 PCM Transmitter: Quantization c Samy S. Soliman (Cairo University) ELCN / 58

33 Uniform Mid-Rise Quantization Quantizer Characteristic: Mid-Rise Staircase The origin lies in the middle of a rise c Samy S. Soliman (Cairo University) ELCN / 58

34 Uniform Mid-Tread Quantization Quantizer Characteristic: Mid-Tread Staircase The origin lies in the middle of a tread c Samy S. Soliman (Cairo University) ELCN / 58

35 Quantization Error Definition It is the difference between the input signal, m, and the output signal ν Notes: q = m ν Maximum error: q max = ± 1 step size 2 max min Step size: = L As the step width, the quantization error It is better to use binary weighted number of levels, i.e. L = 2 R bits/sample c Samy S. Soliman (Cairo University) ELCN / 58

36 Signal-to-Noise Ratio (SNR) The signal-to-noise ratio (SNR) is one of the performance measures used to describe communication systems. Quantization error is usually more significant than pulse detection errors. SNR It is the ratio of the useful signal power to the noise power. Assuming a uniform quantizer with ±m p peak levels, the average quantization noise level can be evaluated as N q = q 2 = 2 12 = m2 p 3L 2 Quantizer s Output SNR SNR = m 2 = 3L2 N q mp 2 P c Samy S. Soliman (Cairo University) ELCN / 58

37 Non-Uniform Quantization Motivation The SNR is a function of the signal average power, it can be different from one user to another. It is needed to have SNR levels close to each other. The solution is to use smaller quantization steps for smaller signal amplitudes. Achieved through compressing the signal (µ-law or A-Law), then applying a uniform quantizer. This is equivalent to non-uniform quantization. At the reconstruction end, and inverse process is applied using expander. The combined system is called Compander. c Samy S. Soliman (Cairo University) ELCN / 58

38 Non-Uniform Quantization µ-law Quantizer y = ln(1 + µ ˆm) ln(1 + µ) 3L 2 SNR [ln(1 + µ)] 2 A-Law Quantizer A ˆm, 0 ˆm 1/A 1 + ln(a) y = 1 + ln(a ˆm), 1/A ˆm ln(a) c Samy S. Soliman (Cairo University) ELCN / 58

39 Non-Uniform µ-law Quantization c Samy S. Soliman (Cairo University) ELCN / 58

40 Non-Uniform A-Law Quantization c Samy S. Soliman (Cairo University) ELCN / 58

41 Encoding (Digital Baseband Modulation) 1 Encoding is used to make the transmitted signal more robust to noise, interference and other channel impairments. 2 It translates the discrete set of sample values to a more appropriate form. 3 Binary codes give the maximum advantage over the effects of noise in a transmission medium, because a binary symbol withstands a relatively high level of noise and it is easy to generate. c Samy S. Soliman (Cairo University) ELCN / 58

42 Encoding: Line Codes Line codes are used for the electrical representation of binary data stream. 1 Unipolar NRZ signaling 2 Polar NRZ signaling 3 Unipolar RZ signaling 4 Bipolar BRZ signaling (Alternate Mark Inversion) 5 Split-Phase signaling (Manchester Code) c Samy S. Soliman (Cairo University) ELCN / 58

43 Line Codes Activity: Identify each of the following line codes c Samy S. Soliman (Cairo University) ELCN / 58

44 Line Codes Line codes usually differ in: 1 Spectral characteristics (power spectral density and bandwidth efficiency): BW should be as small as possible + no DC component. 2 Power Efficiency: for a given BW and a specified detection error probability, the transmitted power should be as small as possible. 3 Error detection capability (Interference and noise immunity): should be possible to detect and preferably correct errors. 4 Bit synchronization capability: should be possible to extract timing or clock information from the line code. 5 Implementation cost and complexity c Samy S. Soliman (Cairo University) ELCN / 58

45 Bit Rate - Transmission Bandwidth - Output SNR A baseband signal with maximum power P Watts and bandwidth B Hz, sampled at the Nyquist rate, 2B Hz, and quantized into L = 2 R PCM levels, using a uniform quantizer with ±m p peak levels, to be transmitted over a channel of efficiency η bits/sec/hz Bit Rate Transmission Bandwidth Output SNR R b = 2BR B T = R b η SNR = 3P mp 2 2 2R SNR db = 10 log(snr) = 10 log ( 3P m 2 p ) + 6R db c Samy S. Soliman (Cairo University) ELCN / 58

46 Regeneration 1 This is one of the most important features of PCM 2 It provides the ability to control the effects of distortion and noise 3 It is done by a chain of Regenerative Repeaters located at sufficiently close spacings along the transmission route Notes While it is not possible to compensate for the quantization process due to the lost values, the regeneration process can overcome the effects of: Attenuation Distortion Random noise This is done through: Detection Regeneration c Samy S. Soliman (Cairo University) ELCN / 58

47 Block Diagram of a Regenerative Repeater The input, at A, is a distorted PCM wave. The output, at B, is the regenerated PCM wave. c Samy S. Soliman (Cairo University) ELCN / 58

48 Regenerative Repeaters 1 Except for delay, the regenerated signal is exactly the same as the signal originally transmitted (under ideal circumstances) 2 Regenerative repeaters perform the following functions: Equalization To compensate for the effects of amplitude and phase distortion Timing To sample the equalized pulses at instants of maximum signal-to-noise ratio (SNR) Decision Making By comparing each sample to a threshold so that a clean pulse, that represents 0 or 1, is retransmitted. c Samy S. Soliman (Cairo University) ELCN / 58

49 Decoding Definition It is the process of generating a pulse whose amplitude is the linear sum of all the pulses in the codeword, with each pulse being weighted by its place value in the code. Note: This process is done after regenerating the received pulses one last time Decoding results a Quantized PAM signal c Samy S. Soliman (Cairo University) ELCN / 58

50 Filtering Definition It is the process of passing the decoder s output through a LPF with cutoff frequency equal to the message bandwidth. Note: For an error-free transmission path, the recovered signal is similar to the original signal with the exception of distortion introduced by the quantization process. c Samy S. Soliman (Cairo University) ELCN / 58

51 Examples on PCM Systems c Samy S. Soliman (Cairo University) ELCN / 58

52 Example 1 Question A signal m(t) band-limited to 3 KHz is sampled at a rate 33.3% higher than the Nyquist rate. The maximum acceptable error in the sample amplitude (the maximum quantization error) is 0.5% of the peak amplitude m p. The quantized samples are binary coded. Find the minimum bit rate to transmit the encoded binary signal. If 24 such signals are time-division-multiplexed, determine the bit rate of the multiplexed signal. c Samy S. Soliman (Cairo University) ELCN / 58

53 Example 2 Question The ASCII code has 128 characters (symbols) which are binary coded. If a certain computer generates 100,000 characters per second, determine the following: 1 The number of bits required per character 2 The number of bits per second required to transmit the computer output 3 For error-detection, an additional bit, called parity bit, is added to the code of each character. Modify the answers of the previous 2 parts accordingly. c Samy S. Soliman (Cairo University) ELCN / 58

54 Example 3 Question A CD records audio signals using PCM. Assume the audio signal bandwidth is 15 KHz. 1 What is the Nyquist rate? 2 If the Nyquist samples are quantized into L = 65, 536 levels and then binary coded. What is the number of bits required per sample? 3 Determine the number of bits per second required to encode the audio signal 4 If the transmission channel supports a transmission rate of 2 bps/hz. What is the minimum bandwidth required to transmit the encoded signal? 5 If practical CDs use 44, 100 samples per second. Determine the transmission bit rate and the minimum bandwidth required to transmit the encoded signal c Samy S. Soliman (Cairo University) ELCN / 58

55 Example 4 Question Five telemetry signals, each of bandwidth 1 KHz, are to be transmitted simultaneously by binary PCM. The maximum tolerable error in sample amplitudes is 0.2% of the peak signal amplitude. The signal must be sampled at least 20% above the Nyquist rate. Framing and synchronization require additional 0.5% extra bits. Determine the minimum possible data rate that must be transmitted and the minimum bandwidth required for transmission (assuming channel efficiency of 2 bps/hz). c Samy S. Soliman (Cairo University) ELCN / 58

56 References B. P. Lathi and Zhi Ding (2010) Modern Digital and Analog Communication Systems, 4th Edition. Oxford University Press. Simon Haykin and Michael Moher (2010) Communication Systems, 5th Edition. John Wiley. c Samy S. Soliman (Cairo University) ELCN / 58

57 Thank You Questions? c Samy S. Soliman (Cairo University) ELCN / 58

Time division multiplexing The block diagram for TDM is illustrated as shown in the figure

Time division multiplexing The block diagram for TDM is illustrated as shown in the figure CHAPTER 2 Syllabus: 1) Pulse amplitude modulation 2) TDM 3) Wave form coding techniques 4) PCM 5) Quantization noise and SNR 6) Robust quantization Pulse amplitude modulation In pulse amplitude modulation,