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					                      MC-DS-CDMA
                          vs.
                      OFDM-CDMA

                        Andrew S. Ling
                      Laurence B. Milstein




Center for Wireless
COMMUNICATIONS                               10/18/2010
                              Outline

    Introduction
    Review of previous results
    Current work




    Center for Wireless
    COMMUNICATIONS                      10/18/2010
                             Objective
To compare the performances of the MC-DS-CDMA and OFDM-
CDMA systems, assuming equal:


    Bandwidth
    Information rate
    Transmitted power

    Maximal-ratio combining
    Waveform shaping (raised-cosine filter) will result in non-
     overlapping sub-bands



    Center for Wireless
    COMMUNICATIONS                                                 10/18/2010
                                 Approach
    Waveform shaping in OFDM:




                          OFDM              FDM


    From a systems perspective, we can view the OFDM-CDMA
     system as a MC-DS-CDMA system with a processing gain of N=1
     on each sub-carrier.


    Center for Wireless
    COMMUNICATIONS                                           10/18/2010
                                        Comparison


                  1               2                 1                 2           MC-DS-CDMA




       1 2            1   2   1   2 1   2   1   2       1 2   1   2       1   2   OFDM-CDMA




    OFDM potentially has greater frequency diversity
    OFDM is more susceptible to Doppler effects and channel
     parameter estimation errors
    OFDM also has a higher peak-to-average power ratio

    Center for Wireless
    COMMUNICATIONS                                                                        10/18/2010
                          Research Question

    When is it better to divide a given bandwidth into many narrow
     sub-bands (OFDM-CDMA), as opposed to fewer relatively-wide
     sub-bands (MC-DS-CDMA)?




    Center for Wireless
    COMMUNICATIONS                                                10/18/2010
                           Base Model

We start off with a simple model and assume:

     No narrow-band interference
     No Doppler effects
     No error-correction coding (aside from repetition coding)
     Perfect knowledge of channel state information




    Center for Wireless
    COMMUNICATIONS                                                10/18/2010
                                  Parameters

    MC-DS-CDMA:
        M1 = M = # of parallel data symbols sent per channel use
        R1 = # of repetitions per data symbol
        N = processing gain per sub-band

    OFDM-CDMA:
        M2 = M = # of parallel data symbols sent per channel use
        R2 = # of repetitions per data symbol

                It can be easily shown that R2 = NR1.


    Center for Wireless
    COMMUNICATIONS                                                 10/18/2010
                                  Scenario #1

                          (f)c        (f)c – coherence bandwidth of the channel



                 1         2           1                2             MC-DS-CDMA




     1 2 1 2 1            2 1 2 1 2        1 2 1 2 1           2      OFDM-CDMA




    MC-DS-CDMA: Frequency non-selective (flat) fading in each
     sub-band
    OFDM-CDMA: Correlated block fading

    Center for Wireless
    COMMUNICATIONS                                                                  10/18/2010
                         Correlated Block Fading
                              (f)c


           1                    2             1                 2       MC-DS-CDMA




1 2 1 2 1                     2 1 2 1 2           1 2 1 2 1         2   OFDM-CDMA
  
 
 N OFDM-CDMA
sub - bands per block     correlated              independent
                            fading                   fading


                      N
            Rb          # of repetition s per data symbol per block
                      M
       MR2
            # of blocks  # of sub - bands in MC - DS - CDMA system
        N
Center for Wireless
COMMUNICATIONS                                                                 10/18/2010
                            Frequency Diversity
    MC-DS-CDMA:

                 freq. diversity  R1

    OFDM-CDMA (worst-case – perfect correlation):
                                   MR2
                 freq. diversity 
                                    N
                                  MR1  R1


     We expect the OFDM-CDMA system to have better performance.



    Center for Wireless
    COMMUNICATIONS                                           10/18/2010
                      Performance Comparison




                                               R1 = 1



                                               R1 = 2




                                               R1 = 4


                                               (MR2/N) = 4



Center for Wireless
COMMUNICATIONS                                          10/18/2010
                                          Scenario #2
                                                      (f)c – coherence bandwidth of the channel

                 1                  2                 1                  2           MC-DS-CDMA

                                  (f)c


      1 2             1   2   1    2 1    2   1   2       1 2    1   2       1   2   OFDM-CDMA




    MC-DS-CDMA: Frequency selective fading in each sub-band
     (# of resolvable paths = L = N)
    OFDM-CDMA: Frequency non-selective (flat) fading in each
     sub-band

    Center for Wireless
    COMMUNICATIONS                                                                                 10/18/2010
                           Frequency Diversity
    OFDM-CDMA:
              freq. diversity  R2

    MC-DS-CDMA (rectangular MIP):
              freq. diversity  R1
              path diversity (per sub - band)  L

     overall diversity  R1L  R1 N  R2

     For an exponential MIP, we expect the MC-DS-CDMA system to
     perform worse.


    Center for Wireless
    COMMUNICATIONS                                           10/18/2010
                      Performance Comparison




                                  OFDM-CDMA




                                               R1N = 128,
                                               256, 512


Center for Wireless
COMMUNICATIONS                                        10/18/2010
                          Summary of Results
    Scenario #1: (f)c = BW of one MC-DS-CDMA sub-band
                           Pe, OFDMCDMA  Pe, MC-DS-CDMA

    Scenario #2: (f)c = BW of one OFDM-CDMA sub-band

                Rectangular MIP:
                           Pe, OFDMCDMA  Pe, MCDS CDMA

                Exponential MIP:

                          Pe, OFDMCDMA  Pe, MCDS CDMA


    Center for Wireless
    COMMUNICATIONS                                           10/18/2010
                                        Current Work
    Repeat analysis of both scenarios, taking into account parameter
     estimation errors.


                1                 2                  1                 2           MC-DS-CDMA




     1 2            1     2   1   2 1    2   1   2       1 2   1   2       1   2   OFDM-CDMA



    The energy-per-repetition in the OFDM-CDMA system is (1/N)th
     the energy-per-repetition in the MC-DS-CDMA system.


    Center for Wireless
    COMMUNICATIONS                                                                        10/18/2010
                                       Current Work
    Noisier channel estimates in the OFDM-CDMA system than in the
     MC-DS-CDMA system.
    Maximal-ratio combiner:
                              R
                     Z     g Z   i   i
                              i 1
                        optimal                ts
                                 gain coefficien
                     (functionof channelestimates)

    We expect the parameter estimation errors to have a more
     damaging effect on the OFDM-CDMA system.




    Center for Wireless
    COMMUNICATIONS                                              10/18/2010
                          Channel Estimation: Approach

    Send a pilot tone on each sub-carrier
    Assume the pilot and data spreading sequences are orthogonal
     over a bit interval
    Channel estimator for each sub-carrier
    Demodulated signals for each sub-band are weighted by the
     channel estimates and then combined




    Center for Wireless
    COMMUNICATIONS                                                  10/18/2010
                         MC-DS-CDMA Transmitter
                                    Rate 1/R1
                                 repetition code

                                  Symbol                    Bank of MR1                 
     (k
    dh )         S/P                                                                              Re{}                  s ( k ) (t )
                                  Mapper                     Modulators

                       M parallel             MR1 symbols
                      data symbols


      MC-DS-CDMA modulator at sub-carrier fi,m (i=1,…,R , m=1,…,M)                                         1


           Pilot channel
                                                                              Chip wave-shaping
                      all +1's               A                                     filter

                                     (k
                                   C pn)           
                                                             Impulse                                                    si(,km) (t )
                                                                                   H(f)
           Data channel                                     Modulator
                        agk, m
                         ( )
                                             B         Impulse period = Tc
                                                                                            j ( 2f i ,m t  i(,k ) )
                                                         Energy/chip = Ec               e                        m

                                       (k )
                                   C   dn
                 Spreading sequence of length N
Center for Wireless
COMMUNICATIONS                                                                                                                          10/18/2010
                              MC-DS-CDMA Receiver
                                                                 Bank of M
                   Bank of MR1              Symbol               Maximal-                                ˆ(
r (t )
                   Demodulators            De-Mapper               Ratio
                                                                                          P/S            d mk )
                                                                 Combiners

                                            MR1 symbols                        M symbols



MC-DS-CDMA demodulator at sub-carrier fi,m (i=1,…,R , m=1,…,M)                                     1


   Lowpass equivalent response
     of r(t) at frequency fi,m
                                                             t = n 1 Tc
                                                                                  N 1

                                                                                 
                          ~ (t )       ~
                          ri , m       hi ,m (t )  h(t )                                     Yi , m
                                                                                 n1  0
                                   Lowpass equivalent response
                                    of bandpass matched filter
                                          centered at fi,m              (k
                                                                      C dn1)
                                                        Data spreading sequence of length N
    Center for Wireless
    COMMUNICATIONS                                                                                            10/18/2010
                        MC-DS-CDMA Estimator

MC-DS-CDMA estimator at sub-carrier fi,m                                   (i=1,…,R1, m=1,…,M)


                                               t = n2Tc
                                                                  N I 1
              ~ (t )
              ri , m     ~
                         hi ,m (t )  h(t )                     
                                                                  n2  0
                                                                                Wi ,m

                                                          (k
                                                        C pn)2
                                         Pilot spreading sequence of length N

      Maximal-ratio combiner:
                                      R1 *        
                             Z m  Re Wi ,mYi ,m 
                                      i 1        

  Center for Wireless
  COMMUNICATIONS                                                                          10/18/2010
                          OFDM-CDMA Transmitter
                                    Rate 1/R2
                                 repetition code

                                  Symbol                    Bank of MR2                  
     (k
    dh )         S/P                                                                               Re{}                  s ( k ) (t )
                                  Mapper                     Modulators

                       M parallel             MR2 symbols
                      data symbols


      OFDM-CDMA modulator at sub-carrier fi,m                                             (i=1,…,R2, m=1,…,M)

           Pilot channel
                                                                              Chip wave-shaping
                      all +1's               A                                     filter

                                     (k
                                   C pn)           
                                                             Impulse                                                     si(,km) (t )
                                                                                   H(f)
           Data channel                                     Modulator
                        agk, m
                         ( )
                                             B         Impulse period = Tc
                                                                                             j ( 2f i ,m t  i(,k ) )
                                                         Energy/chip = Ec                e                        m

                                       (k )
                                   C   dn

                  nth chip of spreading sequence             n  g  MR2  (i  1) M  ( m  1)
Center for Wireless
COMMUNICATIONS                                                                                                                           10/18/2010
                              OFDM-CDMA Receiver
                                                                  Bank of M
                   Bank of MR2               Symbol               Maximal-                          ˆ(
r (t )
                   Demodulators             De-Mapper               Ratio
                                                                                          P/S       d mk )
                                                                  Combiners

                                            MR2 symbols                          M symbols



OFDM-CDMA demodulator at sub-carrier fi,m (i=1,…,R , m=1,…,M)                                   2


  Lowpass equivalent response
    of r(t) at frequency fi,m
                                                              t = nTc
                          ~ (t )       ~
                          ri , m       hi ,m (t )  h(t )                          Yi , m
                                   Lowpass equivalent response
                                    of bandpass matched filter
                                          centered at fi,m                (k
                                                                        C dn )
                                                         nth chip of data spreading sequence
    Center for Wireless
    COMMUNICATIONS                                                                                      10/18/2010
                           OFDM-CDMA Estimator

OFDM-CDMA estimator at sub-carrier fi,m                                          (i=1,…,R2, m=1,…,M)


                                                        t = nTc
                  ~ (t )     ~
                  ri , m     hi ,m (t )  h(t )                             Wi ,m

                                                                    (k
                                                                  C pn)
                                                   nth chip of pilot spreading sequence
      Maximal-ratio combiner:
                                        R2 *        
                               Z m  Re Wi ,mYi ,m 
                                        i 1        

  Center for Wireless
  COMMUNICATIONS                                                                                10/18/2010
                             Next Time

    Bit error probability expressions for the two systems for both
     scenarios
    Look at various trade-offs




    Center for Wireless
    COMMUNICATIONS                                                    10/18/2010

				
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