# MIMO with MUMS by ewghwehws

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```									MIMO with MUMS

2E1367 Project Course in DSP

Group Red 04
2004.5.28
Outline
 Introduction                          Implementation
   MIMO systems
   MUMS
 Theory for 3 MIMO
schemes                               Results
   Weighted Orthogonal Space-time
Block Coding
   Differential Space-time
Modulation
   Spatial Multiplexing
 System Model
Introduction
 MIMO systems
   Multiple Input Multiple Output communication systems for
a higher data rate and better quality.
 MUMS
   A test-bed with four radio nodes (Tx1,Tx2, Rx1,Rx2)
   Two antennas each node
   WIDELAB radio equipment
Theory - WOSTBC
 Weighted Orthogonal Space-time Block Coding
(WOSTBC)
 Alamouti Space-time Coding-----encoder
h11

Tx1 h21           Rx1
TX1    TX2
Time t     S0     S1
h12
Time t +T   -S1*   S0*
h22
Tx2               Rx2
Theory - WOSTBC
 Alamouti Space-time Coding----Receiver

RX1        RX2
h11
Time t        r0         r2
Tx1 h21           Rx1   Time t +T       r1         r3
h12
r 0  h11 s0  h12  s1  n0
h22
Tx2               Rx2   r1  h11 s1 *  h12  s0 *  n1
r 2  h21 s0  h22  s1  n2
r 3  h21 s1 *  h22  s0 *  n3
Theory - WOSTBC
 Alamouti Space-time Coding----Decoder

s0  h11* r 0  h12  r1*  h21* r 2  h22  r 3 *
ˆ
s1  h12 * r 0  h11 r1*  h22 * r 2  h21 r 3 *
ˆ
s0  (| h11 |2  | h21 |2  | h12 |2  | h22 |2 )  s0  N 0
ˆ
ˆ1  (| h11 |2  | h21 |2  | h12 |2  | h22 |2 )  s1  N1
s
r 0 r1
                Decoder                s 0, s1
ˆ ˆ
r 2 r 3
Theory - Weighting
 Goal: To maximize the SNR at the receiver
 Idea: Put more power on the transmitter that
has a higher gain of channels
If                                             h11

h11  h21        h12        h22
2      2           2           2
Tx1 h21           Rx1

Allot full power to TX1              h12

h22
Tx2               Rx2
VICE VERSA
Theory –Differential Space-time Modulation
 Modulation                 Optimal Unitary Group Codes (n = t= 2 )

Optimal Unitary Group
Codes                          R             M                G

 1 0 
0.5         BPSK           0  1
      

 j 0  0  1
Bits block                 G       1.5         QPSK        0  j , 1 0 
            
Modulator
w8 0  0  1
2            8PSK              ,    
 0 w*8  1 0 
       

j / 4
Notation:w8  e
Theory –Differential Space-time Modulation
 Differential Encoding
1  1
X0  D                       D
1 1 
X k  X k 1Gk
Gk                 Xk

Z 1
Theory –Differential Space-time Modulation
 Differential Decoder

GG

ˆ  arg max Re Tr GY Y
G                   k  k 1   
Re TrG1

Choose the G matrix
Maximize the value
.                  .

Yk                   Yk Yk 1      .                  .                         ˆ
G
{} +                    .                  .
.                  .
.                  .

Z 1                        Re TrG m 
Theory – Spatial Multiplexing
 Utilize the feedback information of channel condition
 Water Filling: maximize the information capacity

Receiver:                                             H
S1                                    ˆ
s1
r  HWs  v  U H  H W s  v            W                        G
S2                                    ˆ
s2
TX       RX
s  Gr
Singular Value Decomposition (SVD):
 s  H W s  U H v
*

H  U H  H VH

W  UW W VW
Theory – Spatial Multiplexing
 Solution of W
Start M=2

U W  VH         VW  I
1                1
       (1   2 i 1 2 )
M

 H ,i
W ,max 0                                 M
W  
 0      W ,min 
   M  M 1                    2

2
   2 , i  1,2
W ,i
H ,i
 Solution of G
No             W ,M  0
G U
2
*
H
Yes
End
Theory – Spatial Multiplexing
 Adaptive modulation over time and space
 QoS Based Water Filling
QoS: BER threshold 
Mapping function of SNR to BER:                 i  F ( i , M i )

               W ,i H ,i
2     2

Step 1:       W ,i  WF ( H )                i 
2

Step 2:        i  F ( i , M i )          Mi

Notation: M i: modulation order               i : SNR                i : BER
System Model
Transmitter

Modulation       Frame            Up            Pulse              Up
Packing         sampling       shaping          conversion

Receiver

Down           Matched        Sync      down         Frequency
conversion        filter                sampling      offset comp

Demodulation      Detection       Channel
Estimation
Implementation - Frame packing (TX)
 Three kinds of frames                                BPSK
 Sync frame                                   Sync + freq_offset

32 tr symb
BPSK alamouti
 Training frame                   Modulation identification

16 tr symb        2 mod_id symb            14 zero symb
BPSK orthogonal                              Noise estimation
Channel estimation

 Data frame                  BPSK / QPSK / 16QAM

32 data symb
Implementation - Frame packing (RX)
 Feedback buffer
 First byte                  Unused

7      6   5    4   3      2    1      0

MOD_ID bits      WEIGHT_ID bits
00    BPSK           00       TX1 more power
01    QPSK           01       TX2 more power
10   16QAM           10        Equal power
11    Unused         11          Unused
Implementation - Program flow
32 * 5
Feedback delay: 5 frames T frame         3.3ms
48000
Feedback buffer size: 4 bytes
Read 1st FB                                     Read 2nd FB
Send tr frame                         Send tr frame                                    Send tr frame
sync                      Receive 1st FB                           Receive 2nd FB
TX      0    1   2      3   4     5   6     7      8   9   10      11   12   13   14   15   16   17   …

FB1                                        FB2

RX      0    1   2      3   4     5   6     7      8   9   10      11   12   13   14   15   16   17   …

Estimate channel                           Estimate channel                        Estimate channel
Write FB                                   Write FB                                Write FB
Implementation - Frequency offset I
 Least squares line fitting
Slope
j *( 2 *f *n   0 )   (n)
r0 (n)  s0 (n) * e                             -0.4
the phase of training unwrapped

-0.45

(n)
-0.5

Im[ r0 (n)]
(n)  arctan(               )                 -0.55

Re[ r0 (n)]
-0.6

f  0.002                                    -0.65
0   5   10       15        20         25   30   35

(96 Hz )                                                                    n
Implementation - Frequency offset II
 Frequency offset compensation

Before                                                         After

Signal Space of 16QAM
Signal Space of 16QAM
5                                                            4

4
3
3
2
2

1                                                            1

0                                                            0

-1
-1
-2
-2
-3
-3
-4

-5                                                            -4
-5   -4   -3   -2      -1     0     1       2   3   4   5     -4   -3   -2    -1       0       1     2   3   4
Implementation - Design parameters I
 SNR threshold

BER
BPSK
QPSK
16-QAM

Target BER =10-3

SNR

20dB         50dB
Implementation - Design parameters II
 Power weight threshold
Tx1 power            Tx2 power
h11
Tx1           Rx1   tot _ power _ received | h11 |2  | h21 |2  | h12 |2  | h22 |2

h21
Receiver                                  Transmitter
Tx1 _ power _ received
h12                                          0.8                  90% power to Tx1
tot _ power _ received
Tx2     h22   Rx2      Tx1 _ power _ received
 0.2                  10% power to Tx1
tot _ power _ received

else                               50% power to Tx1
Implementation - Real time issues
 Code optimization (processing speed and memory space)
 Complex number (LDDW)
 Floating point division (extract the exponent)
 Trigonometric functions (C67x FastRTS Library, Cisoid Table)
Results
 Throughput
48000
theoretical _max_ throughput            * no _ bits _ per _ symb
5

48000
pratical _ max_ throughput            * no _ bits _ per _ symb *
5
67  1  9
no _ bits _ per _ symb  1,2,4                         0.8507
67

no _ correct _ bits _ received
measured _ throughput 
tot _ time

67 * 32 * 5
tot _ time                 223.3ms
48000
Results
 Throughput (cont’d)
theoretical_max_throughput           BPSK: 9.6K bps (8.16K bps)
(pratical_max_throughput)
QPSK: 19.2K bps (16.3K bps)

16QAM: 38.4K bps (32.6K bps)

Measured_throughput (alamouti)              BPSK: 8.15K bps
QPSK: 19.15K bps
16QAM: 30.72K bps
Measured throughput (alamouti with          32.02K bps
adaptive modulation)
Results
SISO
MIMO
 Simulations
-3
-1       BER performance of adaptive modulation                                       x 10                          average data rate
10                                                 WOSTBC
SISO
DSTM
10
Spatial Multiplexing
adaptive MIMO
9             BPSK
QPSK
-2                                                                                             16QAM
10                                                                                8
adaptive SISO

7
BER

Rate
6

-3
10                                                                                5

4

3

-4
10                                                                                2
5              10                     15                        20               5                        10                       15   20
SNR(dB)                                                                                    SNR(dB)

MIMO: lower BER                                                                           MIMO: higher data rate

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