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Fundamental of Transmissions

Fundamental of Transmissions. Dr. Farahmand Updated: 2/9/2009. Medium. TX. RX. What is telecommunications?. Conveying information between two points or between one and multi-points Transmitting information wirelessly is achieved via electromagnetic signals (E)

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Fundamental of Transmissions

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  1. Fundamental of Transmissions Dr. Farahmand Updated: 2/9/2009

  2. Medium TX RX What is telecommunications? • Conveying information between two points or between one and multi-points • Transmitting information wirelessly is achieved via electromagnetic signals (E) • Electric current flowing through a wire creates magnetic field around the wire • An alternating electric current flowing through a wire creates electromagnetic waves • Electromagnetic radiation is waves of energy • These waves collectively called electromagnetic spectrum

  3. Signal Characteristics • Analog (continuous) or digital (discrete) • Periodic or aperiodic • Components of a periodic electromagnet wave signal • Amplitude (maximum signal strength) – e.g., in V • Frequency (rate at which the a periodic signal repeats itself) – expressed in Hz • Phase (measure of relative position in time within a single period) – in deg or radian (2p = 360 = 1 period)

  4. Sine Waves

  5. Sound Wave Examples Each signal is represented by x(t) = sin (2pf.t) f = 5Kz f = 1Kz A dual tone signal with f1 and f2 is represented by x(t) = sin (2pf1.t) + sin (2pf2.t)

  6. The simplest signal is a sinusoidal wave A sine wave can be expressed in time or space (wavelength) Wavelength is the distance the signal travels over a single cycle Wavelength is a function of speed and depends on the medium (signal velocity) Periodic Signal Characteristics lf=v Exact speed light through vacuum is 299,792,458 m/s

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

  8. Periodic Signal Characteristics • Consider the following signal • Consists of two freq. component (f) and (3f) with BW = 2f Second harmonic BW What is the Max amplitude of this component? f 3f http://www.jhu.edu/~signals/listen-new/listen-newindex.htm

  9. Periodic Signal Characteristics S(t)=sin(2pft) S(t)=1/3[sin(2p(3f)t)] S(t)= 4/p{sin(2pft) +1/3[sin(2p(3f)t)]}

  10. Frequency Domain Representation S(t)= 4/p{sin(2pft) +1/3[sin(2p(3f)t)]} frequency domain function for a single square pulse that has the value 1{s(t)=1} between –X/2 and X/2, and is 0 {s(t)=1} elsewhere Refer to NOTES!

  11. Example: What is f1? What is f2? Which case has larger data rate? (sending more bits per unit of time) Data Rate & Frequency • f1 = 2(1/10^-3)=2KHz • Case I data rate=one bit per (0.25msec) •  4 Kbps • f2 = 1 KHz  data rate=2Kbps • Case 1 has higher data rate (bps)

  12. Bandwidth and Data Rate • Case 1: • Assume a signal has the following components: f, 3f, 5f ; f=10^6 cycles/sec • What is the BW? • What is the period? • How often can we send a bit? • What is the data rate? • Express the signal equation in time domain • Case 2: • Assume a signal has the following components: f, 3f, 5f; f=2x10^6 cycles/sec • What is the BW? • What is the period? • How often can we send a bit? • What is the data rate? • Case 3: • Assume a signal has the following components: f, 3f ; f=2x10^6 cycles/sec • What is the BW? • What is the period? • How often can we send a bit? • What is the data rate? • Express the signal equation in time domain BW=4MHz T=1usec 1 bit every 0.5usec Data rate=2*f=2bit/usec=2MHz BW=8MHz (5 x 2 - 2=8) T= ½ usec 1 bit every 0.25usec Data rate=2*f=2bit/0.5 usec=4MHz BW=4MHz T=0.5 usec 1 bit every 0.25usec Data rate=2*f=4bit/usec=4MHz Remember: Greater BW  larger cost but Lower BW  more distortion;

  13. Nyquist Formula and Bandwidth • Assuming noise free system and assuming that only one bit is provided to represent the signal: • Nyquist’s formula states the limitation of the data rate due to the bandwidth: • If the signal transmission rate is 2B, then a signal with frequency of less or equal B is required to carry this signal: TR(f)=2Bf£B • If bandwidth is B (Hz) the highest signal rate that can be carried is 2B (bps): f=BTR(f)£2B • Example: if the highest frequency is 4KHz (bandwidth) a sampling rate of 8 Kbps is required to carry the signal Remember: Channel Capacity = (number of bit) x (signal bandwidth)

  14. Example: Log2(8)=ln(8)/ln(2)=3 Channel CapacityNyquist’s formulation when multilevel signaling is present • channel capacity (C) is the tightest upper bound on the amount of information that can be reliably transmitted over a communications channel (max. allowable data rate) • What if the number of signal levels are more than 2 (we use more than a single bit to represent the sate of the signal)? • C = Maximum theoretical Channel Capacity in bps • M = number of discrete signals (symbols) or voltage levels • n = number of bits per symbol Remember: More bits per symbol  more complexity!

  15. Channel Capacity Example: • Voice has a BW of 3100 Hz. calculate the channel capacity • Assuming we use 2 signal levels • Assuming we use 8 signal levels •  channel capacity required to pass a voice signal: • Channel capacity (or Nyquist capacity) is 2 x 3100 cycles/sec = 6.1Kbps – note in this case one bit is being used to represent two distinct signal levels. • If we use 8 signal levels: channel capacity: 2x3100x3=18600 bps

  16. S/N Ratio • The signal and noise powers S and N are measured in watts or volts^2, so the signal-to-noise ratio here is expressed as a power ratio, not in decibels (dB) Example: Assume signal strength is 2 dBm and noise strength is 5 mW. Calculate the SNR in dB. 2dBm 1.59 mW SNR = 10log(1.59/5)=-5dB

  17. Signal ImpairmentsAttenuation • Strength of a signal falls off with distance over transmission medium • Attenuation factors for guided media: • Received signal must have sufficient strength so that circuitry in the receiver can interpret the signal • Signal must maintain a level sufficiently higher than noise to be received without error • Typically signal strength is reduced exponentially • Expressed in dB Attenuation is greater at higher frequencies, causing distortion

  18. Signal ImpairmentsAttenuation Impacts • Lowers signal strength • Requires higher SNR • Can change as a function of frequency • More of a problem in analog signal (less in digital) • Higher frequencies attenuate faster • Using equalization can improve – higher frequencies have stronger strength

  19. Signal ImpairmentsDelay Distortion • In bandlimited signals propagation velocity is different for different frequencies • Highest near the center frequency • Hence, bits arrive out of sequence •  resulting in intersymbol interference •  limiting the maximum bit rate!

  20. Categories of Noise • Thermal Noise • Intermodulation noise • Crosstalk • Impulse Noise

  21. Thermal Noise • Thermal noise due to agitation of electrons • Present in all electronic devices and transmission media • Cannot be eliminated • Function of temperature • Particularly significant for satellite communication • When the signal is received it is very weak

  22. Thermal Noise • Amount of thermal noise to be found in a bandwidth of 1Hz 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) – zero deg. C is 273.15 • Expressed in dBW 10log(No/1W)

  23. Thermal Noise • Noise is assumed to be independent of frequency • Thermal noise present in a bandwidth of B Hertz (in watts): or, in decibel-watts 

  24. Thermal Noise (MATLAB Example) %MATLAB CODE: T= 10:1:1000; k= 1.3803*10^-23; B=10^6; No=k*T; N=k*T*B; N_in_dB=10*log10(N); semilogy(T,N_in_dB) title(‘Impact of temperature in generating thermal noise in dB’) xlabel(‘Temperature in Kelvin’) ylabel(‘Thermal Noise in dB’)

  25. Other Types of Noise • Intermodulation noise – occurs if signals with different frequencies share the same medium • Interference caused by a signal produced at a frequency that is the sum or difference of original frequencies • Crosstalk – unwanted coupling between signal paths • Impulse noise – irregular pulses or noise spikes • Short duration and of relatively high amplitude • Caused by external electromagnetic disturbances, or faults and flaws in the communications system Question: Assume the impulse noise is 10 msec. How many bits of DATA are corrupted if we are using a Modem operating at 64 Kbps with 1 Stop bit?

  26. Other Types of Noise - Example Intermodulation noise Impulse noise Crosstalk

  27. Channel Capacity with Noise and Error • An application of the channel capacity concept to an additive white Gaussian noise channel with B Hz bandwidth and signal-to-noise ratio S/N is the Shannon–Hartley theorem: • Establishing a relation between error rate, noise, signal strength, and BW • If the signal strength or BW increases, in the presence of noise, we can increase the channel capacity • Establishes the upper bound on achievable data rate (theoretical) • Does not take into account impulse and attenuation Note: S/N is not in dB and it is log base 2!

  28. Noise Impact on Channel Capacity • Presence of noise can corrupt the signal • Unwanted noise can cause more damage to signals at higher rate • For a given noise level, greater signal strength improves the ability to send signal • Higher signal strength increases system nonlinearity  more intermodulation noise • Also wider BW  more thermal noise into the system  increasing B can result in lower SNR

  29. Example of Nyquist Formula and Shannon–Hartley Theorem p/4 • What is the wavelength associated with the highest energy level? • Calculate the BW of this signal. • Assuming the SNR = 24 dB, Calculate the maximum channel capacity. • Using the value of the channel capacity, calculate how many signal levels are required to generate this signal? • How many bits are required to send each signal level? • Express the mathematical expression of this signal in time domain. • What type of signal, more likely, is this? (TV, Visible light, AM, Microwave) – Next slide p/3x4 3MHz 4MHz l=108 m B=4-3=1 MHz SNRdB(24)log-1(24/10) 102.4= 251 C=Blog2(1+S/N)=8Mbps C=2Blog2MM=16 2n=Mn=4 Signal Type: AM http://www.adec.edu/tag/spectrum.html

  30. Radio-frequency spectrum: commercially exploited bands http://www.britannica.com/EBchecked/topic-art/585825/3697/Commercially-exploited-bands-of-the-radio-frequency-spectrum

  31. Expression Eb/N0 • Ratio of signal energy per bit to noise power density per Hertz • R = 1/Tb; • R = bit rate; • Tb = time required to send one bit; • S = Signal Power (1W = 1J/sec) • Eb=S.Tb • No = Thermal noise (W/Hz) • The bit error rate for digital data is a function of Eb/N0 • Given a value for Eb/N0 to achieve a desired error rate, parameters of this formula can be selected • As bit rate R increases, transmitted signal power must increase to maintain required Eb/N0 Note that as R increases power must increase as well to maintain signal quality

  32. SNR & Expression Eb/N0 • Using Thermal noise within the bandwidth of B Hertz (in watts): • N=NoxB • Using Shannon’s Theorem – Channel Capacity in the presence of noise • The relation between SNR and Eb/No will be (R=C=Data rate) • C/B expressed in bps/Hz and called Spectral Density Q: What will be Eb/No if the spectral density is 6 bps/Hz???

  33. 10^-4 8.4 dB Probability of Error Question: Assume we require Eb/No = 8.4 dB to achieve bit error rate of 10^-4. Assume temperature is 17oC and data rate is set to 2.4 Kbps. Calculate the required level of the received signal in W and dBW.

  34. 10^-4 8.4 dB Probability of Error 8.4 dB  6.91 17oC  290oKelvin R=2400 bps K=1.38*10^-23 Eb/No=S/(KTR) S=-161 dBW Question: Assume we require Eb/No = 8.4 dB to achieve bit error rate of 10^-4. Assume temperature is 17oC and data rate is set to 2.4 Kbps. Calculate the required level of the received signal in W and dBW.

  35. Review: Power in Telecommunication Systems • Remember: • Example 1: if P2=2mW and P1 = 1mW  10log10(P2/P1)=3.01 dB • Example 2: if P2=1KW and P1=10W 20dB • What if dB is given and you must find P2/P1? • P2/P1 = Antilog(dB/10) = 10 dB/10 . • Example 3: if dB is +10 what is P2/P1? • P2/P1 = Antilog(+10/10) = 10 +10/10 = 10

  36. Colors and Wavelengths lf=v ColorRedOrangeYellowGreenBlueViolet Wavelength (nm)780 - 622 622 - 597597 - 577577 - 492492 - 455455 - 390 Frequency (THz)384 - 482482 - 503503 - 520520 - 610610 - 659659 - 769 1 terahertz (THz) = 10^3 GHz = 10^6 MHz = 10^12 Hz,  1 nm = 10^-3 um = 10^-6 mm = 10^-9 m. The white  light is a mixture of the colors of the visible spectra. Wavelengths is a common way of describing light waves.  Wavelength = Speed of light in vacuum / Frequency.

  37. Colors and Wavelengths

  38. Colors and Wavelengths

  39. References • Online calculator: http://www.std.com/~reinhold/BigNumCalc.html • Wavelengths and lights http://www.usbyte.com/common/approximate_wavelength.htm & http://eosweb.larc.nasa.gov/EDDOCS/Wavelengths_for_Colors.html • Learn about decibel http://www.phys.unsw.edu.au/jw/dB.html

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