May 2007
doc.: IEEE 802.22-07/0xx
IEEE P802.22 Wireless RANs
Text for full band diversity interleaving
Last Updated - Date: 2007-05-08
Author(s):
Name
Isabelle Siaud
Company
Orange Labs
Orange Labs
John Benko
Address
Rue du Clos Courtel
35510 CessonSévigné France
801 Gateway Blvd,
S San Francisco,
CA USA
Phone
+33 299 124 629
1-650-875-1593
email
isabelle.siaud@orangeftgroup.com
john.benko@orangeftgroup.com
Abstract
This document presents both informative and normative text for a frequency interleaver to
backup
the
presentation,
22-07-0117-01-000_Enhanced_Bit_and_Frequency_
Interleaving given in the March 2007 meeting.
.
Notice: This document has been prepared to assist IEEE 802.22. It is offered as a basis for discussion and is not binding on the
contributing individual(s) or organization(s). The material in this document is subject to change in form and content after
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Release: The contributor grants a free, irrevocable license to the IEEE to incorporate material contained in this contribution,
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accepts that this contribution may be made public by IEEE 802.22.
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A.1.1.1 Introduction and Motivation (Informative)
The interleaving algorithm proposed here can be used to interleave (1) encoded bits at the binary level and (2) to allocate subcarriers in OFDMA symbols. The same algorithm is utilized for downstream and upstream sub-carrier mapping allocation
with appropriate permutations rules for these two configurations.
The interleaving algorithm, L(k) is a turbo-based structure using an interleaving unit I(k) integrated in an iterative structure.
Desired permutations rules provided by the algorithm, are generated with three integer parameters {p,q,j}. The block
interleaving system
L( k )  I (p,qj ) is built on an iterative structure described by the interest iteration (j) and two integer
parameters p and q that generate in a scalable way, desired interleaving patterns. The originality of the algorithm is to exactly
control in an algebraic way the interleaving spreading
L( s )  eff I (p,qj )( s )
between interleaved samples while preserving
special data multiplexing, ensuring an equivalent multi-stream interleaving processing performed onto a single stream.
Interleaving parameters {p,q,j} are selected to increase the interleaving spreading L(s) between adjacent samples and
samples separated by s-1 samples. S values are chosen depending on the interleaving implementation and interleaving
spreading criteria. In a second step, for the s ={s0, s1, …,sq} targeted values, the interleaving parameters {p,q,j} are selected
to generate the appropriate interleaving pattern that make increase the interleaving spreading and satisfy technical
requirements of the system.
The annex gives the technical background for the algorithm.
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A.1.1.2 Interleaver algorithm for full channel interleaving (diversity mode) - Normative
Interleaving for full channel interleaving shall use the block interleaving algorithm I p( ,jq) (k ) , described in this
section. Parameters that fully describe the interleaving are: K, the number of interleaved sub-carriers, p, the
interleaving partition size (integer), q, an integer parameter q and j, the iteration number. I p( ,jq) (k ) is based on an
interleaving function L(k), built on a serial combination of two algebraic functions L0,p and L1,p,q, characterized by
two inputs and one output. Inputs of the function L0,p are fed with the input index position and the feedback of the
previous iteration of the algorithm, I p( ,jq1) (k ) , while function L1,p,q is fed with the incremental k (position index of
samples 0, 1, ….K-1) and the output of the function L0,p associated with the current iteration.
L0 and L1 functions are expressed, for j=1, as follow:
L0, p (k )   k  k  p K , k  0,...., K  1
I p , q (k )  L1, p , q (k )   K  p  k  q  p  L0, p (k ) 
I p , q (k )   K  p  k  q  p   k  kp K 
(1)
K
K
The interleaving algorithm expressed for the iteration j={1,2} as:


L(2)
0, p ( k )    k  p  I p , q ( k ) 
K

I p(2), q (k )   K  p  k  p  q  L(2)
0, p ( k ) 
I
(2)
p,q
K
(k )   K  p  k  p  q   k  p  I p , q (k )  
K K

The extension to the j-th iteration is given by:
L(0 ,jp) ( k )    k  p  I (p ,qj 1 ) ( k )
I
( j)
p ,q
K
( k )   K  p  k  q  p  L(0 ,jp) ( k )
K
(2)
I (p ,qj ) ( k )   K  p  k  q  p   k  p  I (p ,qj 1 ) ( k ) 
K K

A.1.1.3 Sub-carrier allocation in upstream configuration - Normative
In a pure diversity implementation, 60 sub-channels of 28 sub-carriers are allocated in an OFDMA structure. Each subchannel is composed of 24 data tones and 4 pilot tones.
In this configuration, the interleaving is performed upon blocks of 1680 tones (28x60), K=1680, where pilot tones are
included in the interleaving process. The interleaving pattern I(k), as described in section A.1.1.2, shall be used with
interleaving parameters {p,q, j} as defined in the Table 1 below. Table 1 also gives informative interleaving speading
distances.
Interleaving
depth K
Interleaving
set up
Permutation
1680
Interleaving
parameters
p
q
j
21
2
3
Interleaving spreading L(s)
S=1
589
S=2
S=4
502
236
S=24
264
S=48
528
Table 1: Interleaving parameters for the sub-carrier mapping allocation (upstream).
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A.1.1.4 Sub-carrier allocation in downstream configuration - Normative
In a pure diversity implementation, 60 sub-channels of 28 sub-carriers are allocated in an OFDMA structure, with each subchannel composed of 24 data tones.
Data tones are first mixed and allocated in each sub-channel in the frequency and time domains. Pilot tones are then placed in
the OFDMA symbol at fixed positions.
In this configuration, the interleaving is performed upon blocks of 1440 tones (24x60, 48x30). The interleaving spreading is
optimized for s values ranged from {1, …., 23}/{1,…, 47} and between sub-channels ([s]28=0, [s]48=0). Secondly, the
permutations between each subset of 24/48 sub-carriers have to be different when the concerned sub-channels are allocated to
the same user in the time domain.
The selected interleaving parameters are summarized below. Three sets of parameters are given, to support an optional
dynamic implementation of the algorithm where three successive permutations rules (P1, P2, P3) are successively
implemented in a periodic pattern for successive OFDM symbols in the OFDMA downlink structure (see Figure 1 below).
The sub-channel mapping allocation shall be hence attributed in different ways by splitting interleaved data tones in subchannels and mapping them in the time and frequency domain. In the case where static interleaving is used, parameter set P1
should be used.
Interleaving
depth K
Interleaving
Permutation
Interleaving
parameters
p
q
j
Interleaving spreading L(s)
S=1
S=2
S=4
S=24
S=48
P1
1440
40
2
2
559
322
644
456
528
P2
1440
10
2
3
421
598
244
24
48
P3
1440
32
2
3
577
286
572
252
336
Table 2: Interleaving parameters for the sub-carrier mapping allocation.
Three different permutation rules
L2(k)
K=1440
Y2(k)=x(L2(k))
L3(k)
K=1440
Y1(k)=x(L1(k))
L1(k)
K=1440
f
f
t
Permutation rule #1
Permutation rule #2
Permutation rule #3
Permutation rule #1
OFDM symbol #1
OFDM symbol #2
OFDM symbol #3
OFDM symbol #1
Figure 1: Dynamic implementation of the sub-carrier mapping allocation for the DS
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Annex 1 : Technical Background for the algorithm (informative)
The block interleaving processing with a size K consists in first reading sequentially a K sized input sequence S
and writes it out in a sequence S' following a dedicated interleaving pattern given here by I (p,qj ) where p and q are
integer parameters of the algorithm and (j) the selected iteration providing the desired interleaving pattern. Sample
index k at both output and input of the interleaving is ranged from 0 to K-1. That is, the k-th output, written to
location k in the output vector, is read from location I (p,qj ) in the input vector. Interleaving processing is described
by:
S'( k )  S( I (p,qj ) ( k ))
(3)
L(k)
0
Y(k)
0
L(k+s)
L(0)
k'
k
k+s
Y(k)=X(k')
k'=L(k)
Fig. A1: Interleaving procedure
The interleaving algorithm resorts from advanced studies and is set aside for fulfilling proper technical
requirements. First, the maximization of the interleaving spreading between samples separated by s-1 samples is
an important criterion to ensure reduced correlations at the input decoder. For that purpose, several s values are
selected in a multi-level interleaving spreading maximization criterion to select interleaving patterns providing
high spreading in a multi-level scale. Secondly, interleaving scrambles data and breaks special data multiplexing
used to optimize system performance. We focus the interleaving design on a dedicated algorithm which preserves
special data multiplexing. Technical requirements are detailed in the next section.
A.1.2 Technical requirements
A.1.2.1 The maximization of the interleaving spreading
It consists in selecting interleaving patterns I (p,qj ) , ie interleaving parameters {p, q, j} that increase the
interleaving spreading given by
L(s)  eff I (pj,q) (s) 


Min
I (pj,q) (k  s)  I (pj,q) (k ) .
0k K 1
Some targeted s values are considered in connection with the interleaving implementation.
The interleaving spreading eff I (p,qj ) ( s ) between samples separated with s-1 samples corresponds to lowest absolute
value of the dispersion Pp ,q , j ( s ) and the function K  Pp ,q , j ( s ) . For the iteration 1, we have:
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Pp ,q ( s )  I p ,q ( k  s )  I p ,q ( k ),

eff I p ,q ( s )  Min Pp ,q ( s ) ,K  Pp ,q ( s )

I p ,q ( k )   K  p  k  q  p    k  p  k )K 
(4)
K
I p ,q ( k  s )   K  p  k  s  q  p   ( k  s )  p  ( k  s ))K 
Pp ,q ( s )  s   q  p  s( p  1 )K
 s   q  p  s( 1  p ) ,
K

I p ,q ( s )  Min 
e ff
K  s   q  p  s( 1  p )K








K
(5)
For the iteration j, we have:
Pp ,q , j ( s )  I (p ,qj ) ( k  s )  I (p ,qj ) ( k )
Pp ,q , j ( s )  s  q  p  ( s  p  Pp ,q , j 1( s ))
(6)
K
 s   q  p( s  p  P

p ,q , j 1 ( s )) K





 K  s   q  p( s  p  Pp ,q , j 1 ( s )) 
K 

eff I (p ,qj ) ( s )  Min 
These algebraic functions are used to select appropriate interleaving parameters {p,q,j} and generate desired
interleaving patterns that provide the desired interleaving spreading for s targeted values.
At the binary level
L(s) maximisation in each data symbol imposes s={1,…,Ncbps-1} where Ncbps is the number of encoded bits
per data sub-carrier. L(s) maximisation between adjacent sub-carriers is carried out with [s]Ncbps=0. For these
targeted values, selected {p,q,j} parameters that provide the relevant permutations rules are the parameters
providing the largest L(s).
At the sub-carrier level
The interleaving spreading maximisation is processed upon successive sub-carriers within each sub-channel and
between sub-channels in considering {p,q,j} parameters that provide max values of L(s) with [s]Nsubchannel_size=0.
The interleaving partitioning preservation
It consists in keeping unchanged after the interleaving processing, a distributed p-sized data multiplexing
associated with p virtual parallel streams (Fig.A1).
Virtual stream # 0
stream #0
Interleaving
X(k)
Interleaving
Y(k)
Interleaving
P/S
S/P
Interleaving
Y(k)
S/P
Y( k )  X( I (p,qj )( k ))
Interleaving
Stream # p-1
Virtual stream #p-1
x0 x1 x2.. xpo-1 xpo xp-1 xpxp+1 …...x2p-1 xpq x1+pqx2+pq x3+pq ..xp(q+1)-1
x'0 x'1 x'2 x'3 …x'p-1 x'p x'p+1….. x'2p-1
x'pq x'1+pqx'2+pq x'3+pq ..x'p(q+1)-1
Fig. A2: The equivalent multi-stream interleaving structure
In that way, the algorithm preserves an interleaving partitioning associated with a virtual partitioning of p
independent data streams where the interleaving processing is equivalent to a fictitious p-parallel interleaving
processing independently carried out on each virtual data stream (right part of Fig.1). The integer parameter p is
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one parameter of the interleaving proposal which provides the interleaving partitioning size. This property is
translated by the equation:
I ( j )( k )  k   0
 p,q
p
(7)
In that way, the interleaving processing does not break dedicated data multiplexing resulting from pre and post
processing.
The basic interleaving function I(k) is characterized by two inputs and one output. One of the inputs is fed with
the initial index position of the input sequence S and the second one is fed with the interleaving pattern output of
the previous iteration. The interleaving pattern I p( ,jq) (k ) results from the iteration (j), p and q parameters using the
same basic interleaving function I(k). The basic structure I(k) is also a serial combination of two functions Lo,p
and L1,p,q characterized with two inputs and one output.
( j)
I p ,q
I p , q (k )
k
(2)
I
I
I p ,q (k )
(k )
I
I
( j)
k
Lo
( j 1)
I p ,q (k )
I p ,q (k )
L1
I p( ,jq) (k )  I1 (k , L0(pj ) (k ))
Fig. 3: The turbo-based interleaving structure
Static & Dynamic
set-up
IFFT
FFT
X

k
WNkm
X
FFT
X
( 1)m
(N
1)m
WN FFT
FFT
Multipath Channel
sn ( t )
WN0m
Tcp Insertion
Guard sub-carrier Insertion
sub-carrier
Allocation In(k)
And pilot insertion
sub-carrier Modulation
Binary interleaving
Puncturing
FEC coding
Information binary source
X
+
AWGN
DIC ={rule#1,#2,..,#N'}
( j)
I p , q (k )
k
I
I
I p ,q (k )
I p,q (2) (k )
I
OFDM
symbol
OFDM
symbol
- symbol
OFDM
I
Interleaver
rule #1
Interleaver
rule #2
Interleaver
rule #N'
Figure 1: Implementation of the interleaving proposal at the binary and sub-carrier levels
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Annex 2 : Backup Material
Graphical representation of interleaving for DownStream
Interleaving patterns are represented for two sub-channel sizes (24 and 48 data tones). This graphical
representation includes three successive sub-channels using the same relative tone indexes in a sub-channel.
K=1440 {p, q, j}={40,2,2}
data symbol index
1400
1200
1000
800
600
400
200
0
0
10
20
30
40
k relative sub-carrier index in a sub-channel
sub-channel#1
sub-channel#2
sub-channel#3
Figure 2: Permutation rule #1
The second permutation rule #2 is similar for each sub-channel composed of 24 data tones. This permutation shall
be implemented in a pure diversity configuration.
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K=1440 {p, q, j}={10,2,3}
data symbol index
1400
1200
1000
800
600
400
200
0
0
5
10
15
20
k relative sub-carrier index in a sub-channel
sub-channel#1
sub-channel#2
sub-channel#3
K=1440 {p, q, j}={10,2,3}
data symbol index
1400
1200
1000
800
600
400
200
0
0
10
20
30
40
k relative sub-carrier index in a sub-channel
sub-channel#1
sub-channel#2
sub-channel#3
Figure 3 : Permutation rule #2
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K=1440 {p, q, j}={32,2,3}
data symbol index
1400
1200
1000
800
600
400
200
0
0
5
10
15
20
k relative sub-carrier index in a sub-channel
sub-channel#1
sub-channel#2
sub-channel#3
K=1440 {p, q, j}={32,2,3}
data symbol index
1400
1200
1000
800
600
400
200
0
0
10
20
30
40
k relative sub-carrier index in a sub-channel
sub-channel#1
sub-channel#2
sub-channel#3
Figure 4 : Permutation rule #2
Graphical representation of interleaving for UpStream
The next figures provide the positions of symbols upon data and pilot tones in the case of 28 (24D+4P) subchannel size.
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K=1680, {p,q,j}={21,2, 3}
1800
data symbol index
1500
1200
900
600
300
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
relative sub-carrier index in sub-channel
sub-channel #3
sub-channel #1
sub-channel #2
Figure 5: Permutation rule #1
The second permutation rule #2 is similar for each sub-channel composed of 24 data tones. This permutation shall
be implemented in a pure diversity configuration.
K=1680, {p,q,j}={5,2, 3}
1800
data symbol index
1500
1200
900
600
300
0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
relative sub-carrier index in sub-channel
sub-channel #1
sub-channel #2
sub-channel #3
Figure 6 : Permutation rule #2
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K=1680, {p,q,j}={168, 2, 3}
1800
data symbol index
1500
1200
900
600
300
0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
relative sub-carrier index in sub-channel
sub-channel #1
sub-channel #2
sub-channel #3
Figure 7 : Permutation rule #3
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