ECS455: Chapter 5 OFDM

Transcription

1 ECS455: Chapter 5 OFDM 1 Dr.Prapun Sukompong prapun.com/ec455 Office Hour: BKD Tueday 9:30-10:30 Friday 14:00-16:00

2 2 OFDM: Overview Let S 1, S 2,, S N be the information ymbol. The dicrete baeband OFDM modulated ymbol can be expreed a Some reference may ue different contant in the front Note that: N kt ( t) S k exp j, 0 t T N k 0 T 1 2 kt N 1 Sk 1 0, texp j T k 0 N T N 1 1 2kt 2kt Re ( t) ReSkco ImSkin N k 0 T T c k t Some reference may tart with different time interval, e.g. [-T /2, +T /2]

3 OFDM Application Wi-Fi: a and g verion DVB-T (the terretrial digital TV broadcat ytem ued in mot of the world outide North America) DMT (the tandard form of ADSL - Aymmetric Digital Subcriber Line) WiMAX 3

4 4 Single-Uer OFDM

5 Motivation Firt, we tudy the wirele channel. There are a couple of difficult problem in communication ytem over wirele channel. Alo want to achieve high data rate (throughput) 5

6 ECS455: Chapter 5 OFDM 5.1 Wirele Channel 6 Dr.Prapun Sukompong prapun.com/ec455 Office Hour: BKD Tueday 9:30-10:30 Friday 14:00-16:00

7 Single Carrier Tranmiion Baeband: N 1 t p t kt k0 Paband: x t Re k 1 t p t 0, T j2 fct t e 1, t 0, T 0, otherwie. 1.2 (a) (b) Time Time

8 Multipath Propagation In a wirele mobile communication ytem, a tranmitted ignal propagating through the wirele channel often encounter multiple reflective path until it reache the receiver We refer to thi phenomenon a multipath propagation and it caue fluctuation of the amplitude and phae of the received ignal. We call thi fluctuation multipath fading. 8

9 Wirele Comm. and Multipath Fading The ignal received conit of a number of reflected ray, each characterized by a different amount of attenuation and delay. r t x t h t n t x t n t v i0 i i t h1 t 0.5 t 0.2 t 0.2T 0.3 t 0.3T 0.1 t 0.5T h2 t 0.5 t 0.2 t 0.7T 0.3 t 1.5T 0.1 t 2.3T h t i0 (b) (a) (b) v i i Time Time Time

10 Frequency Domain The tranmitted ignal (envelope) 1 P(f) f H 1 (f) 1.5 Channel with weak multipath f H 2 (f) 1.5 Channel with trong multipath f 10

11 COST 207 Channel Model Baed on channel meaurement with a bandwidth of 8 10MHz in the 900MHz band ued for 2G ytem uch a GSM. 11 [Fazel and Kaier, 2008, Table 1-1]

12 3GPP LTE Channel Model 12 [Fazel and Kaier, 2008, Table 1-3]

13 3GPP 6-tap typical urban (TU6) Delay profile and frequency repone of 3GPP 6-tap typical urban (TU6) Rayleigh fading channel in 5 MHz band. 13 [3GPP TS GPP; Technical Specification Group GSM/EDGE Radio Acce Network; Radio Tranmiion and Reception (Releae 7)]

14 Equalization Chapter 11 of [Goldmith, 2005] Delay pread caue ISI In a broad ene, equalization define any ignal proceing technique ued at the receiver to alleviate the ISI problem caued by delay pread. [Goldmith, 2005] Higher data rate application are more enitive to delay pread, and generally require high-performance equalizer or other ISI mitigation technique. Signal proceing can alo be ued at the tranmitter to make the ignal le uceptible to delay pread. Ex. pread pectrum and multicarrier modulation 14

15 Equalizer deign Balance ISI mitigation with noie enhancement Both the ignal and the noie pa through the equalizer Nonlinear equalizer uffer le from noie enhancement than linear equalizer, but typically entail higher complexity. Mot equalizer are implemented digitally after A/D converion Such filter are mall, cheap, eaily tuneable, and very power efficient. The optimal equalization technique i maximum likelihood equence etimation (MLSE). Unfortunately, the complexity of thi technique grow exponentially with the length of the delay pread, and i therefore impractical on mot channel of interet. Viterbi algorithm 15

16 Simple Analog Equalizer 16 xt H f Heq f nt 1 H f Remove all ISI Diadvantage: If ome frequencie in the channel frequency repone H( f ) are greatly attenuated, the equalizer H eq (f ) = 1/ H( f ) will greatly enhance the noie power at thoe frequencie. If the channel frequency repone H( f ) ha a pectral null (= 0 for ome frequency), then the power of the new noie i infinite. Even though the ISI effect are (completely) removed, the equalized ytem will perform poorly due to it greatly reduced SNR. x t n t

17 17 Linear v. Non-linear Equalizer Need to balance mitigation of the effect of ISI with maximizing the SNR of the pot-equalization ignal. Linear digital equalizer In general work by inverting the channel frequency repone Eay to implement and to undertand conceptually Typically uffer from more noie enhancement Not ued in mot wirele application Nonlinear equalizer Do not invert the channel frequency repone Suffer much le from noie enhancement Deciion-feedback equalization (DFE) i the mot common Fairly imple to implement and generally perform well.

18 [Goldmith, 2005, Fig. 11.2] Equalizer Type Symbol-by-ymbol (SBS) equalizer: remove ISI from each ymbol and then detect each ymbol individually. Sequence etimator (SE): detect equence of ymbol, o the effect of ISI i part of the etimation proce. 18

19 Tranveral Structure Linear and nonlinear equalizer are typically implemented uing a tranveral or lattice tructure. The tranveral tructure i a filter with N 1 delay element and N tap with tunable complex weight. Heq z wi z L il i N 2L1 19 The length of the equalizer N i typically dictated by implementation conideration Large N uually entail higher complexity.

20 Time-varying Multipath Channel Impule Repone: L = number of reolvable path i (t) = complex-valued path gain of the ith path Uually aumed to be independent complex Gauian procee reulting in Rayleigh fading becaue each reolvable path i the contribution of a different group of many irreolvable path. i = time delay of the ith path Tranfer function: H f, t L1, h t t i0 i i 20 L = 16-path exponential power delay profile with a decay factor of 1.0 db and a time delay eparation of 150 n between adjacent path (correponding to the rm delay pread of 0.52 μ). 5 GHz carrier frequency and 4 km/h terminal peed. [Adachi, Garg, Takaoka, and Takeda, 2005, Figure 2]

21 Adaptive Equalization Equalizer mut typically have an etimate of the channel (impule or frequency repone) Since the wirele channel varie over time, the equalizer mut learn the frequency or impule repone of the channel (training) and then update it etimate of the frequency repone a the channel change The proce of equalizer training and tracking i often referred to a adaptive equalization. Blind equalizer do not ue training Learn the channel repone via the detected data only 21

22 Equalization for Digital Cellular Telephony GSM Ue adaptive equalizer Equalize echo up to 16 m after the firt ignal received Correpond to 4.8 km in ditance. One bit period i 3.69 m. Hence, echo with about 4 bit length delay can be compenated The direct equence preading employed by CDMA (IS-95) obviate the need for a traditional equalizer. If the tranmiion bandwidth i large (for example 20 MHz), the complexity of traightforward high-performance equalization tart to become a eriou iue. 22

23 Wirele Propagation [Bahai, 2002, Fig. 2.1] 23

24 Three tep toward modern OFDM 1. Solve Multipath problem Multicarrier modulation (FDM) 2. Gain Spectral Efficiency Orthogonality of the carrier 3. Achieve Efficient Implementation FFT and IFFT 24

25 ECS455: Chapter 5 OFDM 5.2 Multi-Carrier Tranmiion 25 Dr.Prapun Sukompong prapun.com/ec455 Office Hour: BKD Tueday 9:30-10:30 Friday 14:00-16:00

26 Single-Carrier Tranmiion [Karim and Sarraf, 2002, Fig 3-1] 26

27 Multi-Carrier Tranmiion Convert a erial high rate data tream on to multiple parallel low rate ub-tream. Each ub-tream i modulated on it own ub-carrier. Time domain perpective: Since the ymbol rate on each ub-carrier i much le than the initial erial data ymbol rate, the effect of delay pread, i.e. ISI, ignificantly decreae, reducing the complexity of the equalizer. 27 [Fazel and Kaier, 2008, Fig 1-4]

28 Frequency Diviion Multiplexing Frequency Domain Perpective: Even though the fat fading i frequency-elective acro the entire OFDM ignal band, it i effectively flat in the band of each low-peed ignal. [The flatne aumption i the ame one that you ued in Riemann approximation of integral.] 28 [Myung and Goodman, 2008]

29 Frequency Diviion Multiplexing To facilitate eparation of the ignal at the receiver, the carrier frequencie were paced ufficiently far apart o that the ignal pectra did not overlap. Empty pectral region between the ignal aured that they could be eparated with readily realizable filter. The reulting pectral efficiency wa therefore quite low. 29

30 Multi-Carrier (FDM) v. Single Carrier Single Carrier Single higher rate erial cheme Multipath problem: Far more uceptible to inter-ymbol interference (ISI) due to the hort duration of it ignal element and the higher ditortion produced by it wider frequency band Complicated equalization Multi-Carrier (FDM) Parallel cheme. Each of the parallel ubchannel can carry a low ignalling rate, proportional to it bandwidth. Long duration ignal element and narrow bandwidth in ub-channel. Complexity problem: If built traightforwardly a everal (N) tranmitter and receiver, will be more cotly to implement. BW efficiency problem: The um of parallel ignalling rate i le than can be carried by a ingle erial channel of that combined bandwidth becaue of the unued guard pace between the parallel ubcarrier. 30

31 FDM (con t) Before the development of equalization, the parallel technique wa the preferred mean of achieving high rate over a diperive channel, in pite of it high cot and relative bandwidth inefficiency. 31

32 OFDM OFDM = Orthogonal frequency diviion multiplexing One of multi-carrier modulation (MCM) technique Parallel data tranmiion (of many equential tream) A broadband i divided into many narrow ub-channel Frequency diviion multiplexing (FDM) High pectral efficiency The ub-channel are made orthogonal to each other over the OFDM ymbol duration T. Spacing i carefully elected. Allow the ub-channel to overlap in the frequency domain. Allow ub-carrier to be paced a cloe a theoretically poible. 32

33 Vector: 33 Orthogonality Two vector/function are orthogonal if their inner product i zero. The ymbol a b 1 1 n *, k k 0 k 1 a n b n a b a b a b Time-domain: *, 0 a b a t b t dt Frequency domain: * A, B A f B f df 0 i ued to denote orthogonality. Example: in t t 2 k 1 and co 2 k 2 on 0, T T T e t j2 n T Example: Complex conjugate t 3 and 5 t t on 1,1 9 on 0, T

34 Orthogonality in Communication CDMA TDMA FDMA 1 1 t S c t S f S C f k k k k k0 k0 1 1 t S c t kt S f C f S e k k k0 k0 where c(t) i time-limited to [0,T]. Thi i a pecial cae of CDMA with c t ct kt 1 S f S C f k f k 0 k where C(f) i frequency-limited to [0,f]. Thi i a pecial cae of CDMA with C f C f kf k k where j2 fkt The c k are non-overlapping in time domain. c k c k The C k are non-overlapping in freq. domain.

35 OFDM Let S 1, S 2,, S N be the information ymbol. The dicrete baeband OFDM modulated ymbol can be expreed a N kt ( t) S k exp j, 0 t T N k 0 T 1 2 kt N 1 Sk 1 0, texp j T k 0 N T c k t Another pecial cae of CDMA! 35 Note that: N 1 1 2kt 2kt Re ( t) ReSkco ImSkin N k 0 T T

36 OFDM: Orthogonality T * 2k1t 2 2 k exp exp T 0 T k t ck tc t dt j j dt 1 2 T 0 2 k1 k2 t T, k k exp j dt T 0, k k When k k, 1 2 When k k, 1 2 T * k 1 1 k 2 0 c t c t dt dt T T 2 k k t c t c t dt j k * k exp j2 k1 k2 T 0 T 11 0 j2 k k 1 2 T

37 Frequency Spectrum N kt ( t) S k 1 0, texp j T k 0 N T 1 1 ct 0, T N N 2 kt k ck t c t exp j Ck f C f C f kf T T j2 f 2 1 t C f T e inct f c k t 1 t T in c T f T T, 2 2 T f 1 T Thi i the term that make the technique FDM. 37 N1 N1 ( t) S c t S( f ) S C f k k k k k0 k0 N 1 1 j2 f kf N k 0 S k 2 e T in c T T f kf

38 Subcarrier Spacing S N kt () t S k 1 0, texp j T k 0 N T f 1 N N 1 k 0 j2 S e T in c T f kf k T f kf 2 f 1 T Each QAM ignal carrie one of the original input complex number. OFDM N eparate QAM ignal, FDM at N frequencie eparated by the ignalling rate. 38 Spectrum Overlap in OFDM The pectrum of each QAM ignal i of the form with null at the center of the other ubcarrier.

39 Normalized Power Denity Spectrum Flatter when have more ub-carrier 39 [Fazel and Kaier, 2008, Fig 1-5]

40 Time-Domain Signal Real and Imaginary component of an OFDM ymbol i the uperpoition of everal harmonic modulated by data ymbol [Bahai, 2002, Fig 1.7] 40 N kt ( t) S k exp j, 0 t T N k 0 T N 1 1 2kt 2kt Re ( t) ReSkco ImSkin N k 0 T T in-phae part quadrature part

41 Summary So, we have a cheme which achieve Large ymbol duration (T ) and hence le multipath problem Good pectral efficiency One more problem: There are o many carrier! 41