Mobile Communications TCS 455

Transcription

1 Mobile Counication TCS 455 Dr. Prapun Sukopong Lecture 24 1 Office Hour: BKD Tueday 14:00-16:00 Thurday 9:30-11:30

2 Announceent Read Chapter 9: Section 1.2 fro [Bahai, Multi-carrier Digital Counication: Theory And Application Of OFDM, 2002] Uploaded to the SIIT online lecture note yte. 2

3 Chapter 5 OFDM 3 Office Hour: BKD Tueday 14:00-16:00 Thurday 9:30-11:30

4 4 OFDM Let S 1, S 2,, S N be the inforation ybol. The dicrete baeband OFDM odulated ybol can be expreed a Soe reference ay 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 ISkin N k 0 T T c k t Soe reference ay tart with different tie interval, e.g. [-T /2, +T /2]

5 Chapter 5 OFDM Wirele Channel 5 Office Hour: BKD Tueday 14:00-16:00 Thurday 9:30-11:30

6 Three tep toward OFDM 1. Solve Multipath Multicarrier odulation (FDM) 2. Gain Spectral Efficiency Orthogonality of the carrier 3. Achieve Efficient Ipleentation FFT and IFFT 6

7 Chapter 5 OFDM Multi-Carrier Traniion 7 Office Hour: BKD Tueday 14:00-16:00 Thurday 9:30-11:30

8 FDM: Better or Wore? Coparion with a ingle higher rate erial chee The parallel yte, if built traightforwardly a everal tranitter and receiver, will certainly be ore cotly to ipleent. Each of the parallel ubchannel can carry a low ignalling rate, proportional to it bandwidth. The u of thee ignalling rate i le than can be carried by a ingle erial channel of that cobined bandwidth becaue of the unued guard pace between the parallel ub-carrier. The ingle channel will be far ore uceptible to inter-ybol interference. Thi i becaue of the hort duration of it ignal eleent and the higher ditortion produced by it wider frequency band, a copared with the long duration ignal eleent and narrow bandwidth in ub-channel in the parallel yte. 8

9 FDM (3) Before the developent of equalization, the parallel technique wa the preferred ean of achieving high rate over a diperive channel, in pite of it high cot and relative bandwidth inefficiency. 9

10 OFDM OFDM = Orthogonal frequency diviion ultiplexing One of ulti-carrier odulation (MCM) technique Parallel data traniion (of any equential trea) A broadband i divided into any narrow ub-channel Frequency diviion ultiplexing (FDM) High pectral efficiency The ub-channel are ade orthogonal to each other over the OFDM ybol duration T. Spacing i carefully elected. Allow the ub-channel to overlap in the frequency doain. Allow ub-carrier to be paced a cloe a theoretically poible. 10

11 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

12 Frequency Spectru 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 in ct f c k t 1 t T in c T f T T, 2 2 T f 1 T Thi i the ter that ake the technique FDM. 12 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 inc T T f kf

13 Subcarrier Spacing f 1 T OFDM FDM Spectru Overlap in OFDM 13

14 Tie-Doain Signal Real and Iaginary coponent of an OFDM ybol i the uperpoition of everal haronic odulated by data ybol [Bahai, 2002, Fig 1.7] 14 N kt ( t) S k exp j, 0 t T N k 0 T N 1 1 2kt 2kt Re ( t) Re Skco I Skin N k 0 T T

15 Suary So, we have a chee which achieve Large ybol duration (T ) and hence le ultipath proble Good pectral efficiency One ore proble: There are o any carrier! 15

16 Dicrete Fourier Tranfor (DFT) N kt ( t) S k exp j, 0 t T N k 0 T Saple the ignal in tie doain: T N n n Sk exp j N N k 0 T N k exp N k 0 k n T kn S j N IDFT S n N N 16

17 17 DFT

18 18 DFT

19 19 DFT

20 Efficient Ipleentation: (I)FFT [Bahai, 2002, Fig. 2.9] 20

21 FFT The hitory of the FFT i coplicated. A with any dicoverie and invention, it arrived before the (coputer) world wa ready for it. Uually done with N a power of two. Not only i it very efficient in ter of coputing tie, but i ideally uited to the binary arithetic of digital coputer. Reference: E. Oran Brigha, The Fat Fourier Tranfor, Prentice-Hall,

22 DFT Saple Here are the point [n] on the continuou-tie verion (t): n T n N N kn Sk exp j N k 0 N 0 nn N IDFT S n T

23 Overapling

24 Overapling (2) Increae the nuber of aple point fro N to LN on the interval [0,T ]. L i called the over-apling factor. T L n n n n LN N 0 nn 0 n LN T 24 N 1 L 1 2 n Sk exp j N k 0 T k T 1 N 1 2 kn n Sk exp j LN N k 0 LN N kn LN Sk exp j LN k 0 LN N N 1 NL1 1 2kn 2kn L N Sk exp j 0exp j LN k 0 LN k N LN NL1 1 2 kn L N Sk exp j L N IDFT S n LN k 0 LN Zero padding: S k Sk, 0k N 0, N k LN

25 Overapling: Suary T N point LN point L n n N IDFTSn n n L N IDFT S n N LN 0 nn 0 n LN T Zero padding: S k Sk, 0k N 0, N k LN

26 26 OFDM ipleentation by IFFT/FFT

27 Chapter 5 OFDM Cyclic Prefix 27 Office Hour: BKD Tueday 14:00-16:00 Thurday 9:30-11:30

28 Cyclic Prefix Can we eliinate the ultipath proble? 28

29 N n L L-1 N N-1 Convolution x Flip Shift Multiply Add h h = h 0 h 1 x hn xhn h n h N 1 h N h N + L 2 29

30 N n n L L-1 L L-1 N N-1 N N-1 Circular Convolution x x h h h = h 0 h = h 0 h 1 h 1 h n h n h N 1 h N 1 30 Replicate x Then, perfor the uual convolution only on n = 0 to N-1 h N h N + L 2