Report

9. Multi Carrier Modulation and OFDM Transmission of Data Through Frequency Selective Time Varying Channels We have seen a wireless channel is characterized by time spread and frequency spread. Frequency Spread S ( , F ) F FDMAX RMS RMS MEAN Time Spread Single Carrier Modulation in Flat Fading Channels • if symbol duration >> time spread then there is almost no Inter Symbol Interference (ISI). channel TS 1 0 time Problem with this: Low Data Rate!!! 1 0 phase still recognizable … in the Frequency Domain • this corresponds to Flat Fading channel 1 / TS Frequency Frequency Flat Freq. Response Frequency Single Carrier Modulation in Frequency Selective Channels • if symbol duration ~ time spread then there is considerable Inter Symbol Interference (ISI). channel time 1 0 ? ? phase not recognizable One Solution: we need equalization channel equalizer time 1 time 0 1 0 Channel and Equalizer Problems with equalization: • it might require training data (thus loss of bandwidth) • if blind, it can be expensive in terms computational effort • always a problem when the channel is time varying The Multi Carrier Approach • let symbol duration >> time spread so there is almost no Inter Symbol Interference (ISI); • send a block of data using a number of carriers (Multi Carrier) “symbol” 1 “symbol” 0 time 0 1 time 1 0 time channel Compare Single Carrier and Multi Carrier Modulation SC Frequency 1 Frequency 1 One symbol Frequency 0 1 0 1 1 1 Block of symbols 1 1 Flat Fading Channel: Easy Demod channel MC subcarriers 0 0 1 0 1 1 1 Frequency Each subcarrier sees a Flat Fading Channel: Easy Demod Structure of Multi Carrier Modulation In MC modulation each “MC symbol” is defined on a time interval and it contains a block of data OFDM Symbol data data data data time TSymbol data t Tg Tb guard interval with data interval Tg MAX MAX channel time spread Guard Time We leave a “guard time” between blocks to allow multipath TX Guard Time Tg Data Block the “guard time” is long enough, so the multipath in one block does not affect the next block Data Block Tb TSymbol data+guard RX RX Tg TX NO Inter Block Interference! MC Signal Transmitted Signal: s(t ) Re e j 2FC t x(t ) FC carrierfrequency Baseband Complex Signal: k x(t ) NF 2 c e j 2kF t k k k 0 NF 2 0 t TSymbol kF subcarrier frequencyoffset ck data “Orthogonal” Subcarriers and OFDM t guard interval Tg Tb data interval 1 Choose: F Tb N F F F FC Orthogonality: 1 Tb t 0 Tb e t0 j 2Fk t j 2F t e F Fk FC kF 1 dt Tb t 0 Tb e t0 j 2 ( k ) Ft 1 if k dt 0 if k Orthogonality at the Receiver Transmitted subcarrier j 2Fk t Channel (LTI) e t 0 Received subcarrier Tg Tb x(t ) ck e j 2Fk t k 0 t Tg Tb h(t ) t H ( F ) FTh(t ) 0 Tg Tb Tg transient steady state response response y (t ) ck H ( Fk )e j 2 Fk t k Tg t Tg Tb still orthogonal at the receiver!!! 1 1 ck H ( Fk ) Tb Tg Tb y(t )e Tg j 2Fk t dt OFDM symbols in discrete time Let • FS be the sampling frequency; • N NF be the number of data samples in each symbol; • F 1 /N TS FS / N the subcarriers spacing Then: 1 x(nTS ) N with NF 2 c e k k NF 2 j 2k FF ( n L ) s 1 N NF 2 c e k k Tg L TS the guard time. NF 2 jk 2N ( n L ) n 0,.., L N 1 Summary OFDM Symbol # samples # subcarriers guard L data N NF TIME: 0 Tg Tb Sampling Interval TS 1 / FS t Freq spacing F FS / N FREQUENCY: FS / 2 N F F S 2 N 0 N F FS 2 N FS / 2 F OFDM Symbol and FFT 1 x[n L] N NF 2 c e jk 2N n k k NF 2 NF 2 1 N c e 1 N N 1 k 1 jk 2N n k X [k ]e 1 N jk 2N n 1 c e j ( N k ) 2N n k k NF 2 IFFTX [k ] k 0 Where: X [k ] ck , k 1,..., N F / 2 X [ N k ] ck , k 1,..., N F / 2 X [k ] 0, otherwise positive subcarriers negative subcarriers unused subcarriers Guard Time with Cyclic Prefix (CP) x[ L],...,x[ L N 1] IFFTX [k ], k 0,...,N 1 0 L N 1 L CP IFFT{ X } N CP from the periodicity x[n] x[ N n] x[0] x[ N ] x[1] x[ N 1] ... x[ L 1] x[ L N 1] OFDM Demodulator See each block: y[n] 0 L 1 n L N 1 No Inter Block Interference y[n L] h[n]* x[n L] 2 j kn 1 N 1 h[n]* X [k ]e N N k 0 2 j kn 1 N 1 H [k ] X [k ]e N IFFT H [k ] X [k ] N k 0 H [k ] X [k ] FFTy[ L],...,y[ L N 1] with H[k ] FFT h[0],..., h[L 1],0,...,0 k 0,..., N 1 Overall Structure of OFDM Comms System X [ 0] X [1] X X [ N 1 ] IFFT N H [0] X [0] H [ 1 ] X [ 1 ] W Y H [ N 1 ] X [ N 1 ] +CP P/S NL N NL h[n] w[n] FFT -CP S/P NL N N NL Simple One Gain Equalization To recover the transmitted signal you need a very simple one gain equalization: received transm. noise Y [k ] H [k ] X [k ] W [k ] channel Use simple Wiener Filter: Xˆ [k ] H *[k ] H [k ] 2 2 W Y [k ] OFDM as Parallel Flat Fading Channels Significance: a Freq. Selective Channel becomes N Flat Fading Channels h(t ) X m [0] X m [ N 1] x(t ) w(t ) y(t ) OFDM Mod OFDM Demod Frequency Selective channel N Flat Fading Channels Wm [0] X m [0] H [ 0] X m [ N 1] H [ N 1] Ym [0] Wm [ N 1] Ym[ N 1] Ym [0] Ym[ N 1] OFDM Parameters Summarize basic OFDM Parameters: • FS sampling rate in Hz • N length of Data Field in number of samples • L length of Cyclic Prefix in number of samples • NF N total number of Data Subcarriers guard data data t / TS L guard guard N time 0 NF / N frequency F / FS IEEE 802.11a: Frequency Bands: 5.150-5.350 GHz and 5.725-5.825 GHz (12 channels) Modulation OFDM Range: 100m IEEE 802.11g Frequency Bands: 2.412-2.472GHz Modulation: OFDM Range: 300m Channel Parameters: FCC Example: the Unlicensed Band 5GHz U-NII (Unlicensed National Information Infrastructure) • 8 channels in the range 5.15-5.35GHz 30 MHz 20MHz 30 MHz 5150 5180 5200 5300 FC • 4 channels in the range 5.725-5.825GHz 5320 5350 F (MHz) Channel Parameters: Example IEEE802.11 In terms of a Transmitter Spectrum Mask (Sec. 17.3.9.2 in IEEE Std 802.11a-1999) 0dB Typical Signal Spectrum 20dB 28dB 40dB 30 20 11 9 FC Typical BW~16 MHz 9 11 20 30 F (MHz) In either case: FS 20MHz Sampling frequency N 64 L 16 FFT size Cyclic Prefix CP N 16 Tg 16 / 20 0.8 sec DATA N 64 Tb 64 / 20 3.2 sec Sub-carriers: (48 data + 4 pilots) + (12 nulls) = 64 NULL c1 c26 N F 52 NULL c 26 c1 Frequency Pilots at: -21, -7, 7, 21 0 1 0 26 38 63 63 IFFT x0 N 64 x63 Time Frequencies: F 20 MHz / 64 312.5kHz 38 64 26 63 1 8.125 26 k 8.125 F ( MHz ) Subcarriers index 16 .25 MHz DATA F (MHz) FCARRIER 10 FCARRIER 20MHz 1 / Ts FCARRIER 10 Time Block: Ts TFFT / 64 50109 sec TG 0.8 sec TFFT 3.2 sec TFRAME 4.0 sec time Overall Implementation (IEEE 802.11a with 16QAM). 1. Map encoded data into blocks of 192 bits and 48 symbols: data Encode Buffer Interleave (192 bits) …010011010101… 48 Map to 16QAM … 1110 0111 1000 … 1101 4 4x48=192 bits a +1+j3 -1+j +3-j3 … +1-j 48 Overall Implementation (IEEE 802.11a with 16QAM). 2. Map each block of 48 symbols into 64 samples time domain frequency domain xm [0] null 0 0 +1+j3 … -3-j +3-j3 … +1-j 24 data 2 pilots null 24 data 2 pilots am [ ] 26 27 27 64 26 64 X m [k ] 1: 48 1 2 1 1 64 IFFT k 0 : 63 26 1 1 62 63 xm [62] xm [63] xm [n] n 0 : 63 26 xm [1] k Channel Parameters: Physical Frequency Spread S ( , F ) F FDMAX kHz Time Spread MAX 1 10 sec outdoor MAX 10 50 n sec indoor Constraints on OFDM Symbol Duration: MAX Tg Tb 1/ FD MAX 106 sec to minimize CP overhead 103 sec roughly!!! for channel Time Invariant Summary of OFDM and Channel Parameters Channel: 2. Doppler Spread MAX sec FDMAX Hz 3. Bandwidth BW Hz 1. Max Time Spread FS Hz 4. Channel Spacing OFDM (design parameters): 1. Sampling Frequency FS 2. Cyclic Prefix L MAX FS 3. FFT size (power of 2) 4L N FS / FDMAX 4. Number of Carriers NF N BW / FS integer integer integer Example: IEEE802.11a Channel: 1. Max Time Spread MAX 0.5 sec 2. Doppler Spread FDMAX 50 Hz 3. Bandwidth BW 16 MHz 4. Channel Spacing FS 20MHz OFDM (design parameters): 1. Sampling Frequency FS 20MHz 2. Cyclic Prefix L 16 0.5 20 10 3. FFT size (power of 2) N 64 20 106 / 50 integer 4. Number of Carriers NF 52 64 16 / 20 integer Applications: various Area Networks According to the applications, we define three “Area Networks”: • Personal Area Network (PAN), for communications within a few meters. This is the typical Bluetooth or Zigbee application between between personal devices such as your cell phone, desktop, earpiece and so on; • Local Area Network (LAN), for communications up 300 meters. Access points at the airport, coffee shops, wireless networking at home. Typical standard is IEEE802.11 (WiFi) or HyperLan in Europe. It is implemented by access points, but it does not support mobility; • Wide Area Network (WAN), for cellular communications, implemented by towers. Mobility is fully supported, so you can move from one cell to the next without interruption. Currently it is implemented by Spread Spectrum Technology via CDMA, CDMA-2000, TD-SCDMA, EDGE and so on. The current technology, 3G, supports voice and data on separate networks. For (not so) future developments, 4G technology will be supporting both data and voice on the same network and the standard IEEE802.16 (WiMax) seems to be very likely More Applications 1. WLAN (Wireless Local Area Network) standards and WiFi. In particular: • IEEE 802.11a in Europe and North America • HiperLAN /2 (High Performance LAN type 2) in Europe and North America • MMAC (Mobile Multimedia Access Communication) in Japan 2. WMAN (Wireless Metropolitan Network) and WiMax • IEEE 802.16 3. Digital Broadcasting • Digital Audio and Video Broadcasting (DAB, DVB) in Europe 4. Ultra Wide Band (UWB) Modulation • a very large bandwidth for a very short time. 5. Proposed for IEEE 802.20 (to come) for high mobility communications (cars, trains …)