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									  OFDM as a Multicarrier Modulation:
A Convenient Framework for Time-Frequency
   Processing in Wireless Communications


               Jacek Ilow, Ph.D.
              Associate Professor

  Department of Electrical and Computer Engineering
                Dalhousie University
                   Halifax,Canada
         J.ilow@dal.ca
         http://www.dal.ca/~jilow
         http://radio-1.ee.dal.ca/~ilow
                            OFDM History
• High-data-rate communications systems are limited not by noise, but
  often more significantly by the intersymbol interference (ISI) due to
  the memory of the dispersive communications channel.
    – If the symbol rate exceeds the duration of channel impulse response
      (CIR), mechanisms must be implemented in order to combat the effects of
      ISI.
        • Channel equalization techniques can be used to suppress the echoes caused by
          the channel.
        • Significant research efforts have been invested into the development of such
          channel equalizers


    – Another approach is to utilize an FDM system which employs a set of
      subcarriers in order to transmit information in parallel subchannels over
      the same channel.
        • The data throughput of each channel is only a fraction of the data rate of the
          single-carrier system having the same throughput.
                         Frequency Selective Channel


    Why OFDM?

    Single Carrier                                             Multicarrier
    • Uses the entire bandwidth                                • Splits bandwidth into subchannels
    • Short symbol times                                       • Sends information in parallel
    • This causes ISI                                          • OFDM: orthogonal subcarriers
                                                                       1


                                                                     0.8
                              frequency response




                                                                                  frequency response
                                                                     0.6



    OFDM is a considerable option when the channel introduces ISI    0.4


                                                                     0.2



    Applications: ADSL, DAB, DVB, Hiperlan/2, ...                      0


                                                                     -0.2


                                                   frequency
OFDM – Orthogonal Frequency Division Multiplexing
                                                                     -0.4
                                                                                                                                     frequency
                                                                            0.5                        1   1.5   2   2.5   3   3.5       4  4.5   5
                                                                                                                                                      2001-05-31
FDM (Frequency Division Multiplexing) Vs. OFDM
Frequency

                                                             Power
                                                FDMA

                                           Bc


                                                cos(2pf0t)
Bm          Frequency channel                   X            BPF

                                 Serial         X            BPF
                                 Time
                                  To                                 S
                                Parallel    cos(2pf1t)
                                 (S/P)
                                                X            BPF

                                            cos(2pfN-1t)
                                  OFDM History
•   In 1971, Weinstein suggested using a digital implementation based on the DFT.
     –   The DFT is by its nature cyclically redundant in the frequency domain.
     –   The associated harmonically related frequencies can be used as a set of subchannels carriers
         required by the OFDM system.
  Multipath can be described in two domains:
  time and frequency
Time domain: Impulse response




               time                         time
                                                                         time

                              Impulse response

Frequency domain: Frequency response

                       time                                                time


                       time                      f                         time


 Sinusoidal signal as input   Frequency response     Sinusoidal signal as output
    Modulation techniques:
    monocarrier vs. multicarrier
Channel

          Channelization                                   N carriers

                                                                                    Similar to
                                Guard bands
                                                                                   FDM technique

                    B                                          B
            Pulse length ~1/B                         Pulse length ~ N/B
  – Data are transmited over only one carrier   – Data are shared among several carriers
                                                  and simultaneously transmitted

       Drawbacks                                  Advantages
                                                                                       Furthermore
      – Selective Fading                          – Flat Fading per carrier
                                                                                  – It is easy to exploit
      – Very short pulses                         – N long pulses                 Frequency diversity
     – ISI is compartively long                   – ISI is comparatively short    – It allows to deploy
                                                                                   2D coding techniques
     – EQs are then very long                     – N short EQs needed
                                                                                  – Dynamic signalling
     – Poor spectral efficiency                   – Poor spectral efficiency
       because of band guards                       because of band guards



                   To improve the spectral efficiency:
                                     Eliminate band guards between carriers
                          To use orthogonal carriers (allowing overlapping)
Orthogonal Frequency Division Modulation

            N carriers
                                           Symbol: 2 periods of f0


                                                                          Transmit
                           f
                                                                      +
                                            Symbol: 4 periods of f0

                                                                                            f
                  B
                                           Symbol: 8 periods of f0
                                                                                     Channel frequency
  Data coded in frequency domain Transformation to time domain:                      response
                                 each frequency is a sine wave
                                 in time, all added up.


                                                                              Decode each frequency
                                                                              bin separately
  Receive
                                    time                                  f

                                                              B

               Time-domain signal          Frequency-domain signal
       Each subcarrier is modulated at a low enough rate that dispersion
       (ISI) is not a problem. Subcarriers must be spaced so that they do
       not interfere.

           S(f)




                                 f0         f1               fN-1
                                            Bandwidth, B

                  cos(2pf0t)
                      x               LPF         Detector

                      x               LPF         Detector
r(t)                                                                P/S
                  cos(2pf1t)


                      x               LPF         Detector
                  cos(2pfN-1t)                 Demodulator
         Orthogonal Frequency Division Multiplexing (OFDM)
OFDM is a special case of multicarrier transmission that permits
subchannels to overlap in frequency without mutual interference 
increased spectral efficiency.
OFDM exploits signal processing technology to obtain cost-effective means
of implementation.
Mulitple users can be supported by allocating each user a group of
subcarriers.




                             Bandwidth, ~ B/2
                        Spectrum of OFDM Signal



When N is large, the power spectral density (PSD) of the transmitted signal is




                         PSD of OFDM Signal
OFDM transmission system (time continuous)
    Transmitter                                                                             Channel
                              ld(M)             d0 (i)
                                      Mod.                               g (t)
                                                                          0

                                                d1 (i)
              b(i b )                 Mod.                               g (t)               sa (t)
                                                                                   S
                                                                          1
     Source             S/P


                                                dN-1(i)
                                      Mod.                              gN-1(t)
                                                                                             channel
                                                                                              ca(t)
    Receiver                                              T
                              ld(M)            ^
                                               d0 (i)
                                      Demod.                             h0 (t )            (t)
                                                              ^0(t )
                                                              s
              ^                                ^
              b(i b )                          d1 (i)
                                      Demod.                             h1 (t )   ^a (t)
                                                                                   s
                                                              ^
                                                              s1 (t )
     Dest.              P/S

                                               ^
                                               dN-1 (i)
                                      Demod.                            hN-1 (t)
                                                          ^N-1(t)
                                                          s


                                             OFDM Basics
      Mathematical Description of an OFDM System 1/2
                                  N 1
•   time continuous        s(t )   dn (i) g  t  iTS  e j 2p f nt
                                              
                                              
                                                        
                                                        
    representation of an          n0                      

    OFDM transmitter:
                                g (t )  rect  t /TS  , f n  nf  n /TS
                                               
                                               
                                                       
                                                       
                                                       

                                  N 1          j 2p nt /TS
                                 dn (i) e                   , iTS  t   i 1TS
                                                                          
                                                                               
                                                                                
                                                                               
                                  n0


•   time discrete                               N 1       j 2p nkTA /TS
    representation of
                       sk (i)  s(t) t iT kT   dn(i) e               ,            k [0,1,2,..., N 1]
                                          S   A n0
    an OFDM transmitter:
                               N  TS /TA
                                 N 1
                                dn (i) e j 2p nk / N = IDFT d0(i), d1(i),..., d N 1(i)
                                                              
                                                              
                                                                                          
                                                                                          
                                                                        
                                                                                                
                                                                                                 
                                 n0


                                         OFDM Basics
     Mathematical Description of an OFDM System 2/2

                                N 1
•   time discrete       dn (i)   rk (i) e j 2p kn/ N
                        ˆ
    representation of           k 0
    an OFDM receiver:         = DFT r0(i), r1(i),..., rN 1(i)
                                                              
                                                              
                                        
                                                              
                                                               




•   Complete System:
                        ˆ
                        d  DFTN IDFTN (r)c  
                                 
                                 
                                                 
                                                 
                                    
                                                         
                                                          




                                 OFDM Basics
Symbol Rate Model of an OFDM System
    Transmitter                                                                      Discrete
                     ld(M)            d0 (i)               s0 (i)                    Channel
                             Mod.                0     0


                                      d1 (i)               s1 (i)
                             Mod.                1     1
                                                                            s(i,k)
    Source     S/P                               IDFT                 P/S

                                                                                           ga (t)
                                      dN-1 (i)             sN-1(i)
                             Mod.                N-1 N-1                                       sa (t)

                                                                                       channel
                                                                                         ca (t)
    Receiver
                     ld(M)             d0 (i)               r0 (i)
                             Demod.              0     0                              (t)
                                                                                               ra (t)
                                       d1 (i)               r1 (i)                         ha (t)
                             Demod.              1     1
                                                                            r(i,k)
     Dest.     P/S                                   DFT              S/P

                                                                                      TA
                                       dN-1(i)              rN-1(i)
                             Demod.              N-1 N-1




                               OFDM Basics
    Including a “cyclic prefix”
To combat the time dispersion: including ‘special’ time guards in the symbol transitions

                                           co p y
                                                                                                 Furthemore it converts Linear conv. = Cyclic conv.
      CP
                                                    T                                                                         (Method: overlap-save)
                                             Tc


                                  Without the Cyclic Prefix                                                                            Including the Cyclic Prefix
                                            Symbol: 8 periods of fi
                                                                                                                                               CP             Symbol: 8 periods of fi
       Passing the channel h(n)




                                                                                                            Passing the channel h(n)
                                                                                                Yi(t)
                                                                                                                                                                                             Yi(t)


                                            Channel: h( n) =( 1 ) –n/ n   n=0 ,…,2 3



                                                                                                Yi(t)


                                                                                                                                       Initial transient     The inclusion of a CP       Final transient
                                                                                                                                       remains within      maintains the orthogonality   remains within
               Initial transient               Loss of orthogonality                   Decaying transient
                                                                                                                                            the CP                                          the CP


                                                                                               Yj(t)                                                                                        Yj (t)



                                              Symbol: 4 periods of fi                                                                                         Symbol: 4 periods of fi




                                            CP functions:
                                                – It acomodates the decaying transient of the previous symbol
                                                – It avoids the initial transient reachs the current symbol
                          OFDM Modulator
                                                      cos(2pfct)

                                               Real       x
  Bit
Stream            S/P     IDFT         P/S                     S    BPF   s(t)

                                               Img         x

                                                       sin(2pfct)



                          OFDM Demodulator
             x      LPF

  r(t)   cos(2pfct)                                                  Received
                          A/D    S/P         DFT        P/S             Bit
            p/2                                                       Stream

             x      LPF
                    IEEE 802.11 Wireless LAN
•   IEEE 802.11 standard:
     –   unlicensed frequency spectrum: 900Mhz, 2.4Ghz, 5.1Ghz, 5.7Ghz




                                                   and 802.11b           802.11a
Frequency Band
The 802.11 Protocol Stack
   www.ieee802.org/11/
                       802.11a System Specification
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 GI2       T1         T2      GI      OFDM Symbol   GI   OFDM Symbol

Short training sequence:              Long training sequence:
AGC and frequency offset              Channel estimation
  •    Sampling (chip) rate: 20MHz
  •    Chip duration: 50ns
  •    Number of FFT points: 64
  •    FFT symbol period: 3.2ms
  •    Cyclic prefix period: 16 chips or 0.8ms
         –   Typical maximum indoor delay spread < 400ns
         –   OFDM frame length: 80 chips or 4ms
         –   FFT symbol length / OFDM frame length = 4/5
  •    Modulation scheme
         –   QPSK: 2bits/sample
         –   16QAM: 4bits/sample
         –   64QAM: 6bits/sample
  •    Coding: rate ½ convolutional code with constraint length 7
                      OFDM Transmitter
                 (HIPERLAN/2 / IEEE802.11a)
                                            d0(i)
                                     Map.
                                     Mod.

                                            d1(i)
                                     Map.
                                                             N
    source      CC         S/P              d2(i)     IDFT       PS/GI       DAC
                                     Map.
                                 .
                                 .
                                 .
                                            dN-1(i)
                                     Map.


•   channel coding (convolutional codes with Viterbi decoding)
•   IDFT: discrete realized filter bank (very efficient FFT)
•   cyclic prefix / guard interval (GI) prevents intersymbol interference (ISI)


                                       OFDM Basics
    OFDM Receiver (HIPERLAN/2 / IEEE802.11a)
                        e                               0
                                             d0(i)
                                                               Mod.
                                                              Demap.
                                                       e1
                                             d1(i)
                                                              Demap.
                         SYNC     N                                                  -1
ADC          PE              -1
                                      DFT              e2                  P/S    CC       dest.
                          GI                 d2(i)
                                                              Demap.
                                                                       .
                                                       eN-1            .         Viterbi
                                                                       .
                                             dN-1(i)                             decoder
•     Synchronization
       – FFT window position (time domain)
       – sample and modulation frequency correction
•     Pre equalizer (PE) for impulse compression
•     OFDM: Orthogonal Frequency Division Multiplexing
       – separate multiplicative channel correction on each subcarrier
       – equalizer coefficient design: en = 1 / Cn       circular convolution




                                            OFDM Basics
               Channel Estimation (CE): Training Symbols
•              burst structure of HIPERLAN/2 and IEEE802.11a
               –   short symbols for AGC and raw synchronization
               –   training sequence (TS): 2 identical symbols per subcarrier (52)
               –   data OFDM symbols with 48 user data and 4 pilot symbols each
               –   pilot symbols for fine synchronization (insufficient for channel estimation)



           f
16.5 MHz




             AGC                                                       …
           0 SYNC             TS



               0          8        16         24                                              t in ms

                                             Channel Estimation
Spectrum Mask
                                    Power Spectral Density




                                   -20 dB

                                   -28 dB


                                   -40 dB


   -30      -20    -11 -9                   9 11       20      30
                                f carrier
                                                             Frequency (MHz)

• Requires extremely linear power amplifier design.
Carrier orthogonality by Discrete Multi-Tone (DMT)
       modulation enables their partial overlap




                                   OFDM spectra of individual subcarriers


                        •   DMT used in Digital Subscribe Line (xDSL)
                        •   Usable frequency band is separated into 256 small
                            frequency bands (or subchannels) of 4.3125 kHz each
                            (ADSL)
                        •   Within each subchannel, modulation uses quadrature
                            amplitude modulation (QAM)
                        •   By varying the number of bits per symbol within a
                            subchannel, the modem can be rate-adaptive
                        •   DMT uses the fast Fourier transform (FFT) algorithm
                            for modulation and demodulation

								
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