outline wireless phy: modulation and demodulation -...

Wireless PHY: Modulation and Demodulation

Y. Richard Yang

09/6/2012

2

Outline

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

❍  frequency shifting

3

Admin

❒  First assignment to be posted by this weekend

❒ Any feedback on pace and coverage

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Recap: Fourier Series of Periodic Function

❒ A periodic function g(t) on [a, a+T] can be decomposed as:

❒  For periodic function on [0, 1]

g(t) = G[k]ej2π k

Tt

k=−∞

∞

∑

G[k]= 1T

g(t)e− j2π k

Ttdt

a

a+T∫

g(t) = G[k]e j2πk tk=−∞

∞

∑

G[k]= g(t)e− j2πk t dt0

1∫

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Fourier Transform

❒  For those who are curious, we do not need it formally

❒  Problem: what if g(t) is not periodic ❒ Approach:

❍ Truncate g(t) beyond [-L/2, L/2] (i.e., set = 0) and then repeat to define gL(t)

gL (t) = GL[k]ej2π k

Lt

k=−∞

∞

∑ GL[k]= 1L

gL (t)e− j2π k

Ltdt

−L/2

L/2∫

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Fourier Transform

GL[k]= 1L

gL (t)e− j2π k

Ltdt

−L/2

L/2∫ GL[k]= Δf G( fk )

gL (t) = G( fk )ej2π fk t

k=−∞

∞

∑ Δf

fk =kL G( fk ) = gL (t)e− j2π fk t dt

−∞

∞

∫Define Δf = 1L

GL[k]= 1L

gL (t)e− j2π k

Ltdt

−L/2

L/2∫

≈ G( f )e j2π ft df−∞

∞

∫

Fourier Transform

G( f ) = g(t)e− j2π f t dt−∞

∞

∫ f (t) = G( f )e j2π ft df−∞

∞

∫

Recap: Discrete Domain Analysis

❒  FFT: Transforming a sequence of numbers x0, x1, …, xN-1 to another sequence of numbers X0, X1, …, XN-1

❒ Note

❒ Hence Xk is the coefficient for k Hz harmonics if the FFT N samples are for one sec

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G[k]= g(t)e− j2πkt0

1

∫ dt ≈ g( nN )e− j2πk nN

n=0

N−1

∑ 1N

8

FFT Analysis vs Sample Rate

X1

Nfft=Nsample

X2 XNfft/2

1Hz 2Hz Nfft/2 Hz

Nsample

N fft

2Nsample

N fft

Nsample

2

The freq. analysis resolution:

Nsample

N fft

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Frequency Domain Analysis Examples Using GNURadio

❒  spectrum_2sin_plus ❍ Audio ❍  FFT Sink ❍ Scope Sink ❍ Noise

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❒  spectrum_1sin_rawfft ❍ Raw FFT

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❒  spectrum_2sin_multiply_complex ❍ Multiplication of a sine first by

•  a real sine and then by •  a complex sine

to observe spectrum

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Takeaway from the Example

❒ Advantages of I/Q representation

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I/Q Multiplication Also Called Quadrature Mixing

spectrum of complex signal x(t)

spectrum of complex signal x(t)ej2f0t

spectrum of complex signal x(t)e-j2f0t

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Basic Question: Why Not Send Digital Signal in Wireless Communications?

❒ Signals at undesirable frequencies ❍  suppose digital frame repeat every T seconds,

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, …

1

0 digital signal

t

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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

UMTS (TDD) 1900 -

1920, 2020 - 2025

AMPS , TDMA , CDMA

824 - 849,

869 - 894

TDMA , CDMA , GSM

1850 - 1910,

1930 - 1990

PDC

810 - 826,

940 - 956,

1429 - 1465,

1477 - 1513

Cordless

Phones

CT1+ 885 - 887, 930 -

932

CT2

864 - 868

DECT

1880 - 1900

PACS 1850 - 1910, 1930 -

1990

PACS - UB 1910 - 1930

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

2400 - 2483

5150 - 5350, 5725 - 5825

IEEE 802.11

2471 - 2497

5150 - 5250

Others RF - Control

27, 128, 418, 433,

868

RF - Control

315, 915

RF - Control

426, 868

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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

)1(log2 NSW +

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Frequencies for Communications

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: λ = c/f

wave length λ, speed of light c ≅ 3x108m/s, frequency f

1 Mm 300 Hz

10 km 30 kHz

100 m 3 MHz

1 m 300 MHz

10 mm 30 GHz

100 µm 3 THz

1 µm 300 THz

visible light VLF LF MF HF VHF UHF SHF EHF infrared UV

optical transmission coax cable twisted pair

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Why Not Send Digital Signal in Wireless Communications?

voice

Transmitter

20-20KHz

Antenna: size ~ wavelength

At 3 KHz, λ =cf

=3×108

3×103=100km

Antenna too large! Use modulation to transfer

to higher frequency

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Outline

❒  Recap ❒  Frequency domain examples ❒  Basic concepts of modulation

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❒  The information source ❍  Typically a low frequency signal ❍  Referred to as baseband signal

q  Carrier q  A higher frequency sinusoid q  Example cos(2π10000t)

q  Modulated signal q  Some parameter of the carrier (amplitude, frequency, phase)

is varied in accordance with the baseband signal

Basic Concepts of Modulation Basic Concept of Modulation

  The information source   Typically a low frequency signal   Referred to as the “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

x(t)

t

X(f)

f

Modulator baseband

carrier Modulated signal

7/8/10 5 Flynn/Katz

Basic Concept of Modulation





x(t)

t

X(f)

f

Modulator baseband


7/8/10 5 Flynn/Katz






x(t)

t

X(f)

f

Modulator baseband


7/8/10 5 Flynn/Katz






x(t)

t

X(f)

f

Modulator baseband


7/8/10 5 Flynn/Katz

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Types of Modulation

❒ Analog 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)

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Outline

❒  Recap ❒  Frequency domain examples ❒  Basic concepts of modulation ❒ Amplitude modulation

Amplitude Modulation (AM)   Block Diagram

  Time Domain

  Frequency Domain

m x +

Ac cos �ct

x(t) xAM(t)=Ac [1+mx(t)]cos �ct

X(f)

f -fm fm

XAM(f)

f -fc fc

Signal information is contained in the sidebands

7/8/10 7 Flynn/Katz 23

Example: Amplitude Modulation (AM)

❒  Block diagram

❒ Time domain

❒  Frequency domain


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz 24

Example: am_modulation Example

❒ Setting ❍ Audio source (sample 32K) ❍ Signal source (300K, sample 800K) ❍ Multiply

❒ Two Scopes

❒  FFT Sink

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Example AM Frequency Domain

Note: There is always the negative freq. in the freq. domain. 26

Problem: How to Demodulate AM Signal?


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz

27

Outline

❒  Recap ❒  Frequency domain examples ❒  Basic concepts of modulation ❒ Amplitude modulation ❒ Amplitude demodulation

❍ 

28

Outline

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

❍  frequency shifting

29

Design Option 1

❒ Step 1: Multiply signal by e-jfct

❍  Implication: Need to do complex multiple multiplication

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Design Option 1 (After Step 1)

-2fc

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Design Option 1 (Step 2)

❒ Apply a Low Pass Filter to remove the extra frequencies at -2fc

-2fc

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Design Option 1 (Step 1 Analysis)

❒ How many complex multiplications do we need for Step 1 (Multiply by e-jfct)?

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Design Option 2: Quadrature Sampling

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Quadrature Sampling: Upper Path (cos)

35


36


37

Quadrature Sampling: Lower Path (sin)

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Quarature Sampling: Putting Together

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Exercise: SpyWork

❒  Setting: a scanner scans 128KHz blocks of AM radio and saves 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)

outline wireless phy: modulation and demodulation -...

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