1 CODING FOR MULTIPLE ANTENNAS WITH LINEAR AND NONLINEAR (BLAST) INTERFACES DIMACS WORKSHOP, OCTOBER 2002 EZIO BIGLIERI (work done with A. Nordio, G. Taricco,

1

CODING FOR MULTIPLE ANTENNAS WITH LINEAR AND NONLINEAR (BLAST) INTERFACES

DIMACS WORKSHOP, OCTOBER 2002

EZIO BIGLIERI(work done with A. Nordio, G. Taricco, and A. Tulino)

2

OUTLINE

SYSTEM MODEL AND BASIC ASSUMPTIONS LINEAR AND NONLINEAR RECEIVERS ZERO-FORCING AND MMSE BLAST ITERATIVE RECEIVER CODING FOR NONLINEAR RECEIVERS SIMULATION RESULTS

3

SYSTEM MODEL

mimo channel with t transmit and r receive antennas

fading constant over N symbol intervals independent rayleigh fading channel perfect csi at receiver

4

H

TX RX

5

SYSTEM MODEL

6

INTRODUCING AN INTERLEAVER

Pairwise error probability with ML detection:

E E

7

INTRODUCING AN INTERLEAVER

Spatial interference

8

INTRODUCING AN INTERLEAVER

9

INTRODUCING AN INTERLEAVER

OPTIONS FOR REMOVING 1:

• r

10

INTRODUCING AN INTERLEAVER

OPTIONS FOR REMOVING 1:

• r • Alamouti-type coding

11

INTRODUCING AN INTERLEAVER

OPTIONS FOR REMOVING 1:

• r • Alamouti-type coding• Introducing a row-interleaver

12

INTRODUCING AN INTERLEAVER

A random row interleaver yields

13

LINEAR INTERFACE

A

Metric used:

14

NONLINEAR INTERFACE

G +

L decoder

+ –

reduce spatial interference

L has zero diagonal elements

15

NONLINEAR INTERFACE

G +

L decoder

+ –

reduce spatial interference

L strictly upper triangular: Allows t iterations BLASTL with zero diagonal elements ITERATIVE RECEIVER

16

Use a soft estimate of the transmitted code word X in the form

BLAST INTERFACE

17

BLAST algorithm: step 1

18

BLAST algorithm: step 1

19

BLAST algorithm: step 1

20

BLAST algorithm: step 1

21

BLAST algorithm: step 2

22

ZF BLAST

23

ZF BLAST

24

MMSE BLAST

25

MMSE BLAST

26

NONLINEAR ITERATIVE INTERFACE

A +

L decoder

+ –

estimate of spatial interference L has zero diagonal elements:

L = AH - diag(AH)

27

NONLINEAR ITERATIVE INTERFACE

estimate of spatial interference:

28

CODING FOR NONLINEAR INTERFACES

...encoder

vertical coding:

coded symbols are spread across TX antennas

29

...

horizontal coding:

each TX antenna is

encoded separately

encoder

encoder

encoder

CODING FOR NONLINEAR INTERFACES

30

...encoder

vertical coding:

no preliminary decisions available

to increase the reliability of symbols

detected and used for cancellation

CODING FOR NONLINEAR INTERFACES

31

horizontal coding:

interference cancellation

is limited by the weakest code

...

encoder

encoder

encoder

CODING FOR NONLINEAR INTERFACES

32

horizontal + vertical coding:

each TX antenna transmits

a subcode of a larger code

...

encoder

CODING FOR NONLINEAR INTERFACES

33

SIMULATION RESULTS

(8,4,4) Extended Hamming code

34

35

36

37

38

39

40

41