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An introduction to multiple ante

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					                Promises of Wireless
                   MIMO Systems

                   Mattias Wennström
                   Uppsala University
                         Sweden

Mattias
Wennström
Signals &
Systems Group
                             Outline
                •   Introduction...why MIMO??
                •   Shannon capacity of MIMO systems Telatar, AT&T 1995
                •   The ”pipe” interpretation
                •   To exploit the MIMO channel
                    – BLAST Foschini, Bell Labs 1996
                    – Space Time Coding Tarokh, Seshadri & Calderbank 1998
                    – Beamforming
                • Comparisons & hardware issues
                • Space time coding in 3G & EDGE
                                                Release ’99

Mattias
Wennström
Signals &
Systems Group
                     Why multiple antennas ????
                   • Frequency and time processing are at limits
                   • Space processing is interesting because it
                     does not increase bandwidth


                outdoor                                                         indoor
                                             ”Specular” ”Scattering”
                                              channels   channels
                    Phased array
                       range extension,
                    interference reduction                               MIMO
                                                                        Systems
                               Adaptive Antennas                       (diversity)
Mattias                          interference cancellation
Wennström
Signals &
Systems Group
                      Initial Assumptions

                •   Flat fading channel (Bcoh>> 1/ Tsymb)
                •   Slowly fading channel (Tcoh>> Tsymb)
                •   nr receive and nt transmit antennas
                •   Noise limited system (no CCI)
                •   Receiver estimates the channel perfectly
                •   We consider space diversity only


Mattias
Wennström
Signals &
Systems Group
                ”Classical” receive diversity
                                     H11


                                      H21


                                       PT  *
                     C  log 2 det I  2 HH 
                                    σ nt    

                   = log2[1+(PT/s2)·|H|2]       [bit/(Hz·s)]

                     Capacity increases logarithmically   H = [ H11 H21]
Mattias
Wennström            with number of receive antennas...
Signals &
Systems Group
                Transmit diversity / beamforming

                                         H11


                                          H12


                  Cdiversity = log2(1+(PT/2s2)·|H|2)     [bit/(Hz·s)]


                 Cbeamforming = log2(1 +(PT/s2 )·|H|2)          [bit/(Hz·s)]

                 • 3 dB SNR increase if transmitter knows H
                 • Capacity increases logarithmically with nt
Mattias
Wennström
Signals &
Systems Group
                  Multiple Input Multiple Output systems

                                                                             H       H12 
                                               H11                       H   11
                                                                              H 21   H 22 
                                                                                           
                                    H21
                         H12

                                                     H22
                       Cdiversity = log2det[I +(PT/2s2 )·HH†]=           Where the i are the
                                                                         eigenvalues to HH†

                                       P                   P      
                            log 2 1  T 2 1   log 2 1  T 2 2 
                                    2s                  2s        

                Interpretation:                1
                      Transmitter                                Receiver
                                               2
Mattias
Wennström         m=min(nr, nt) parallel channels,
Signals &         equal power allocated to each ”pipe”
Systems Group
                            MIMO capacity in general
                    H unknown at TX                       H known at TX
                                    P                         m
                                                                      p 
                C  log 2 det  I  2T HH *            C   log 2 1  i 2 i 
                               s nt                        i 1        s 
                   m
                                 PT   
                  log 2 1  2 i                   Where the power distribution over
                           s nt 
                                                       ”pipes” are given by a water filling
                  i 1
                                                       solution
                                                                                    
                     m  min( nr , nt )
                                                            m         m
                                                                         1
                                                       PT   pi     
                                                                        
                                                            i 1   i 1  i 
                                                                             

                              p1                  1
                             p2                   2

Mattias                      p3                   3
Wennström
Signals &
                             p4                   4
Systems Group
                       The Channel Eigenvalues

                Orthogonal channels HH† =I, 1= 2= …= m= 1

                             m
                                         P     
                Cdiversity   log 2 1  2T i   min(nt , nr )  log 2 (1  PT / s 2 nt )
                             i 1     s nt 

                  • Capacity increases linearly with min( nr , nt )
                  • An equal amount of power PT/nt is allocated
                    to each ”pipe”



                       Transmitter                                  Receiver
Mattias
Wennström
Signals &
Systems Group
                      Random channel models and
                         Delay limited capacity

                       • In stochastic channels,
                           the channel capacity becomes a random
                           variable


                Define : Outage probability Pout = Pr{ C < R }
                Define : Outage capacity R0 given a outage
                probability Pout = Pr{ C < R0 }, this is the delay
                limited capacity.


Mattias         Outage probability approximates the
Wennström
                Word error probability for coding blocks of approx length100
Signals &
Systems Group
                Example : Rayleigh fading channel
                 Hij CN (0,1)

                       Ordered eigenvalue
                       distribution for
                       nr= nt = 4 case.




Mattias
Wennström                   nr=1            nr= nt
Signals &
Systems Group
                       To Exploit the MIMO Channel

                                         Bell Labs Layered
                                         Space Time Architecture

                                                         • nr  nt required
                                                         • Symbol by symbol detection.
                            Time
                                                         Using nulling and symbol
                s1 s1 s1 s1 s1 s1                        cancellation
                s2 s2 s2 s2 s2 s2
                s3 s3 s3 s3 s3 s3
                                    V-BLAST
                                                         • V-BLAST implemented -98
                                                         by Bell Labs (40 bps/Hz)
                s0 s1 s2 s0 s1 s2
                   s0 s1 s2 s0 s1   D-BLAST              • If one ”pipe” is bad in BLAST
                      s0 s1 s2 s0                        we get errors ...
Mattias
Wennström
Signals &
Systems Group   {G.J.Foschini, Bell Labs Technical Journal 1996 }
                               Space Time Coding

                • Use parallel channel to obtain diversity not
                   spectral efficiency as in BLAST
                • Space-Time trellis codes : coding and diversity
                                      gain (require Viterbi detector)
                • Space-Time block codes : diversity gain
                               (use outer code to get coding gain)
                • nr= 1 is possible
                • Properly designed codes acheive diversity of nr nt


                *{V.Tarokh, N.Seshadri, A.R.Calderbank
Mattias
                Space-time codes for high data rate wireless communication:
Wennström
                 Performance Criterion and Code Construction
Signals &
                , IEEE Trans. On Information Theory March 1998 }
Systems Group
                 Orthogonal Space-time Block Codes

                                                                               Block of T
                                                                               symbols

                          Constellation
                            mapper
                Data in
                                                                               nt transmit
                                                         STBC                      antennas



                                                    • K input symbols, T output symbols T K
                   Block of K
                     symbols                        • R=K/T is the code rate
                                                    • If R=1 the STBC has full rate
                                                    • If T= nt the code has minimum delay
                                                    • Detector is linear !!!
Mattias
Wennström       *{V.Tarokh, H.Jafarkhani, A.R.Calderbank
Signals &       Space-time block codes from orthogonal designs,
Systems Group   IEEE Trans. On Information Theory June 1999 }
                    STBC for 2 Transmit Antennas

                                                      Full rate and
                                                      minimum delay
                            c0     c1 
                                      *
                [ c0 c1 ]          * 
                             c1    c0 
                                            Antenna

                                    Time


                 Assume 1 RX antenna:
                Received signal at time 0   r0  h1c0  h2 c1  n0
                Received signal at time 1   r1   h1c1  h2 c0  n1
                                                      *       *
Mattias
Wennström
Signals &
Systems Group
                                       r  Hc  n

                     r0         h1       h2           n0        c0 
                r   * ,     H *          *
                                                  ,   n   * ,    c 
                    r1         h2        h1          n1         c1 

                                                  ~
                   ~  H*r  H*Hc  H*n  H 2 c  n
                   r                        F
                       Diagonal matrix due to orthogonality


                    The MIMO/ MISO system is in fact
                    transformed to an equivalent SISO system
                    with SNR

                    SNReq = || H ||F2 SNR/nt                       1 2
Mattias
Wennström             || H ||F2 = 1 2
Signals &
Systems Group
                The existence of Orthogonal STBC
                • Real symbols :   For nt =2,4,8 exists delay optimal
                                   full rate codes.
                                   For nt =3,5,6,7,>8 exists full rate
                                   codes with delay (T>K)
                • Complex symbols : For nt =2 exists delay optimal
                                   full rate codes.
                                   For nt =3,4 exists rate 3/4 codes
                                   For nt > 4 exists (so far)
                                   rate 1/2 codes

                                                     s1      0     s2    s3 
                Example: nt =4, K=3, T=4             0       s1     *
                                                                    s3    s2 
                                                                           *

                          R=3/4 s1 s2     s3    *
                                                 
                                                      s2    s3    *
                                                                    s1    0 
                                                                              
                                                     *                    * 
Mattias                                              s3      s2   0     s1 
Wennström
Signals &
Systems Group
                  Outage capacity of STBC
                                 SNR                                   SNR         
                         log 2 1             Cdiversity  log 2 det  I     HH  
                                            2
                CSTBC                  H   F
                                    nt                                     nt      


                                                                   Optimal capacity


                                                        STBC is optimal
                                                          wrt capacity if
                                                          HH† = || H ||F2
                                                          which is the case for
                                                        • MISO systems
                                                        • Low rank channels

Mattias
Wennström
Signals &
Systems Group
                Performance of the STBC…
                (Rayleigh faded channel)


                The PDF of
                || H ||F2 = 1 2 ..  m   Assume BPSK modulation
                                              BER is then given by
                                                                       2nr nt  1
                                                              nr nt
                                                    1 
                                              Pb                   
                                                                       nn       
                                                    4SNR             r t 
                                                         Diversity gain
                                                         nrnt which is
                                                         same as for
                                                         orthogonal
                                                         channels
                   nt=4 transmit antennas and
Mattias
Wennström          nr is varied.
Signals &
Systems Group
                        MIMO With Beamforming




                  Requires that channel H is known at the transmitter
                  Is the capacity-optimal transmission strategy if
                           1       1
                                        SNR
                          2       1
                Which is often true for line of sight (LOS) channels


                                                Only one ”pipe” is used


Mattias         Cbeamforming = log2(1+SNR·1)                 [bit/(Hz·s)]
Wennström
Signals &
Systems Group
                            Comparisons...
                2 * 2 system. With specular component (Ricean fading)




                                                                        One dominating
                                                                        eigenvalue. BF puts
                                                                        all energy into
                                                                         that ”pipe”


Mattias
Wennström
Signals &
Systems Group
                Correlated channels / Mutual coupling ...
                                          When angle spread (D)
                                          is small, we have a
                                          dominating eigenvalue.
                                          The mutual coupling
                                          actually
                                          improves the performance
                                          of the STBC by making the
                                          eigenvalues ”more equal”
                                          in magnitude.




Mattias
Wennström
Signals &
Systems Group
                 WCDMA Transmit diversity concept
                  (3GPP Release ’99 with 2 TX antennas)


                •2 modes                        Open loop mode is exactly the
                                                2 antenna STBC  s0  s1 
                                                                        *
                     • Open loop (STTD)                                    * 
                     • Closed loop (1 bit / slot feedback)        s1      s0 

                         • Submode 1 (1 phase bit)
                         • Submode 2 (3 phase bits / 1 gain bit)


                The feedback bits (1500 Hz) determines the beamformer weights
                Submode 1 Equal power and bit chooses phase between
                          {0,180} / {90/270}
                Submode 2 Bit one chooses power division {0.8 , 0.2} / {0.2 , 0.8}
                and 3 bits chooses phase in an 8-PSK constellation
Mattias
Wennström
Signals &
Systems Group
                       GSM/EDGE Space time coding proposal

                  • Frequency selective channel …
                  • Require new software in terminals ..
                  • Invented by Erik Lindskog
                   Time Reversal Space Time Coding                          (works for 2 antennas)


                                Block

                       S1(t)
                                        Time reversal   Complex conjugate
                S(t)

                        S2(t)
                                        Time reversal   Complex conjugate     -1


Mattias
Wennström
Signals &
Systems Group
                 ”Take- home message”
                • Channel capacity increases linearly
                 with min(nr, nt)
                • STBC is in the 3GPP WCDMA proposal




Mattias
Wennström
Signals &
Systems Group

				
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