Outline. Wireless PHY: Modulation and Demodulation. Admin. Page 1. G[k] = 1 T. g(t)e j2πk t dt. G[k] = = k L. ) = g L (t)e j2π f k t dt.

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1 Outline Wireless PHY: Modulation and Demodulation Y. Richard Yang Admin and recap Basic concepts o modulation Amplitude modulation Amplitude demodulation requency shiting 9/6/22 2 Admin First assignment to be posted by this weekend Any eedback on pace and coverage Recap: Fourier Series o Periodic Function A periodic unction g(t) with period T on [a, a+t] can be decomposed as: G[k]e j2π k T t k= G[k] = T a a+t g(t)e j2π k T t dt 3 For periodic unction with period on [, ] G[k] = G[k]e j2πk t k= g(t)e j2πk t dt 4 Fourier Transorm Fourier Transorm G L [k] = L L/2 L/2 g L (t)e j2π k L t dt For those who are curious, we do not need it ormally Deine k = k L Δ = L Ĝ( k ) = g L (t)e j2π k t dt Problem: Fourier series or periodic unction g(t), what i g(t) is not periodical? G L [k] = L/2 g L (t)e j2π k L t dt G L [k] = Δ L/2 L Ĝ( k ) Approach: Truncate g(t) beyond [-L/2, L/2] (i.e., set = ) and then repeat to deine g L (t) g L (t) = G L [k]e j2π k L t G L [k] = L/2 g L (t)e j2π k L t dt L/2 k= L 5 g L (t) = Ĝ( k )e j2π k t Δ k= Ĝ( )e j2π t d Let L grow to ininity, we derive Fourier Transorm: Ĝ( ) = g(t)e j2π t dt Ĝ( )e j2π t d 6 Page

2 Fourier Series vs Fourier Transorm Fourier series For periodical unctions, e.g., [, ] Fourier transorm For non periodical unctions Recap: Discrete Domain Analysis FFT: Transorming a sequence o numbers x, x,, x N- to another sequence o numbers X, X,, X N- G[k]e j2πk t k= G[k] = g(t)e j2πk t dt Ĝ( ) = g(t)e j2π t dt Ĝ( )e j2π t d Note G[k] = g(t)e j2πkt dt g( N n )e j2πk N n N n= N Recap: Discrete Domain Analysis FFT Analysis vs Sample Rate FFT: Transorming a sequence o numbers x, x,, x N- to another sequence o numbers X, X,, X N- Nt=Nsample X X 2 X Nt/2 Hz 2Hz Nt/2 Hz Interpretation: consider x, x,, x N- as sampled values o a periodical unction deined on [, ] X k is the coeicient (scaled by N) or k Hz harmonics i the FFT N samples span one sec N sample N t 2N sample N t The req. analysis resolution: N sample N sample 2 9 N t Frequency Domain Analysis Examples Using GNURadio spectrum_2sin_plus Audio FFT Sink Scope Sink Noise Frequency Domain Analysis Examples Using GNURadio spectrum_sin_rawt Raw FFT 2 Page 2

Frequency Domain Analysis Examples Using GNURadio spectrum_2sin_multiply_complex Multiplication o a sine irst by a real sine and then by a complex sine to observe spectrum Takeaway rom the Example

3 Frequency Domain Analysis Examples Using GNURadio spectrum_2sin_multiply_complex Multiplication o a sine irst by a real sine and then by a complex sine to observe spectrum Takeaway rom the Example Advantages o I/Q representation 3 4 I/Q Multiplication Also Called Quadrature Mixing Basic Question: Why Not Send Digital Signal in Wireless Communications? Signals at undesirable requencies suppose digital rame repeat every T seconds, then according to Fourier series decomposition, signal decomposes into requencies at /T, 2/T, 3/T, let T = ms, generates radio waves at requencies o KHz, 2 KHz, 3 KHz, spectrum o complex signal x(t) spectrum o complex signal x(t)e j2t spectrum o complex signal x(t)e -j2t digital signal t 5 6 Frequencies are Assigned and Regulated Spectrum and Bandwidth: Shannon Channel Capacity Cellular Phones Cordless Phones Wireless LANs Others Europe USA Japan GSM , AMPS, TDMA, CDMA PDC 486/46-467, , 8-826, 496, 89-95/ , 96, TDMA, CDMA, GSM , 7-785/ , UMTS (FDD) 92-98, 2-29 UMTS (TDD) 9-92, CT , 93 - PACS 85-9, 93 - PHS CT2 PACS - UB 9-93 JCT DECT 88-9 IEEE IEEE I EEE HIPERLAN , , RF - Control RF - Control RF - Control 27, 28, 48, 433, 35, , The maximum number o bits that can be transmitted per second by a physical channel is: S W log 2 ( + N ) where W is the requency range o the channel, and S/N is the signal noise ratio, assuming Gaussian noise 7 8 Page 3

wavelength 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

4 Frequencies or Communications Why Not Send Digital Signal in Wireless Communications? twisted pair Mm 3 Hz km 3 khz coax cable m 3 MHz m 3 MHz mm 3 GHz µm 3 THz optical transmission µm 3 THz VLF LF MF HF VHF UHF SHF EHF inrared visible light UV voice 2-2KHz Transmitter Antenna: size ~ wavelength 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/ wave length λ, speed o light c 3x 8 m/s, requency 9 At 3 KHz, λ = c = =km Antenna too large! Use modulation to transer to higher requency 2 Outline Basic Concepts o Modulation Recap Basic concepts o modulation The inormation source Typically a low requency signal Reerred to to as as the baseband baseba signal x(t) er q Carrier q A higher requency sinusoid q Example cos(2πt) t baseband carrier X() Modulator Modulated signal q Modulated signal q Some parameter o the carrier (amplitude, requency, phase) is varied in accordance with the baseband signal 2 22 Types o Modulation Analog modulation Amplitude modulation (AM) Frequency modulation (FM) Double and signal sideband: DSB, SSB Outline Recap Basic concepts o modulation Amplitude modulation Digital modulation Amplitude shit keying (ASK) Frequency shit keying: FSK Phase shit keying: BPSK, QPSK, MSK Quadrature amplitude modulation (QAM) Page 4

Example: Amplitude Modulation (AM) Example: am_modulation Example Block diagram x(t) m x + A c cos c t Time me domain Domain x AM (t)=a c [+mx(t)]cos c t Setting Audio source (sample 32K) Signal

5 Example: Amplitude Modulation (AM) Example: am_modulation Example Block diagram x(t) m x + A c cos c t Time me domain Domain x AM (t)=a c [+mx(t)]cos c t Setting Audio source (sample 32K) Signal source (3K, sample 8K) Multiply Two Scopes Frequency Domain domain X() X AM () sideba FFT Sink - m m - c c Example AM Frequency Domain Problem: How to Demodulate AM Signal? Note: There is always the negative req. in the req. domain. 27 X() - m m sideba X AM () - c c 28 Outline Admin and recap Basic concepts o modulation Amplitude modulation Amplitude demodulation requency shiting Design Option Step : Multiply signal by e -j2πct Implication: Need to do complex multiple multiplication 29 3 Page 5

6 Design Option (Ater Step ) Design Option (Step 2) Apply a Low Pass Filter to remove the extra requencies at -2 c -2 c -2 c 3 32 Design Option (Step Analysis) Design Option 2: Quadrature Sampling How many complex multiplications do we need or Step (Multiply by e -j2πct )? Quadrature Sampling: Upper Path (cos) Quadrature Sampling: Upper Path (cos) Page 6

Quadrature Sampling: Upper Path (cos) Quadrature Sampling: Lower Path (sin) 37 38 Quadrature Sampling: Lower Path (sin) Quadrature Sampling: Lower Path (sin) 39 4 Exercise: SpyWork Quarature

7 Quadrature Sampling: Upper Path (cos) Quadrature Sampling: Lower Path (sin) Quadrature Sampling: Lower Path (sin) Quadrature Sampling: Lower Path (sin) 39 4 Exercise: SpyWork Quarature Sampling: Putting Together Setting: a scanner scans 28KHz blocks o AM radio and saves each block to a ile. SpyWork: Scan the block in a saved ile to ind radio stations and tune to each station (each AM station has KHz) 4 42 Page 7

Outline. Wireless PHY: Modulation and Demodulation. Admin. Page 1. g(t)e j2πk t dt. G[k] = 1 T. G[k] = = k L. ) = g L (t)e j2π f k t dt.

Outline. Wireless PHY: Modulation and Demodulation. Admin. Page 1. g(t)e j2πk t dt. G[k] = 1 T. G[k] = = k L. ) = g L (t)e j2π f k t dt. Outline Wireless PHY: Modulation and Demodulation Y. Richard Yang Admin and recap Basic concepts o modulation Amplitude demodulation requency shiting 09/6/202 2 Admin First assignment to be posted by this