Wireless PHY: Frequency-Domain Analysis Y. Richard Yang 09/4/2012
Outline Recap Frequency domain analysis Introduction to modulation
Recap: Wireless and Mobile Computing Driven by infrastructure and device technology global infrastructures device miniaturization and capabilities software development platforms Challenges: wireless channel: unreliable, open access mobility portability changing environment heterogeneity
Overview of Wireless Physical Layer source coding bit stream channel coding analog signal sender modulation receiver bit stream source decoding channel decoding demodulation
Wireless Physical Layer Example: Wireless: 802.11
Our Objective Understand key issues and techniques in the design of wireless physical layer Key approach: identify the problem and then the solution(s).
Outline Recap Frequency domain analysis Modulation Characteristic of wireless channels and potential impacts
Fourier Series: Decomposing into a Collection of Harmonics A periodic real function g(t) on [-π, π] can be decomposed as a set of harmonics (cos, sin): Time domain 1 1 http://en.wikipedia.org/wiki/Fourier_series t t decomposition periodical signal set bk = 0
Fourier Analysis http://en.wikipedia.org/wiki/Fourier_series
Fourier Analysis http://en.wikipedia.org/wiki/Fourier_series
Fourier Analysis: Example http://en.wikipedia.org/wiki/Fourier_series http://en.wikipedia.org/wiki/File:Periodic_identity_function.gif
Fourier Series: An Alternative Representation A problem of the expression It contains both cos() and sin(), and hence is somehow complex to manipulate. http://en.wikipedia.org/wiki/Fourier_series
Fourier Series: Using Euler’s formula Applying Euler’s formula We have http://en.wikipedia.org/wiki/Fourier_series
Fourier Series: Using Euler’s formula http://en.wikipedia.org/wiki/Fourier_series
Making Sense of Complex Numbers http://en.wikipedia.org/wiki/Fourier_series What is the effect of multiplying c by ejπ/2? What is the effect of multiplying c by j?
Making Sense of Complex Numbers http://en.wikipedia.org/wiki/Fourier_series
Making Sense of Complex Numbers: Conjugate http://en.wikipedia.org/wiki/Fourier_series
Summary of Progress: Fourier Analysis of Real Function on [-π, π] http://en.wikipedia.org/wiki/Fourier_series
Defining Decomposition in a General Interval A periodic function g(t) on [a, a+T] can be decomposed as: http://en.wikipedia.org/wiki/Fourier_series
Defining Decomsition on [0, 1] http://en.wikipedia.org/wiki/Fourier_series
ej2πft Making Sense of ej2πft http://en.wikipedia.org/wiki/Fourier_series
Making Sense of ej2πft G[f]e-j2πft ej2πft ϕ=2πft ϕ=-2πft e-j2πft http://en.wikipedia.org/wiki/Fourier_series
Two Domain Representations See examples: spectrum_2in.m Two representations: time domain; frequency domain Knowing one can recover the other
Example: Frequency Analysis of sine and cosine See examples: spectrum_2in.m
Example: Frequency Analysis of sine and cosine
Example: Frequency Domain’s View of Euler’s Formula
From Integral to Computation http://en.wikipedia.org/wiki/Fourier_series
Discrete Domain Analysis Transforming a sequence of numbers x0, x1, …, xN-1 to another sequence of numbers X0, X1, …, XN-1 Inverse DFFT
Frequency Analysis Examples Using GNURadio spectrum_2sin_plus FFT Scope spectrum_1sin_rawfft Raw FFT spectrum_2sin_multiply_complex Multiplication of 2 sines Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Quadrature Mixing spectrum of complex signal x(t) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns. spectrum of complex signal x(t) spectrum of complex signal x(t)ej2f0t spectrum of complex signal x(t)e-j2f0t
Signals at undesirable frequencies Basic Question: Why Not Send Digital Signal in Wireless Communications? Signals at undesirable frequencies suppose digital frame length T, then signal decomposes into frequencies at 1/T, 2/T, 3/T, … let T = 1 ms, generates radio waves at frequencies of 1 KHz, 2 KHz, 3 KHz, … $22 billion: Amount operators paid the U.S. government over the past ten years for spectrum. Source Burton Group. 1 digital signal t
Frequencies are Assigned and Regulated Europe USA Japan Cellular Phones GSM 450 - 457, 479 486/460 467,489 496, 890 915/935 960, 1710 1785/1805 1880 UMTS (FDD) 1920 1980, 2110 2190 (TDD) 1900 1920, 2020 2025 AMPS , TDMA CDMA 824 849, 869 894 1850 1910, 1930 1990 PDC 810 826, 940 956, 1429 1465, 1477 1513 Cordless CT1+ 885 887, 930 932 CT2 864 868 DECT 1900 PACS 1910, 1930 UB 1910 PHS 1895 1918 JCT 254 380 Wireless LANs IEEE 802.11 2400 2483 HIPERLAN 2 5150 5350, 5470 5725 902 928 I EEE 802.11 5350, 5725 5825 2471 2497 5250 Others RF Control 27, 128, 418, 433, 315, 915 426, 868
Spectrum and Bandwidth: Shannon Channel Capacity 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
Frequencies for Communications twisted pair coax cable optical transmission 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 VLF LF MF HF VHF UHF SHF EHF infrared visible light UV VLF = Very Low Frequency UHF = 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 3x108m/s, frequency f
Why Not Send Digital Signal in Wireless Communications? Transmitter voice Antenna: size ~ wavelength 20-20KHz At 3 KHz, $22 billion: Amount operators paid the U.S. government over the past ten years for spectrum. Source Burton Group. Antenna too large! Use modulation to transfer to higher frequency
Basic Concept of Modulation The information source Typically a low frequency signal 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
Types of Modulation Analog modulation Digital modulation Amplitude modulation (AM) Frequency modulation (FM) Double and signal sideband: DSB, SSB Digital modulation Amplitude shift keying (ASK) Frequency shift keying: FSK Phase shift keying: BPSK, QPSK, MSK Quadrature amplitude modulation (QAM) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Example: Amplitude Modulation (AM) Block diagram Time domain Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns. Frequency domain
Problem: How to Demodulate AM Signal? Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Quadrature Sampling (Software Radio Foundation) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Quadrature Sampling: Upper Path (cos) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Quadrature Sampling: Upper Path (cos) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Quadrature Sampling: Upper Path (cos) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Quadrature Sampling: Lower Path (sin) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Quadrature Sampling: Lower Path (sin) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Quadrature Sampling: Lower Path (sin) Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
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.
Software AM Radio Receiver Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Modulation Modulation of digital signals known as Shift Keying Amplitude Shift Keying (ASK): Frequency Shift Keying (FSK): 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
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(2ft), 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 d1d2
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 ?
Fourier Series: An Alternative Representation A problem of the expression contains both cos() and sin(). Using Euler’s formula: http://en.wikipedia.org/wiki/Fourier_series
Implementing Wireless: From Hardware to Software
Making Sense of the Transform http://en.wikipedia.org/wiki/Fourier_series
Relating the Two Representations http://en.wikipedia.org/wiki/Fourier_series