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					Multi-user CDMA
      Enhancing capacity of wireless
      cellular CDMA
                                   Topics Today
                             Dealing without multi-user reception:
                              asynchronous CDMA
                                SNR
                                power balance - near-far effect
                             Multi-user detection (MUD) classification and properties
                                The conventional detector (non-MUD, denotations)
                                Maximum likelihood sequence detection
                                Linear detectors
                                    Decorrelating detector

                                    Minimum mean-square error detector

                                    Polynomial expansion detector

                                Subtractive interference cancellation
                                    Serial and parallel cancellation techniques




Timo O. Korhonen, Helsinki University of Technology                                      2
                   s1 (t ) 2 P1


                   s2 (t ) 2 P2                                                        Asynchronous CDMA
                                                                                                        voltage at the I&D*
                                                                                                        at the decision instant

                                                                                                                    U
                   sU (t ) 2 PU                                                              m j (tm )  m jj   mij  n j
                                                                                             ˆ
                                                                                                                   i 1
                                                                      ˆ
                                                                      m j (tm )                                    i j


                                                                                    signal
                                                                                   voltage         ISI & noise voltage
                            v j (t )
                                                                                                        signal power for the j:th user
            The j:th user experiences the SNR:
                                                 m2                                          m2
                       SNR j                     jj
                                                                                             jj

                                      
                                                     
                                                          2
                                                              
                                                                       
                                                                                  
                                                                                   2
                                                                                          
                                                                                                         
                                                                                                          2
                                                                                                            
                                    E    mij  n j               E    mij    2E    mij n j    E n 2 
                                                                                                                    j
                                       i i, jj
                                                            
                                                                        i  j  
                                                                           i, j
                                                                                          
                                                                                              i, j       
                                                                                                   0


                                                          MAI                                channel noise

                                                                                               *Integrate and dump receiver
Timo O. Korhonen, Helsinki University of Technology                                                                                  3
                                   Practical CDMA receiver
                                                                                                 Effective BW
 from channel                                                tm                                  is defined by:
                          LPF                            0
                                                                  u (t )   decision
                                                                                                                                    2
                                                                                                      V ( f )df 
                                                                                                     0           
                                                                                             Beff               
                                                 local code                     phasing of
                                                                                sampling

                                                      Lc Pj  WPj / R
                                                                                                        V 2 ( f )df
                                                                                                                0


                                                                                                 for rectangular
                                                                   2
                                                             m                                   spectra:
              SNR j                                               jj

                             
                                       
                                        2
                                               
                                                              
                                                               2
                                                                 
                           E    mij    2E    mij n j    E n 2 
                                                                                                    V( f )
                                                                         j                                                S0
                             
                               i, j        
                                                  i, j                                                                         f
                                                       0           N 0 Beff  PN
                                       U
                                                                                              BN
                                      P
                                      i 1
                                             i
                                                                                                         B S 
                                                                                                                              2

                                      i j                                                    Beff       N 0             2
                                                                                                                                   BN
                                                                                                                BN S      0

                                                                                                        Lc Pj
        Hence, SNR upper bound for the j:th user is SNR j                                  U

                                                                                             P  N B
                                                                                             i 1
                                                                                                    i           0   eff

                                                                                             i j
Timo O. Korhonen, Helsinki University of Technology                                                                                      4
                   Perfect power control
             Equal received powers for U users means that Pi   i 1 Pi  (U  1) Pj
                                                                                                           U
       
                                                                                                           i j

                                                                                                        Lc Pj
            Therefore the j:th user’s SNR equals ( SNR)0 
                                                                                                N 0 Beff  (U  1) Pj
             and the number of users is
                                      1     1                                                 1     1 
                          U  1  Lc                                     U max  lim 1  Lc             1 
                                                                                                                      Lc
                                      SNRo SNR1                                  SNR1 
                                                                                                SNRo SNR1        SNR0
            where* (for BPSK)                                          U max
                                       Pj             PW         2 Eb
                  SNR1  Lc                           j
                                                             
                                   Beff N 0           PN R       No
            Number of users is
             limited by
                channel AWGN level N0
                                                                                                                          Eb/No
                processing gain Lc
                                                                                 SNR0 / 2                                 (=SNR1/2)
                                                                                            AWGN level decreases
                received power Pr

                                                                         *SNR1: received SNR without multiple access interference
Timo O. Korhonen, Helsinki University of Technology                                                                                   5
               Unequal received powers - the near-far -effect
            Assume all users apply the same power but their distance to the
             receiving node is different. Hence the power from the i:th node is
                                                        P  P0 / dia
                                                         i


             where d is the distance, and a is the propagation attenuation
             coefficient (a = 2 for free space, in urban area a = 3…5 )
            Express the power ratio of the i:th and j:th user at the common
             reception point                                        a
                                                               dj 
                                 Po  Pdia  Pj d a  Pi  Pj  
                                       i          j
                                                               di 
            Therefore, the SNR of the j:th user is
                                                      Lc Pj                                Lc Pj
                                  SNR j                      U
                                                                      SNR j                             a
                                                N 0 Beff   Pi
                                                                                                U
                                                                                                    d 
                                                                                 N 0 Beff  Pj   j 
                                                              i 1
                                                                                               i 1  d i 
                                                              i j
                                                                                                i j




Timo O. Korhonen, Helsinki University of Technology                                                           6
       The near-far effect in asynchronous CDMA
            Grouping the previous yields condition
                                                      a
                                           U
                                                dj        1     1 
                                           d 
                                          i 1  i 
                                                       Lc             U 1
                                                            SNR0 SNR1 
                                          i j

            Multiple-access interference (MAI) power should not be larger
             than what the receiver sensitivity can accommodate
            Note the manifestation of near-far -effect because just one larger
             sum term on the left side of the equation voids it
            Example: Assume that all but one transmitter have the same
             distance to the receiving node. The one transmitter has the
             distance d1=dj /2.5 and a=3.68, SNR0=14, SNR1=25,
             Rb = 30 kb/s, Beff = 20 MHz, then
                           a                                                                 1     1 
               U
                   dj                                              (2.5)3.68  U  2  Lc           
                d   (2.5)3.68  U  2                                                   SNR0 SNR1 
              i 1  i                                             
              i j                                                  U  2  2.53.68  L  1  1   14
                                                                                        c            
               Lc,BPSK  (2/ Tc ) /(1/ Tb )  2Tb / Tc  2Tb Beff                          SNR0 SNR1 
Timo O. Korhonen, Helsinki University of Technology                                                          7
            By using the perfect power balance the number of users is
                                                             1          1 
                                                 U  1  Lc                   42
                                                             ( SNR)0 ( SNR)1 
            Hence the presence of a single user so near has dropped the
             number of users into almost 1/3 part of the maximum number
            If this user comes closer than
                                                           d1  d j / 2.78

             all the other users will be rejected, e.g. they can not communicate
             in the system in the required SNR level. This illustrates the near-
             far effect
            To minimize the near-far effect efficient power control is should be
             adaptively realized in asynchronous CDMA-systems




Timo O. Korhonen, Helsinki University of Technology                                    8
                                   Fighting against Multiple Access
                                   Interference
                           CDMA system can be realized by spreading codes having
                            low cross -correlation as Gold codes (asynchronous
                            usage) or Walsh codes (synchronous usage)
                           Multipath channel with large delay spread can destroy
                            code cross-correlation properties
                               a remedy: asynchronous systems with large code gain
                                assume other users to behave as Gaussian noise (as
                                just analyzed!)
                           Additional compensation of MAI yields further capacity
                            (increases receiver sensitivity). This can be achieved by
                               Code waveform design (BW-rate/trade-off)
                               Power control (minimizes near-far effect)
                               FEC- and ARQ-systems
                               Diversity-systems: - Spatial - Frequency - Time
                               multi-user detection


Timo O. Korhonen, Helsinki University of Technology                                     9
                                   MAI versus ISI (Inter-Symbolic
                                   Interference)
                                           Note that there exists a strong parallelism between the
                                            problem of MAI and that of ISI:
                                              Asynchronous channel of K-users behaves the same
                                              way as a single user channel having ISI with *memory
                                              depth of K-1

                                           Hence, a number of multi-user detectors have their
                                            equalizer counter parts as:
                                              maximum likelihood

                                              zero-forcing

                                              minimum mean square

                                              decision feedback

                                           General classification of multi-user detectors:
                                              linear

                                              subtractive
                                                              *This could be generated for instance by a multipath
                                                              channel having K-1 taps
Timo O. Korhonen, Helsinki University of Technology                                                                  10
                               Maximum-likelihood sequence detection
                                    Optimum multi-user detection applies maximum-likelihood
                                     principle:
                                       Considering the whole received sequence, find the
                                       estimate for the received sequence that has the
                                       minimum distance to the allowed sequences
                                    The ML principle
                                       has the optimum performance provided transmitted
                                        symbols equal alike
                                       has large computational complexity - In exhaustive
                                        search 2NK vectors to be considered! (K users, N bits)
                                       requires estimation of received amplitudes and phases
                                        that takes still more computational power
                                       can be implemented by using Viterbi-decoder that is
                                        ‘practically optimum’ ML-detection scheme to reduce
                                        computational complexity by surviving path selections
                                    We discuss first the conventional detector (by following the
                                     approach we already had to familiarize to denotations)

Timo O. Korhonen, Helsinki University of Technology                                                 11
                                   Formulation: Received signal
                                    Assume
                                       single path AWGN channel
                                       perfect carrier synchronization
                                       BPSK modulation
                                    Received signal is therefore
                                                               K
                                                      r (t )   Ak (t ) g k (t )d k (t )  n(t )
                                                               k 1

                                     where for K users
                                            Ak (t ) is the amplitude
                                                      g k (t ) is the spreading code waveform
                                                      d k (t ) is the data modulation of the k:th user
                                                      n(t ) is the AWGN with N0/2 PSD

                                    Note that there are Lc chips/bit (Lc : processing gain)

Timo O. Korhonen, Helsinki University of Technology                                                      12
                                   Conventional detection (without MUD)
                                   for multiple access
                                    The conventional DS receiver for K users consists of K
                                     matched filters or correlators:
                                      r (t )                     Tb
                                                                                           ˆ
                                                                                           d1
                                                                0    x(t )dx   decision

                                                      g1 (t )
                                                                 Tb
                                                                                           ˆ
                                                                                           d2
                                                                0    x(t )dx   decision

                                                      g2 (t )

                                                                 Tb
                                                                                           ˆ
                                                                                           dK
                                                                0    x(t )dx   decision

                                                      gK (t )

                                    Each user is detected without considering background
                                     noise (generated by the spreading codes of the other
                                     users) to be deterministic (Assumed to be genuine
                                     AWGN)
Timo O. Korhonen, Helsinki University of Technology                                             13
                                   Output for the K:th user without MUD
                                    Detection quality depends on code cross- and
                                     autocorrelation              1
                                                        i ,k   gi (t ) g k (t )dt
                                                                 Tb T         b

                                    Hence we require a large autocorrelation and small
                                     crosscorrelation (small ISI)
                                                                  i ,k  1, i  k
                                                          
                                                          0  i ,k  1, i  k
                                    The output for the K:th user consist of the signal, MAI and
                                     filtered Gaussian noise terms (as discussed earlier)
                                                    1
                                                yk  T r (t ) g k (t )dt
                                                    Tb           b



                                                                                           1
                                                      yk  Ak d k   i 1 i ,k Ai di       T n(t ) g k (t )dt
                                                                        K

                                                                        ik                Tb   b



                                                      yk  Ak d k  MAI k  zk
                                    Received SNR of this was considered earlier in this
                                     lecture
Timo O. Korhonen, Helsinki University of Technology                                                                 14
                                   Matrix notations to consider
                                   detection for multiple access
                                    Assume a three user synchronous system with
                                     a matched filter receiver
                                                   y1  A1d1   2,1 A2 d 2  3,1 A3 d3  z1
                                                  
                                                   y2  1,2 A1d1  A2 d 2  3,2 A3 d3  z2
                                                  y   Ad   A d  A d  z
                                                   3     1,3 1 1      2,3 2 2        3 3     3


                                           y1   1            2,1   3,1   A1   0      0   d1   z1 
                                           y               1      3,2   0    A2     0   d 2    z2 
                                           2   1,2                                           
                                           y3   1,3
                                                            2,3     1  0
                                                                                   0      A3   d3   z3 
                                                                                                  
                                     that is expressed by the matrix-vector notation as
                                                            y  RAd  z
                                          matched filter outputs                             noise
                                                                                     data
                                                      correlations between     received amplitudes
                                                      each pair of codes


Timo O. Korhonen, Helsinki University of Technology                                                                15
                                   The data-term and the MAI-term
                                    Matrix R can be partitioned into two parts by setting
                                                      y  RAd  z with R  I  Q
                                      Note that hence Q contains off-diagonal elements or R
                                     (or the crosscorrelations)
                                    and therefore MF outputs y  RAd  z can be expressed
                                     as
                                                y  (I  Q) Ad  z  Ad  QAd  z

                                    Therefore the term Ad contains the decoupled data and
                                     QAd represents the MAI
                                    Objective of all MUD schemes is to cancel out the MAI-
                                     term as effectively as possible (constraints to
                                     hardware/software complexity and computational
                                     efficiency)


Timo O. Korhonen, Helsinki University of Technology                                           16
                                   Asynchronous and synchronous channel
                                    In synchronous detection decisions can be made bit-by-bit
                                    In asynchronous detection bits overlap and multi-user
                                     detection is based on taking all the bits into account
                                                                K
                                                      r (t )   Ak (t ) g k (t )d k (t   k )  n(t )
                                                               k 1

                           asynchronous ch.                                               synchronous ch.

User 1                 1                3             5                User 1            1             3   5
User 2                        2                4           6           User 2            2             4   6




             1  2 Tb  1                                    3Tb   2         1          Tb  1           3Tb   1
                                    The matrix R contains now partial correlations that exist
                                     between every pair of the NK code words (K users, N bits)

Timo O. Korhonen, Helsinki University of Technology                                                                        17
                                   Asynchronous channel correlation matrix
                                    In this example the correlation matrix extends to 6x6
                                     dimension:
                                                        y  RAd  z

                                                     1      2,1    0      0       0      0 
                                                           1      3,2    0       0      0 
                                                     1,2                                       
                                                     0      2,3    1      4,3    0      0 
                                                  R
                                                     0      0      3,4    1      5,4    0   
                                                     0      0       0      4,5    1      6,5 
                                                                                               
                                                     0
                                                            0       0      0      5,6    1   

                                    Note that the resulting matrix is sparse because most of
                                     the bits do not overlap
                                    Sparse matrix - algorithms can be utilized to reduce
                                     computational difficulties (memory size & computational
                                     time)
Timo O. Korhonen, Helsinki University of Technology                                                 18
                                   Decorrelating detector
                                    The decorrelating detector applies the inverse of the
                                     correlation matrix to suppress MAI
                                                          Ldec  R 1
                                     and the data estimate is therefore
                                                           ˆ
                                                           d dec  R 1y
                                                          R 1 ( A d  Q A d  z )
                                                                     RAd

                                                          Ad  R 1z  Ad  z dec
                                    We note that the decorrelating detector eliminates
                                     the MAI completely!
                                    However, channel noise is filtered by the inverse of
                                     correlation matrix - This results in noise enhancement!
                                    Decorrelating detector is mathematically similar to zero
                                     forcing equalizer as applied to compensate ISI


Timo O. Korhonen, Helsinki University of Technology                                             19
                                   Decorrelating detector properties
                                   summarized
                               

                                     PROS:
                                    Provides substantial performance improvement over
                                     conventional detector under most conditions
                                    Does not need received amplitude estimation
                                    Has computational complexity substantially lower that the
                                     ML detector (linear with respect of number of users)
                                    Corresponds ML detection when the energies of the users
                                     are not know at the receiver
                                    Has probability of error independent of the signal energies
                               

                                     CONS:
                                    Noise enhancement
                                    High computational complexity in inverting matrix R


Timo O. Korhonen, Helsinki University of Technology                                            20
                                    Polynomial expansion (PE) detector
                                     Many MUD techniques require inversion of R. This can be
                                      obtained efficiently by PE
                                                        NS
                                                 L   w R i  R 1 d PE  L PE y
                                                                    ˆ
                                                                   PE          i
                                                                        i 0
                                                            NS
                                                d PE   wi R i y  w0 R 0 y w1R1 y...  wN S R N S y
                                                ˆ
                                                            i 0
                                     For finite length message a finite length PE series can
                                      synthesize R-1 exactly. However, in practice a truncated
                                      series must be used for continuous signaling

                                                                                                                    ˆ
                                                                                                                    d PE  L PE y
                                         y          Weight                           Weight
                                                  multiplication
                                                                         Ry                         R2 y     Weight
                                                                                   multiplication          multiplication


          matched
r (t )     filter                                       R                              R                       R
           bank
                                                       w0                           w1                     w2
                                    y                                   Ry                          R2 y

 Timo O. Korhonen, Helsinki University of Technology                                                                          21
                                   Mathcad-example
                                                                   NS
                                                             R   wi R i
                                                              1

                                                                   i 0


         R 1 


                                                                            = series expansion
                                                                              of R-1 (to 2. degree)




                                                                                   wi
                                                       R2

Timo O. Korhonen, Helsinki University of Technology                                                   22
                                   Minimum mean-square error (MMSE)
                                   detector
                                    Based on solving MMSE optimization problem with
                                                           E[ d  Ly ]
                                                                     2


                                     that should be minimized
                                    This leads into the solution
                                            dˆ  LMMSE y  R  ( N0 / 2)A 2  1 y
                                                                             
                                    One notes that under high SNR this solution is the same
                                     as decorrelating receiver
                                    This multi-user technique is equal to MMSE linear
                                     equalizer used to combat ISI
                                    PROS: Provides improved noise behavior with respect of
                                     decorrelating detector
                                    CONS:
                                       Requires estimation of received amplitudes and
                                        noise level
                                       Performance depends also on powers of
                                        interfering users
Timo O. Korhonen, Helsinki University of Technology                                            23
                                   Successive interference cancellation
                                   (SIC)                                ˆ
                                                                        d




                                                                                                                       To the next stage
                                                                                                                   1

                                                                               ˆ
                                                                               A1 (t  Tb )   g1 (t   1  Tb )
                                                                 ˆ
                                                                 d1
                                        MF
                          r (t )                      decision
                                                                                                 - s1 (t  Tb )
                                                                                                   ˆ
                                       user 1
                                                                 r (t  Tb )
                                                           Tb
                                                                                               +         r1 (t )
                                    Each stage detects, regenerates and cancels out a user
                                    First the strongest user is cancelled because
                                       it is easiest to synchronize and demodulate
                                       this gives the highest benefit for canceling out the
                                         other users
                                    Note that the strongest user has therefore no use for this
                                     MAI canceling scheme!
                                    PROS: Small HW requirements and large performance
                                     improvement when compared to conventional detector
                                    CONS: Processing delay, signal reordered if their powers
                                     changes, in low SNR:s performance suddenly drops
Timo O. Korhonen, Helsinki University of Technology                                                                                        24
                                   Parallel interference cancellation (PIC)
        r (t  Tb )

ˆ
d1 (0)                                                   s1 (t  Tb )
                                                         ˆ                        -                              ˆ
                                                                                                                 d1 (1)
                                                                         ˆ
                                                                          si (t )
                   ˆ
                   A1 (t  Tb )                                         i 1
                                                                                      +
ˆ                                                       s2 (t  Tb )
                                                        ˆ                                                        ˆ
d2 (0)
                                                                         si (t ) -
                                                                          ˆ
                                                                        i2
                                                                                          matched
                                                                                                       decisions d2 (1)
                                                                                                          and
                   ˆ
                   A2 (t  Tb )                       spreader                             filter
                                                                                                         stage
                                                                                           bank
ˆ                                                       sK (t  Tb )
                                                        ˆ                                                        ˆ
                                                                                                        weights d K (1)
d K (0)
                                                                         s (t ) -
                                                                          ˆ
                                                                        i K
                                                                               i

                  ˆ
                  AK (t  Tb )                                                                 y  (I  Q) Ad  z
                amplitude                                               parallel                     Ad  QAd  z
                estimation                                              summer
  initial             With equal weights for all stages the data estimates for
                               

  data                each stages are
  estimates                     ˆ                ˆ
                               d(m  1)  y  QAd(m) y  Ad  QAd  z
 minimization tends to cancel MAI                     ˆ
                                         Ad  QA(d  d(m))  z
                                    Number of stages determined by required accuracy
                                     (Stage-by-stage decision-variance can be monitored)
Timo O. Korhonen, Helsinki University of Technology                                                                25
                                     PIC properties

                                    SIC performs better in non-power controlled channels
                                    PIC performs better in power balanced channels
                                    Using decorrelating detector as the first stage
                                       improving first estimates improves total performance
                                       simplifies system analysis
                                     Doing a partial MAI cancellation at each stage with the
                PIC variations




                                 

                                     amount of cancellation increasing for each successive
                                     stage
                                       tentative decisions of the earlier stages are less
                                        reliable - hence they should have a lower weight
                                       very large performance improvements have achieved
                                        by this method
                                       probably the most promising suboptimal MUD




Timo O. Korhonen, Helsinki University of Technology                                            26
                                   Benefits and limitations of multi-user
                                   detection
                               PROS:
                                    Significant capacity improvement - usually signals of the
                                     own cell are included
                                    More efficient uplink spectrum utilization - hence for
                                     downlink a wider spectrum may be allocated
                                    Reduced MAI and near-far effect - reduced precision
                                     requirements for power control
                                    More efficient power utilization because near-far effect
                                     is reduced
                               CONS:
                                    If the neighboring cells are not included interference
                                     cancellation efficiency is greatly reduced
                                    Interference cancellation is very difficult to implement in
                                     downlink reception where, however, larger capacity
                                     requirements exist (DL traffic tends to be larger)

Timo O. Korhonen, Helsinki University of Technology                                                27

				
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