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

Outline Admin and recap Frequency domain examples Basic concepts of modulation Amplitude modulation Amplitude demodulation Digital modulation

Admin First assignment to be posted by this weekend

Recap: Why Not Send Digital Signal in Wireless Communications? Frequency assignment/allocation Match to antenna characteristics

Recap: Modulation Basic concepts the information source (baseband) carrier modulated signal

Recap: Amplitude Modulation (AM) Block diagram Time domain Frequency domain

Recap: Demod of AM Design option 1: multiply modulated signal by e-jfct Design option 2: quadrature sampling

Quarature Sampling: Putting Together Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

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

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

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

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

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

Implementing a 3-rd Order FIR Filter An array of size N+1 for h compute y[n] xn-3 xn-2 xn-1 xn xn+1 * * * * h3 h2 h1 h0

Implementing a 3-rd Order FIR Filter An array of size N+1 for h compute y[n+1] xn-3 xn-2 xn-1 xn xn+1 * * * * h3 h2 h1 h0

Key Question: How to Determine h? 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 Remember that we consider x as samples of time domain function g(t) on [0, 1] and (repeat in other intervals) 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 g(t) time h(t)

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

Fourier Series of y=g*h

In English, you can integrate Fubini’s Theorem In English, you can integrate first along y and then along x first along x and then along y at (x, y) grid They give the same result See http://en.wikipedia.org/wiki/Fubini's_theorem

Fourier Series of y=g*h

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

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

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

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

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

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

LPF Design Example #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

Outline Recap Amplitude demodulation Digital modulation frequency shifting low pass filter Digital modulation

Modulation Modulation of digital signals also known as Shift Keying Amplitude Shift Keying (ASK): vary carrier amp. according to bit value Frequency Shift Keying (FSK) pick carrier freq according to bit value Phase Shift Keying (PSK): 1 t

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

Phase Shift Keying: QPSK 11 10 00 01 Q I A t QPSK (Quadrature Phase Shift Keying): 2 bits coded as one symbol symbol determines shift of sine wave often also transmission of relative, not absolute phase shift: DQPSK - Differential QPSK

Quadrature Amplitude Modulation Quadrature Amplitude Modulation (QAM): combines amplitude and phase modulation It is possible to code n bits using one symbol 2n discrete levels 0000 0001 0011 1000 Q I 0010 φ a Example: 16-QAM (4 bits = 1 symbol) Symbols 0011 and 0001 have the same phase φ, but different amplitude a. 0000 and 1000 have same amplitude but different phase

Exercise Suppose fc = 1 GHz (fc1 = 1 GHz, fc0 = 900 GHz for FSK) Bit rate is 1 Mbps Encode one bit at a time Bit seq: 1 0 0 1 0 1 Q: How does the wave look like for? 11 10 00 01 Q I A t

Generic Representation of Digital Keying (Modulation) Sender sends symbols one-by-one Each symbol has a corresponding signaling function g1(t), g2(t), …, gM(t), each has a duration of symbol time T Exercise: What is the setting for BPSK? for QPSK?

Checking Relationship Among gi() BPSK 1: g1(t) = -sin(2πfct) t in [0, T] 0: g0(t) = sin(2πfct) t in [0, T] Are the two signaling functions independent? Hint: think of the samples forming a vector, if it helps, in linear algebra Ans: No. g1(t) = -g0(t)

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

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

Example: Matched Filter Detection Basic idea consider each gm[0,T] as a point (with coordinates) in a space compute the coordinate of the received signal s[0,T] check the distance between gm[0,T] and the received signal s[0,T] pick m* that gives the lowest distance value

Computing Coordinates Pick orthogonal bases {f1(t), f2(t), …, fN(t)} for {g1(t), g2(t), …, gM(t)} Compute the coordinate of gm[0,T] as cm = [cm1, cm2, …, cmN], where Compute the coordinate of the received signal r[0,T] as r = [r1, r2, …, rN] Compute the distance between r and cm every cm and pick m* that gives the lowest distance value

Example: Matched Filter => Correlation Detector received signal

Spectral Density of BPSK Spectral Density = bit rate ------------------- width of spectrum used b fc : freq. of carrier Rb =Bb = 1/Tb b fc

Phase Shift Keying: Comparison fc: carrier freq. Rb: freq. of data 10dB = 10; 20dB =100 BPSK A QPSK t 11 10 00 01

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

Signal Propagation

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

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

Real Antennas Q: Assume frequency 1 Ghz,  = ? Real antennas are not isotropic radiators 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) Not good for spectrum usage/sharing The wavelength can be extremely large to build portal devices e.g., T = 1 us -> f=1/T = 1MHz -> wavelength = 3x108/106 = 300m

Figure for Thought: Real Measurements

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

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

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

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

JTC Indoor Model for PCS: Path Loss Shadowing path loss follows a log-normal distribution (i.e. L is normal distribution) with mean: 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 Lf : a floor penetration loss factor (dB) n: the number of floors between base station and mobile terminal

JTC Model at 1.8 GHz

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

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

Multipath Effect (A Simple Example) Assume transmitter sends out signal cos(2 fc t) d1 d2 phase difference:

Multipath Effect (A Simple Example) Suppose at d1-d2 the two waves totally destruct. (what does it mean?) Q: where are places the two waves construct?

Option 1: Change Location If receiver moves to the right by /4: d1’ = d1 + /4; d2’ = d2 - /4; -> By moving a quarter of wavelength, destructive turns into constructive. Assume f = 1G, how far do we move?

Option 2: Change Frequency

Multipath Delay Spread RMS: root-mean-square

Multipath Effect (moving receiver) example d d1 d2 Suppose d1=r0+vt d2=2d-r0-vt d1d2

Derivation See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)

Waveform v = 65 miles/h, fc = 1 GHz: fc v/c = 109 * 30 / 3x108 = 100 Hz 10 ms deep fade Q: How far does a car drive in ½ of a cycle?

Multipath with Mobility

Effect of Small-Scale Fading no small-scale fading

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

JTC Model: Delay Spread Residential Buildings

Multipath Can Cause ISI Dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI) Assume 300 meters delay spread, the arrival time difference is 300/3x108 = 1 ns if symbol rate > 1 Ms/sec, we will have serious ISI In practice, fractional ISI can already substantially increase loss rate signal at sender LOS pulse multipath pulses signal at receiver LOS: Line Of Sight

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

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

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 use fade margin—increase power or reduce distance bit/packet error rate at deep fade diversity equalization; spread-spectrum; OFDM; directional antenna ISI

Backup Slides

Received Signal d2 d1 receiver

Multipath Fading with Mobility: A Simple Two-path Example r(t) = r0 + v t, assume transmitter sends out signal cos(2 fc t) r0 More detail see page 16 Eqn. (2.13): http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter2.pdf

Received Waveform v = 65 miles/h, fc = 1 GHz: 10 ms deep fade v = 65 miles/h, fc = 1 GHz: fc v/c = 109 * 30 / 3x108 = 100 Hz Why is fast multipath fading bad?

Small-Scale Fading

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

RMS: root-mean-square Delay Spread RMS: root-mean-square

Multipath Can Cause ISI dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI) Assume 300 meters delay spread, the arrival time difference is 300/3x108 = 1 ms if symbol rate > 1 Ms/sec, we will have serious ISI In practice, fractional ISI can already substantially increase loss rate signal at sender LOS pulse multipath pulses signal at receiver LOS: Line Of Sight

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

Dipole: Radiation Pattern of a Dipole http://www.tpub.com/content/neets/14182/index.htm http://en.wikipedia.org/wiki/Dipole_antenna

Free Space Signal Propagation 1 t at distance d ?