Wireless PHY: Digital Demodulation and Wireless Channels Y. Richard Yang 09/13/2012

2 Outline r Admin and recap r Digital demodulation r Wireless channels

3 Admin r Assignment 1 posted

4 r Demodulation r Low pass filter and FIR r Convolution Theorem r Digital modulation/demodulation r ASK, FSK, PSK r General representation Recap

QPSK Demodulation/Decoding 5 sin( 2πf c t ) cos( 2πf c t ) [a 01,b 01 ] [a 10,b 10 ] [a 00,b 00 ] [a 11,b 11 ] [a x,b x ] Q: how to decode?

Look into Noise 6 r Assume sender sends g m (t) [0, T] r Receiver receives x(t) [0, T] r Consider one sample where w[i] is noise r Assume white noise, i.e., prob w[i] = z is

7 Likelihood r What is the likelihood (prob.) of observing x[i]? m it is the prob. of noise being w[i] = x[i] – g[i] r What is the likelihood (prob.) of observing the whole sequence x? m the product of the probabilities

Likelihood Detection 8 r Suppose we know r Maxim likelihood detection picks the m with the highest P{x|g m }. r From the expression We pick m with the lowest ||x-g m || 2

Back to QPSK 9

QPSK Demodulation/Decoding 10 sin( 2πf c t ) cos( 2πf c t ) [a 01,b 01 ] [a 10,b 10 ] [a 00,b 00 ] [a 11,b 11 ] [a x,b x ] Q: what does maximum likelihood det pick?

General Matched Filter Detection: Implementation for Multiple Sig Func. 11 r Basic idea m consider each g m [0,T] as a point (with coordinates) in a space m compute the coordinate of the received signal x[0,T] m check the distance between g m [0,T] and the received signal x[0,T] m pick m* that gives the lowest distance value

Computing Coordinates 12 r Pick orthogonal bases {f 1 (t), f 2 (t), …, f N (t)} for {g 1 (t), g 2 (t), …, g M (t)} r Compute the coordinate of g m [0,T] as c m = [c m1, c m2, …, c mN ], where r Compute the coordinate of the received signal x[0,T] as x = [x 1, x 2, …, x N ] r Compute the distance between r and c m every cm and pick m* that gives the lowest distance value

Example: Matched Filter => Correlation Detector 13 received signal x

14 BPSK vs QPSK BPSK QPSK f c : carrier freq. R b : freq. of data 10dB = 10; 20dB = A t

BPSK vs QPSK r A major metric of modulation performance is spectral density (SD) r Q: what is the SD of BPSK vs that of QPSK? r Q: Why would any one use BPSK, given higher QAM? 15 Spectral Density = bit rate width of spectrum used

Context r Previous demodulation considers only additive noise, and does not consider wireless channel’s effects r We next study its effects 16

17 Outline r Admin and recap r Digital demodulation r Wireless channels

Signal Propagation

19 r Isotropic radiator: a single point m equal radiation in all directions (three dimensional) m only a theoretical reference antenna r Radiation pattern: measurement of radiation around an antenna zy x z yx ideal isotropic radiator Antennas: Isotropic Radiator Q: how does power level decrease as a function of d, the distance from the transmitter to the receiver?

20 Free-Space Isotropic Signal Propagation r In free space, receiving power proportional to 1/d² (d = distance between transmitter and receiver) r Suppose transmitted signal is cos(2  ft), the received signal is m P r : received power m P t : transmitted power m G r, G t : receiver and transmitter antenna gain m (=c/f): wave length Sometime we write path loss in log scale: Lp = 10 log(Pt) – 10log(Pr)

21 Log Scale for Large Span dB = 10 log(times) Slim/Gates ~100B Obama ~10M ~10K 1000 times 40 dB 10,000 times 30 dB 10,000 x 1, = 70 dB

22 Path Loss in dB dB = 10 log(times) source 10 W d1 1 mW 1 uW 1000 times 40 dB 10,000 times 30 dB 10,000 x 1, = 70 dB power d2

23 dBm (Absolute Measure of Power) dBm = 10 log (P/1mW) source 10 W d1 1 mW 1 uW 1000 times 40 dB 10,000 times 30 dB 10,000 x 1, = 70 dB power d2 40 dBm -30 dBm

24 Number in Perspective (Typical #)

25 Exercise: 915MHz WLAN (free space) r Transmit power (Pt) = 24.5 dBm r Receive sensitivity = dBm r Receiving distance (Pr) = r Gt=Gr=1

26 Two-ray Ground Reflection Model r Single line-of-sight is not typical. Two paths (direct and reflect) cancel each other and reduce signal strength m P r : received power m P t : transmitted power m G r, G t : receiver and transmitter antenna gain m h r, h t : receiver and transmitter height

27 Exercise: 915MHz WLAN (Two-ray ground reflect) r Transmit power (Pt) = 24.5 dBm r Receive sensitivity = dBm r Receiving distance (Pr) = r Gt=Gr=hr=ht=1

28 Real Antennas r Real antennas are not isotropic radiators r Some simple antennas: quarter wave /4 on car roofs or half wave dipole /2  size of antenna proportional to wavelength for better transmission/receiving /4 /2 Q: Assume frequency 1 Ghz, = ?

29 Figure for Thought: Real Measurements

30 r Receiving power additionally influenced by m shadowing (e.g., through a wall or a door) m refraction depending on the density of a medium m reflection at large obstacles m scattering at small obstacles m diffraction at edges reflection scattering diffraction shadow fading refraction Signal Propagation: Complexity

31 Signal Propagation: Complexity Details of signal propagation are very complicated We want to understand the key characteristics that are important to our understanding

32 Outline r Admin and recap r Digital demodulation r Wireless channels m Intro m shadowing

33 Shadowing r Signal strength loss after passing through obstacles r Same distance, but different levels of shadowing: It is a random, large-scale effect depending on the environment

Example Shadowing Effects 34 i.e. reduces to ¼ of signal 10 log(1/4) = -6.02

35 JTC Indoor Model for PCS: Path Loss A: an environment dependent fixed loss factor (dB) B: the distance dependent loss coefficient, d : separation distance between the base station and mobile terminal, in meters L f : a floor penetration loss factor (dB) n: the number of floors between base station and mobile terminal Shadowing path loss follows a log-normal distribution (i.e. L is normal distribution) with mean:

36 JTC Model at 1.8 GHz

37 Outline r Admin and recap r Digital demodulation r Wireless channels m Intro m Shadowing m Multipath

38 r Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction Multipath

39 r Example: reflection from the ground or building Multipath Example: Outdoor ground

40 Multipath Effect (A Simple Example) d1d1 d2d2 phase difference: Assume transmitter sends out signal cos(2  f c t)

Multipath Effect (A Simple Example) r Where do the two waves totally destruct? r Q: where do the two waves construct? 41

Option 1: Change Location r If receiver moves to the right by /4: d 1 ’ = d 1 + /4; d 2 ’ = d 2 - /4; -> 42 By moving a quarter of wavelength, destructive turns into constructive. Assume f = 1G, how far do we move?

Option 2: Change Frequency 43 r Change frequency:

44 Multipath Delay Spread RMS: root-mean-square

45 Multipath Effect (moving receiver) d1d1 d2d2 example Suppose d 1 =r 0 +vt d 2 =2d-r 0 -vt d1  d2 d

Derivation 46 See for cos(u)-cos(v)

Derivation 47 See for cos(u)-cos(v)

Derivation 48 See for cos(u)-cos(v)

Derivation 49 See for cos(u)-cos(v)

Derivation 50 See for cos(u)-cos(v)

Derivation 51 See for cos(u)-cos(v)

52 Waveform v = 65 miles/h, f c = 1 GHz:f c v/c = 10 ms deep fade Q: How far does a car drive in ½ of a cycle? 10 9 * 30 / 3x10 8 = 100 Hz

53 Multipath with Mobility

54 Effect of Small-Scale Fading no small-scale fading small-scale fading

55 signal at sender Multipath Can Spread Delay signal at receiver LOS pulse multipath pulses LOS: Line Of Sight Time dispersion: signal is dispersed over time

56 JTC Model: Delay Spread Residential Buildings

57 signal at sender Multipath Can Cause ISI signal at receiver LOS pulse multipath pulses LOS: Line Of Sight Dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI) Assume 300 meters delay spread, the arrival time difference is 300/3x10 8 = 1 ns  if symbol rate > 1 Ms/sec, we will have serious ISI In practice, fractional ISI can already substantially increase loss rate

58 r Channel characteristics change over location, time, and frequency small-scale fading Large-scale fading time power Summary: Wireless Channels path loss log (distance) Received Signal Power (dB) frequency signal at receiver LOS pulse multipath pulses

59 Preview: Challenges and Techniques of Wireless Design Performance affected Mitigation techniques Shadow fading (large-scale fading) Fast fading (small-scale, flat fading) Delay spread (small-scale fading) received signal strength bit/packet error rate at deep fade ISI use fade margin— increase power or reduce distance diversity equalization; spread- spectrum; OFDM; directional antenna

60 Representation of Wireless Channels r Received signal at time m is y[m], h l [m] is the strength of the l-th tap, w[m] is the background noise: r When inter-symbol interference is small: (also called flat fading channel)

Backup Slides 61

Received Signal 62 d2 d1 receiver

63 Multipath Fading with Mobility: A Simple Two-path Example r(t) = r0 + v t, assume transmitter sends out signal cos(2  f c t) r0r0

64 Received Waveform v = 65 miles/h, f c = 1 GHz:f c v/c = 10 9 * 30 / 3x10 8 = 100 Hz 10 ms Why is fast multipath fading bad? deep fade

65 Small-Scale Fading

66 signal at sender Multipath Can Spread Delay signal at receiver LOS pulse multipath pulses LOS: Line Of Sight Time dispersion: signal is dispersed over time

67 Delay Spread RMS: root-mean-square

68 signal at sender Multipath Can Cause ISI signal at receiver LOS pulse multipath pulses LOS: Line Of Sight dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI) Assume 300 meters delay spread, the arrival time difference is 300/3x10 8 = 1 ms  if symbol rate > 1 Ms/sec, we will have serious ISI In practice, fractional ISI can already substantially increase loss rate

69 r Channel characteristics change over location, time, and frequency small-scale fading Large-scale fading time power Summary: Wireless Channels path loss log (distance) Received Signal Power (dB) frequency

70 Dipole: Radiation Pattern of a Dipole

Free Space Signal Propagation t 101 t 101 t at distance d ?

Why Not Digital Signal (revisited) r Not good for spectrum usage/sharing r The wavelength can be extremely large to build portal devices m e.g., T = 1 us -> f=1/T = 1MHz -> wavelength = 3x10 8 /10 6 = 300m 72

Exercise r Suppose fc = 1 GHz (fc1 = 1 GHz, fc0 = 900 GHz for FSK) r Bit rate is 1 Mbps r Encode one bit at a time r Bit seq: r Q: How does the wave look like for? Q I A t