Wireless PHY: Modulation and Channels Y. Richard Yang 09/6/2012

2 Outline r Recap r Frequency domain examples r Introduction to modulation

3 Frequency Domain Analysis Examples Using GNURadio r spectrum_2sin_plus m Audio m FFT Sink m Scope Sink m Noise

4 Frequency Domain Analysis Examples Using GNURadio r spectrum_1sin_rawfft m Raw FFT

5 Frequency Domain Analysis Examples Using GNURadio r spectrum_2sin_multiply_complex m Multiplication of a sine first by a real sine and then by a complex sine to observe spectrum

6 Takeaway of the Example r Advantages of I/Q representation

7 Quadrature Mixing spectrum of complex signal x(t) spectrum of complex signal x(t)e j2f0t spectrum of complex signal x(t)e -j2f0t

8 Basic Question: Why Not Send Digital Signal in Wireless Communications? r Signals at undesirable frequencies m suppose digital frame length T, then signal decomposes into frequencies at 1/T, 2/T, 3/T, … m let T = 1 ms, generates radio waves at frequencies of 1 KHz, 2 KHz, 3 KHz, … 1 0 digital signal t

9 Frequencies are Assigned and Regulated

10 Spectrum and Bandwidth: Shannon Channel Capacity r The maximum number of bits that can be transmitted per second by a physical channel is: where W is the frequency range of the channel, and S/N is the signal noise ratio, assuming Gaussian noise

11 Frequencies for Communications VLF = Very Low FrequencyUHF = Ultra High Frequency LF = Low Frequency SHF = Super High Frequency MF = Medium Frequency EHF = Extra High Frequency HF = High Frequency UV = Ultraviolet Light VHF = Very High Frequency Frequency and wave length:  = c/f wave length, speed of light c  3x10 8 m/s, frequency f 1 Mm 300 Hz 10 km 30 kHz 100 m 3 MHz 1 m 300 MHz 10 mm 30 GHz 100  m 3 THz 1  m 300 THz visible light VLFLFMFHFVHFUHFSHFEHFinfraredUV optical transmission coax cabletwisted pair

12 Why Not Send Digital Signal in Wireless Communications? voice Transmitter 20-20KHz Antenna: size ~ wavelength At 3 KHz, Antenna too large! Use modulation to transfer to higher frequency

13 Outline r Recap r Frequency domain examples r Basic concepts of modulation

14 r The information source m Typically a low frequency signal m Referred to as baseband signal  Carrier  A higher frequency sinusoid  Example cos(2π10000t)  Modulated signal  Some parameter of the carrier (amplitude, frequency, phase) is varied in accordance with the baseband signal Basic Concepts of Modulation

15 Types of Modulation r Analog modulation m Amplitude modulation (AM) m Frequency modulation (FM) m Double and signal sideband: DSB, SSB r Digital modulation m Amplitude shift keying (ASK) m Frequency shift keying: FSK m Phase shift keying: BPSK, QPSK, MSK m Quadrature amplitude modulation (QAM)

16 Outline r Recap r Frequency domain examples r Basic concepts of modulation r Amplitude modulation

17 Example: Amplitude Modulation (AM) r Block diagram r Time domain r Frequency domain

18 Example: am_modulation Example r Setting m Audio source (sample 32K) m Signal source (300K, sample 800K) m Multiply r Two Scopes r FFT Sink

19 Example AM Frequency Domain Note: There is always the negative freq. in the freq. domain.

20 Problem: How to Demodulate AM Signal?

21 Outline r Recap r Frequency domain examples r Basic concepts of modulation r Amplitude modulation r Amplitude demodulation

22 Design Option 1 r Step 1: Multiply signal by e -jfct m Implication: Need to do complex multiple multiplication

23 Design Option 1 (After Step 1) -2f c

24 Design Option 1 (Step 2) r Apply a Low Pass Filter to remove the extra frequencies at -2f c -2f c

25 Design Option 1 (Step 1 Analysis) r How many complex multiplications do we need for Step 1 (Multiply by e -jfct )?

26 Design Option 2: Quadrature Sampling

27 Quadrature Sampling: Upper Path (cos)

28 Quadrature Sampling: Upper Path (cos)

29 Quadrature Sampling: Upper Path (cos)

30 Quadrature Sampling: Lower Path (sin)

31 Quadrature Sampling: Lower Path (sin)

32 Quadrature Sampling: Lower Path (sin)

33 Quarature Sampling: Putting Together

34 Exercise: SpyWork r Setting: a scanner scans 128KHz blocks of AM radio and save each block to a file (see am_rcv.py). r SpyWork: Scan the block in a saved file to find radio stations and tune to each station (each AM station has 10 KHz)

35 Remaining Hole: Designing LPF r Frequency domain view freq B-B freq B-B

36 Design Option 1 freq B-B freq B-B compute freq zeroing out not want freq compute time signal Problem of Design Option 1?

37 Impulse Response Filters r GNU software radio implements filtering using m Finite Impulse Response (FIR) filters m Infinite Impulse Response (IIR) Filters r FIR filters are more commonly used r Filtering is common in networks/communications (and AI and …)

38 FIR Filter r An N-th order FIR filter h is defined by an array of N+1 numbers: r Assume input sequence x0, x1, …,

39 Implementing a 3-rd Order FIR Filter r An array of size N+1 for h xnxn x n-1 x n-2 x n-3 h0h0 h1h1 h2h2 h3h3 **** x n+1 compute y[n]

40 Implementing a 3-rd Order FIR Filter r An array of size N+1 for h xnxn x n-1 x n-2 x n-3 h0h0 h1h1 h2h2 h3h3 **** x n+1 compute y[n+1]

41 FIR Filter is also called convolution between x (as a vector) and h (as a vector), denoted as Key Question: How to Determine h?

g*h in the Continuous Time Domain 42 r Remember that we consider x as samples of time domain function g(t) on [0, 1] and (repeat in other intervals) r We also consider h as samples of time domain function h(t) on [0, 1] (and repeat in other intervals) for (i = 0; i< N; i++) y[t] += h[i] * g[t-i];

Visualizing g*h 43 g(t) h(t) time

Visualizing g*h 44 g(t) h(t) time t

Fourier Series of y=g*h 45

Fubini’s Theorem r In English, you can integrate m first along y and then along x m first along x and then along y m at (x, y) grid They give the same result 46 See

Fourier Series of y=g*h 47

Summary of Progress So Far 48 y = g * h => Y[k] = G[k] H[k] is called the Convolution Theorem, an important theorem.

Applying Convolution Theorem to Design LPF 49 r Choose h() so that m H() is close to a rectangle shape m h() has a low order (why?)

Applying Convolution Theorem to Design LPF 50 r Choose h() so that m H() is close to a rectangle shape m h() has a low order (why?)

Sinc Function 51 r The h() is often related with the sinc(t)=sin(t)/t function f 1/2-1/2 1

FIR Design in Practice 52 r Compute h m MATLAB or other design software m GNU Software radio: optfir (optimal filter design) m GNU Software radio: firdes (using a method called windowing method) r Implement filter with given h m freq_xlating_fir_filter_ccf or m fir_filter_ccf

LPF Design Example 53 r Design a LPF to pass signal at 1 KHz and block at 2 KHz

LPF Design Example 54 #create the channel filter # coefficients chan_taps = optfir.low_pass( 1.0, #Filter gain 48000, #Sample Rate 1500, #one sided mod BW (passband edge) 1800, #one sided channel BW (stopband edge) 0.1, #Passband ripple 60) #Stopband Attenuation in dB print "Channel filter taps:", len(chan_taps) #creates the channel filter with the coef found chan = gr.freq_xlating_fir_filter_ccf( 1, # Decimation rate chan_taps, #coefficients 0, #Offset frequency - could be used to shift 48e3) #incoming sample rate

55 Outline r Recap r Frequency domain examples r Basic concepts of modulation r Amplitude modulation r Amplitude demodulation r Digital modulation

56 r Modulation of digital signals also known as Shift Keying r Amplitude Shift Keying (ASK): m vary carrier amp. according to bit value r Frequency Shift Keying (FSK) o pick carrier freq according to bit value r Phase Shift Keying (PSK): 101 t 101 t 101 t Modulation

57 r BPSK (Binary Phase Shift Keying): m bit value 0: sine wave m bit value 1: inverted sine wave m very simple PSK r Properties m robust, used e.g. in satellite systems Q I 01 Phase Shift Keying: BPSK

58 Phase Shift Keying: QPSK Q I A t r QPSK (Quadrature Phase Shift Keying): m 2 bits coded as one symbol m symbol determines shift of sine wave m often also transmission of relative, not absolute phase shift: DQPSK - Differential QPSK

59 r Quadrature Amplitude Modulation (QAM): combines amplitude and phase modulation r It is possible to code n bits using one symbol m 2 n discrete levels Q I 0010 φ a Quadrature Amplitude Modulation r Example: 16-QAM (4 bits = 1 symbol) r Symbols 0011 and 0001 have the same phase φ, but different amplitude a and 1000 have same amplitude but different phase

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

Generic Representation of Digital Keying (Modulation) r Sender sends symbols one-by-one r Each symbol has a corresponding signaling function g 1 (t), g 2 (t), …, g M (t), each has a duration of symbol time T r Exercise: m What is the setting for BPSK? for QPSK? 61

Checking Relationship Among g i () 62 r BPSK m 1: g 1 (t) = -sin(2πf c t) t in [0, T] m 0: g 0 (t) = sin(2πf c t) t in [0, T] r Are the two signaling functions independent? m Hint: think of the samples forming a vector, if it helps, in linear algebra m Ans: No. g 1 (t) = -g 0 (t)

Checking Relationship Among g i () 63 r QPSK m 11: sin(2πf c t + π/4) t in [0, T] m 10: sin(2πf c t + 3π/4) t in [0, T] m 00: sin(2πf c t - 3π/4) t in [0, T] m 01: sin(2πf c t - π/4) t in [0, T] r Are the four signaling functions independent? m Ans: No. They are all linear combinations of sin(2πf c t) and cos(2πf c t). m We call sin(2πf c t) and cos(2πf c t) the bases. m They are orthogonal because the integral of their product is 0.

Discussion: How does the Receiver Detect Which g i () is Sent? 64 r Assume synchronized (i.e., the receiver knows the symbol boundary). m This is also called coherent detection

Example: Matched Filter Detection 65 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 s[0,T] m check the distance between g m [0,T] and the received signal s[0,T] m pick m* that gives the lowest distance value

Computing Coordinates 66 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 r[0,T] as r = [r 1, r 2, …, r 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 67 received signal

68 Spectral Density of BPSK b R b =B b = 1/T b b f c : freq. of carrier fcfc Spectral Density = bit rate width of spectrum used

69 Phase Shift Keying: Comparison BPSK QPSK f c : carrier freq. R b : freq. of data 10dB = 10; 20dB = A t

Question 70 r Why would any one use BPSK, given higher QAM?

Signal Propagation

72 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?

73 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)

74 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, = ?

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 75

76 Figure for Thought: Real Measurements

77 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

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

79 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 80 i.e. reduces to ¼ of signal 10 log(1/4) = -6.02

81 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:

82 JTC Model at 1.8 GHz

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

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

85 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 Suppose at d 1 -d 2 the two waves totally destruct. (what does it mean?) r Q: where are places the two waves construct? 86

Option 1: Change Location r If receiver moves to the right by /4: d 1 ’ = d 1 + /4; d 2 ’ = d 2 - /4; -> 87 By moving a quarter of wavelength, destructive turns into constructive. Assume f = 1G, how far do we move?

Option 2: Change Frequency 88 r Change frequency:

89 Multipath Delay Spread RMS: root-mean-square

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

Derivation 91 See for cos(u)-cos(v)

92 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

93 Multipath with Mobility

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

95 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

96 JTC Model: Delay Spread Residential Buildings

97 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

98 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

99 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)

100 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

Backup Slides 101

Received Signal 102 d2 d1 receiver

103 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

104 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

105 Small-Scale Fading

106 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

107 Delay Spread RMS: root-mean-square

108 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

109 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

110 Dipole: Radiation Pattern of a Dipole

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

112 Fourier Series: An Alternative Representation r A problem of the expression contains both cos() and sin(). r Using Euler’s formula:

113 Implementing Wireless: From Hardware to Software

114 Making Sense of the Transform

115 Relating the Two Representations