Fundamentals of Wireless Transmissions

Transcription

1 Fundamentals of Wireless Transmissions Dr. Farahmand Updated: 9/15/14

2 Overview (1) Week 1 Demo Energy and waves Dipole Antennas Signal characteristics and spectrum Bandwidth Signal power (Vpeak and Vrms) Antenna concept XBEE modules TinyOS RF Transceivers Antenna Cables Signal propagation Free Space Transmission Model Isotropic and other types of antenna Antenna Gain and efficiency Loss and attenuation Receiver sensitivity Maximum separation

3 Wireless Communication Systems 1- Antenna - Channel Multiplexer Modulator Converter Electromagnetic Energy Electromagnetic Energy Converter De modulator De multiplexer

4 A simple Wireless Transmitter Audio Transformer Oscillator

5 Waves and Propagation Consider waving a charged ping pong ball at 10 hertz [1] n Using an megameter-wave receiver we can detect a signal Let s pretend vibrating a single electron at radio frequency.

6 Waves and Propagation - Demo

7 Electromagnetic Energy (Radio Waves) Electromagnetic waves are used to transmit signals (electric impulses) Waves are deformation (disturbance) of medium n Temporary disturbance of medium (e.g., Heat Waves) n This is how energy is being transmitted EM Wave consists of n Electric field (red) n Magnetic Field (blue) n Both traveling at the speed of light (3x10^8 m/s) n plane polarized wave travels in X direction Remember: Visible light is EM energy with very high frequency The basic idea behind an electromagnet is simple: By running electric current through a wire, you can create a magnetic field. Applet:

8 EM Radiation Properties Wave Model n When radiation distance and time scale is large n Wave properties (speed, freq, wavelength) Particle Model n When radiation distance and time scale is small n Discrete packets of energy is released (photons) n Described by photon-energy expression (E=hf) this is energy per photon n Remember photons transport energy Atom absorbs photonà excites electronsà photoionization Atom losses energy à atom emits a photonà generating light

9 EM Waves Classification EM waves can be classified according to their frequencies

10 Colors and Wavelengths

11 EM Radiation Signals can be converted à EM waves Antennas are used to enhance radiated waves Radiated waves have typical signal properties à We need to learn about signal properties first! à Given such properties how is the system capacity impacted! RF Signal Conversion Signals EM Waves Antenna EM Radiation - Enhanced Waves Signal Properties Radio (electromagnetic) waves Signal Freq. and spectrum

12 Wave-properties Signal Characteristics Analog (continuous) or digital (discrete) Periodic or aperiodic Components of a periodic electromagnet wave signal n Amplitude (maximum signal strength) e.g., in V n Frequency (rate at which the a periodic signal repeats itself) expressed in Hz n Phase (measure of relative position in time within a single period) in deg or radian (π = 360 = 1 period) Periodic: S( t) = S( t + T) S( t) = Asin( πft + ϕ) ϕ = phase A = amplitude f = frequncy T = period = 1/ f

13 Sine Waves

14 Sound Wave Examples Each signal is represented by x(t) = sin (πf.t) f = 5Kz f = 1Kz A dual tone signal with f1 and f is represented by x(t) = sin (πf1.t) + sin (πf.t)

15 Periodic Signal Characteristics The simplest signal is a sinusoidal wave A sine wave can be expressed in time or space (wavelength) n n Wavelength is the distance the signal travels over a single cycle Wavelength is a function of speed and depends on the medium (signal velocity) λ = vf λf=v T = 1/ f v = 3x10 8 m / sec Exact speed light through vacuum is 99,79,458 m/s

16 More about signals.

17 Taylor Series Complex signals are often broken into simple pieces Signal requirements n n n Can be expressed into simpler problems Is linear The first few terms can approximate the signal Example: The Taylor series of a real or complex function ƒ(x) is the power series

18 Signal Representation We can represent all complex signals as harmonic series of simpler signals Frequency components of the square wave with amplitude A can be expressed as s( t) 4 = A π K = 1/ odd sin(πkft) k

19 Square Wave S(t)=sin(πft) S(t)=1/3[sin(π(3f)t)] S(t)= 4/π{sin(πft) +1/3[sin(π(3f)t)]} s( t) = 4 A π K = 1/ odd sin(πkft) k

20 Square Wave K=1,3,5 K=1,3,5, 7 Frequency Components of Square Wave s( t) = 4 A π K = 1/ odd sin(πkft) k K=1,3,5, 7, 9,.. Fourier Expansion

21 Periodic Signals A Periodic signal/function can be approximated by a sum (possible infinite) sinusoidal signals. Consider a periodic signal with period T A periodic signal can be Real or Complex The fundamental frequency: ωo Example: n Prove that x(t) is periodic: Periodic Re al Complex ω T o o x( t) = π / T o = π / ω x( t) = cos( ω t + θ) o x( t + nt ) = x( t) = o = cos( ω t o Ae jω t o x( t) + θ )

22 Signal Generation No Modulation

23 Signal Generation - Modulated

24 RF Source

25 Frequency Spectrum We can plot the frequency spectrum or line spectrum of a signal n In Fourier Series k represent harmonics n Frequency spectrum is a graph that shows the amplitudes and/or phases of the Fourier Series coefficients Ck. Amplitude spectrum Ck =4A/k.pi The lines Ck are called line spectra because we indicate the values by lines s( t) = 4 A π K = 1/ odd sin(πkft) k

26 Examples

27 Periodic Signal Characteristics A signal can be made of many frequencies n All frequencies are multiple integer of the fundamental frequency n Spectrum of a signal identifies the range of frequencies the signal contains n Absolute bandwidth is defined as: Highest_Freq Lowest_Freq n 3-dB Bandwidth in general is defined as the frequency ranges where a signal has its most of energies Signal data rate n n n Information carrying capacity of a signal Expressed in bits per second (bps) Typically, the larger frequency à larger data rate Example à

28 Periodic Signal Characteristics Consider the following signal n Consists of two freq. component (f) and (3f) with BW = f S( t) = ( 4 / π) sin( πft) + ( 4 / 3π ) sin( π( 3 f ) t) Fundamental _ freq = f Max_ freq = 3 f Abs_ BW = 3 f f = f BW What is the Max amplitude of this component? f 3f

29 Calculating Signal Power Sinusoidal signals RMS (Root Mean Square) or effective value of the sine waveform (single tone): Average Power is calculated using RMS value and expressed in Watts Instantaneous power is V^/ V P = Vp / = V = RMS R RMS 0.707Vp Vp=Vpeak (not peak-to-peak) Read for more information:

30 RMS Concept Examples Find the Vrms for a square wave signal!

31 Power in Telecommunication Systems Power change can have large dynamic range Remember: x then x Hence 10 = y log(10 ) = log y x = Example 1: if P=mW and P1 = 1mW à 10log 10 (P/P1)=3.01 db Example : if P=1KW and P1=10W à 0dB What if db is given and you must find P/P1? n P/P1 = Antilog(dB/10) = 10 db/10. Example 3: if db is +10 what is P/P1? n P/P1 = Antilog(+10/10) = /10 = 10 log y We tend to express power in dbw or dbm

32 Converting and Amplification Watt, dbw, dbm, db Conversions: Watt to dbw & dbm P =10(W ) =10 log(10) =10dBW =10 log( mw /1mW ) =10 4 = 40dBm For more see:

33 dbm

34 Wireless Systems

35 Antenna An antenna is an electrical conductor (transducer) n Converts time-varying current/voltage signals into EM waves (and vise versa) Antennas RX and TX EM EM waves n Transmission - radiates electromagnetic energy into space n Reception - collects electromagnetic energy from space In two-way communication, the same antenna can be used for transmission and reception n Antenna characteristics are the same for transmitting or receiving electromagnetic energy The antenna can receive on one frequency and transmit on another

36 Isotropic Radiation We assume power is radiated spherically n The source be surrounded by a sphere or radius d n A perfect Omni directional power (isotropic antenna) We measure directionality based on how much of the isotropic radiation is focused in a certain direction n This is referred to as the antenna directionality or antenna Gain

37 Isotropic Antenna A single source of transmission n Sphere of radiation with radius d n Uniform flux lines (just like the sun) Power flux density =P den = Transmit Power/A Sphere (W/m^) Received power (W): n n Also called power intercepted Aer is effective aperture or area (m^) n Aer is based on the physical area P r = P den = P t 4π d P t 4π d A er

38 Antenna Directionality or Gain Power density can be increased by changing its directionality n That is transmitting or receiving more in certain directions n This is referred to as the antenna gain (Gt) Equivalent Isotropic Radiated Power (EIRP) P r = P t G t 4π d A er = EIRP 4π d A er Let s discuss G, Ae, and EIRP!

39 Antenna Gain & Effective Area Power gain is expressed relative to isotropic (assume ohmic loss very small η=1; note: η>=1 ) P r = P G t t 4π d A er = EIRP 4π d A er Also known as Hertzian Dipole For Isotropic G = 4π η λ Ae = G λ 4π η A e = 4π f η c A e η is efficiency of the system (later)

40 Different Antenna Types

41 Receiver Effective Area On the receiver side the larger the antenna the more of the radiated power can be captured (intercepted) n Pr = P den. Aer (in Watt) n Aer is the physical effective area of the receiver antenna P r = P t 4π d A er = P t G t G r = P t G t G r λ 4π d 1 4π (d / λ ) Also known as Range Eqn. Or Friis Or Free Space Eqn.

42 Antenna Gain & Effective Area P r = P t G t 4π d A er Both TX and RX antennas can have gains The receiver gain is directly related to its effective area n Note that larger Aeff à more gain à more power TX and RX Remember: G r = η 4π A er λ G t = η 4π A et λ η is efficiency of the system (later)

43 Equivalent Isotropic Radiated Power EIRP= Pt.Gt n Indicates signal strength radiated n Can be expressed in dbi or dbd dbi represents the power density with respect to an isotropic antenna dbd represents the power density with respect to a dipole antenna n Note: dbi = dbd +.15dB For example: n Calculate EIRP if a 1 dbi gain antenna is fed with 15 dbm of power 1 dbi + 15dBm = 7 dbm (500 mw)

44 Example: Antenna Gain Given a parabolic antenna with radius of 1 meter used to send WiFi (80.11b) channel ; Assume the effective area of the parabolic is 0.56A(Face Area) and η=1: n Find the gain and its effective area. n What is the gain in db? MATLAB CODE: Face_Area=0.56*pi*r*r; f=.417*10^9; c=3*10^8; l=c/f Gain=(4*pi*Face_Area*f*f)/(c*c) Gain_in_db=10*log10(Gain) G 4πA λ 4πf c See next slide for freq. bands in b = e = A e

45 Example: Antenna Gain 80.11b Frequency Band (GHz) In the United States and Canada there are 11 channels available for use in the 80.11b.4GHz WiFi Frequency range. This standard is defined by the IEEE. Average

46 Receiver Sensitivity GPS Receiver What is the minimum level of signal power the receiver can receive and still process it properly? P r (min) = P G t t 4πd A P (min) = P G G λ t t r er r η(4πd) In this case, given d à we find Pr(min)

47 Maximum Distance Covered Using sensitivity: min max ) (4 ) (4 4 r t t t r t t r r t t r P G G P d d G G P P A d G P P = = = π η λ π η λ π η=1 if no ohmic loss!

48 Sensitivity and RSSI Remember: EIRP à signal strength radiated Power strength can be adjusted in the routers/wireless devices There are two well-known values for link quality estimation: n n Received Signal Strength Indicator (RSSI) Determines the total energy of the signal Higher RSSI à more signal energy Higher RSSI à less packet error ratio (PER) Link Quality Indicator (LQI) Measurement is performed per packet No standard as to how to implement RSSI n Difficult to compare performances of difference devices to one another

49 Example: Power Transmission in XBEE XBEE has a threshold sensitivity of -44dBm and it can transmit with maximum of 10 dbm. What is the maximum distance two XBEE transceivers can be separated from one another? (assume: free space, Gt=Gr=1; no ohmic loss, f=.417ghz) d max = P max t G G t r ( 4π ) P min r η λ

50 Signal Distortion n n n Received signal conditions must have sufficient strength so that circuitry in the receiver can interpret the signal must maintain a level sufficiently higher than noise to be received without error Signal can be distorted: (1) High Noise; () Low Signal Strength Low Signal Strength is due to Attenuation (loss of energy) There are many sources contributing to signal attenuation Strength of signal falls off with distance over transmission medium (free space) à Free Space Loss (signal spreading) Ohmic loss converting to heat Note: Equalizing attenuation improves distortion By equalizing we can ensure that the signal performs the same over the entire frequency band

51 Loss in Free Space Model Note that Lpath is the loss due to signal spreading as it travels (not due to converting to heat or ohmic loss) Note: n as wave length increases more loss occurs n the impact of distance and wavelength are very drastic P L r = path EIRP G = (4π ) r (4π ) ( d / λ ) 1 ( d How does loss changes as the frequency increases? / λ )

52 Free Space Loss The signal disperses with distance Free space loss, for ideal isotropic antenna L path = P t P r = ( ) 4πd ( 4πfd) λ P t = signal power at transmitting antenna P r = signal power at receiving antenna λ = carrier wavelength d = propagation distance between antennas c = speed of light (» 3 10^8 m/s) where d and λ are in the same units (e.g., meters) = c When there is loss (db)à we have to subtract!

53 Free Space Loss (in db) Free space loss equation can be represented as L path_ db P P t = 10log = 0log ; r 4πd λ P t P r ( λ) + 0log( ) 1.98 db = 0 log d + Attenuation (loss) is greater at higher frequencies, causing distortion

54 Other Factors Impacting Attenuation Mismatch between the source and antenna Propagation loss (passing though walls) Absorption (due to hitting building) Antenna ohmic loss (converting to heat) P r = EIRP G L sys = L 1 L L = r ( 1/ L ) (1/ L path sys n L i i L sys _ db =10 log(l 1 )+10log(L )+10 log(l )+... )

55 Free Space Loss: A different view P = EIRP G r r (4π ) 1 ( d / λ ) Free space loss accounting for gain of other antennas P ( ) ( ) ( ) 4π d λd ( cd ) t Lend to end = = η = η = η Pr GrGtλ Aer Aet f A er A et G t = gain of transmitting antenna G r = gain of receiving antenna A et = effective area of transmitting antenna A er = effective area of receiving antenna G G r t = = 4πA er λ 4πA et λ

56 ..Free Space Loss Free space loss accounting for gain of other antennas can be recast as P ( 4π ) ( d ) ( λd ) ( cd ) L t Lend to end = = η = η = η Pr GrGtλ Ar At f end to end _ db = 0log ( λ) + 0 log( d ) 10 log( A A ) ( f ) + 0log( d) 10log( A t A ) dB = r Note that as λ increases frequency decreases and Hence, the total attenuation increases! A A 0 log + r t t r

57 Free Space Loss and Frequency Note that, ASSUMING THERE IS NO GAIN CHANGE, as f increases the loss increases! L L end to end _ db end to end _ db = = L db 0log Pt = 10log P r 4πfd = 0log c ( λ) + 0 log( d ) 10 log( A A ) t r Two approaches ( f ) + 0log( d) 10log( A t A ) dB = r 0 log + Note that, IF WE ACCOUNT FOR GAIN, as frequency increases total attenuation decreases! Frequency impacts gain!

58 Efficiency We define the efficiency of antenna (system) using η eff n Note the total power transmitted: P r + P loss = P total η eff = P r Ptotal = P r Pr + P loss TX (Pt) RX (Pr) Electromagnetic Energy

59 Example: Find the received power in a cell phone Notes Refer to Notes Example A

60 Example: Compare the received power for different antennas Notes Refer to Notes Example B

61 References Stallings, William. Wireless Communications & Networks, /E. Pearson Education India, 009.Stallings, William. Wireless Communications & Networks, /E. Pearson Education India, 009. Black, Bruce A., et al. Introduction to wireless systems. Prentice Hall PTR, 008. Rappaport, Theodore S. Wireless communications: principles and practice. Vol.. New Jersey: Prentice Hall PTR, 1996.