1. Some charts from Stallings, modified and added to1 Communications Systems, Signals, and Modulation Session 3 Nilesh Jha

2. About Channel Capacity Impairments, such as noise, limit data rate that can be achieved Channel Capacity – the maximum rate at which data can be transmitted over a given communication path, or channel, under given conditions

3. Transmission Impairments Signal received may differ from signal transmitted Analog - degradation of signal quality Digital - bit errors Caused by Attenuation and attenuation distortion Delay distortion Noise

4. Attenuation Signal strength falls off with distance Depends on medium Received signal strength: must be enough to be detected must be sufficiently higher than noise to be received without error Attenuation is an increasing function of frequency

5. Noise (1) Additional EM energy and signals on the receiver Thermal -- usually inserted by receiver circuits Due to thermal agitation of electrons Uniformly distributed White noise Intermodulation Signals that are the sum and difference of original frequencies sharing a medium, and falling within the desired signal’s passband

6. Noise (2) Crosstalk A signal from one line or channel is picked up by another Impulse Irregular pulses or spikes e.g. External electromagnetic interference Short duration High amplitude Multipath See in later Sessions, causes distortions

7. Signal-to-Noise Ratio Ratio of the power in a signal to the power contained in the noise that’s present at a particular point in the transmission Typically measured at a receiver Signal-to-noise ratio (SNR, or S/N) A high SNR means a high-quality signal, low number of required intermediate repeaters SNR sets upper bound on achievable data rate

8. Signals and Noise High SNR Lower SNR

9. Concepts Related to Channel Capacity Data rate - rate at which data can be communicated (bps) Bandwidth - the bandwidth of the transmitted signal as constrained by the transmitter and the nature of the transmission medium (Hertz) Noise - average level of noise over the communications path Error rate - rate at which errors occur Error = transmit 1 and receive 0; transmit 0 and receive 1

10. Nyquist Bandwidth For binary signals (two voltage levels) C = 2B With multilevel signaling C = 2B log 2 M M = number of discrete signal or voltage levels

11. Shannon Capacity Formula Equation: Represents theoretical maximum that can be achieved In practice, somewhat lower rates achieved Formula assumes white noise (thermal noise) Worse when other forms of noise are included Impulse noise Attenuation distortion or delay distortion Interference

12. Example of Nyquist and Shannon Formulations Spectrum of a channel between 3 MHz and 4 MHz ; SNR dB = 24 dB Using Shannon’s formula

13. Example of Nyquist and Shannon Formulations How many signaling levels are required?

14. Multiplexing Capacity of transmission medium usually exceeds capacity required for transmission of a single signal Multiplexing - carrying multiple signals on a single medium More efficient use of transmission medium

15. Multiplexing

16. Reasons for Widespread Use of Multiplexing Cost per kbps of transmission facility declines with an increase in the data rate Cost of transmission and receiving equipment declines with increased data rate Most individual data communicating devices require relatively modest data rate support

17. Multiplexing Techniques Frequency-division multiplexing (FDM) Takes advantage of the fact that the useful bandwidth of the medium exceeds the required bandwidth of a given signal --- different users at different frequency bands or subbands Time-division multiplexing (TDM) Takes advantage of the fact that the achievable bit rate of the medium exceeds the required data rate of a digital signal --- different users at different time slots

18. Frequency-division Multiplexing

19. Time-division Multiplexing

20. Multiplexing and Multiple Access Both refer to the sharing of a communications resource, usually a channel Multiplexing usually refers to sharing some resource by doing something at one site --- eg, at the multiplexer Often a static or pseudo-static allocation of fractions of the multiplexed channel, eg, a T1 line. Often refers to sharing one resource. The division of the resource can be made on frequency, or time, or other physical feature Multiple Access shares an asset in a distributed domain ie, multiple users at different places sharing an overall media, and using a scheme where it is divided into channels based on frequency, or time or another physical feature Usually dynamic

21. Factors Used to Compare Modulation and Encoding Schemes Signal spectrum With fewer higher frequency components, less bandwidth required --- Spectrum Efficiency For wired comms: with no DC component, AC coupling via transformer possible --- DC components cause problems Transfer function of a channel is worse near band edges -- always better to constrain signal spectrum well inside the spectrum available Synchronization and Clocking Determining when 0 phase occurs -- carrier synch Determining beginning and end of each bit position -- bit sync Determining frame sync --- usually layer above physical

22. Signal Modulation/Encoding Criteria: Demodulating/Decoding Accurately What determines how successful a receiver will be in interpreting an incoming signal? Signal-to-noise ratio = SNR signal power/noise power Note: power = energy per unit time Data rate (R) Bandwidth (BW) An increase in data rate increases bit error rate An increase in SNR decreases bit error rate An increase in bandwidth allows an increase in data rate

23. Factors Used to Compare Modulation/Encoding Schemes Signal interference and noise immunity --- Performance in the presence of interference and noise For a given signal power level, the effect of noise and interference is then labeled the Power Efficiency For digital modulation, Prob. Of Bit Error = function (SNR) where N includes the interference terms More exactly, Prob. Bit Error = function (Energy per bit/Noise power density, with noise including interference and other noise like terms) --- see next chart Cost and complexity Usually the higher the signal and data rates require a higher complexity and greater the cost

24. A Figure of Merit in Communications: Noise Immunity For digital modulation one bottom line Figure of Merit (FOM) is Probability of Bit Error (Psub e) -- Lowest for Most Accurate Decoding of Bit Stream Prob. Bit Error= function of (Eb/Nsub 0) Many functions for many different modulation and coding types have been computed - usually decreases with increasing Eb/Nsub 0 Eb=energy per bit Nsub 0=noise spectral density; Noise Power N= (Nsub 0)* BW Note: Includes Interference and Intermodulation and Crosstalk (Eb/Nsub 0) is a critically important number for digital comms Eb/Nsub0=(SNR)*(BW/R) ---- important formula -- derive it SNR is signal to noise ratio, a ratio of power levels BW is signal bandwidth, R is data rate in bits/sec For analog modulation the FOM is SNR Signal quality given by subjective statistical scores -- voice: 1-5 (high) FM requires a lower SNR than AM for the same signal quality

25. Basic Modulation/Encoding Techniques Digital data to analog signal --- Digital Modulation Amplitude-shift keying (ASK) Amplitude difference of carrier frequency Frequency-shift keying (FSK) Frequency difference near carrier frequency Phase-shift keying (PSK) Phase of carrier signal shifted

26. Basic Encoding Techniques

27. Amplitude-Shift Keying One binary digit represented by presence of carrier, at constant amplitude Other binary digit represented by absence of carrier where the carrier signal is Acos(2πf c t)

28. Amplitude-Shift Keying Susceptible to sudden gain changes Inefficient modulation technique On voice-grade lines, used up to 1200 bps Used to transmit digital data over optical fiber

29. Binary Frequency-Shift Keying (BFSK) Two binary digits represented by two different frequencies near the carrier frequency where f 1 and f 2 are offset from carrier frequency f c by equal but opposite amounts

30. Binary Frequency-Shift Keying (BFSK) Less susceptible to error than ASK On voice-grade lines, used up to 1200bps Used for high-frequency (3 to 30 MHz) radio transmission Can be used at higher frequencies on LANs that use coaxial cable

31. Multiple Frequency-Shift Keying (MFSK) More than two frequencies are used More bandwidth efficient but more susceptible to error f i = f c + (2i – 1 – M)f d f c = the carrier frequency f d = the difference frequency M = number of different signal elements = 2 L L = number of bits per signal element

32. Multiple Frequency-Shift Keying (MFSK) To match data rate of input bit stream, each output signal element is held for: T s =LT seconds where T is the bit period (data rate = 1/T) So, one signal element encodes L bits

33. Multiple Frequency-Shift Keying (MFSK) Total bandwidth required 2Mf d Minimum frequency separation required 2f d =1/T s Therefore, modulator requires a bandwidth of W d =2 L /LT=M/T s

34. Multiple Frequency-Shift Keying (MFSK)

35. Phase Shift Keying (PSK) The signal carrier is shifted in phase according to the input data stream 2 level PSK, also called binary PSK or BPSK or 2-PSK, uses 2 phase possibilities over which the phase can vary, typically 0 and 180 degrees -- each phase represents 1 bit can also have n-PSK -- 4-PSK often is 0, 90, 180 and 270 degrees --- each phase then represents 2 bits Each phase called a ‘symbol’ Each bit or groups of bits can be represented by a phase value (eg, 0 degrees, or 180 degrees), or bits can be based on whether or not phase changes (differential keying, eg, no phase change is a 0, a phase change is a 1) --- DPSK

36. Phase-Shift Keying (PSK) Two-level PSK (BPSK) Uses two phases to represent binary digits

37. Phase-Shift Keying (PSK) Differential PSK (DPSK) Phase shift with reference to previous bit Binary 0 – signal burst of same phase as previous signal burst Binary 1 – signal burst of opposite phase to previous signal burst

38. Phase-Shift Keying (PSK) Four-level PSK (QPSK) Each element represents more than one bit

39. Quadrature PSK More efficient use by each signal element (or symbol) representing more than one bit e.g. shifts of  /2 (90 o ) In QPSK each element or symbol represents two bits Can use 8 phase angles and have more than one amplitude -- then becomes QAM then (combining PSK and ASK) QPSK used in different forms in a many cellular digital systems Offset-QPSK: O-QPSK: The I (0 and 180 degrees) and Q (90 and 270 degrees) quadrature bits are offset from each other by half a bit --- becomes a more efficient modulation, with phase changes not so abrupt so better spectrally, and more linear Pi/4-QPSK is a similar approach to O-QPSK, also used

40. Multilevel Phase-Shift Keying (MPSK) Multilevel PSK Using multiple phase angles multiple signals elements can be achieved D = modulation rate, baud R = data rate, bps M = number of different signal elements or symbols = 2 L L = number of bits per signal element or symbol eg, 4-PSK is QPSK, 8-PSK, etc

41. Quadrature Amplitude Modulation QAM is a combination of ASK and PSK Two different signals sent simultaneously on the same carrier frequency

42. Quadrature Amplitude Modulation

43. Quadrature Amplitude Modulation (QAM) The most common method for quad (4) bit transfer Combination of 8 different angles in phase modulation and two amplitudes of signal Provides 16 different signals (or ‘symbols’), each of which can represent 4 bits (there are 16 possible 4 bit combinations)

44. 90 45 0 135 180 225 270 315 amplitude 1 amplitude 2 Quadrature Amplitude Modulation Illustration -- example of Constellation Diagram Notice that there are 16 circles or nodes, each represents a possible amplitude and phase, and each represents 4 bits Obviously there are many such constellation diagrams possible --- the technical issue winds up being that as the nodes get closer to each other any noise can lead to the receiver confusing them, and making a bit error

45. Performance of Digital Modulation Schemes Bandwidth or Spectral Efficiency ASK and PSK bandwidth directly related to bit rate FSK bandwidth related to data rate for lower frequencies, but to offset of modulated frequency from carrier at high frequencies Determined by C/BW ie bps/Hz Noise Immunity or Power Efficiency: In the presence of noise, bit error rate of PSK and QPSK are about 3dB superior to ASK and FSK ---- ie, x2 less power for same performance Determined by BER as function of Eb/Nsub0

46. Spectral Performance Bandwidth of modulated signal (B T ) ASK, PSKB T =(1+r)R FSKB T =2DF+(1+r)R R = bit rate 0 < r < 1; related to how signal is filtered DF = f 2 -f c =f c -f 1

47. SPECTRAL Performance Bandwidth of modulated signal (B T ) MPSK MFSK L = number of bits encoded per signal element M = number of different signal elements

48. In Stallings

50. By Sklar, from Gibson Power-Bandwidth Efficiency Plane

51. Analog Modulation Techniques Analog data to analog signal Also called analog modulation Amplitude modulation (AM) Angle modulation Frequency modulation (FM) Phase modulation (PM)

52. AM MODULATION Top left: source (baseband) signal to be modulated; bottom left: modulated signal, carrier lines inside white; right: demodulated after it is transmitted and received (note after 1.e-3 similarity except for attenuation)

53. Input Voice and Received Voice after Transmission and Reception, Using FM --- Only a Little Noise -- Notice Similarity

54. Input Voice and Received Voice after Transmission and Reception, Using FM --- Lots More Noise in Channel -- Notice that Received Signal is NOT What Was Transmitted

55. Amplitude Modulation cos2  f c t = carrier x(t) = input signal n a = modulation index Ratio of amplitude of input signal to carrier a.k.a double sideband transmitted carrier (DSBTC)

56. Spectrum of AM signal

57. Amplitude Modulation Transmitted power P t = total transmitted power in s(t) P c = transmitted power in carrier

58. Single Sideband (SSB) Variant of AM is single sideband (SSB) Sends only one sideband Eliminates other sideband and carrier Advantages Only half the bandwidth is required Less power is required Disadvantages Suppressed carrier can’t be used for synchronization purposes

59. Angle Modulation Angle modulation Phase modulation Phase is proportional to modulating signal n p = phase modulation index

60. Angle Modulation Frequency modulation Derivative of the phase is proportional to modulating signal n f = frequency modulation index

61. Angle Modulation Compared to AM, FM and PM result in a signal whose bandwidth: is also centered at f c but has a magnitude that is much different Angle modulation includes cos(  (t)) which produces a wide range of frequencies Thus, FM and PM require greater bandwidth than AM

62. Angle Modulation Carson’s rule where The formula for FM becomes

63. Coding Encoding sometimes is used to refer to the way in which analog data is converted to digital signals eg, A/D’s, PCM or DM Source Coding refers to the way in which basic digitized analog data can be compressed to lower data rates without loosing any or to much information -- eg, voice, video, fax, graphics, etc. Channel coding refers to signal transformations used to improve the signal’s ability to withstand the channel propagation impairments --- two types waveform coding --- transforms signals (waveforms) into better ones --- able to withstand propagation errors better --- this refers to different modulation schemes, M’ary signaling, spread spectrum Sequence coding, also generally labelled error coding or FEC, transforms data bits sequences into ones less error prone, by inserting redundant bits in a smart way -- eg, block and convolutional codes

64. Basic Encoding Techniques Analog data to digital signal Used for digitization of analog sources Pulse code modulation (PCM) Delta modulation (DM) After the above, usually additional processing done to compress signal to achieve similar signal quality with fewer bits --- called source coding

65. Analog to Digital Conversion Once analog data have been converted to digital signals, the digital data: can be transmitted using NRZ-L can be encoded as a digital signal using a code other than NRZ-L can be modulated to an analog signal for wireless transmission, using previously discussed techniques

66. Pulse Code Modulation Based on the sampling theorem Each analog sample is assigned a binary code Analog samples are referred to as pulse amplitude modulation (PAM) samples The digital signal consists of block of n bits, where each n-bit number is the amplitude of a PCM pulse

67. Pulse Code Modulation

68. By quantizing the PAM pulse, original signal is only approximated Leads to quantizing noise Signal-to-noise ratio for quantizing noise Thus, each additional bit increases SNR by 6 dB, or a factor of 4

69. Delta Modulation Analog input is approximated by staircase function Moves up or down by one quantization level (  ) at each sampling interval The bit stream approximates derivative of analog signal (rather than amplitude) 1 is generated if function goes up 0 otherwise

70. Delta Modulation

71. Two important parameters Size of step assigned to each binary digit (  ) Sampling rate Accuracy improved by increasing sampling rate However, this increases the data rate Advantage of DM over PCM is the simplicity of its implementation

72. Source Coding Voice or Speech or Audio Basic PCM yields 4 KHz*2 samples/Hz*8 bits/sample=64 Kbps -- music/etc up to 768 Kbps Coding can exploit redundancies in the speech waveform -- one way is LPC, linear predictive coding --- predicts what’s next, sends only the changes expected RPE and CELP (Code Excited LPC) used in cell phones, using LPC, at rates of 4 to 9.6 to 13 kbps Graphics and Video: eg, JPEG or GIF, MPEG

73. Reasons for Growth of Digital Modulation and Transmission Growth in popularity of digital techniques for sending analog or digital source data Cheaper components used in creating the modulations and doing the encoding, and similarly on the receivers Best performance in terms of immunity to noise and in terms of spectral efficiency --- improved digital modulation and channel coding techniques Great improvements in digital voice and video compression Voice to about 8 Kbps at good quality, video varies to below 1 Mbps provide increased capacity in terms of numbers of users in given BW Dynamic and efficient multiple access and multiplexing techniques using TDM, TDMA and CDMA, even when some larger scale Frequency Allocations (FDMA) -- labeled as combinations Easier and simpler implementation interfaces to the digital landline networks and IP

74. Duplex Modes Duplex modes refer to the ways in which two way traffic is arranged One way vs two way: simplex (one way only), half duplex (both ways, but only one way at a time), duplex (two ways at the same time) If duplex, question is then how one separates the two ways In wired systems, it could be in different wires (or cables, fibers, etc) Both wired and wireless one way is to separate the two paths in frequency --- FDD, frequency division duplex If two frequencies, or frequency bands, are separate enough, no cross interference Cellular systems are all FDD It’s clean and easy to do, good performance, but it limits channel assignments and is not best for asymmetric traffic TDD is time division duplex, same frequencies are used both ways, but time slots are assigned one way or the other Good for asymmetrical traffic, allows more control through time slot reassignments But strong transmissions one way could interfere with other users Mostly not used in cellular, but 3G has one such protocol, and low tier portables also