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IMT Advanced

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Pakistan Telecommunication Authority

OFDM is a high-speed wireless transmission technology that divides the available spectrum into multiple orthogonal subcarriers. It is implemented as OFDMA to support multi-user communication. OFDM provides advantages over single carrier transmission by combating inter-symbol interference and frequency selective fading. It works by encoding data over multiple carrier frequencies, with spacing between carriers chosen so that the carriers are orthogonal to each other. This allows high data rates without overlapping signals at a receiver.

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Core Technologies for 4G: OFDM Prof. Chung G. Kang KOREA University ccgkang@korea.ac.kr 4G Mobile (IMT Advanced) System and Applications
OFDM: Overview • High-speed wireless transmission technology • Implemented as a useful means of multiple access to support the multi-user communication, as OFDMA (Orthogonal Frequency Division Multiple Access) • Adopted for the candidate radio interface technologies for IMT-Advanced in ITU-R
• Rayleigh Fading Channel Model • Time Dispersion due to Multi-path Fading MOBILE Moving directionRoad Buildings i 2 ( cos ) 1 ( ) Re ( ) c d i i n j f f t R i i s t As t e              cd f c v f where RMS Delay Spread (t) t t ( )t ( )t Ideal Channel Non-ideal Channel Broadband Wireless Channel (1)
• Ideal Channel vs. Non-ideal Channel +( )s t ( )s t ( )n t ( )h t - Ideal channel ( )h t | ( ) |H f - Non-ideal channel ft ( )h t | ( ) |H f ft ( )t ( )t ( )t Broadband Wireless Channel (2)
• Delay Spread and Inter-Symbol Interference (ISI) Symbol 1 Ts s < Ts 0 1 2 3 Symbol 1 1 2 3 Symbol 2 s >> Ts Ts 0 1 2 3 1 2 3 ( ) 0 1 1 2 2 3 3, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )h t t t t t= + - + - + -% % % % %t a d t a d t t a d t t a d t t Broadband Wireless Channel (3) Higher-speed transmission suffers from the more multipath fading (more ISI)!
• Delay Spread and Frequency Selectivity ( )h t | ( ) |H f ft 1( )t ( )t ( )h t t 1( )t ( )t 2( )t  | ( ) |H f f Bc Bc ~ s ~ s Bs - Frequency flat - Frequency selective Bs Bs : Signal Bandwidth Bc: Coherence Bandwidth Broadband Wireless Channel (4) Ts Ts
( ) 1 2 2, ( ) ( ) ( ) ( )h t t tt a d t a d t t= + -% % % • General Fading Channel Broadband Wireless Channel (5) Channel varies with both frequency and time, i.e., frequency selectivity varies with the times, depending on the mobile speed
Equalizer Channel Equalization 0 T ( )h t { }nx { }ny 0h 1h 2 0 2 1 1 3 0 3 1 2 y h x h x n y h x h x n       • Optimum Channel Equalization - Maximum likelihood sequence equalization (MLSE) + n 2 3 0 1 2 3 Given { , } and { , }, determine { , } y y h h x x  2 3 2* * 2 2 3 2 0 2 1 1 3 0 3 1 2 ( , ) ˆ ˆ( , ) min ( ) { ( )} x x S x x y h x h x y h x h x           - Illustrative example {1, 1}nx   ˆ{ }nx where {(1,1),(1, 1),( 1,1),( 1, 1)}S       2 | | 2 4S   In general, | | L S M where M is the number of symbols and L is the number of multi-paths Too complex!
Discrete Fourier Transform (DFT) 2 ( ) ( ) j ft X f x t e dt     ( )X f ( )x t ( ) n s n X f X f T            ( )X f nx sT 1/ sT 2 0 kN j n N k n n X x e     nx N N kX f f k DFT:
Serial to Parallel Conv. x x x + Modulator RF • Transmitter sT 0cos2 f t 1cos2 f t 1cos2 Nf t  OFDM: Basic Concept (1) sN T 1/s sR T sN T { }nx 0x 1x 1Nx  sN T ( )b t ( )s t Orthogonality:   0 cos2 cos2 0 sNT i jf t f t dt   for all i j 1 0 ( ) cos2 N n n n s t x f t     OFDM symbol
• Receiver OFDM: Basic Concept (2) ( )s t Down Conv. x 0cos2 f t sN T x x 1cos2 f t 1cos2 Nf t  1x 1Nx  Serial to Parallel Conv. De- modulator 0x 0 0 0 1 1 2 ( )cos(2 ) 2 cos(2 ) cos(2 ) 2 cos(2 ) cos(2 ) 2 cos(2 ) cos(2 ) sNT n n n n n N N n n s t f t dt x f t f t x f t f t x f t f t x                        Too many carriers…. How to implement this?
0f • OFDM = N Parallel Narrowband Channels 0x OFDM: Basic Concept (3) 1f 3f2f 1x 2x
OFDM: Basic Concept (4) 0 • Time Domain: OFDM Symbol • Frequency Domain: Subcarriers ( ) cos(2 ) (0, )n n ns t x f t rect T  ( ) ( )*sinc( ) sinc( ( )) n n n n n S f x f f fT x f f        (0, )rect T T sT N T  0x 1x 1Nx  0 t T  1cos(2 )f t 2cos(2 )f t 3cos(2 )f t
OFDM: Implementation (1) • Block Diagram 1 2 ( / ) 0 N j k N n n k k x X e      1 2 ( / ) 0 1 2 ( / ) 0 N j k N n k nk N j k N n n kk Y y e a x e aX              { }kX { }kY 0x 1x 1Nx  - Illustration: single-path channel ˆ/k kX Y a
• Block Diagram kX kH kY ?k k kY H X { }kX { }kY 0x 1x 1Nx  - Illustration: multi-path channel OFDM: Implementation (2)
Cyclic Prefix (1) 1 0 2 exp 2 k n n H h jk n           0 1 2 0 H H   2 0 2 exp 3 k n n X x jk n           0 1 2 3 0 0 X X X    2 0 2 exp 3 k n n Y y jk n           0 1 2 5 1 2 3 1- 2 3 Y Y Y     k k kY H X • Effect of Multi-path Channel - Illustrating example
1 0 2 exp 2 k n n H h jk n           0 1 2 0 H H   2 0 2 exp 3 k n n X x jk n                   2 0 3 2 exp][ n n njkykY  0 1 2 6 0 0 Y Y Y    , 1,2k k kY H X k  0 1 2 3 0 0 X X X    Cyclic Prefix (2) • Effect of Multi-path Channel - Illustrating example Cyclic prefix
• Guard Interval vs. Cyclic Prefix - Inter-symbol Interference (ISI) & guard Interval - Inter-carrier Interference & cyclic prefix  Zero-valued guard interval FFT interval Guard interval Cyclic prefix Guard interval  FFT interval No ICI and no ISI No ISI but ICI Guard interval Cyclic Prefix (3)
subTGT sym sub GT T T  No guard interval Orthogonality maintained by inserting CP ISI can be avoided by the guard interval Cyclic Prefix (4) • Effect of CP: Illustration
FFT period FFT periodGI Subcarrier #1 Subcarrier #2 CP Delayed Subcarrier #2
f t Effective BW FFT size Guard interval TG Effective symbol duration Tsub copy 1 1 0 1 2 1 1{ , , , , , , , , , }N L N N N L N L N NX X X X X X X X X X        0x 1x 1Nx  OFDM: Overall Picture • OFDM Symbol in 3D OFDM Symbol
OFDM: Performance • Effect of Delay Spread (b) Delay exceeds guard time by 3% of the FFT interval. (c) Delay exceeds guard time by 10% of the FFT interval. - What if delay exceeds the guard time (CP)?
Windowing • Power Spectrum Density - The side-lobe of spectrum decreases with the larger number of subcarriers - The out-of-band spectrum decreases slowly, due to a sinc function - Raised cosine windowing
Guard Band Guard BandData Subcarrier BandGuard Band Guard BandData Subcarrier Band - Adjacent Channel Interference (ACI) - Guard Band Guard Band & ACI • Illustrative Example: N = 1024 (IEEE 802.16e) Channel 1 Channel 2 Channel 3 Adjacent channel interference Channel 2 Unused Subcarriers for guard band
SNR Coded OFDM - Some subcarriers suffered by frequency selective fading must be protected by forward error correction (FEC) coding • Why Coded OFDM?
OFDM: Block Diagram • Overall Block Diagram
Water-filling (1) { }kX { }kY 0x 1x 1Nx  • System Model , 1,2, , 1n n n ny h x n N    - The frequency selective channel transformed to a parallel channel • AWGN Capacity 21 0 0 | | log 1 N n n P h C N           - Total capacity = sum capacity of each channel where 2 {| | }, 0,1,2, , 1nP E x n N   What if we allocate the different power to each subcarrier?
Water-filling (2) • Power Allocation Problem for a Parallel Channel - Assume that each subcarrier is allocated with power Pn. - Problem statement - Optimal power allocation: where the Lagrange multiplier is chosen such that the power constraint is met: 0 1 2 1 ,..., 0 0 m ax log 1 , c c N c N n n N P P n P h C N              1,...,0,0, 1 0    cnc N n n NnPPNP c             2 0* ~ 1 n n h N P  .~ 11 1 0 2 0 P h N N cN n n c                  subject to
Water-filling (3) • Water-filling Interpretation - If P units of water per sub-carrier are filled into the vessel, the depth of the water at subcarrier n is the power allocated to that sub-carrier Height of the water surface - Optimal power allocation: The better a channel, the more power! Inverse of Channel gain             2 0* ~ 1 n n h N P 
• Illustrative Example x x Rb bps/Wb Hz Digital Modulation Base Station x x Digital Demodulation Information bits for User 1 Rc >> Rb bps x + C1 C2 Rb bps/Wb Hz User 1 User 2 Multiple Access: CDMA (1) C1
• Processing Gain & Interference 0 b b required required EC R I N W             1 b b R T  1 c W T  Processing Gain = b b c W T R T  0 6 10 3 (dB) (dB) 1.2288 10 6 10 log 6 21.1 15.1dB 9.6 10 b required brequired EC W I N R                       - Example:  0 9,600Hz; 1.2288MHz; / 6dBb b required R W E N   Multiple Access: CDMA (2)
• Processing Gain & Data Rate - Processing gain varies with the data rate for the fixed chip rate system - Example: Rc = 1.2288Mcps  The higher the data rate is, the lower the processing gain is!  To maintain the processing gain, more bandwidth is required for higher data rate Rb = 9.6kbps  PG = 128 Rb = 4.8kbps  PG = 256 - Example: For W = 20Mbps with PG = 128, Rb = W/PG ~ 150kbps  The maximum possible data is limited to 150kbps with CDMA! Rc Rb 2Rb Multiple Access: CDMA (3) • Illustrative Example Chip
Serial to Parallel Converter X X X + Modulator RF sT 0cos2 f t 1cos2 f t 1cos2 Nf t  sNT sNT sNT • Orthogonal Frequency Division Multiplexing (OFDM) X X X + RF )(ts 0cos2 f t 1cos2 f t 1cos2 Nf t  sNT • Orthogonal Frequency Division Multiple Access (OFDMA) sNT User 0 User 1 User N-1 Modulator Modulator Modulator Multiple Access: OFDMA (1) 0x 1x 1Nx  ( )s t 0x 1x 1Nx 
User #2 User #1 • OFDMA Concept  Multiuser OFDM (OFDM + FDMA) - Subchannel: a set of subcarrier as a basic resource allocation unit - Why OFDMA? Multiple Access: OFDMA (2)
• Multiple Access with OFDM - Resource units: Subchannels or Resource Block Frequency Time OFDM symbol Subchannel Multiple Access: OFDMA (3) Subframe Subcarrier User 1 User 2 User 3 User 4 By assigning different time/frequency slots to users, they can be kept orthogonal, no matter how much the delay spread is….
Cellular OFDMA (1) 0 max max 0 0 2 max ( ) ( ) ( ) ( ) ( ) ( )u u k k k k k k P d N N d dC PNI N d p d d N            • Co-channel Interference in OFDMA Network max uN p N  maxN Cell F0 Cell F1 Fully loaded Loading factor = p uN 0 bEC R I N W   cf) CDMA 1/Processing Gain 0( )d 1( )d 2( )d - C/I ratio for subcarrier P -500 0 500 -800 -600 -400 -200 0 200 400 600 800 in meter inmeter 10 20 30 40 50 60 - Downlink
• Subcarrier Allocation for Interference Averaging - Example x1 x2 X1 X2 Without frequency hopping With frequency hopping - Interference averaging with frequency hopping  interference diversity Cellular OFDMA (2)
• Hopping Pattern for Subcarrier Allocation - To design the hopping patterns with a period of Nc OFDM symbols that are as apart as possible for neighbor BSs (Nc: prime number)  Every user hops over all the sub-carriers in each period  frequency diversity  Each user occupies different sub-carriers in any OFDM symbol time - Latin square  Nc x Nc matrix  Example: Nc = 5 Cellular OFDMA (3)
• Orthogonal Latin Squares - Latin squares that gives exactly one time/sub-carrier collision for every pair of virtual channels of two base stations  Ra and Rb are orthogonal if a is not equal to b - Generation rule:  Example: a = 2 & Nc = 5 • Inter-BS Synchronization - OFDM symbol-level synchronization required Cellular OFDMA (4)
• OFDM Parameters: Numerology (TDD) Nominal Channel Bandwidth (W) 8.75MHz Over-sampling Factor (n) 8/7 Sampling Frequency (Fs) 10 MHz FFT Size (Nfft) 1,024 Sub-Carrier Spacing ( f) 9.765625kHz Useful Symbol Time (Tb ) 102.4 µs Cyclic Prefix (CP) Tg=1/8 Tb Symbol Time (Ts ) 115.2 µs TDD Number of OFDM symbols per Frame 42 TTG + RTG (µs) 161.6 Number of Guard Sub-Carriers Left 80 Right 79 Number of Used Sub-Carriers 865 IEEE 802.16e: PHY Parameters Tg Tb Ts sF nW 1/bT f  /s fftf F N  1/ 9.765625 kHzbf T   2 8.75MHz 9.765625kHz 896m fftN    1024fftN   (9.765625)(1024) 10MHzs fftF f N    / 10/8.75 8/ 7sn F W    102.4 μsbT 
• TDD Frame Structure 115.2us IEEE 802.16e: Frame Structure 24 symbols 12 symbols
• Downlink Syntax Value Notes Total # of subcarriers 768 768 = 24 bands * 4 bins/band * 8 subcarriers/bin # of frames / sec 200 1 / 5 ms/frame = 200 (frames/sec) OFDM symbols / frame 42 42 symbols = 27 DL symbols + 15 UL symbols OFDM symbol rate 5400 200 (frames/sec) * 27 (symbols/frame) = 5400 (symbols/sec) Data subcarrier rate 4.1472 5400 (symbols/sec)* 768 (subcarriers/symbol) = 4.1472 (Msubcarriers/sec) Max. bits/subcarrier Min. bits/subcarrier 5 5/36 MAX: R = 5/6 coding & 64 QAM  5/6 * log2(64) = 5 (bits/subcarrier) MIN: R = 1/12 coding & QPSK  1/12 * log2(4) = 5/36 (bits/subcarrier) Max. data rate (Mbps) Min. data rate (Mbps) 20.736 0.576 4.1472 (Msubcarriers/sec) * 5 (bits/subcarrier) = 20.736 (Mbps) 4.1472 (Msubcarriers/sec) * 5/36 (bits/subcarrier) = 576 (kbps) IEEE 802.16e: Data Rate • Uplink Syntax Value Notes OFDM symbol rate 3000 200 (frames/sec) * 15 (symbols/frame) = 3000 (symbols/sec) Data subcarrier rate 2.3040 3000 (symbols/sec)* 768 (subcarriers/symbol) = 2.304 (Msubcarriers/sec) Max. bits/subcarrier Min. bits/subcarrier 10/3 5/36 MAX: R = 5/6 coding & 16 QAM  5/6 * log2(16) = 10/3 (bits/subcarrier) MIN: R = 1/12 coding & QPSK  1/12 * log2(4) = 5/36 (bits/subcarrier) Max. data rate (Mbps) Min. data rate (Mbps) 7.68 0.320 2.304 (Msubcarriers/sec) * 10/3 (bits/subcarrier) = 7.68 (Mbps) 2.304 (Msubcarriers/sec) * 5/36 = 320 (kbps)
IEEE 802.16m (1) • Basic Frame Structure - The number of OFDMA symbols varies with the length of CP. - Type-1, type-2, type-3, type-4 subframes
IEEE 802.16m (2) • Frame Structure with Type-1 Subframe (FDD) - 5MHz, 10MHz, 20MHz bandwidth
IEEE 802.16m (3) • Frame Structure with Type-1 Subframe (TDD)
• OFDM Parameters: Numerology (FDD) Nominal Channel Bandwidth (MHz) 5 7 8.75 10 20 Over-sampling Factor 28/25 8/7 8/7 28/25 28/25 Sampling Frequency (MHz) 5.6 8 10 11.2 22.4 FFT Size 512 1024 1024 1024 2048 Sub-Carrier Spacing (kHz) 10.937500 7.812500 9.765625 10.937500 10.937500 Useful Symbol Time Tu (µs) 91.429 128 102.4 91.429 91.429 Cyclic Prefix (CP) Tg=1/8 Tu Symbol Time Ts (µs) 102.857 144 115.2 102.857 102.857 FDD Number of OFDM symbols per Frame 48 34 43 48 48 Idle time (µs) 62.857 104 46.40 62.857 62.857 Cyclic Prefix (CP) Tg=1/16 Tu Symbol Time Ts (µs) 97.143 136 108.8 97.143 97.143 FDD Number of OFDM symbols per Frame 51 36 45 51 51 Idle time (µs) 45.71 104 104 45.71 45.71 Cyclic Prefix (CP) Tg=1/4 Tu Symbol Time Ts (µs) 114.286 160 128 114.286 114.286 FDD Number of OFDM symbols per Frame 43 31 39 43 43 Idle time (µs) 85.694 40 8 85.694 85.694 Number of Guard Sub-Carriers Left 40 80 80 80 160 Right 39 79 79 79 159 Number of Used Sub-Carriers 433 865 865 865 1729 Number of Physical Resource Unit (18x6) in a type-1 sub-frame 24 48 48 48 96 IEEE 802.16m (4)
• OFDM Parameters: Numerology (TDD) Nominal Channel Bandwidth (MHz) 5 7 8.75 10 20 Over-sampling Factor 28/25 8/7 8/7 28/25 28/25 Sampling Frequency (MHz) 5.6 8 10 11.2 22.4 FFT Size 512 1024 1024 1024 2048 Sub-Carrier Spacing (kHz) 10.937500 7.812500 9.765625 10.937500 10.937500 Useful Symbol Time Tu (µs) 91.429 128 102.4 91.429 91.429 Cyclic Prefix (CP) Tg=1/8 Tu Symbol Time Ts (µs) 102.857 144 115.2 102.857 102.857 TDD Number of OFDM symbols per Frame 47 33 42 47 47 TTG + RTG (µs) 165.714 248 161.6 165.714 165.714 Cyclic Prefix (CP) Tg=1/16 Tu Symbol Time Ts (µs) 97.143 136 108.8 97.143 97.143 TDD Number of OFDM symbols per Frame 50 35 44 50 50 TTG + RTG (µs) 142.853 240 212.8 142.853 142.853 Cyclic Prefix (CP) Tg=1/4 Tu Symbol Time Ts (µs) 114.286 160 128 114.286 114.286 TDD Number of OFDM symbols per Frame 42 30 38 42 42 TTG + RTG (µs) 199.98 200 136 199.98 199.98 Number of Guard Sub-Carriers Left 40 80 80 80 160 Right 39 79 79 79 159 Number of Used Sub-Carriers 433 865 865 865 1729 Number of Physical Resource Units (18x6) in a type-1 sub-frame 24 48 48 48 96 IEEE 802.16m (5)
• Frame Structure - FDD - TDD 3GPP LTE (1)
Subframe #0 DwPTS Subframe #2 Subframe #3 Subframe #4 Subframe #5 Subframe #7 Subframe #8 Subframe #9 GP UwPTS DwPTS GP UwPTS Subframe #0 DwPTS Subframe #2 Subframe #3 Subframe #4 Subframe #5 Subframe #7 Subframe #8 Subframe #9 GP UwPTS Subframe #6 One radio frame (10 ms) 10 ms switch-point periodicty 5 ms switch-point periodicty : DL subframe : UL subframe DwPTS GP UwPTS : Special subframe Configuration 0 1 2 3 4 5 5 Switch-point periodicity 5 ms 5 ms 5 ms 10 ms 10 ms 10 ms 10 ms Subframe number 0 1 2 3 4 5 6 7 8 9 D D D D D D D S S S S S S S U U U U U U U U U D U U D U U D D U D D U D D D D D D D S S S D D D S U U U D D D U U U D D D D U U D D D D D D Uplink-downlink allocations • Periodic Switch-Point Operation for TDD Frame Structure 3GPP LTE (2)
DL symbN slotT 0l 1DL symb  Nl RB sc DL RBNN RB scN RB sc DL symb NN  ),( lk 0k 1RB sc DL RB  NNk • Slot Structure and Physical Resource Element: Downlink ( , )k l RB sc DL RB NN - Resource grid subcarriers and DL symbN OFDM symbols - Resource element Each element in the resource grid, uniquely defined by the index pair - Resource block RB scNDL symbN To describe the mapping of certain physical channels to resource elements, in terms of OFDM symbols and consecutive subcarriers 3GPP LTE (3)
Nominal Channel Bandwidth (MHz) 1.4 3 5 10 15 20 Over-sampling Factor 48/35 96/75 43/28 43/28 43/28 43/28 Sampling Frequency (MHz) 1.92 3.84 7.68 15.36 23.04 30.72 FFT Size 128 256 512 1024 1536 2048 Sub-Carrier Spacing (kHz) 15 15 15 15 15 15 Useful Symbol Time Tu (µs) 66.7 66.7 66.7 66.7 66.7 66.7 Normal Cyclic Prefix (CP) Tg=4.7us Symbol Time Ts (µs) 71.4 71.4 71.4 71.4 71.4 71.4 FDD Number of OFDM symbols per Half Frame 70 70 70 70 70 70 Idle time (µs) . . . . . . Extended Cyclic Prefix (CP) Tg=16.7us Symbol Time Ts (µs) 83.4 83.4 83.4 83.4 83.4 83.4 FDD Number of OFDM symbols per Half Frame 60 60 60 60 60 60 Idle time (µs) . . . . . . Number of Guard Sub-Carriers Left 28 38 106 212 318 424 Right 28 38 106 212 318 424 Number of Used Sub-Carriers 72 180 300 600 900 1200 Number of Physical Resource elements (12x7) in a resource block 6 15 25 50 75 100 • OFDM Parameters: FDD 3GPP LTE (1)
Nominal Channel Bandwidth (MHz) 1.4 3 5 10 15 20 Over-sampling Factor 48/35 96/75 43/28 43/28 43/28 43/28 Sampling Frequency (MHz) 1.92 3.84 7.68 15.36 23.04 30.72 FFT Size 128 256 512 1024 1536 2048 Sub-Carrier Spacing (kHz) 15 15 15 15 15 15 Useful Symbol Time Tu (µs) 66.7 66.7 66.7 66.7 66.7 66.7 Normal Cyclic Prefix (CP) Tg=4.7us Symbol Time Ts (µs) 71.4 71.4 71.4 71.4 71.4 71.4 TDD Number of OFDM symbols per Half Frame 68 68 68 68 68 68 GP (µs) 142.8 142.8 142.8 142.8 142.8 142.8 Extended Cyclic Prefix (CP) Tg=16.7us Symbol Time Ts (µs) 83.4 83.4 83.4 83.4 83.4 83.4 TDD Number of OFDM symbols per Half Frame 59 59 59 59 59 59 GP (µs) 83.4 83.4 83.4 83.4 83.4 83.4 Number of Guard Sub-Carriers Left 28 38 106 212 318 424 Right 28 38 106 212 318 424 Number of Used Sub-Carriers 72 180 300 600 900 1200 Number of Physical Resource elements (12x7) in a resource block 6 15 25 50 75 100 • OFDM Parameters: TDD 3GPP LTE (2)

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IMT Advanced

  • 1. Core Technologies for 4G: OFDM Prof. Chung G. Kang KOREA University ccgkang@korea.ac.kr 4G Mobile (IMT Advanced) System and Applications
  • 2. OFDM: Overview • High-speed wireless transmission technology • Implemented as a useful means of multiple access to support the multi-user communication, as OFDMA (Orthogonal Frequency Division Multiple Access) • Adopted for the candidate radio interface technologies for IMT-Advanced in ITU-R
  • 3. • Rayleigh Fading Channel Model • Time Dispersion due to Multi-path Fading MOBILE Moving directionRoad Buildings i 2 ( cos ) 1 ( ) Re ( ) c d i i n j f f t R i i s t As t e              cd f c v f where RMS Delay Spread (t) t t ( )t ( )t Ideal Channel Non-ideal Channel Broadband Wireless Channel (1)
  • 4. • Ideal Channel vs. Non-ideal Channel +( )s t ( )s t ( )n t ( )h t - Ideal channel ( )h t | ( ) |H f - Non-ideal channel ft ( )h t | ( ) |H f ft ( )t ( )t ( )t Broadband Wireless Channel (2)
  • 5. • Delay Spread and Inter-Symbol Interference (ISI) Symbol 1 Ts s < Ts 0 1 2 3 Symbol 1 1 2 3 Symbol 2 s >> Ts Ts 0 1 2 3 1 2 3 ( ) 0 1 1 2 2 3 3, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )h t t t t t= + - + - + -% % % % %t a d t a d t t a d t t a d t t Broadband Wireless Channel (3) Higher-speed transmission suffers from the more multipath fading (more ISI)!
  • 6. • Delay Spread and Frequency Selectivity ( )h t | ( ) |H f ft 1( )t ( )t ( )h t t 1( )t ( )t 2( )t  | ( ) |H f f Bc Bc ~ s ~ s Bs - Frequency flat - Frequency selective Bs Bs : Signal Bandwidth Bc: Coherence Bandwidth Broadband Wireless Channel (4) Ts Ts
  • 7. ( ) 1 2 2, ( ) ( ) ( ) ( )h t t tt a d t a d t t= + -% % % • General Fading Channel Broadband Wireless Channel (5) Channel varies with both frequency and time, i.e., frequency selectivity varies with the times, depending on the mobile speed
  • 8. Equalizer Channel Equalization 0 T ( )h t { }nx { }ny 0h 1h 2 0 2 1 1 3 0 3 1 2 y h x h x n y h x h x n       • Optimum Channel Equalization - Maximum likelihood sequence equalization (MLSE) + n 2 3 0 1 2 3 Given { , } and { , }, determine { , } y y h h x x  2 3 2* * 2 2 3 2 0 2 1 1 3 0 3 1 2 ( , ) ˆ ˆ( , ) min ( ) { ( )} x x S x x y h x h x y h x h x           - Illustrative example {1, 1}nx   ˆ{ }nx where {(1,1),(1, 1),( 1,1),( 1, 1)}S       2 | | 2 4S   In general, | | L S M where M is the number of symbols and L is the number of multi-paths Too complex!
  • 9. Discrete Fourier Transform (DFT) 2 ( ) ( ) j ft X f x t e dt     ( )X f ( )x t ( ) n s n X f X f T            ( )X f nx sT 1/ sT 2 0 kN j n N k n n X x e     nx N N kX f f k DFT:
  • 10. Serial to Parallel Conv. x x x + Modulator RF • Transmitter sT 0cos2 f t 1cos2 f t 1cos2 Nf t  OFDM: Basic Concept (1) sN T 1/s sR T sN T { }nx 0x 1x 1Nx  sN T ( )b t ( )s t Orthogonality:   0 cos2 cos2 0 sNT i jf t f t dt   for all i j 1 0 ( ) cos2 N n n n s t x f t     OFDM symbol
  • 11. • Receiver OFDM: Basic Concept (2) ( )s t Down Conv. x 0cos2 f t sN T x x 1cos2 f t 1cos2 Nf t  1x 1Nx  Serial to Parallel Conv. De- modulator 0x 0 0 0 1 1 2 ( )cos(2 ) 2 cos(2 ) cos(2 ) 2 cos(2 ) cos(2 ) 2 cos(2 ) cos(2 ) sNT n n n n n N N n n s t f t dt x f t f t x f t f t x f t f t x                        Too many carriers…. How to implement this?
  • 12. 0f • OFDM = N Parallel Narrowband Channels 0x OFDM: Basic Concept (3) 1f 3f2f 1x 2x
  • 13. OFDM: Basic Concept (4) 0 • Time Domain: OFDM Symbol • Frequency Domain: Subcarriers ( ) cos(2 ) (0, )n n ns t x f t rect T  ( ) ( )*sinc( ) sinc( ( )) n n n n n S f x f f fT x f f        (0, )rect T T sT N T  0x 1x 1Nx  0 t T  1cos(2 )f t 2cos(2 )f t 3cos(2 )f t
  • 14. OFDM: Implementation (1) • Block Diagram 1 2 ( / ) 0 N j k N n n k k x X e      1 2 ( / ) 0 1 2 ( / ) 0 N j k N n k nk N j k N n n kk Y y e a x e aX              { }kX { }kY 0x 1x 1Nx  - Illustration: single-path channel ˆ/k kX Y a
  • 15. • Block Diagram kX kH kY ?k k kY H X { }kX { }kY 0x 1x 1Nx  - Illustration: multi-path channel OFDM: Implementation (2)
  • 16. Cyclic Prefix (1) 1 0 2 exp 2 k n n H h jk n           0 1 2 0 H H   2 0 2 exp 3 k n n X x jk n           0 1 2 3 0 0 X X X    2 0 2 exp 3 k n n Y y jk n           0 1 2 5 1 2 3 1- 2 3 Y Y Y     k k kY H X • Effect of Multi-path Channel - Illustrating example
  • 17. 1 0 2 exp 2 k n n H h jk n           0 1 2 0 H H   2 0 2 exp 3 k n n X x jk n                   2 0 3 2 exp][ n n njkykY  0 1 2 6 0 0 Y Y Y    , 1,2k k kY H X k  0 1 2 3 0 0 X X X    Cyclic Prefix (2) • Effect of Multi-path Channel - Illustrating example Cyclic prefix
  • 18. • Guard Interval vs. Cyclic Prefix - Inter-symbol Interference (ISI) & guard Interval - Inter-carrier Interference & cyclic prefix  Zero-valued guard interval FFT interval Guard interval Cyclic prefix Guard interval  FFT interval No ICI and no ISI No ISI but ICI Guard interval Cyclic Prefix (3)
  • 19. subTGT sym sub GT T T  No guard interval Orthogonality maintained by inserting CP ISI can be avoided by the guard interval Cyclic Prefix (4) • Effect of CP: Illustration
  • 20. FFT period FFT periodGI Subcarrier #1 Subcarrier #2 CP Delayed Subcarrier #2
  • 21. f t Effective BW FFT size Guard interval TG Effective symbol duration Tsub copy 1 1 0 1 2 1 1{ , , , , , , , , , }N L N N N L N L N NX X X X X X X X X X        0x 1x 1Nx  OFDM: Overall Picture • OFDM Symbol in 3D OFDM Symbol
  • 22. OFDM: Performance • Effect of Delay Spread (b) Delay exceeds guard time by 3% of the FFT interval. (c) Delay exceeds guard time by 10% of the FFT interval. - What if delay exceeds the guard time (CP)?
  • 23. Windowing • Power Spectrum Density - The side-lobe of spectrum decreases with the larger number of subcarriers - The out-of-band spectrum decreases slowly, due to a sinc function - Raised cosine windowing
  • 24. Guard Band Guard BandData Subcarrier BandGuard Band Guard BandData Subcarrier Band - Adjacent Channel Interference (ACI) - Guard Band Guard Band & ACI • Illustrative Example: N = 1024 (IEEE 802.16e) Channel 1 Channel 2 Channel 3 Adjacent channel interference Channel 2 Unused Subcarriers for guard band
  • 25. SNR Coded OFDM - Some subcarriers suffered by frequency selective fading must be protected by forward error correction (FEC) coding • Why Coded OFDM?
  • 26. OFDM: Block Diagram • Overall Block Diagram
  • 27. Water-filling (1) { }kX { }kY 0x 1x 1Nx  • System Model , 1,2, , 1n n n ny h x n N    - The frequency selective channel transformed to a parallel channel • AWGN Capacity 21 0 0 | | log 1 N n n P h C N           - Total capacity = sum capacity of each channel where 2 {| | }, 0,1,2, , 1nP E x n N   What if we allocate the different power to each subcarrier?
  • 28. Water-filling (2) • Power Allocation Problem for a Parallel Channel - Assume that each subcarrier is allocated with power Pn. - Problem statement - Optimal power allocation: where the Lagrange multiplier is chosen such that the power constraint is met: 0 1 2 1 ,..., 0 0 m ax log 1 , c c N c N n n N P P n P h C N              1,...,0,0, 1 0    cnc N n n NnPPNP c             2 0* ~ 1 n n h N P  .~ 11 1 0 2 0 P h N N cN n n c                  subject to
  • 29. Water-filling (3) • Water-filling Interpretation - If P units of water per sub-carrier are filled into the vessel, the depth of the water at subcarrier n is the power allocated to that sub-carrier Height of the water surface - Optimal power allocation: The better a channel, the more power! Inverse of Channel gain             2 0* ~ 1 n n h N P 
  • 30. • Illustrative Example x x Rb bps/Wb Hz Digital Modulation Base Station x x Digital Demodulation Information bits for User 1 Rc >> Rb bps x + C1 C2 Rb bps/Wb Hz User 1 User 2 Multiple Access: CDMA (1) C1
  • 31. • Processing Gain & Interference 0 b b required required EC R I N W             1 b b R T  1 c W T  Processing Gain = b b c W T R T  0 6 10 3 (dB) (dB) 1.2288 10 6 10 log 6 21.1 15.1dB 9.6 10 b required brequired EC W I N R                       - Example:  0 9,600Hz; 1.2288MHz; / 6dBb b required R W E N   Multiple Access: CDMA (2)
  • 32. • Processing Gain & Data Rate - Processing gain varies with the data rate for the fixed chip rate system - Example: Rc = 1.2288Mcps  The higher the data rate is, the lower the processing gain is!  To maintain the processing gain, more bandwidth is required for higher data rate Rb = 9.6kbps  PG = 128 Rb = 4.8kbps  PG = 256 - Example: For W = 20Mbps with PG = 128, Rb = W/PG ~ 150kbps  The maximum possible data is limited to 150kbps with CDMA! Rc Rb 2Rb Multiple Access: CDMA (3) • Illustrative Example Chip
  • 33. Serial to Parallel Converter X X X + Modulator RF sT 0cos2 f t 1cos2 f t 1cos2 Nf t  sNT sNT sNT • Orthogonal Frequency Division Multiplexing (OFDM) X X X + RF )(ts 0cos2 f t 1cos2 f t 1cos2 Nf t  sNT • Orthogonal Frequency Division Multiple Access (OFDMA) sNT User 0 User 1 User N-1 Modulator Modulator Modulator Multiple Access: OFDMA (1) 0x 1x 1Nx  ( )s t 0x 1x 1Nx 
  • 34. User #2 User #1 • OFDMA Concept  Multiuser OFDM (OFDM + FDMA) - Subchannel: a set of subcarrier as a basic resource allocation unit - Why OFDMA? Multiple Access: OFDMA (2)
  • 35. • Multiple Access with OFDM - Resource units: Subchannels or Resource Block Frequency Time OFDM symbol Subchannel Multiple Access: OFDMA (3) Subframe Subcarrier User 1 User 2 User 3 User 4 By assigning different time/frequency slots to users, they can be kept orthogonal, no matter how much the delay spread is….
  • 36. Cellular OFDMA (1) 0 max max 0 0 2 max ( ) ( ) ( ) ( ) ( ) ( )u u k k k k k k P d N N d dC PNI N d p d d N            • Co-channel Interference in OFDMA Network max uN p N  maxN Cell F0 Cell F1 Fully loaded Loading factor = p uN 0 bEC R I N W   cf) CDMA 1/Processing Gain 0( )d 1( )d 2( )d - C/I ratio for subcarrier P -500 0 500 -800 -600 -400 -200 0 200 400 600 800 in meter inmeter 10 20 30 40 50 60 - Downlink
  • 37. • Subcarrier Allocation for Interference Averaging - Example x1 x2 X1 X2 Without frequency hopping With frequency hopping - Interference averaging with frequency hopping  interference diversity Cellular OFDMA (2)
  • 38. • Hopping Pattern for Subcarrier Allocation - To design the hopping patterns with a period of Nc OFDM symbols that are as apart as possible for neighbor BSs (Nc: prime number)  Every user hops over all the sub-carriers in each period  frequency diversity  Each user occupies different sub-carriers in any OFDM symbol time - Latin square  Nc x Nc matrix  Example: Nc = 5 Cellular OFDMA (3)
  • 39. • Orthogonal Latin Squares - Latin squares that gives exactly one time/sub-carrier collision for every pair of virtual channels of two base stations  Ra and Rb are orthogonal if a is not equal to b - Generation rule:  Example: a = 2 & Nc = 5 • Inter-BS Synchronization - OFDM symbol-level synchronization required Cellular OFDMA (4)
  • 40. • OFDM Parameters: Numerology (TDD) Nominal Channel Bandwidth (W) 8.75MHz Over-sampling Factor (n) 8/7 Sampling Frequency (Fs) 10 MHz FFT Size (Nfft) 1,024 Sub-Carrier Spacing ( f) 9.765625kHz Useful Symbol Time (Tb ) 102.4 µs Cyclic Prefix (CP) Tg=1/8 Tb Symbol Time (Ts ) 115.2 µs TDD Number of OFDM symbols per Frame 42 TTG + RTG (µs) 161.6 Number of Guard Sub-Carriers Left 80 Right 79 Number of Used Sub-Carriers 865 IEEE 802.16e: PHY Parameters Tg Tb Ts sF nW 1/bT f  /s fftf F N  1/ 9.765625 kHzbf T   2 8.75MHz 9.765625kHz 896m fftN    1024fftN   (9.765625)(1024) 10MHzs fftF f N    / 10/8.75 8/ 7sn F W    102.4 μsbT 
  • 41. • TDD Frame Structure 115.2us IEEE 802.16e: Frame Structure 24 symbols 12 symbols
  • 42. • Downlink Syntax Value Notes Total # of subcarriers 768 768 = 24 bands * 4 bins/band * 8 subcarriers/bin # of frames / sec 200 1 / 5 ms/frame = 200 (frames/sec) OFDM symbols / frame 42 42 symbols = 27 DL symbols + 15 UL symbols OFDM symbol rate 5400 200 (frames/sec) * 27 (symbols/frame) = 5400 (symbols/sec) Data subcarrier rate 4.1472 5400 (symbols/sec)* 768 (subcarriers/symbol) = 4.1472 (Msubcarriers/sec) Max. bits/subcarrier Min. bits/subcarrier 5 5/36 MAX: R = 5/6 coding & 64 QAM  5/6 * log2(64) = 5 (bits/subcarrier) MIN: R = 1/12 coding & QPSK  1/12 * log2(4) = 5/36 (bits/subcarrier) Max. data rate (Mbps) Min. data rate (Mbps) 20.736 0.576 4.1472 (Msubcarriers/sec) * 5 (bits/subcarrier) = 20.736 (Mbps) 4.1472 (Msubcarriers/sec) * 5/36 (bits/subcarrier) = 576 (kbps) IEEE 802.16e: Data Rate • Uplink Syntax Value Notes OFDM symbol rate 3000 200 (frames/sec) * 15 (symbols/frame) = 3000 (symbols/sec) Data subcarrier rate 2.3040 3000 (symbols/sec)* 768 (subcarriers/symbol) = 2.304 (Msubcarriers/sec) Max. bits/subcarrier Min. bits/subcarrier 10/3 5/36 MAX: R = 5/6 coding & 16 QAM  5/6 * log2(16) = 10/3 (bits/subcarrier) MIN: R = 1/12 coding & QPSK  1/12 * log2(4) = 5/36 (bits/subcarrier) Max. data rate (Mbps) Min. data rate (Mbps) 7.68 0.320 2.304 (Msubcarriers/sec) * 10/3 (bits/subcarrier) = 7.68 (Mbps) 2.304 (Msubcarriers/sec) * 5/36 = 320 (kbps)
  • 43. IEEE 802.16m (1) • Basic Frame Structure - The number of OFDMA symbols varies with the length of CP. - Type-1, type-2, type-3, type-4 subframes
  • 44. IEEE 802.16m (2) • Frame Structure with Type-1 Subframe (FDD) - 5MHz, 10MHz, 20MHz bandwidth
  • 45. IEEE 802.16m (3) • Frame Structure with Type-1 Subframe (TDD)
  • 46. • OFDM Parameters: Numerology (FDD) Nominal Channel Bandwidth (MHz) 5 7 8.75 10 20 Over-sampling Factor 28/25 8/7 8/7 28/25 28/25 Sampling Frequency (MHz) 5.6 8 10 11.2 22.4 FFT Size 512 1024 1024 1024 2048 Sub-Carrier Spacing (kHz) 10.937500 7.812500 9.765625 10.937500 10.937500 Useful Symbol Time Tu (µs) 91.429 128 102.4 91.429 91.429 Cyclic Prefix (CP) Tg=1/8 Tu Symbol Time Ts (µs) 102.857 144 115.2 102.857 102.857 FDD Number of OFDM symbols per Frame 48 34 43 48 48 Idle time (µs) 62.857 104 46.40 62.857 62.857 Cyclic Prefix (CP) Tg=1/16 Tu Symbol Time Ts (µs) 97.143 136 108.8 97.143 97.143 FDD Number of OFDM symbols per Frame 51 36 45 51 51 Idle time (µs) 45.71 104 104 45.71 45.71 Cyclic Prefix (CP) Tg=1/4 Tu Symbol Time Ts (µs) 114.286 160 128 114.286 114.286 FDD Number of OFDM symbols per Frame 43 31 39 43 43 Idle time (µs) 85.694 40 8 85.694 85.694 Number of Guard Sub-Carriers Left 40 80 80 80 160 Right 39 79 79 79 159 Number of Used Sub-Carriers 433 865 865 865 1729 Number of Physical Resource Unit (18x6) in a type-1 sub-frame 24 48 48 48 96 IEEE 802.16m (4)
  • 47. • OFDM Parameters: Numerology (TDD) Nominal Channel Bandwidth (MHz) 5 7 8.75 10 20 Over-sampling Factor 28/25 8/7 8/7 28/25 28/25 Sampling Frequency (MHz) 5.6 8 10 11.2 22.4 FFT Size 512 1024 1024 1024 2048 Sub-Carrier Spacing (kHz) 10.937500 7.812500 9.765625 10.937500 10.937500 Useful Symbol Time Tu (µs) 91.429 128 102.4 91.429 91.429 Cyclic Prefix (CP) Tg=1/8 Tu Symbol Time Ts (µs) 102.857 144 115.2 102.857 102.857 TDD Number of OFDM symbols per Frame 47 33 42 47 47 TTG + RTG (µs) 165.714 248 161.6 165.714 165.714 Cyclic Prefix (CP) Tg=1/16 Tu Symbol Time Ts (µs) 97.143 136 108.8 97.143 97.143 TDD Number of OFDM symbols per Frame 50 35 44 50 50 TTG + RTG (µs) 142.853 240 212.8 142.853 142.853 Cyclic Prefix (CP) Tg=1/4 Tu Symbol Time Ts (µs) 114.286 160 128 114.286 114.286 TDD Number of OFDM symbols per Frame 42 30 38 42 42 TTG + RTG (µs) 199.98 200 136 199.98 199.98 Number of Guard Sub-Carriers Left 40 80 80 80 160 Right 39 79 79 79 159 Number of Used Sub-Carriers 433 865 865 865 1729 Number of Physical Resource Units (18x6) in a type-1 sub-frame 24 48 48 48 96 IEEE 802.16m (5)
  • 48. • Frame Structure - FDD - TDD 3GPP LTE (1)
  • 49. Subframe #0 DwPTS Subframe #2 Subframe #3 Subframe #4 Subframe #5 Subframe #7 Subframe #8 Subframe #9 GP UwPTS DwPTS GP UwPTS Subframe #0 DwPTS Subframe #2 Subframe #3 Subframe #4 Subframe #5 Subframe #7 Subframe #8 Subframe #9 GP UwPTS Subframe #6 One radio frame (10 ms) 10 ms switch-point periodicty 5 ms switch-point periodicty : DL subframe : UL subframe DwPTS GP UwPTS : Special subframe Configuration 0 1 2 3 4 5 5 Switch-point periodicity 5 ms 5 ms 5 ms 10 ms 10 ms 10 ms 10 ms Subframe number 0 1 2 3 4 5 6 7 8 9 D D D D D D D S S S S S S S U U U U U U U U U D U U D U U D D U D D U D D D D D D D S S S D D D S U U U D D D U U U D D D D U U D D D D D D Uplink-downlink allocations • Periodic Switch-Point Operation for TDD Frame Structure 3GPP LTE (2)
  • 50. DL symbN slotT 0l 1DL symb  Nl RB sc DL RBNN RB scN RB sc DL symb NN  ),( lk 0k 1RB sc DL RB  NNk • Slot Structure and Physical Resource Element: Downlink ( , )k l RB sc DL RB NN - Resource grid subcarriers and DL symbN OFDM symbols - Resource element Each element in the resource grid, uniquely defined by the index pair - Resource block RB scNDL symbN To describe the mapping of certain physical channels to resource elements, in terms of OFDM symbols and consecutive subcarriers 3GPP LTE (3)
  • 51. Nominal Channel Bandwidth (MHz) 1.4 3 5 10 15 20 Over-sampling Factor 48/35 96/75 43/28 43/28 43/28 43/28 Sampling Frequency (MHz) 1.92 3.84 7.68 15.36 23.04 30.72 FFT Size 128 256 512 1024 1536 2048 Sub-Carrier Spacing (kHz) 15 15 15 15 15 15 Useful Symbol Time Tu (µs) 66.7 66.7 66.7 66.7 66.7 66.7 Normal Cyclic Prefix (CP) Tg=4.7us Symbol Time Ts (µs) 71.4 71.4 71.4 71.4 71.4 71.4 FDD Number of OFDM symbols per Half Frame 70 70 70 70 70 70 Idle time (µs) . . . . . . Extended Cyclic Prefix (CP) Tg=16.7us Symbol Time Ts (µs) 83.4 83.4 83.4 83.4 83.4 83.4 FDD Number of OFDM symbols per Half Frame 60 60 60 60 60 60 Idle time (µs) . . . . . . Number of Guard Sub-Carriers Left 28 38 106 212 318 424 Right 28 38 106 212 318 424 Number of Used Sub-Carriers 72 180 300 600 900 1200 Number of Physical Resource elements (12x7) in a resource block 6 15 25 50 75 100 • OFDM Parameters: FDD 3GPP LTE (1)
  • 52. Nominal Channel Bandwidth (MHz) 1.4 3 5 10 15 20 Over-sampling Factor 48/35 96/75 43/28 43/28 43/28 43/28 Sampling Frequency (MHz) 1.92 3.84 7.68 15.36 23.04 30.72 FFT Size 128 256 512 1024 1536 2048 Sub-Carrier Spacing (kHz) 15 15 15 15 15 15 Useful Symbol Time Tu (µs) 66.7 66.7 66.7 66.7 66.7 66.7 Normal Cyclic Prefix (CP) Tg=4.7us Symbol Time Ts (µs) 71.4 71.4 71.4 71.4 71.4 71.4 TDD Number of OFDM symbols per Half Frame 68 68 68 68 68 68 GP (µs) 142.8 142.8 142.8 142.8 142.8 142.8 Extended Cyclic Prefix (CP) Tg=16.7us Symbol Time Ts (µs) 83.4 83.4 83.4 83.4 83.4 83.4 TDD Number of OFDM symbols per Half Frame 59 59 59 59 59 59 GP (µs) 83.4 83.4 83.4 83.4 83.4 83.4 Number of Guard Sub-Carriers Left 28 38 106 212 318 424 Right 28 38 106 212 318 424 Number of Used Sub-Carriers 72 180 300 600 900 1200 Number of Physical Resource elements (12x7) in a resource block 6 15 25 50 75 100 • OFDM Parameters: TDD 3GPP LTE (2)