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Small-Scale Fading and Multipath measurements consists of PPT of UPTU Unit-1 Part 2

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- 1. Unit-I (P-II) Small-Scale Fading and Multipath measurements 1Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 2. I. Fading • Fading: rapid fluctuations of received signal strength over short time intervals and/or travel distances • Caused by interference from multiple copies of Tx signal arriving @ Rx at slightly different times • Three most important effects: 1. Rapid changes in signal strengths over small travel distances or short time periods. 2. Changes in the frequency of signals. 3. Multiple signals arriving a different times. When added together at the antenna, signals are spread out in time. This can cause a smearing of the signal and interference between bits that are received. 2 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 3. • Fading signals occur due to reflections from ground & surrounding buildings (clutter) as well as scattered signals from trees, people, towers, etc. – often an LOS path is not available so the first multipath signal arrival is probably the desired signal (the one which traveled the shortest distance) – allows service even when Rx is severely obstructed by surrounding clutter 3 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 4. • Even stationary Tx/Rx wireless links can experience fading due to the motion of objects (cars, people, trees, etc.) in surrounding environment off of which come the reflections • Multipath signals have randomly distributed amplitudes, phases, & direction of arrival – vector summation of (A ∠θ) @ Rx of multipath leads to constructive/destructive interference as mobile Rx moves in space with respect to time 4 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 5. • received signal strength can vary by Small-scale fading over distances of a few meter (about 7 cm at 1 GHz)! 1. This is a variation between, say, 1 mW and 10-6 mW. 2. If a user stops at a deeply faded point, the signal quality can be quite bad. 3. However, even if a user stops, others around may still be moving and can change the fading characteristics. 4. And if we have another antenna, say only 7 to 10 cm separated from the other antenna, that signal could be good. 5 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 6. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 6 • fading occurs around received signal strength predicted from large-scale path loss models
- 7. Physical Factors Influencing Fading in Mobile Radio Channel (MRC) 1) Multipath Propagation • # and strength of multipath signals • time delay of signal arrival – large path length differences → large differences in delay between signals • urban area w/ many buildings distributed over large spatial scale – large # of strong multipath signals with only a few having a large time delay • suburb with nearby office park or shopping mall – moderate # of strong multipath signals with small to moderate delay times • rural → few multipath signals (LOS + ground reflection) 7 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 8. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 8 2) Speed of Mobile – relative motion between base station & mobile causes random frequency modulation due to Doppler shift (fd) – Different multipath components may have different frequency shifts. 3) Speed of Surrounding Objects – also influence Doppler shifts on multipath signals – dominates small-scale fading if speed of objects > mobile speed • otherwise ignored
- 9. 4) Tx signal bandwidth (Bs) The mobile radio channel (MRC) is modeled as filter w/ specific bandwidth (BW) The relationship between the signal BW & the MRC BW will affect fading rates and distortion, and so will determine: a) if small-scale fading is significant b) if time distortion of signal leads to inter-symbol interference (ISI) An MRC can cause distortion/ISI or small-scale fading, or both. But typically one or the other. 9 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 10. Doppler Shift • motion causes frequency modulation due to Doppler shift (fd) • v : velocity (m/s) • λ : wavelength (m) • θ : angle between mobile direction and arrival direction of RF energy » + shift → mobile moving toward S » − shift → mobile moving away from S 10 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 11. • Two Doppler shifts to consider above 1. The Doppler shift of the signal when it is received at the car. 2. The Doppler shift of the signal when it bounces off the car and is received somewhere else. • Multipath signals will have different fd’s for constant v because of random arrival directions!! 11 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 12. • Note: What matters with Doppler shift is not the absolute frequency, but the shift in frequency relative to the bandwidth of a channel. – For example: A shift of 166 Hz may be significant for a channel with a 1 kHz bandwidth. – In general, low bit rate (low bandwidth) channels are affected by Doppler shift. 12 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 13. . MRC Impulse Response Model • Impulse response is wideband characterization containing all the information required to analyze the radio X’mission through channel. • We can Model the MRC as a linear filter with a time varying characteristics due to position of Rx. • Vector summation of random amplitudes & phases of multipath signals results in a "filter“ • That is to say, the MRC takes an original signal and in the process of sending the signal produces a modified signal at the receiver. 13 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 14. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 14 • Time variation due to mobile motion results in time delay of multipath signals varies with location of Rx Can be thought as a "location varying" filter. As mobile moves with time, the location changes with time; hence, time-varying characteristics. • The MRC has a fundamental bandwidth limitation → model as a band pass filter
- 15. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 15 Assume Rx moving along X –axis with constant velocity v. For fixed d channel can be modeled as linear time invariant system But for different d signal received at Rx will vary due to multipath and Doppler shift. That is the channel response is dependent on d so impulse response Should be expressed as h(d,t).
- 16. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 16 Let x(t)-transmitted signal than received signal y(d,t) at d Ca be expressed as convolution of x(t) & h (d,t) For causal system h (d,t)=0, for t<0 eq reduces to If v is constant d=vt than
- 17. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 17 As v is constant so y(vt,t) is function of t, so If v is assumed to be constant for short distance, = x’mitted bandpass waveform =received bandpass waveform = impulse response of multipath radio channel
- 18. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 18
- 19. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 19 • How is the impulse response of an MRC determined? – “channel sounding” → like radar – transmit short time duration pulse (not exactly an impulse, but with wide BW) and record multipath echoes @ Rx
- 20. • short duration Tx pulse ≈ unit impulse • define excess delay bin as • amplitude and delay time of multipath returns change as mobile moves • Fig. 5.4, pg. 184 → MRC is time variant 1i i 20 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 21. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 21 • model multipath returns as a sum of unit impulses – ai ∠ θ i = amplitude & phase of each multipath signal – N = # of multipath components – ai is relatively constant over an local area • But θ i will change significantly because of different path lengths (direct distance plus reflected distance) at different locations.
- 22. • The useful frequency span of the model : • The received power delay profile in a local area: • Assume the channel impulse response is time invariant, or WSS 2 ( ) ( ; )b P k h t 2 / 22 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 23. Relationship between Bandwidth and Received Power • A pulsed, transmitted RF signal of the form 23 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 24. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 24 • For wideband signal
- 25. • The average small-scale received power – The average small scale received power is simply the sum of the average powers received in each multipath component – The Rx power of a wideband signal such as p(t) does not fluctuate significantly when a receiver is moved about a local area. 25 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 26. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 26 • CW signal (narrowband signal ) is transmitted in to the same channel
- 27. • Average power for a CW signal is equivalent to the average received power for a wideband signal in a small-scale region. • The received local ensemble average power of wideband and narrowband signals are equivalent. • Tx signal BW > Channel BW Rx power varies very small • Tx signal BW < Channel BW large signal fluctuations (fading) occur – The duration of baseband signal > excess delay of channel – due to the phase shifts of the many unsolved multipath components 27 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 28. 28 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 29. • The Fourier Transform of hb ( t,τ) gives the spectral characteristics of the channel → frequency response • MRC filter passband → “Channel BW” or Coherence BW = Bc – range of frequencies over which signals will be transmitted without significant changes in signal strength – channel acts as a filter depending on frequency – signals with narrow frequency bands are not distorted by the channel 29 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 30. 30 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 31. 31 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 32. 32 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 33. 33 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 34. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 34
- 35. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 35
- 36. Small scale Multipath measurement • Direct RF pulse(uses wideband pulse bistatic radar) • Spread Spectrum sliding correlator channel sounding Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 36
- 37. Channel Sounder: Pulse type 37 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 38. Disadvantages • Interference • If first pulse is faded severe fading occurs • Phase of multipath is not received Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 38
- 39. Channel Sounder: PN Type 39 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 40. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 40 •Pseudo –noise is added to carrier signal •The power sprctrum envelope of X’mitted SS is given by- •With BW=2Rc •at receiver again PN sequence is added to incoming SS signal but with slower clock rate . •This is called as SLIDING CORRELATION.
- 41. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut. 41 •Processing gain is given by:- •The time resolution of MPC with SS using SC is given by
- 42. Channel Sounder: Swept Freq. type 42 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 43. IV. Multipath Channel Parameters • Derived from multipath power delay P (τk) : relative power amplitudes of multipath signals (absolute measurements are not needed) Relative to the first detectable signal arriving at the Rx at τ0 – use ensemble average of many profiles in a small localized area →typically 2 − 6 m spacing of measurements→ to obtain average small-scale response 43 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 44. 44 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 45. • Time Dispersion Parameters – “excess delay” : all values computed relative to the time of first signal arrival τo – mean excess delay → – RMS delay spread → – Central moment where Avg( τ2) is the same computation as above as used for except that • A simple way to explain this is “the range of time within which most of the delayed signals arrive”. Do not rerlyon absolute power 45 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 46. – outdoor channel ~ on the order of microseconds – indoor channel ~ on the order of nanoseconds 46 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 47. • maximum excess delay ( τX): the largest time where the multipath power levels are still within X dB of the maximum power level – worst case delay value – depends very much on the choice of the noise threshold 47 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 48. • τ and στ provide a measure of propagation delay of interfering signals – Then give an indication of how time smearing might occur for the signal. – A small στ is desired. – The noise threshold is used to differentiate between received multipath components and thermal noise 48 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 49. • Coherence BW (Bc) and Delay Spread ( ) – The Fourier Transform of multipath delay shows frequency (spectral) characteristics of the MRC – Bc : statistical measure of frequency range where MRC response is flat • MRC response is flat = passes all frequencies with ≈ equal gain & linear phase • amplitudes of different frequency components are correlated • if two sinusoids have frequency separation greater than Bc, they are affected quite differently by the channel 49 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 50. – amplitude correlation → multipath signals have close to the same amplitude → if they are then out-of-phase they have significant destructive interference with each other (deep fades) – so a flat fading channel is both “good” and “bad” • Good: The MRC is like a bandpass filter and passes signals without major attenuation from the channel. • Bad: Deep fading can occur. 50 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 51. –so the coherence bandwidth is “the range of frequencies over which two frequency components have a strong potential for amplitude correlation.” (quote from textbook) 51 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 52. • estimates – 0.9 correlation → Bc ≈ 1 / 50 (signals are 90% correlated with each other) – 0.5 correlation → Bc ≈ 1 / 5 Which has a larger bandwidth and why? • specific channels require detailed analysis for a particular transmitted signal – these are just rough estimates 52 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 53. • A channel that is not a flat fading channel is called frequency selective fading because different frequencies within a signal are attenuated differently by the MRC. – Note: The definition of flat or frequency selective fading is defined with respect to the bandwidth of the signal that is being transmitted. 53 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 54. • Bc and στ are related quantities that characterize time-varying nature of the MRC for multipath interference from frequency & time domain perspectives 54 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 55. • these parameters do NOT characterize the time-varying nature of the MRC due to the mobility of the mobile and/or surrounding objects – that is to say, Bc and characterize the statics, (how multipath signals are formed from scattering/reflections and travel different distances) – Bc and στ do not characterize the mobility of the Tx or Rx. 55 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 56. • Doppler Spread (BD) & Coherence Time (Tc) – BD : measure of spectral broadening of the Tx signal caused by motion → i.e., Doppler shift • BD = max Doppler shift = fmax = vmax / λ • In what direction does movement occur to create this worst case? • if Tx signal bandwidth (Bs) is large such that Bs >> BD then effects of Doppler spread are NOT important so Doppler spread is only important for low bps (data rate) applications (e.g. paging) 56 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 57. • Tc : statistical measure of the time interval over which MRC impulse response remains invariant → amplitude & phase of multipath signals ≈ constant – Coherence Time (Tc) = passes all received signals with virtually the same characteristics because the channel has not changed – time duration over which two received signals have a strong potential for amplitude correlation 57 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.
- 58. – Two signals arriving with a time separation greater than Tc are affected differently by the channel, since the channel has changed within the time interval – For digital communications coherence time and Doppler spread are related by 2 9 0.423 16 c m m T f f 58 Vrince Vimal,Asst.Prof, Deptt Of EC, MIT, MIET Group, Meerut.

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