Multipath can be described in two domains: time and frequency

Transcription

1 Multipath can be described in two domains: and frequency Time domain: Impulse response Impulse response Frequency domain: Frequency response f Sinusoidal signal as input Frequency response Sinusoidal signal as output

2 Introduction to OFDM modulation N carriers Symbol: 2 periods of f 0 f Symbol: 4 periods of f 0 + Transmit f Data coded in frequency domain B Symbol: 8 periods of f 0 Transformation to domain: each frequency is a sine wave in, all added up Channel frequency response Receive N carriers f Decode each frequency bin separately B Time-domain signal Frequency-domain signal

3 Introduction to OFDM (Orthogonal frequency division multiplex) N carriers Time-frequency grid Data Frequency B f 0 Carrier B Features No intercarrier guard bands Controlled overlapping of bands Maximum spectral efficiency (Nyquist rate) Easy implementation using IFFTs Very sensitive to -freq synchronization T=1/f 0 Time One OFDM symbol Intercarrier Separation = Any integer Multiple of 1/(symbol duration) Modulation technique A user utilizes all carriers simultaneously to transmit its data as coded quantity at each frequency carrier, which can be quadrature-amplitude modulated (QAM)

4 OFDM Modulation and Demodulation using FFTs f b0 b1 b2 bn-1 Data coded in frequency domain: one symbol at a IFFT (Inverse fast Fourier transform) d0 d1 d2 d3 dn-1 Data in domain: one symbol at a P/S (Parallel to serial converter) d0, d1, d2,, dn-1 Transmit -domain samples of one symbol d0, d1, d2,, dn-1 Receive -domain samples of one symbol S/P (Serial to parallel converter) d0 d1 d2 d3 dn-1 FFT (Fast Fourier transform) f b0 Decode each b1 frequency bin b2 independently bn-1

5 Loss of orthogonality (by frequency offset) Transmission pulses Reception pulse with offset δ ψ k (t) = exp( jk2πt / T ) y ψ k +m (t) = exp( j2π (k + m)t / T) δ ψ k +m (t) = exp( j2π (k + m + δ )/T) con δ 1/ 2 Interference between channels k and k+m T I m (δ ) = exp( jk 2πt / T)exp( j(k + m + δ )2πt / T)dt = 0 T( 1 exp( j2πδ )) j2π(m + δ) I m (δ) = T sin πδ π m + δ Summing up m m I m2 (δ) Tδ ( ) 2 N 1 1 m 2 m =1 ( Tδ ) for N >> 1(N > 5 Is enough) Interference in db Loss for 8 carriers m=1 m=3 m=5 m= Frequency offset ICI in db Total ICI due to loss of orthogonality δ =005 δ =002 δ =001 δ =0005 δ =0002 δ = Carrier position within the band (N=16) δ assumed rv Gaussian σ=δ Practical limit

6 Loss of orthogonality () Let us assume a misadjustment τ T /2+τ X i = c 0 ψ k (t)ψ * l (t τ )dt + c T /2 1 ψ k (t)ψ * l (t τ )dt T /2+τ T /2 2 consecutive symbols τ senmπ Then X i = 2T T, c 0 c 1 mπ if m=k-l 0, c 0 = c 1 Or approximately, when τ<<t τ X 2mπ i T T = 2 τ mπ T independent on m In average, the interfering power in any carrier is E X i T 2 2 = 4 τ T = 2 τ 2 ICI 20log 2 τ T, τ << T T Per carrier 2 1 Interference in db Loss for 16 carriers 0-5 m= m= m= Relative misadjustment τ Zone of interest ICI in db ICI due to loss of orthogonaliy N=8 assumed a uniform rv Max practical limit N= Standard deviation of the relative misadjustment

7 Including a cyclic prefix to each OFDM symbol To combat the multipath: including guards between the symbols copy CP τ Tc T Without the Cyclic Prefix Including the Cyclic Prefix Symbol: 8 periods of f i CP Symbol: 8 periods of f i Passing the channel h(n) Channel: h(n)=(1) n /n n=0,,23 Ψ i (t) Ψ i (t) Passing the channel h(n) Ψ i(t) Initial transient Loss of orthogonality Decaying transient Initial transient remains within the CP The inclusion of a CP maintains the orthogonality Final transient remains within the CP Ψ j (t) Ψ j (t) Symbol: 4 periods of f i Symbol: 4 periods of f i CP functions: It acomodates the decaying transient of the previous symbol It avoids the initial transient reachs the current symbol

8 Symplified scheme of an OFDM transceiver Transmitter Cyclic prefix (CP) BITS CODER S S P DAC RF P IFFT f 0 Receiver RF ADC Filter S P FFT DECOD P S BITS f 0 PLL, symbol timing Channel estimation frequency offset

9 Windowing of the OFDM symbol Total band used by OFDM: it depends on the number or carriers ACI ACI Wide separation Maintainig a fix bandwidth, if N increases Narrow separation Adjacent channel interference decreases BUT It is interesting to have few carriers as well: To introduce short delay in data gathering and signal processing (FFTs) To have a bigger intercarrier separation --> It reduces the relative frequency offset Compromise Need to shape the OFDM symbols

10 OFDM modulators with symbol shaping a n p(t) e jω nt Equivalent architectures a n e jω nt p(t) Σan p(t) ejωnt p(t) Σa n e jω nt a k a k p(t) e jω kt e jω kt Implemented with FFT After the synchronous reception p(t) even T /2 I = p(t)e j2π(k n)t / T T /2 dt = 2 p(t)cos[2π(n k)t / T]dt T /2 = 0, k n 0 1, k = n 0 The simplest way to maintain symmetry within -T/2<t<T/2 is p(t)=k p(t) cos odd even T/2 Symbol shaping has to be carried out as part of the symbol duration + CP The total ACI can be condiderably reduced PC+T

11 Robustness against the channel and ACI improvement N Virtual OFDM symbols within the slot With guards (Cyclic prefixes), the channel s dispersion is avoided L=N+CP PC PC PC PC PC OFDM symbols with guards (CPs) With smooth transitions between symbols, the adjacent channel interference is minimized PC PC PC PC OFDM symbols with guards and symbol shaping

12 80211a Physical Layer Data Symbol Format t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 GI2 T1 T2 GI OFDM Symbol GI OFDM Symbol Short training sequence: AGC and frequency offset Long training sequence: Channel estimation Training symbols: 4 us each t: 08 us, 16 samples GI2: 16 us, 32 samples T: 32 us, 64 samples Data Symbols: 4 us each GI: 08 us, 16 samples OFDM Symbol: 32 us, 64 samples * Only 52 of the 64 carriers are used * 4 of the 52 carriers are used for pilot carriers (no data) Data rate for each 20 Mhz channel: 20 Msamples per second 250 Ksymbols per second 48 data carriers per symbol 1/2 or 3/4 convolutional code 1 bit/carrier (BPSK) to 6 bits/carrier (64 QAM) Overall: Lowest: 48 * 1 * 1/2 * 250K = 6 Mbps Highest: 48 * 6 * 3/4 * 250K = 54 Mbps Turbo mode supports 108 Mbps using 40 Mhz channel

13 Robustness against errors: random noise and channel-selected errors Random noise: primarily introduced by thermal and circuit noise Channel-selected errors: introduced by magnitude distortion in channel frequency response Time-frequency grid Data bits Frequency B f 0 Bad carriers Frequency response f T=1/f0 Time Errors are no longer random Interleaving is often used to scramble the data bits so that standard error correcting codes can be applied

14 Spectrum Mask Power Spectral Density -20 db -28 db -40 db f carrier Frequency (MHz) Requires extremely linear power amplifier design

15 Adjacent Channel and Alternate Adjacent Channel Rejection Date Minimum A djacent Channel A ltern ate rate S en sib ility R ejection Channel rejection 6 M bps -82 dbm 16 db 32 db 12M bps -79 dbm 13 db 29 db 24M bps -74 dbm 8 db 24 db 36M bps -70 dbm 4 db 20 db 54M bps -65 dbm 0 db 15 db 32 db 16 db Signal Frequency Requires joint design of the anti-aliasing filter and ADC