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 weekend Any eedback on pace and coverage Recap: Fourier Series o Periodic Function A periodic unction g(t) on [a, a+t] can be decomposed as: g(t) = 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 on [0, ] g(t) = G[k] = G[k]e j2πk t k= 0 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: what i g(t) is not periodic Approach: Truncate g(t) beyond [-L/2, L/2] (i.e., set = 0) 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 [k] = L/2 g L (t)e j2π k L t dt G L [k] = Δ L/2 L Ĝ( k ) g L (t) = Ĝ( k )e j2π k t Δ k= Fourier Transorm Ĝ( )e j2π t d Ĝ( ) = g(t)e j2π t dt (t) = Ĝ( )e j2π t d 6 Page
Recap: Discrete Domain Analysis FFT Analysis vs Sample Rate FFT: Transorming a sequence o numbers x 0, x,, x N- to another sequence o numbers X 0, X,, X N- Nt=Nsample X X 2 X Nt/2 Hz 2Hz Nt/2 Hz Note G[k] = g(t)e j2πkt dt g( N n )e j2πk N n 0 N Hence X k is the coeicient or k Hz harmonics i the FFT N samples are or one sec n=0 N 7 N sample 2N sample N t N t The req. analysis resolution: N sample N t N sample 2 8 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 9 0 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 2 Page 2
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 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 j20t spectrum o complex signal x(t)e -j20t digital signal 0 t 3 4 Frequencies are Assigned and Regulated Spectrum and Bandwidth: Shannon Channel Capacity Cellular Phones Cordless Phones Wireless LANs Others Europe USA Japan GSM 450-457, 479 - AMPS, TDMA, CDMA PDC 486/460-467,489-824 - 849, 80-826, 496, 890-95/935-869 - 894 940-956, 960, TDMA, CDMA, GSM 429-465, 70-785/805-850 - 90, 477-53 880 930-990 UMTS (FDD) 920-980, 20-290 UMTS (TDD) 900-920, 2020-2025 CT+ 885-887, 930 - PACS 850-90, 930 - PHS 932 990 895-98 CT2 PACS - UB 90-930 JCT 864-868 254-380 DECT 880-900 IEEE 802. 902-928 IEEE 802. 2400-2483 I EEE 802. 247-2497 HIPERLAN 2 2400-2483 550-5250 550-5350, 5470-550 - 5350, 5725-5825 5725 RF - Control RF - Control RF - Control 27, 28, 48, 433, 35, 95 426, 868 868 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 5 6 Frequencies or Communications Why Not Send Digital Signal in Wireless Communications? twisted pair Mm 300 Hz 0 km 30 khz coax cable 00 m 3 MHz m 300 MHz 0 mm 30 GHz 00 µm 3 THz optical transmission µm 300 THz VLF LF MF HF VHF UHF SHF EHF inrared visible light UV voice 20-20KHz 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 3x0 8 m/s, requency 7 At 3 KHz, λ = c = 3 08 3 0 3 =00km Antenna too large! Use modulation to transer to higher requency 8 Page 3
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(2π0000t) 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 9 20 Types o Modulation Analog modulation Amplitude modulation (AM) Frequency modulation (FM) Double and signal sideband: DSB, SSB Outline Recap Basic concepts o modulation Digital modulation Amplitude shit keying (ASK) Frequency shit keying: FSK Phase shit keying: BPSK, QPSK, MSK Quadrature amplitude modulation (QAM) 2 22 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 (300K, sample 800K) Multiply Two Scopes Frequency Domain domain X() X AM () sideba FFT Sink - m m - c c 23 24 Page 4
Example AM Frequency Domain Problem: How to Demodulate AM Signal? Note: There is always the negative req. in the req. domain. 25 X() - m m sideba X AM () - c c 26 Outline Outline Recap Basic concepts o modulation Amplitude demodulation Admin and recap Basic concepts o modulation Amplitude demodulation requency shiting 27 28 Design Option Design Option (Ater Step ) Step : Multiply signal by e -jct Implication: Need to do complex multiple multiplication -2 c 29 30 Page 5
Design Option (Step 2) Apply a Low Pass Filter to remove the extra requencies at -2 c Design Option (Step Analysis) How many complex multiplications do we need or Step (Multiply by e -jct )? -2 c 3 32 Design Option 2: Quadrature Sampling Quadrature Sampling: Upper Path (cos) 33 34 Quadrature Sampling: Upper Path (cos) Quadrature Sampling: Upper Path (cos) 35 36 Page 6
Quadrature Sampling: Lower Path (sin) Quadrature Sampling: Lower Path (sin) 37 38 Quadrature Sampling: Lower Path (sin) Quarature Sampling: Putting Together 39 40 Exercise: SpyWork Setting: a scanner scans 28KHz blocks o AM radio and saves each block to a ile (see am_rcv.py). SpyWork: Scan the block in a saved ile to ind radio stations and tune to each station (each AM station has 0 KHz) 4 Page 7