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## Iterative detection and decoding to approach MIMO capacity

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Title: Iterative detection and decoding to approach MIMO capacity

1
Iterative detection and decodingto approach MIMO
capacity
• Jun Won Choi

2
Introduction
• MIMO capacity (CSI only at receiver)
• Fast fading scenario Ergodic I.I.D. Rayleigh
• Under fast fading assumption, transmission of
independent data stream with same power is
sufficient to achieve capacity (V-BLAST).
• Capacity achieving Gaussian codes are used at
each antenna as outer code.
• Coding across transmit antennas is needed ?

Teletar, 1999
3
Introduction
• Optimal transmitter structure

Signal processing operation (V-BLAST, D-BLAST,
space-time coding)
AWGN coder (outer code)
H
AWGN coder (outer code)
noise
Inner code
Coding across transmit antennas is needed in slow
4
Introduction
• Maximum a posteriori (MAP) decoder
• Model a received signal as Markov process whose
trellis is formed to include AWGN code,
space-time coding, and MIMO channel.
• Map decoding rule is optimal.
• Computationally infeasible !
• Iterative detection and decoding (IDD)
• Divide decoding job into MIMO detection (inner
code) and AWGN channel decoding (outer code).
• Approximately approach to optimal performance via
information exchange between two constitutional
blocks.

5
Transmitter design example 1 (IDD)
• Turbo-Blast (Haykin 2002)
• Random layered space time coding

Diagonal Layering
AWGN coder
Interleaver
M-ary modul
AWGN coder
Interleaver
M-ary modul
Space-time interleaver
6
Transmitter design example 2
• Space-time bit interleaved coded modulation
(Tonello, 2000)

M-ary mapper
AWGN coder
Interleaver
S/P
M-ary mapper
7
Principle of IDD
• Iterative (MIMO) detection and (channel) decoding

MIMO detector
Deinterleaver
SISO demapper
Information exchange
SISO channel decoder
Interleaver
Soft information is expressed as L-value
Priori LLR
Extrinsic LLR
8
IDD
• SISO Channel decoder
• BCJR algorithm based on trellis-based search
• Low-complexity APP decoder - LOG-MAX algorithm,
Soft output viterbi algorithm (SOVA)
• MIMO detector
• MAP versus Sub-optimal detector with linear
structure

9
Definition (Space-time bit interleaved coded
modulation)
10
Map detector
• Map detector
• A posteriori L-value of the bit

Extrinsic information (output)
11
Map decoder
• Map detection rule
• Log-Max approximation
• Complexity
• Complexity of MAP decoder is exponential in
modulation size, antenna size.

There are combinations for
each hypothesis.
12
List sphere decoding
• Idea (Hochwald, 2003)
• Find the combinations of symbol vector that are
highly likely to be transmitted. It is called
candidate list.
• Define the candidate list, L as
• Then, extrinsic L-value can be find over such
candidate list, i.e.,

13
List sphere decoding
• List sphere decoding
• Efficient tree pruning problem

Form skewed lattice
Number of points
Sphere constraint
Lattice
14
Define the cost metric
Sphere constraint is violated.
Prune sub-tree.
15
List sphere decoding
• Procedure
• 1. Find the points inside sphere by tree search.
• 2. Select closest points. (when number
of points found is larger than predefined list
size)
• 3. Increase radius and restart the search. (when
number of points found is less than list size)
• 4. If candidate list has no common entry with
or , the extrinsic L-value is
set to inf or inf depending on the sign of
entries.
• How to choose B?,
• For true x

16
Turbo-Blast detector
• Turbo-Blast detector
• Sub-optimal detector with linear structure
• Derive based on linear MMSE criterion

Assume that are
available.
Interference cancellation step
Interference nulling step
Let
17
Turbo-Blast detector
• Interference cancellation step
• Interference nulling step

18
Turbo-Blast detector
• Gaussian approximation

Interference noise term
There are only combinations
for each hypothesis.
19
Conclusions
• Capacity achieving MIMO architecture
• Transmitter architecture
• V-BLAST AWGN code for fast fading
• Coding across transmit antenna for slow fading ?
space time coding, D-BLAST, Treaded space time
coding