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Wireless Mesh Networks

Understand the basics of transmission in wireless mesh networks, including time-domain concepts, analog and digital waveforms, and frequency-domain concepts.

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Wireless Mesh Networks

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  1. Wireless Mesh Networks Anatolij Zubow (zubow@informatik.hu-berlin.de) Transmission Fundamentals

  2. Electromagnetic Signal • Is used to transmit information • Function of time (t) • Can also be expressed as a function of frequency (f) • Signal consists of components of different frequencies • More important to an understanding of data transmission 2

  3. Time-Domain Concepts • Analog signal • Signal intensity varies in a smooth fashion over time • No breaks or discontinuities in the signal • Digital signal • Signal intensity maintains a constant level for some period of time and then changes to another constant level • Periodic signal • Analog or digital signal pattern that repeats over time s(t +T ) = s(t ) -∞< t < +∞ • where T is the period of the signal • Otherwise, a signal is aperiodic 3

  4. Analog and Digital Waveforms 1010011101011101001 …….. 4

  5. Examples of Periodic Signal 5

  6. Time-Domain Concepts (cont.) • Aperiodicsignal • Analog or digital signal pattern that doesn't repeat over time • Sine wave is the fundamental analog signal, that can be represented by 3 parameters: • Peak amplitude, frequency, and phase • Peak amplitude (A) • Maximum value or strength of the signal over time; typically measured in volts • Frequency (f ) • Rate, in cycles per second, or Hertz (Hz) at which the signal repeats 6

  7. Time-Domain Concepts (cont.) • Period (T ) • Amount of time it takes for one repetition of the signal • T = 1/f • Equivalent to f • Phase () • Measure of the relative position in time within a single period of a signal • Wavelength () • Distance occupied by a single cycle of the signal • Or, the distance between two points of corresponding phase of two consecutive cycles •  = vT, where v is the velocity of the signal • Special case is v = c = 3∙108m/s (speed of light) 7

  8. Sine Wave Parameters • General sine wave • s(t ) = A sin(2ft + ) • Next figure shows effect of varying each of the three parameters: • (a) A = 1, f = 1 Hz,  = 0; thus T = 1s • (b) Reduced peak amplitude; A=0.5 • (c) Increased frequency; f = 2, thus T = ½ • (d) Phase shift;  = /4 radians (45 degrees) • Note: 2 radians = 360° = 1 period 8

  9. Sine Wave Parameters - s(t ) = A sin(2ft + ) 9

  10. Time vs. Distance • When the horizontal axis is time, as in prev. Fig., graphs display the value of a signal at a given point in space as a function of time • With the horizontal axis in space, graphs display the value of a signal at a given point in time as a function of distance • For a sinusoidal transmission (e.g. radio antenna or loudspeaker) at a particular instant of time, the intensity of the signal varies as a function of distance from the source 10

  11. Time vs. Distance (cont.) • Assumptions: • We’ll only deal with one-dimensional waves (waves that travel along only one axis) • The function describing the wave depends on the coordinate (say x) and time (t): f(x,t) • Observations: • f(x,t) is a periodic function of space: f(x,t) = f(x+λ,t) • f(x,t) is also a periodic function of time: f(x,t) = f(x,t+T) 11

  12. Time vs. Distance (cont.) • Observations: • Angular frequency: ω (omega) = 2πf ; [ω] = radians/sec • Angular wave number: k = 2π/λ; [k] = radians/m • Speed of the wave: v = λ/T = λf = (λ/2π) (2πf) = ω/k; [v] =m/s • Power carried by a wave is proportional to the amplitude squared • General equation of a wave as: f(x,t) = Asin(kx + ωt + Φ), • where ‘x’ is distance, ‘t’ is time, ‘A’ is the amplitude of the wave, ‘k’ is angular wave number, ‘ω‘ angular frequency, and ‘Φ‘ is the phase constant. • (kx + ωt + Φ) is called the phase of the wave, 12

  13. Frequency-Domain Concepts • Fundamental frequency • When all frequency components of a signal are integer multiples of one frequency, it’s referred to as the fundamental frequency • Spectrum • Range of frequencies that a signal contains (e.g. white light) • Absolute bandwidth • Width of the spectrum of a signal • Effective bandwidth (or just bandwidth) • Narrow band of frequencies that most of the signal’s energy is contained in (many signals have infinite bandwidth) 13

  14. Frequency-Domain Concepts (cont.) • An electromagnetic signal will be made up of many frequencies • Fig. represents addition of multiple components: • Components of the signal: sine waves of frequencies f and 3f • Spectrum: f to3f • Absolute bandwidth: 3f – f = 2f 14

  15. Frequency-Domain Concepts (cont.) • Any electromagnetic signal can be shown to consist of a collection of periodic analog signals (sine waves) at different amplitudes, frequencies, and phases (see Fourier analysis) • The period of the total signal is equal to the period of the fundamental frequency • See lecture on signal processing Fourier: Initial work on Fourier series Newton: The physics of the prism 15 Fourier: http://www.gmi.edu/~drussell/Demos/Fourier/Fourier.html

  16. Relationship between Data Rate and Bandwidth • The greater the bandwidth, the higher the information-carrying capacity • Conclusions • Any digital waveform will have infinite bandwidth • BUT the transmission system will limit the bandwidth that can be transmitted • AND, for any given medium, the greater the bandwidth transmitted, the greater the cost • HOWEVER, limiting the bandwidth creates distortions 16

  17. Simply Example • Consider a square wave: positive/negative pulse represents binary 0/1 • Waveform represents 0101… • Pulse duration is 1/(2f)  data rate of 2f bits per second (bps) • Q.: What are the frequency components of this signal? • A.: f+3f, f+3f+5f, f+3f+5f+7f,… s(t ) = A∙4/∙Σ (1/k) sin(2kft) , for k odd • s(t ) has infinite number of frequency components  infinite bandwidth • Peak amplitude of kth frequency components, kf, is only 1/k  most of the energy is in the first few frequency components. • Q.: What happens if we limit the bandwidth to just the first 3 freq. components? • A.: Resulting waveform is close to square waveform 17

  18. Simply Example (cont.) • Case I • Assume that for a receiver the waveform is sufficient close to the square wave (discriminate between 0 and 1) • Let f=106 cycles/s = 1 MHz  T= 10-6 s = 1 µs • The bandwidth of the signal is: (5∙106) – 106 = 4 MHz • One bit occurs every 0.5 µs  data rate of 2∙106 = 2 Mbps • Case II • Similar to case I, except we have a bandwidth of 8 MHz and f = 2 MHz • T= 0.5 µs; one bit occurs every 0.25 µs  data rate of 4 Mbps • Case III • Now the waveform is sufficient • f = 2 MHz and T= 0.5 µs  data rate of 4 Mbps • Bandwidth of the signal is: (3∙2∙106) –2∙106 = 4 MHz • A given bandwidth can support various data rates depending on the ability of the receiver to discern between 0 and 1 18

  19. Data Communication Terms • Data - entities that convey meaning, or information • Signals - electric or electromagnetic representations of data • Transmission - communication of data by the propagation and processing of signals 19

  20. Analog and Digital Data • Analog Data • Continuous values in some interval • E.g. video, audio • Digital Data • Discrete values • E.g. text, integers Fig. Acoustic Spectrum of Speech and Music 20

  21. Decibels and Signal Strength • As the signal propagates along a transmission medium, there will be a loss (attenuation) of signal strength • Gain, losses, and relative levels are expressed in decibels, because • Signal strength often falls of exponentially, so loss can be expressed in decibels, which is a logarithmic unit • Net gain and loss in a cascaded transmission path: simple addition and subtraction • Decibel is the measure of the ratio between 2 signal levels. The decibel gain is given by GdB = 10 log10 Pout / Pin, where Pin the input power level and Pout the output power level • Note: decibel is a measure of relative, not absolute, difference (e.g. loss from 1W to 0.5W is 3 dB) • To refer to absolute level of power – dBm uses 1 mW as the reference (0 dBm = 1 mW): PowerdBm = 10 log PowermW / 1 mW 21

  22. Analog Signals • A continuously varying electromagnetic wave that may be propagated over a variety of media, depending on frequency • Examples of media: • Copper wire media (twisted pair and coaxial cable) • Fiber optic cable • Atmosphere or space propagation • Analog signals can propagate analog and digital data 22

  23. Digital Signals • A sequence of voltage pulses that may be transmitted over a copper wire medium • Example • A constant positive voltage level represents a binary 0 and a constant negative voltage represents a binary 1 • Generally cheaper than analog signaling • Less susceptible to noise interference • Suffer more from attenuation • Digital signals can propagate analog and digital data Attenuation of Digital Signals 23

  24. Analog Signaling 24

  25. Digital Signaling Data 25

  26. Reasons for Choosing Data and Signal Combinations • Digital data, digital signal • Equipment for encoding is less expensive than digital-to-analog equipment • Analog data, digital signal • Conversion permits use of modern digital transmission and switching equipment • Digital data, analog signal • Some transmission media will only propagate analog signals • Examples include optical fiber and satellite • Analog data, analog signal • Analog data easily converted to analog signal 26

  27. Classifications of Transmission Media • Transmission Medium • Physical path between transmitter and receiver • Communication in form of electromagnetic waves • Guided Media • Waves are guided along a solid medium • E.g., copper twisted pair, copper coaxial cable, optical fiber • Unguided Media • Provides means of transmission but does not guide electromagnetic signals • Usually referred to as wireless transmission • E.g., atmosphere, outer space 27

  28. Unguided Media • Transmission and reception are achieved by means of an antenna • Tx: antenna radiates electromagnetic energy into the medium (usually air) • Rx: antenna picks up electromagnetic waves from surrounding medium • Configurations for wireless transmission • Directional – Tx antenna puts out a focused beam (Tx & Rx are aligned) • Omnidirectional – Tx signal is spread out in all directions Electromagnetic Spectrum for Telecommunications 28

  29. Digital Communication System • Wireless Channel (radio/microwave) • Unfavorable transmission medium compared to cable and optical fiber • Shared medium – the same frequency spectrum is used multiple times leading to mutual interference • The communication channel has no “shielding” against electromagnetic interference • The transmission path consists i.a. of a number of parallel paths with different signal propagation delays (echoes). The resulting effect is called delay spread. • The mobility of the transmitter and/or receiver (and/or reflector) leads to Doppler shifts of the received signal. The signal suffers a Doppler spread. • In a digital communication system we can eliminate and benefit from the disadvantages of the wireless channel by adapting the system parameters; this is not possible in an analog communication system. 29

  30. Transmission of Information (Analog/Digital) • Analog Transmission • Main objective: Signal in time and frequency domain • Secondary objective: noise in the channel • Problem: only a small number of ways to combat noise, e.g. increasing transmission power, special modulation techniques (FM,PM) • Digital Transmission • Is totally different – messages are mapped onto symbols • Symbols are transmitted which are adapted in an optimal way to the characteristics of the wireless channel (e.g. noise) • There is no similarity between the message and the transmitted symbol • Example: transmission of audio signals (e.g. radio broadcasting) 30

  31. Analog Transmission • Analog communication system • Noise is directly included in the received signal • The signal s(t) is adapted to the channel in terms of • Spectrum (modulation) • Bandwidth (filtering) • Channel noise (transmission power and type of modulation) • The task of the analog receiver is to reconstruct the sent message s(t) from r(t) • Why is g(t) = s(t) not exactly possible? 31

  32. Analog Transmission • Example: Amplitude modulation (AM) 32

  33. Digital Transmission • Digital communication system • The message signals are converted into digital symbols before transmission. • Thus the time response of the transmission channel is totally different from the message signals at input and output of the digital transmission system. • Output of the digital transmitter: D/A conversion of the symbols • Input of the digital transmitter: A/D conversion of the symbols • Digital symbols have analog time response (in the form of a modulated wave) in the channel. 33

  34. Digital Transmission • Digital symbols are adapted in an optimal way to the characteristics of the wireless channel in terms of • Spectrum (digital modulation) • Bandwidth (pulse shaping  analog time response) • Channel noise (type of digital modulation and error protection) • Noise (thermal) • Echoes (multipath propagation) • Doppler shift (moving sender, receiver, reflector) • Interference (foreign sender) • Man made noise (electromagnetic noise, e.g. sparking) • Statics (electrical discharges in the atmosphere) • Jammer 34

  35. Digital Transmission • Task of the digital receiver is to recognize the transmitted symbols: • Compared to analog receiver symbol reconstruction is not required • This is an advantage, because a digital symbol can still be detected correctly, if its shape was (slightly) changed due to noise in the channel. • Received symbols are correctly detected  digital receiver assigns the arranged bit combination  no error on receiver-side despite altered symbol shape • Wide range of digital modulation techniques, error protection algorithms, and a combination of them 35

  36. Properties of the signals in the physical channel • Analog Signal • In principle all time responses are possible within the allowed spectrum; no forbidden time responses • Problem: • A sent time response superimposed by noise (from the channel) is also a valid time response • A receiver is unable to detect an incorrect time response and therefore cannot remove the noise. • Digital Signal • Sender and receiver agree on the possible (analog) time responses consisting of only predefined symbols • Symbols are chosen in a way to improve the transmission (max. tx rate, min. error rate) 36

  37. Properties of the signals in the physical channel • Digital Signal • Receiver knows all valid symbols • Compares the received time response with all known symbols (e.g. correlation) • Due to noise the received symbols will never perfectly match with a known symbol; instead the similarity to one symbol is high ( decision threshold) • The decision will likely be correct if the energy of the received symbols is higher than the energy of the noise • The detected symbol is mapped onto the arranged bit sequence • Noise is a random variable – it is possible that the receiver will choose the wrong symbol (symbol error) • A symbol error results in one or multiple bit errors • Some bit errors can be corrected by error correction techniques (method depends on the bit error pattern) 37

  38. Block Diagram of a DCS • Main objective: bit error rate reduction Block diagram of the digital sender Block diagram of the digital receiver. Red blocks required for parameter estimation (inner receiver) 38 Demo: www2.rad.com/networks/2006/physical/movie.htm

  39. Block Diagram of a DCS (cont.) • The higher receiver complexity is due to the fact that for demodulation and decoding signals and necessary parameters (e.g. carrier frequency, carrier phase, symbol clock, channel characteristics) have to be obtained from the distorted analog signal (called inner receiver, synchronization). • Without these parameters a demodulation and decoding is not possible. • The more accurate these parameters can be determined, the smaller the bit error rate (BER) of the recovered data stream. 39

  40. DCS – Layered Architecture 40

  41. About Channel Capacity • Impairments, such as noise, limit data rate that can be achieved • For digital data, to what extent do impairments limit data rate? • Channel Capacity • The maximum rate at which data can be transmitted over a given communication path, or channel, under given conditions 41

  42. 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 42

  43. Nyquist Bandwidth • Let us assume a channel that is noise free • Here the limitation on data rate is simply the bandwidth of the signal (B) • For binary signals (two voltage levels) • C = 2B • Data rate that can be supported by B Hz is 2B bps • With multilevel signaling • E.g. 4 possible voltage levels are used as signals • C = 2B log2M • M = number of discrete signal or voltage levels • E.g. M=8 and B=3100 Hz  C=18600 bps • For a given bandwidth, the data rate can be increased by increasing the number of different signal elements 43

  44. Effect of Noise on a Digital Signal • Nyquist’s formula – doubling the bandwidth doubles the data rate • Relationship among data rate, noise, and error rate: • Presence of noise can corrupt one or more bits • If data rate is increased then bits become “shorter” in time  more bits are affected by a given pattern of noise • At a given noise level: data rate error rate 44

  45. 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 resulting in a small bit error rate (BER) • SNR sets upper bound on achievable data rate 45

  46. Shannon Capacity Formula • Equation: • C is the capacity of the channel in bits per second and B is the bandwidth in Hertz • Represents theoretical maximum that can be achieved • In practice, only much lower rates achieved • Formula assumes white noise (thermal noise) • Impulse noise is not accounted for • Attenuation distortion or delay distortion not accounted for • If actual information rate is less than error-free capacity (C), then it is theoretically possible to use a suitable signal code to achieve error-free transmission 46

  47. Thermal Noise • Amount of thermal noise to be found in a bandwidth of 1 Hz in any device or conductor is: • N0 = noise power density in watts per 1 Hz of bandwidth • k = Boltzmann's constant = 1.3803 * 10-23 J/K • T = temperature, in kelvins (absolute temperature) • Noise is assumed to be independent of frequency • Thermal noise present in a bandwidth of B Hertz (in watts): • or, in decibel-watts 47

  48. Example of Nyquist and Shannon Formulations • Spectrum of a channel between 3 MHz and 4 MHz ; SNRdB = 24 dB • Using Shannon’s formula • How many signaling levels are required? 48

  49. Duplexing • Separation of the send and receive signals of a terminal. • Partitioning of the wireless medium prohibits the self-interference of a station so that it does not receive its own transmitted signal. • Note: pathloss attenuation leads to much higher signal strength at a station when sending compared to the received signal strength. 49

  50. Duplexing (Cont.) • Time Division Duplex (separation in time) • Switching point periodically separates a single frequency channel into UL and DL period • Ideal for asymmetric services (UL/DL ratio) • Guard times required (signal propagation durations + Rx/Tx Turnaround) • Frequency Division Duplex (separation in frequency) • DL and UL have different frequency bands of equal size • Suitable for symmetric services but requires paired frequency bands 50

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