Wireless Communication

Transcription

1 Wireless Communication Lecture 3: PHY and OFDM Instructor: Kate Ching-Ju Lin ( 林靖茹 )

2 Reference 1. OFDM Tutorial online: 2. OFDM Wireless LWNs: A Theoretical and Practical Guide By John Terry, Juha Heiskala 3. Next Generation Wireless LANs: n and ac By Eldad Perahia 2

3 Agenda Packet Detection OFDM (Orthogonal Frequency Division Modulation) Synchronization 3

4 What is Packet Detection Detect where is the starting time of a packet It might be easy to detect visually, but how can a device automatically find it? Simplest way: find the energy burst using a threshold Difficulty: hard to determine a good threshold 4

5 Packet Detection Packet Packet Packet A n B n Power ratio M n =A n /B n threshold Double sliding window packet detection Optimal threshold depends on the receiving power 5

6 Packet Detection in Each packet starts with a preamble First part of the preamble is exactly the same with the second part preamble header and data Use cross-correlation to detect the preamble Use double sliding window to calculate the auto-correlation of the signals received in two windows Leverage the key properties: 1) noise is uncorrelated with the preamble, and 2) data payload is also uncorrelated with the preamble 6

7 Packet Detection in preamble preamble preamble preamble preamble preamble preamble preamble A n B n Correlation over time threshold Noise is uncorrelated with noise Noise is uncorrelated with preamble Get a peak exactly when the double windows receives the entire preamble Data is again uncorrelated with noise 7

8 Agenda Packet Detection OFDM (Orthogonal Frequency Division Modulation) Synchronization 8

9 Narrow-Band Channel Model Signal over wireless channels y = hx + n h = α*exp 2jπfδ Rx is the channel between Tx and α: received amplitude, δ: propagation delay How to decode x? x = y/h + n How to learn h? Re-use the known preamble to learn h à since y = hp + n, we get h = y/p The procedure of finding H is called channel estimation 9

10 Why OFDM? Signal over wireless channels y = hx + n à Decoding: x = y/h Work only for narrow-band channels, but not for wide-band channels, e.g., 20 MHz for Channels of different narrow bands will be different! Capacity = BW * log(1+snr) 20MHz frequency 2.45GHz (Central frequency) 10

11 Basic Concept of OFDM Wide-band channel Multiple narrow-band channels Send a sample using the entire band Send samples concurrently using multiple orthogonal sub-channels 11

12 Why OFDM is Better? t t f f Wide-band OFDM: Narrow-band Multiple sub-channels (sub-carriers) carry samples sent at a lower rate Almost same bandwidth with wide-band channel Only some of the sub-channels are affected by interferers or multi-path effect 12

13 Importance of Orthogonality Why not just use FDM (frequency division multiplexing) Not orthogonal Leakage interference from adjacent sub-channels Individual sub-channel Need guard bands between adjacent frequency bands à extra overhead and lower utilization f Guard bands protect leakage interference guard band f 13

14 Difference between FDM and OFDM guard band Frequency division multiplexing f Don t need guard bands Orthogonal sub-carriers in OFDM f 14

15 Key to Achieve Orthogonality: FFT Fast Fourier Transform (FFT) Any waveform is the Sum of Sines Fourier s theorem: ANY waveform in the time domain can be represented by the weighted sum of sines ef1+ 0.5*ef2 ef1+ef2 a*ef1+b*ef2+c*ef3+ Frequencydomain How to generate a square wave? Timedomain

16 Primer of FFT/iFFT ifft: from frequency-domain signals to time-domain signals FFT: from time-domain signals to frequency-domain signals Frequency-domain signal: Amplitude of each freq. a, b, c, d, ifft time-domain signal How can we know the frequency-domain components (a, b, c, ) from this time-domain signal? amplitude c a b f1 f2 f3 FFT frequency

17 Primer of FFT/iFFT ifft: from frequency to time Use periodical waveforms to generate signals c ifft( a b )= amplitude f1 f2 f3 frequency FFT: from time to frequency Extract frequency components of any signal FFT( )= amplitude c a b f1 f2 f3 frequency

18 OFDM Transmitter and Receiver Transmitter Data in 0, 1, 1, 0, 0, 1, 1, 0, Data out amplitude c a b Modulation (BPSK, QAM, etc) Demodulation (BPSK, QAM, etc) f1 f2 f3 a b c Frequency-domain signal d a b c d freq ifft FFT D/A channel time-domain signal + noise A/D Receiver Represent information bits as the amplitudes of orthogonal subcarriers amplitude c a b f1 f2 f3 freq 18

19 OFDM Basic 1. Partition the wide band to multiple narrow subcarriers f 1, f 2, f 3,, f N 2. Represent information bits as the frequencydomain signal (amplitude of each sub-carrier) Example: if we want to send 1, -1, 1, 1, we let 1, -1, 1, 1 be the frequency-domain signals 3. Use ifft to convert the information to the timedomain sent over the air Example: Transmit 1*e f1 + (-1)*e f2 + 1*e f3 + 1*e f4 4. Rx uses FFT to extract information Example: [ ] = FFT(1*e f1 + (-1)*e f2 + 1*e f3 + 1*e f4 ) 19

20 Orthogonal Frequency Division Modulation * X[1] Data X[n] coded in frequency domain f f IFFT * X[2] * X[3] Transformation to time domain: each frequency is a sine wave in time, all added up t transmit receive t FFT f Decode each subcarrier separately X [N] = amplitude of each sub-carrier Time domain signal Frequency domain signal 20

21 Orthogonality of Sub-carriers Time-domain signals: x(t) Frequency-domain signals: X[k] IFFT Encode: frequency-domain samples à time-domain samples x(t) = 1 N N/2 1 X k= N/2 X[k]e j2 kt/n k-th subcarrier FFT Decode: time-domain samples à frequency-domain sample X[k] = N/2 1 X Orthogonality of any two bins : x(t)e 2j kt/n t= N/2 Orthogonal à inner product = 0 N/2 1 X k= N/2 e j2 kt/n e j2 pt/n =0, 8p 6= k 21

22 Orthogonality between Subcarriers Subcarrier frequencies (k/n, k=-n/2,, N/2-1) are chosen so that the subcarriers are orthogonal to each other No guard band is required Two signals are orthogonal if their inner product equals zero N/2 1 X e j2 kt/n e j2 pt/n = N/2 1 X e 2j (k p)t/n k= N/2 = N (k, p) = ( N if p = k 0 if p 6= k k= N/2 X[k]?X[p],k 6= p 22

23 Serial to Parallel Conversion Say we use BPSK and 4 sub-carriers to transmit a stream of samples 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1 Serial-to-parallel conversion of samples Frequency-domain signal c1 c2 c3 c4 symbol IFFT symbol symbol symbol symbol symbol Time-domain signal 0 2-2i i 2 0-2i i i i i i i i Send time-domain samples after parallel-to-serial conversion 0, 2-2i, 0, 2 + 2i, 2, 0-2i, 2, 0 + 2i, -2, 2, 2, 2, -2, 0-2i, -2, 0 + 2i, 0, -2-2i, 0, i, 0, i, 0, -2-2i, 23

24 t1-4 t5-8 t9-12 t13-16 t17-20 t21-24 f1 symbol symbol symbol symbol symbol symbol f2 f3 f4 24

25 t1-4 t5-8 t9-12 t13-16 t17-20 t21-24 f1 symbol symbol symbol symbol symbol symbol f2 f3 1. Send four samples simultaneously in each time-slot 2. but send the same four samples using four time slots f4 à same data rate Send the combined signal as the time-domain signal

26 Why OFDM? combat multipath fading 26

27 Multi-Path Effect y(t) = h(0)x(t) + h(1)x(t 1) + h(2)x(t 2) + = X 4 h(4)x(t 4)=h(t) x(t), Y (f) =H(f)X(f) time-domain convolution frequency-domain 27

28 Current symbol + delayed-version symbol à Signals are destructive in only certain frequencies 28

29 direct delay f1 f2 f3 Current symbol + delayed-version symbol à Signals are destructive in only certain frequencies 29

30 Frequency Selective Fading frequency frequency Frequency selective fading: Only some sub-carriers get affected Can be recovered by proper coding! 30

31 Inter Symbol Interference (ISI) The delayed version of a symbol overlaps with the adjacent symbol One simple solution to avoid this is to introduce a guard-band Guard band 31

32 Cyclic Prefix (CP) However, we don t know the delay spread exactly The hardware doesn t allow blank space because it needs to send out signals continuously Solution: Cyclic Prefix Make the symbol period longer by copying the tail of time-domain samples and glue them in the front CP Symbol i CP Symbol i+1 In , each symbol with 64 samples CP:data = 1:4 à CP: last 16 samples 32

33 Cyclic Prefix (CP) Because of the usage of FFT, the signal is periodic FFT( ) = exp(-2jπδ f )*FFT( ) delayed version original signal Delay in the time domain corresponds to phase shift in the frequency domain Can still obtain the correct signal in the frequency domain by compensating this rotation 33

34 Cyclic Prefix (CP) w/o multipath y(t) à FFT( ) ày[k] = H[k]X[k] w multipath original signal y(t) à FFT( original signal + delayed-version signal ) ày[k] = (H[k] + exp(-2jπδ k )H[k])X[k] = (H [k] +H 2 [k])x[k] = H [k]x[k] Lump the phase shift in H 34

35 Side Benefit of CP Allow the signal to be decoded even if the packet is detected not that accurately decodable undecodable The last sample you actually use for FFT FFT_OFFSET The point you think the first symbol ends Check the parameter FFT_OFFSET in the WARP code. Try to modify it! 35

36 OFDM Diagram Transmitter Modulation Insert S/P IFFT P/S CP D/A channel + noise De-mod remove P/S FFT S/P CP Receiver A/D 36

37 Unoccupied Subcarriers Edge sub-carriers are more vulnerable Frequency might be shifted due to noise or multi-path Leave them unused In , only 48 of 64 bins are occupied bins Is it really worth to use OFDM when it costs so many overheads (CP, unoccupied bins)? 37

38 Agenda Packet Detection OFDM (Orthogonal Frequency Division Modulation) Synchronization 38

39 OFDM Diagram Modulation Transmitter Insert S/P IFFT P/S CP 20MHz D/A baseband Oscillator passband 2.4GHz channel + noise De-mod remove P/S FFT S/P CP Receiver A/D 20MHz baseband Oscillator passband 2.4GHz 39

40 Overview Carrier Frequency Offset (CFO) f c tx f c rx (e.g., TX: GHz, RX: GHz) CFO: Δ f = f tx f rx Time-domain signals: y (t) = y(t) * exp(2jπδ f t) real Sample Frequency Offset (SFO) Sampling rates in Tx and Rx are slightly different (e.g., TX: MHz, RX: MHz) theoretical SFO : = T rx T tx T tx Error accumulates over time Phase rotates 2jπδkφ in the k-th subcarrier Freq.-domain signals: Y [k] = Y[k] * exp(2jπδkφ) constant 40

41 Overview Carrier Frequency Offset (CFO) Calibrate in time-domain y (t) = y(t) * exp(2jπδ f t) * exp(-2jπδ f t) How: Use the preamble Sample Frequency Offset (SFO) Calibrate in frequency-domain Y [k] = Y[k] * exp(2jπδkφ) * exp(-2jπδkφ) How: Use the pilot subcarriers 41

42 Carrier Frequency Offset (CFO) frequency f rx f tx Δ f The oscillators of Tx and Rx are not perfectly synchronized Carrier frequency offset (CFO) Δ f = f tx f rx Leading to inter-carrier interference (ICI) OFDM is sensitive to CFO 42

43 CFO Estimation Up/Down conversion at Tx/Rx Up-convert baseband signal s(t) to passband signal r(t) =s(t)e j2 ftxt h(t, ) Down-convert passband signal r(t) back to y n = r(nt s )e j2 f rxt = s(nt s )e j2 ftxt e j2 frxt h(nt s, ) = s(nt s )e j2 f nt s h(nt s, ) Error caused by CFO, accumulated with time nt s 43

44 CFO Correction in s n S n+n Symbol 1 Symbol 2 Reuse the preamble to calibrate CFO The first half part of the preamble is identical to the second half part s n = s n+n The two transmitted signals are identical: But, the received signals contain different errors y n =(s n h)e j2 y n+n =(s n h)e j2 f nt s à Additional phase rotation Δ f nt s f (n+n)t s à Additional phase rotation Δ f (n+n)t s Find Δ f by taking y n+n / y n 44

45 CFO Correction in y n yn+n =(s n h)e j2 f nt s (s n h)e j2 f (n+n)t s = e j2 f NT s (s n h) 2 To learn CFO Δ f, find the angle of (y n y* n+n )! \ X n y n y N+n ) f T s = 1 2 N \ = 2 f NT s X n! y n yn+n Calibrate the signals to remove phase rotation y n e j2 f nt s =(s n h)e j2 f nt s e j2 f nt s (s n h) Received signals calibration 45

46 Sampling Frequency Offset (SFO) DAC (Tx) ADC (Rx) DAC (at Tx) and ADC (at Rx) never have exactly the same sampling period (T tx T rx ) Tx and Rx may sample the signal at slightly different timing offset SFO : = T rx T tx T tx 46

47 Phase errors due to SFO Assuming no residual CFO, the k-th subcarrier in the received symbol i becomes Y i,n = H k X i,k e j2 k See proof in the next slide All subcarriers experience the same sampling offset, but applied on different frequencies k φ is a constant Each subcarrier is rotated by a constant phase shift 2 Lead to Inter Carrier interference (ICI), which causes loss of the orthogonality of the subcarriers 47

48 Proof of phase errors due to SFO Time-domain Up-convert: Down-convert: r(t) =s(t)e j2 f txt h(t, )+n(t) y i,n = r(t)e j2 f rxt t=(ins +N CP +n)t rx Frequency-domain FFT N CP : N FFT : N S = N FFT + N CP : =0.5+ in S + N CP N FFT : Residual CFO SFO Y i,k = H k X i,k e j2 ( f T FFT + k) Number of samples in CP FFT window size Symbol size a constant indicating the initial phase error of symbol i 48

49 Sample Rotation due to SFO Incremental phase errors in different subcarriers à Signals keep rotating in the I-Q plane Q subcarrier 3 subcarrier 2 xxx x x x x x x x x x x subcarrier 1 I Ideal BPSK signals (No rotation) 49

50 Phase Errors due to SFO and CFO x x phase of H x x x x x x 2πδkφ (SFO) x 1 2πΔ f T FFT φ (Residual CFO) Subcarrier index k Subcarrier i of the received frequency domain signals in symbol n Y i,k = H k X i,k e j2 ( f T FFT + k) SFO: slope; residual CFO: intersection of y-axis 50

51 Data-aided Phase Tracking x x 1 2πδkφ = 2π θk (SFO) regression x x 2πΔ f T FFT φ = 2π η (Residual CFO) WiFi reserves 4 known pilot bits (subcarriers) to compute H k e j2π(η+θk) =Y k /X k Estimate SFO θ k and CFO η by finding the linear regression of the phase changes experienced by the pilot bits Update the channel by H k = H k e 2jπ(η+θk) for every symbol k, and then decode the remaining non-pilot subcarriers Y i,k = H k X i,k e j2 ( + k) = H 0 kx i,k ) ˆX i,k = Y i,k /H 0 k 51

52 After Phase Tracking Q j2 ( + k) X i,k e xxx x x x x x x x x x x X i,k I Decoded signals in the I-Q plane after phase tracking 52

53 OFDM Diagram Transmitter Modulation Insert S/P IFFT P/S CP D/A channel + noise De-mod Phase track remove P/S FFT S/P CP frequency-domain Receiver Correct CFO A/D time-domain 53

54 Quiz Say we want to send (1, -1, 1, 1, -1), and transmit over the air (1,-1,1,1,-1) is the (a) frequency-domain or (b) time-domain signal? is the (a) frequency-domain or (b) time-domain signal What is the Multipath Effect? Why does it cause Deep Fading? 54