Vidyalankar final-essentials of communication systems


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Fundamentals of communication systems

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Vidyalankar final-essentials of communication systems

  1. 1. Essentials Of Communication Systems A Presentation By- A. S. Kurhekar
  2. 2. Overview of Analog Technology <ul><li>Areas of Application </li></ul><ul><ul><li>Old telephone networks </li></ul></ul><ul><ul><li>Most television broadcasting at present </li></ul></ul><ul><ul><li>Radio broadcasting </li></ul></ul>
  3. 3. Analog Signals: The Basics Time Signal Frequency = Cycles/Second Cycle Amplitude
  4. 4. Amplitude and Cycle <ul><li>Amplitude </li></ul><ul><ul><li>Distance above reference line </li></ul></ul><ul><li>Cycle </li></ul><ul><ul><li>One complete wave </li></ul></ul><ul><li>Frequency </li></ul><ul><li>Frequency </li></ul><ul><ul><li>Cycles per second </li></ul></ul><ul><ul><li>Hertz is the unit used for expressing frequency </li></ul></ul><ul><li>Frequency spectrum </li></ul><ul><ul><li>Defines the bandwidth for different analog communication technologies </li></ul></ul>
  5. 5. Frequency Spectrum and Bandwidth <ul><li>Available range of frequencies for communication </li></ul><ul><li>Starts from low frequency communication such as voice and progresses to high frequency communication such as satellite communication </li></ul><ul><li>The spectrum spans the entire bandwidth of communicable frequencies </li></ul>
  6. 6. Frequency Spectrum <ul><li>Low-end </li></ul><ul><ul><li>Voice band </li></ul></ul><ul><li>Middle </li></ul><ul><ul><li>Microwave </li></ul></ul><ul><li>High-end </li></ul><ul><ul><li>Satellite communication </li></ul></ul>Low Frequency High Frequency Radio Frequency Coaxial Cable MHz Voice KHz Satellite Transmission Microwave MHz
  7. 7. An Overview of Digital Technology <ul><li>Areas of Application </li></ul><ul><ul><li>Computers </li></ul></ul><ul><ul><li>New telephone networks </li></ul></ul><ul><ul><li>Phased introduction of digital television technology </li></ul></ul><ul><li>Digital Technology </li></ul><ul><ul><li>Basics </li></ul></ul><ul><ul><li>Digital signals that could be assigned digital values </li></ul></ul><ul><li>Digital computer technology </li></ul><ul><ul><li>Digital signals </li></ul></ul><ul><ul><li>Binary representation </li></ul></ul><ul><ul><ul><li>Encoded into ones and zeros </li></ul></ul></ul>
  8. 8. Digital Signal And Binary Signals <ul><li>Digital signals </li></ul><ul><ul><li>Value limited to a finite set </li></ul></ul><ul><ul><li>Digital systems more robust </li></ul></ul><ul><ul><li>Binary Signals </li></ul></ul><ul><ul><li>Has at most 2 values </li></ul></ul><ul><ul><li>Used to represent bit values </li></ul></ul><ul><ul><li>Bit time T needed to send 1 bit </li></ul></ul><ul><ul><li>Data rate R=1/T bits per second </li></ul></ul>t x(t) t x(t) 1 0 0 0 1 1 0 T
  9. 9. Digital Terms <ul><ul><li>Pulse </li></ul></ul><ul><ul><li>Pulse duration </li></ul></ul><ul><ul><li>Pulse amplitude </li></ul></ul><ul><ul><li>Signal strength </li></ul></ul><ul><li>Clock Speed and Execution Speed </li></ul><ul><ul><li>Pulse duration is inversely proportional to the clock frequency </li></ul></ul><ul><ul><li>Faster the clock speed, the smaller the pulse duration </li></ul></ul><ul><ul><li>Smaller the pulse duration, the faster the execution in general </li></ul></ul>
  10. 10. Performance Metrics <ul><li>Analog Communication Systems </li></ul><ul><ul><li>Metric is fidelity </li></ul></ul><ul><ul><li>Want m(t)  m(t) </li></ul></ul><ul><li>Digital Communication Systems </li></ul><ul><ul><li>Metrics are data rate (R bps) and probability of bit error (P b =p(b  b)) </li></ul></ul><ul><ul><li>Without noise, never make bit errors </li></ul></ul><ul><ul><li>With noise, P b depends on signal and noise power, data rate, and channel characteristics. </li></ul></ul>
  11. 11. Data Rate Limits <ul><li>Data rate R limited by signal power, noise power, distortion, and bit error probability </li></ul><ul><li>Without distortion or noise, can have infinite data rate with P b =0. </li></ul><ul><li>Shannon capacity defines maximum possible data rate for systems with noise and distortion </li></ul><ul><ul><li>Rate achieved with bit error probability close to zero </li></ul></ul><ul><ul><li>In white Gaussian noise channels, C=B log(1+SNR) </li></ul></ul><ul><ul><li>Does not show how to design real systems </li></ul></ul><ul><li>Shannon obtained C=32 Kbps for phone channels </li></ul><ul><ul><li>Get higher rates with modems/DSL (use more BW) </li></ul></ul><ul><ul><li>Nowhere near capacity in wireless systems </li></ul></ul>
  12. 12. Signal Energy and Power <ul><li>The energy in a signal g(t) is </li></ul><ul><li>The power in a signal g(t) is </li></ul><ul><li>Power is often expression in dBw or dBm </li></ul><ul><ul><li>[10 log 10 P] dBW is dB power relative to Watts </li></ul></ul><ul><ul><li>[10 log 10 (P/.001)] dBm is dB power relative to mWatts </li></ul></ul><ul><ul><li>Signal power/energy determines its resistance to noise </li></ul></ul>
  13. 13. The Communication System <ul><li>Communication systems modulate analog signals or bits for transmission over channel. </li></ul><ul><li>The building blocks of a communication system convert information into an electronic format for transmission, then convert it back to its original format after reception. </li></ul><ul><li>Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortion/noise from the channel. </li></ul><ul><li>Digital systems are more robust to noise and interference. </li></ul><ul><li>Performance metric for analog systems is fidelity, for digital it is rate and error probability. </li></ul><ul><li>Data rates over channels with noise have a fundamental capacity limit. </li></ul>
  14. 14. The Backdrop <ul><li>Data rates over channels with noise have a fundamental capacity limit. </li></ul><ul><li>Signal energy and power determine resistance to noise </li></ul><ul><li>Communication system shift, scale, and invert signals </li></ul><ul><li>Unit impulse and step functions important for analysis </li></ul><ul><li>Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions </li></ul><ul><li>Exponentials are eigenfunctions of LTI filters </li></ul><ul><li>Fourier transform is the spectral components of a signal </li></ul><ul><li>Rectangle in time is sinc in frequency; Time-limited signals are not bandlimited and vice versa </li></ul>
  15. 15. Communication System Block Diagram Source Encoder Source Decoder Channel Receiver Text Images Video <ul><li>Source encoder converts message into message signal or bits. </li></ul><ul><li>Transmitter converts message signal or bits into format appropriate for channel transmission (analog/digital signal). </li></ul><ul><li>Channel introduces distortion, noise, and interference. </li></ul><ul><li>Receiver decodes received signal back to message signal. </li></ul><ul><li>Source decoder decodes message signal back into original message. </li></ul>Transmitter
  16. 16. Analysis Outline <ul><li>Channel Distortion and Equalization </li></ul><ul><li>Ideal Filters </li></ul><ul><li>Energy Spectral Density and its Properties </li></ul><ul><li>Power Spectral Density and its Properties </li></ul><ul><li>Filtering and Modulation based on PSD </li></ul>
  17. 17. Channel Distortion <ul><li>Channels introduce linear distortion </li></ul><ul><ul><li>Electronic components introduce nonlinear distortion </li></ul></ul><ul><li>Simple equalizers invert channel distortion </li></ul><ul><ul><li>Can enhance noise power </li></ul></ul>X(f) X(f)+N(f)/H(f) H(f) 1/H(f) N(f) +
  18. 18. Filters <ul><li>Low Pass Filter (linear phase) </li></ul><ul><li>Band Pass Filter (linear phase) </li></ul><ul><li>Most filtering (and other signal processing) is done digitally (A/D followed by DSP) </li></ul>1 -B B 1 1
  19. 19. Energy Spectral Density (ESD) <ul><li>Signal energy: </li></ul><ul><li>ESD measures signal energy per unit Hz. </li></ul><ul><li>ESD of a modulation signal </li></ul>f Contains less information than Fourier Transform (no phase)  g (f) .25[  g (f-f 0 )+  g (f+f 0 )] X cos(2  f 0 t)
  20. 20. Autocorrelation <ul><li>Defined for real signals as  g (t)=g(t) * g(-t) </li></ul><ul><ul><li>Measures signal self-similarity at t </li></ul></ul><ul><ul><li>Can be used for synchronization </li></ul></ul><ul><li>ESD and autocorrelation FT pairs:  g (t)   g (f) </li></ul><ul><li>Filtering based on ESD </li></ul> g (f) |H(f)| 2  g (f) H(f)
  21. 21. Power Spectral Density <ul><li>Similar to ESD but for power signals (P=E/t) </li></ul><ul><li>Distribution of signal power over frequency </li></ul> |G T (f)| 2 1 2T g T (t) -T T   T=  S g (f)
  22. 22. Filtering and Modulation <ul><li>Filtering </li></ul><ul><li>Modulation </li></ul><ul><ul><li>When S g (f) has bandwidth B<f 0 , </li></ul></ul>S g (f) |H(f)| 2 S g (f) H(f) S g (f) .25[S g (f-f 0 )+ S g (f+f 0 )] X cos(2  f c t) otherwise +cross terms
  23. 23. Modulation and Autocorrelation <ul><li>Modulation </li></ul><ul><ul><li>When S g (f) has bandwidth B<f 0 </li></ul></ul><ul><li>Autocorrelation </li></ul>S g (f) .25[S g (f-f 0 )+ S g (f+f 0 )] X cos(2  f c t)
  24. 24. Probability Theory <ul><li>Mathematically characterizes random events. </li></ul><ul><li>Defined on a probability space: (S,{ A i },P(•)) </li></ul><ul><ul><li>Sample space of possible outcomes z i . </li></ul></ul><ul><li>Sample space has a subset of events A i </li></ul><ul><li>Probability defined for these subsets. </li></ul>S A 2       A 3
  25. 25. Probability Measures-I <ul><li>P(S)=1 </li></ul><ul><li>0  P(A)  1 for all events A </li></ul><ul><li>If (A  B)=  then P(AUB)=P(A)+P(B). </li></ul><ul><li>Conditional Probability: </li></ul><ul><ul><li>P(B|A)=P(A  B)/P(A) </li></ul></ul><ul><ul><li>Bayes Rule: P(B|A)=P(A|B)P(B)/P(A) </li></ul></ul><ul><li>Independent Events: </li></ul><ul><ul><li>A and B are independent if P(A  B)=P(B)P(A) </li></ul></ul><ul><ul><li>Independence is a property of P(•) </li></ul></ul><ul><ul><li>For independent events, P(B|A)=P(B). </li></ul></ul>
  26. 26. Probability Measure-II <ul><li>Bernoulli Trials: </li></ul><ul><li>Total Probability Theorem: </li></ul><ul><ul><li>Let A 1 ,A 2 , …, A n be disjoint with  i A i= S </li></ul></ul><ul><ul><li>Then: </li></ul></ul><ul><li>Random Variables and their CDF and pdf </li></ul><ul><ul><li>CDF: F x ( x )=P(x  x ) </li></ul></ul><ul><ul><li>pdf: p x (x)=dF x (x)/dx </li></ul></ul><ul><li>Means, Moments, and Variance </li></ul>A 1 A 2 A 3 S B P 1 P 3 P 2 0 1 2 3 x x x S
  27. 27. Gaussian Random Variables <ul><li>pdf defined in terms of mean and variance </li></ul><ul><li>Gaussian CDF defined by Q function: </li></ul> x  x N (  ,  2 ) Z~ N (  ) Tails decrease exponentially
  28. 28. Several Random Variables <ul><li>Let X and Y be defined on (S,{A i },P(•)) </li></ul><ul><li>Joint CDF F X, Y (x ,y)=P (x  x , y  y ) </li></ul><ul><li>Joint pdf: </li></ul><ul><li>Conditional densities: </li></ul><ul><li>Independent RVs: </li></ul>
  29. 29. Sums of Random Variables and the Central Limit Theorem <ul><li>Sums of RVs: z=x + y </li></ul><ul><ul><li>P z ( z )=p y ( y )  p x ( x ) </li></ul></ul><ul><ul><li>Mean of sum is sum of means </li></ul></ul><ul><ul><li>Variance of sum is sum of variances </li></ul></ul><ul><li>Central Limit Theorem: x 1 ,…,x n i.i.d </li></ul><ul><ul><li>Let y=  i x i , z=(y-E[y])/s Y </li></ul></ul><ul><ul><li>As n  , z becomes Gaussian, E[y]=0, s y 2 =1. </li></ul></ul>
  30. 30. Stationarity, Mean, Autocorrelation <ul><li>A random process is (strictly) stationary if time shifts don’t change probability: </li></ul><ul><ul><li>P(x(t 1 )  x 1 ,x(t 2 )  x 2 ,…,x(t n )  x n )= P(x(t 1 +T)  x 1 ,x(t 2 +T)  x 2 ,…,x(t n +T)  x n ) </li></ul></ul><ul><ul><li>True for all T and all sets of sample times </li></ul></ul><ul><li>Mean of random process: E[x(t)]= </li></ul><ul><ul><li>Stationary process: E[X(t)]= </li></ul></ul><ul><li>Autocorrelation of a random process: </li></ul><ul><ul><li>Defined as R X (t 1 ,t 2 )= E[x(t 1 )x(t 2 )]] </li></ul></ul><ul><ul><li>Stationary process: R x (t 1 ,t 2 )=R X (t 2 -t 1 ) </li></ul></ul><ul><ul><li>Correlation of process samples over time </li></ul></ul>x(t) x
  31. 31. Wide Sense Stationary (WSS) <ul><li>A process is WSS if </li></ul><ul><ul><li>E[x(t)] is constant </li></ul></ul><ul><ul><li>R X (t 1 ,t 2 )= E[X(t 1 )X(t 2 )]]=R X (t 2 -t 1 )= R X (t) </li></ul></ul><ul><ul><li>Intuitively, stationary in 1 st and 2 nd moments </li></ul></ul><ul><li>Ergodic WSS processes </li></ul><ul><ul><li>Have the property that time averages equal probabilistic averages </li></ul></ul><ul><ul><li>Allow probability characteristics to be obtained from a single sample over time </li></ul></ul>
  32. 32. Power Spectral Density (PSD) <ul><li>Defined only for WSS processes </li></ul><ul><li>FT of autocorrelation function: R X (t)  S X (f) </li></ul><ul><li>E[X 2 (t)]=  S X (f) df </li></ul><ul><li>White Noise: Flat PSD </li></ul><ul><ul><li>Good approximation in practice </li></ul></ul><ul><li>Modulation: </li></ul>.5N 0  (  ) .5N 0  S n (f) R n (  ) f S n (f) .25[S n (f-f c )+ S n (f-f c )] X cos(2  f c t+  )
  33. 33. Gaussian Processes <ul><li>z(t) is a Gaussian process if its samples are jointly Gaussian </li></ul><ul><li>Filtering a Gaussian process results in a Gaussian process </li></ul><ul><li>Integrating a Gaussian process results in a Gaussian random variable </li></ul>
  34. 34. Examples of noise in Communication Systems <ul><li>Gaussian processes </li></ul><ul><ul><li>Filtering a Gaussian process yields a Gaussian process. </li></ul></ul><ul><ul><li>Sampling a Gaussian process yields jointly Gaussian RVs </li></ul></ul><ul><ul><li>If the autocorrelation at the sample times is zero, the RVs are independent </li></ul></ul><ul><li>The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise </li></ul><ul><li>In digital communications, the bit value is obtained by integrating the signal, and the probability of error by integrating Gaussian noise </li></ul>
  35. 35. Introduction to Carrier Modulation <ul><li>Basic concept is to vary carrier signal relative to information signal or bits </li></ul><ul><ul><li>The carrier frequency is allocated by a regulatory body like the FCC – spectrum is pretty crowded at this point. </li></ul></ul><ul><li>Analog modulation varies amplitude (AM), frequency (FM), or phase (PM) of carrier </li></ul><ul><li>Digital modulation varies amplitude (MAM), phase (PSK), pulse (PAM), or amplitude/phase (QAM) </li></ul>
  36. 36. Double Sideband (Suppressed Carrier) Amplitude Modulation <ul><li>Modulated signal is s (t)=m(t)cos(2pi f c t) </li></ul><ul><ul><li>Called double-sideband suppressed carrier (DSBSC) AM </li></ul></ul><ul><li>Generation of DSB-SC AM modulation </li></ul><ul><ul><li>Direct multiplication (impractical) </li></ul></ul><ul><ul><li>Nonlinear modulators: Basic premise is to add m(t) and the carrier, then perform a nonlinear operation </li></ul></ul><ul><ul><li>Generates desired signal s(t) plus extra terms that are filtered out. </li></ul></ul><ul><ul><li>Examples include diode/transistor modulators, switch modulators, and ring modulators </li></ul></ul>
  37. 37. Coherent Detection of DSBAM <ul><li>Detector uses another DSB-SC AM modulator </li></ul><ul><li>Demodulated signal: m´(t)=.5cos(f 2 -f 1 )m(t) </li></ul><ul><ul><li>Phase offset: if f 2 -f 1 =  p/2, m´(t)=0 </li></ul></ul><ul><li>Coherent detection via PLL (f 2  f 1 ) required </li></ul><ul><ul><li>Will study at end of AM discussion </li></ul></ul>m(t) cos(  c t+    DSBSC Modulator s(t) DSBSC Modulator LPF m´(t) cos(  c t+    Channel
  38. 38. Introduction to Angle Modulation and FM <ul><li>Information encoded in carrier freq./phase </li></ul><ul><li>Modulated signal is s(t)=A c cos(q(t)) </li></ul><ul><ul><li>q (t)=f (m (t)) </li></ul></ul><ul><li>Standard FM: q (t)=2pf c t+2pk f  m(t)dt </li></ul><ul><ul><li>Instantaneous frequency: f i =f c + k f m(t) </li></ul></ul><ul><ul><li>Signal robust to amplitude variations </li></ul></ul><ul><ul><li>Robust to signal reflections and refractions </li></ul></ul><ul><li>Analysis is nonlinear </li></ul><ul><ul><li>Hard to analyze </li></ul></ul>
  39. 39. FM Bandwidth and Carson’s Rule <ul><li>Frequency Deviation: Df=k f max |m (t)| </li></ul><ul><ul><li>Maximum deviation of w i from w c : w i =w c + k f m(t) </li></ul></ul><ul><li>Carson’s Rule: </li></ul><ul><ul><li>B s depends on maximum deviation from w c AND how fast w i changes </li></ul></ul><ul><li>Narrowband FM: Df<<B m  B s  2B m </li></ul><ul><li>Wideband FM: Df>>B m  B s  2Df </li></ul>B s  2  f+2B m
  40. 40. Spectral Analysis of FM <ul><li>S (t)= A cos (w c t + k f  m (a) da) </li></ul><ul><ul><li>Very hard to analyze for general m(t). </li></ul></ul><ul><li>Let m(t)=cos (w m t): Bandwidth f m </li></ul><ul><li>S(f) sequence of d functions at f=f c ± nf m </li></ul><ul><ul><li>If Df <<f m , Bessel function small for f  (f c  f m ) </li></ul></ul><ul><ul><li>If Df >>f m , significant components up to f c ±Df. </li></ul></ul>S(f) for m(t)=cos(2  f m t) f c f c +f m f c +2f m f c +3f m f c + 4f m f c -4f m f c -3f m f c -2f m f c -f m f … … .5A c J n (  ) B  2  f WBFM .5A c J n (  )
  41. 41. Generating FM Signals <ul><li>NBFM </li></ul><ul><li>WBFM </li></ul><ul><ul><li>Direct Method: Modulate a VCO with m(t) </li></ul></ul><ul><li>Indirect Method </li></ul>m(t) Product Modulator Asin(  c t) s(t) 2  k f  ( ·)dt  (t) -90 o LO + A c cos(  c t) + - Product Modulator (k 1 ,f 1 ) m(t) s 1 (t) Nonlinear Device s 2 (t) BPF s(t)
  42. 42. FM Detection <ul><li>Differentiator and Envelope Detector </li></ul><ul><li>Zero Crossing Detector </li></ul><ul><ul><li>Uses rate of zero crossings to estimate w i </li></ul></ul><ul><li>Phase Lock Loop (PLL) </li></ul><ul><ul><li>Uses VCO and feedback to extract m(t) </li></ul></ul>
  43. 43. Introduction to Digital Modulation <ul><li>Most information today is in bits </li></ul><ul><li>Baseband digital modulation converts bits into analog signals y(t) (bits encoded in amplitude) </li></ul><ul><li>Bandwidth and PSD of y(t) determined by pulse shape p(t) and a k : </li></ul><ul><li>If pulse duration is bit time T b , modulation called non-return to zero (NRZ); if less than T b , called return to zero (RZ) </li></ul>1 0 1 1 0 1 0 1 1 0 On-Off Polar t t T b
  44. 44. Pulse Shaping <ul><li>Pulse shaping is the design of pulse p(t) </li></ul><ul><ul><li>Want pulses that have zero value at sample times nT </li></ul></ul><ul><li>Rectangular pulses don’t have good BW properties </li></ul><ul><li>Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors </li></ul>
  45. 45. Passband Digital Modulation <ul><li>Changes amplitude (ASK), phase (PSK), or frequency (FSK) of carrier relative to bits </li></ul><ul><li>We use BB digital modulation as the information signal m(t) to encode bits, i.e. m(t) is on-off, etc. </li></ul><ul><li>Passband digital modulation for ASK/PSK) is a special case of DSBSC; has form </li></ul><ul><li>FSK is a special case of FM </li></ul>
  46. 46. ASK, PSK, and FSK <ul><li>Amplitude Shift Keying (ASK) </li></ul><ul><li>Phase Shift Keying (PSK) </li></ul><ul><li>Frequency Shift Keying </li></ul>1 0 1 1 1 0 1 1 1 0 1 1 AM Modulation AM Modulation FM Modulation m(t) m(t)
  47. 47. ASK/PSK Demodulation <ul><li>Similar to AM demodulation, but only need to choose between one of two values (need coherent detection) </li></ul><ul><li>Decision device determines which of R 0 or R 1 that R(nT b ) is closest to </li></ul><ul><ul><li>Noise immunity DN is half the distance between R 0 and R 1 </li></ul></ul><ul><ul><li>Bit errors occur when noise exceeds this immunity </li></ul></ul>s(t)  cos(  c t +  ) nT b Decision Device “ 1” or “0” r(nT b ) R 0 R 1 Integrator (LPF)  N a  r(nT b ) r(nT b )+ 
  48. 48. Noise in ASK/PSK <ul><li>Probability of bit error: P b =p (|N ( nT b )|>DN=.5|R 1 -R 0 |) </li></ul><ul><li>N ( n T b ) is a Gaussian RV: N ~ N( m=0,s 2 =.25N o T b ) </li></ul><ul><li>For x~N(0,1), Define Q (z)=p (x>z) </li></ul><ul><li>ASK: </li></ul><ul><li>PSK: </li></ul>s(t)  cos(  c t) nT b R(nT b )+ N(nT b ) “ 1” or “0” + N(t) Channel R 1 R 0  N
  49. 49. FSK Demodulation <ul><li>Minimum frequency separation required to differentiate: </li></ul><ul><ul><li>|f 1 -f 2 |  .5n/T b (MSK uses minimum separation of n=1) </li></ul></ul><ul><ul><li>With this separation, R 1 =0 if “0” sent, R 0 =0 if “1” sent </li></ul></ul><ul><li>Comparator : R 1 =.5AT b if “1’ sent, R 0 =.5AT b if “0” sent </li></ul><ul><li>Comparator outputs “1” if (R 1 +N 1 )-(R 2 +N 2 )>0, otherwise “0” </li></ul><ul><ul><li>Error probability depends on N 1 -N 2 </li></ul></ul>s(t)  cos(2  1 t) R 1 (nT b )+N 1 “ 1” or “0”  cos(  0 t) nT b R 0 (nT b )+N 2 Comparator
  50. 50. FSK Error Probability <ul><li>Analysis similar to ASK/PSK </li></ul><ul><li>P b =p(N 1 -N 2 >.5AT b ) </li></ul><ul><li>Distribution of N 1 -N 2 </li></ul><ul><ul><li>Sum of indep. Gaussians is Gaussian (|f 1 -f 2 |  .5n/T b ) </li></ul></ul><ul><ul><li>Mean is sum of means, Variance is sum of variances </li></ul></ul><ul><ul><li>N 1 ,N 2 ~N(m=0,s 2 =.25N o T b ) (Same as in ASK/PSK) </li></ul></ul><ul><ul><li>N 1 -N 2 ~ N(m=0,s 2 =.5N o T b ) </li></ul></ul><ul><li>P b =p(N 1 -N 2 >.5AT b )= Q(.5AT b /  .5N 0 T b ) </li></ul><ul><li>=Q(  .5T b A 2 /N 0 )=Q(  E b /N 0 ) </li></ul>
  51. 51. Summary of Digital Modulation <ul><li>Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments. </li></ul><ul><li>Digital passband modulation encodes binary bits into the amplitude, phase, or frequency of the carrier. </li></ul><ul><li>ASK/PSK special case of AM; FSK special case of FM </li></ul><ul><li>Noise immunity in receiver dictates how much noise reqd to make an error </li></ul><ul><li>White Gaussian noise process causes a Gaussian noise term to be added to the decision device input </li></ul><ul><li>Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio. </li></ul><ul><li>BPSK has lower error probability than ASK for same energy per bit. </li></ul><ul><li>FSK same error prob. as ASK; less susceptible to amplitude fluctuations. </li></ul>
  52. 52. Performance Degradation <ul><li>Phase offset Dq reduces noise immunity by cos (Dq). </li></ul><ul><li>If noise is not mean zero, causes P b to increase in one direction. </li></ul><ul><li>With timing offset, integrate over [D t , T b +Dt] </li></ul><ul><ul><li>Interference from subsequent bit. </li></ul></ul>
  53. 53. Multilevel Modulation <ul><li>m bits encoded in pulse of duration T s (R b =m/T s ) </li></ul><ul><ul><li> n constant over a symbol time T s , and can take M=2 m different values on each pulse. </li></ul></ul><ul><li>Phase Shift Keying (MPSK) </li></ul><ul><li>Similar ideas in MFSK </li></ul><ul><li>Demodulation similar to binary case </li></ul>Higher data rate more susceptible to noise 00 10 01 11 T s 00 10 01 11
  54. 54. Key Points To Remember <ul><li>PSD and pulse shaping in BB modulation </li></ul><ul><ul><li>PSD depends on pulse shape </li></ul></ul><ul><ul><li>Nyquist pulses avoid ISI: p ( n T b )=0 </li></ul></ul><ul><ul><li>Raised Cosine pulses trade BW efficiency for timing error robustness </li></ul></ul><ul><li>Passband digital modulation for ASK/PSK is a special case of DSBSC; </li></ul><ul><li>FSK is a special case of FM: </li></ul><ul><li>Demodulation uses a decision device to determine if a “1’’ or “0’’ was sent </li></ul><ul><li>Noise can cause the decision device to output an erroneous bit </li></ul>
  55. 55. The Interpretations <ul><li>Communication systems modulate analog signals or bits for transmission over channel. </li></ul><ul><li>The building blocks of a communication system convert information into an electronic format for transmission, then convert it back to its original format after reception. </li></ul><ul><li>Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortion/noise from the channel. </li></ul><ul><li>Digital systems are more robust to noise and interference. </li></ul><ul><li>Performance metric for analog systems is fidelity, for digital it is rate and error probability. </li></ul><ul><li>Data rates over channels with noise have a fundamental capacity limit. </li></ul>
  56. 56. What is Telemetry? <ul><li>Telemetry : The process of measuring at a distance . </li></ul><ul><li>Aeronautical telemetry: The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis </li></ul>
  57. 57. TELEMETERING APPLICATIONS <ul><li>The use of telemetry spectrum is common to many different nations and many purposes </li></ul><ul><ul><li>National defense </li></ul></ul><ul><ul><li>Commercial aerospace industry </li></ul></ul><ul><ul><li>Space applications </li></ul></ul><ul><ul><li>Scientific research </li></ul></ul><ul><li>The primary telemetering applications are </li></ul><ul><ul><li>Range and range support systems </li></ul></ul><ul><ul><ul><li>Land mobile </li></ul></ul></ul><ul><ul><ul><li>Sea ranges </li></ul></ul></ul><ul><ul><ul><li>Air ranges </li></ul></ul></ul><ul><ul><li>Space-based telemetry systems </li></ul></ul><ul><ul><li>Meteorological telemetry </li></ul></ul>
  58. 58. Telemetry Use in Precision Agriculture <ul><li>􀂙 Differential GPS </li></ul><ul><li>􀂙 Mobile phone reporting and control of center pivot irrigation systems </li></ul><ul><li>􀂙 Soil moisture sensor networks </li></ul><ul><li>􀂙 Climate control for high value crops </li></ul><ul><li>􀂙 Real-time monitoring of equipment and people </li></ul>
  59. 59. Current Band-Allocations
  60. 60. Spectrum Encroachments 1435-1525 MHz: Manned Vehicle (L Band) Telemetry 2200-2390 MHz: Manned and Unmanned Vehicle (S Band) Telemetry WARC 92 BBA 97 Terrestrial DAB (Canada), CARIBSS, MediaStar WARC 92 US Alternative 2390 2350 2200 2250 2300 2200-2290 MHz: Unmanned 2360-2390 MHz: Manned 1525 1500 1435 1460 1485 One A/C can easily use over 20MHz of spectrum for a single mission
  61. 61. <ul><li>Thank You !!! </li></ul>