Details on Permutations for DL and UL PHY structures
Document Number:
IEEE C802.16m-08/1468r1
Date Submitted:
2008-11-11
Source:
Seunghyun Kang, HanGyu Cho, Jinsoo Choi, Jin Sam Kwak
Email: {sh_kang, hgcho, emptylie,
samji} @lge.com
LG Electronic Inc.
Venue:
IEEE C802.16m-08/042 “Call for Contributions on Project 802.16m Draft Amendment Content” in
response to the following topic – Downlink and Uplink Physical Structure
Purpose:
To provide details on permutations proposed in amendment texts on DL and UL PHY structures
Notice:
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only the views of the participants listed in the “Source(s)” field above. It is offered as a basis for discussion. It is not binding on
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Introduction


The documents [1] and [2] propose amendment texts
on DL and UL PHY structures in response to “C80216m08_042: Call for Contributions on Project 802.16m Draft
Amendment Content”.
This contribution is focusing on the details of DL/UL
permutations used in those documents in order to help
members understanding permutation rules and related
sequence generation methods therein.
[1] IEEE 802.16m-08/1466, “Proposed Amendment Text on Downlink Physical Structure”
[2] IEEE 802.16m-08/1467, “Proposed Amendment Text on Uplink Physical Structure”
Permutations in subcarrier to resource unit
mapping in 16m
1.
The outer permutation is applied to the PRUs in the units of N1
and N2 contiguous PRUs, where N1=4 and N2 = 1.
- Outer permutation P1 in the unit of N1 contiguous PRUs
- Outer permutation P2 in the unit of N2 contiguous PRUs
2.
3.
Distribute the outer-permuted PRUs into frequency partitions.
Each frequency partition is divided into localized (CRU) and/or
distributed (DRU) resources. Sector specific second-level
permutation can be supported and direct mapping of the
resources for localized resources can be also supported. The
sizes of the distributed/localized resources are flexibly
configured per sector.
- Second-level permutation (or localized/distributed resource grouping)
P3 in the units of PRU
4.
The localized and distributed resources are further mapped into
localized LRUs and distributed LRUs by direct mapping of CRU
and by inner permutation on DRUs, respectively.
- inner permutation P4 in the units of a pair of subcarriers (DL) or tile (UL)
Example of DL subcarrier to resource unit
mapping
: PRU-subband
: PRU
Cell-common
0
10MHz: NPRU=48, N1=4, N2=1, NP-Sub=12, NN1=4, NN2=32
NP-Sub-1
1
Outer permutation P1
in the units of PRU-subband (=N1 contiguous PRUs)
0
NN1-1
1
0 1 2
Outer permutation P2
in the units of PRU
Localized/distributed
resource grouping
Cell-specific
NN2-1
Localized (L)
Path-through
L
Distributed (D)
Inner permutation
in the units of a pair of subcarriers
Freq. partition 1
Localized/distributed
resource grouping
L
D
L
D
L
D
Inner permutation
in the units of a pair of subcarriers
Freq. partition 2
Freq. partition 3
Freq. partition 4
Notes on Permutation Design

There exist several permutations in subchannelization
with various lengths of permutation sequence due to



Cell-common and cell-specific permutations



Frequency partitions
FDM multiplexing of localized and distributed resources
Cell-common outer permutations
Cell-specific second-level permutation and inner permutation
Desirable to distribute permutation units such that
maximum diversity gain can be obtained


For cell-common permutations such as outer permutations P1,
P2, and second-level permutation, distributing permutation units
evenly across the available frequencies is better in terms of
diversity gain
For Inner permutation P4, to be maximally spread the pairs of
subcarriers in time and frequency across the NDRU DRUs in the
distributed resource group is desirable
Permutation sequence generation rule
P[i] = {D· i + O + floor(i / W)} mod N, i = 0,1,…, N – 1
where
D : Distance between two adjacent permutation
indices
O : Initial index offset for the permutation sequence
W = N / GCD(N, NDist), where GCD(x, y) is the greatest
common divisor of x and y
Permutation sequence generation rule


By adding floor(i / W), the permutation sequence
generation rule can be applied to any length N with
any distance D
By using the permutation sequence generation rule,
the generated sequence has almost equidistance
between any two adjacent permutation indices as
follows:
D  1,
( P[i  1]  P[i ]) mod N  
 D,
if (i  1) mod W  0
Otherwise
Outer permutation P1 in the units of PRU-subband
For cell-common outer permutation P1, to evenly
distribute NN1 PRU-subbands across the total NP-Sub PRUsubbands,


D = ceiling(NSub / NN1) and O is cell-common
Ex) NP-Sub = 12 and NN1 = 6


NN1=6 PRU-subbands for allocation with N1 granularity are
evenly distributed with D= ceiling(NSub / NN1)=2, which can
maximize diversity gain
Outer permutation P1
in the units of PRU-subband (=N1 PRUs)
0
1
0
1
NP-Sub-1
NN1-1
For allocation with
N1 granularity
Outer permutation P2 in the units of PRU

For cell-common outer permutation P2, to distribute NN2
PRUs such that each freq. partition can have PRUs well
distributed across the available frequencies,


D = Npart where Npart denotes the number of frequency
partitions and O is cell-common
Ex) NN2 = 24 and Npart = 3 with equal bandwidth

Each frequency partition has 8 evenly distributed PRUs with D=
Npart=3, which can maximize diversity gain
Outer permutation P2
in the units of PRU (N2=1)
0
1
NN1-1
NN2-1
0 1 2
Freq. partition 1
Freq. partition 2
Freq. partition 3
Localized/distributed resource grouping (secondlevel permutation)

In each frequency partition, localized resources (PRUsubbands or PRUs) are reserved evenly distributed
across the available frequencies,
Localized/distributed
resource grouping
Localized (L)
L
Distributed (D)
Freq. partition 1
Localized/distributed
resource grouping
L
D
Freq. partition 2
L
D
Freq. partition 3
L
D
Freq. partition 4
Inner Permutation for DL

Pairing and Renumbering for the data subcarriers across the
NDRU PRUs per OFDMA symbol
Nsym=6
P
P
NDRU=2
P
P
Psc=18
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
Pairing and
Renumbering
across NDRU
PRUs per
OFDMA symbol
P
0
0
P
0
0
0
1
1
0
1
1
1
2
2
1
2
2
2
3
3
2
3
3
3
4
P
3
4
P
4
5
4
4
5
4
5
6
5
5
6
5
6
7
6
6
7
6
7
P
7
7
P
7
P
8
8
P
8
8
8
9
9
8
9
9
9
10
10
9
10
10
10
11
11
10
11
11
11
12
P
11
12
P
12
13
12
12
13
12
13
14
13
13
14
13
14
15
14
14
15
14
15
P
15
15
P
15
Npair,PRU
=(Psc-nl)/2
=8
Npair
= Npair,PRU*NDRU
=16
Inner Permutation for DL


The goal is to form a NDRU distributed LRUs (subchannels)
such that Npair,PRU * Nsym pairs of each subchannel are
maximally spread across the NDRU PRUs
The inner permutation can be performed by (Npair,PRU,
NDRU) block interleaving





Row-wise index writing
Time-variant intra-row permutation
Intra-column permutation
Column-wise index reading
This block interleaving is



To group the renumbered Npair pairs per OFDMA symbol into Npair,PRU
groups with NDRU contiguous pairs for each group and
To select Npair,PRU pairs by choosing a pair per each group and
To change the selected pair per each group with OFDMA symbol
Inner Permutation for DL
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
3
1
4
2
6
9
7
5
14
12
10
13
39
34
29
20
15
10
24
5
6
1
35
30
0
0
1
1
0
1
1
1
2
2
1
2
2
2
3
3
2
3
3
3
4
P
3
4
P
4
5
4
4
5
4
5
6
5
5
6
5
6
7
6
6
7
6
11
11
15
16
17
18
19
19
17
15
18
16
36
31
26
21
16
20
21
22
23
24
22
20
23
21
24
22
17
12
7
2
25
26
27
28
29
25
28
26
29
27
8
3
37
32
27
30
31
32
33
34
33
31
34
32
30
33
28
23
18
13
35
36
37
38
39
Intra-row
permutation
for 1-st
symbol
19
14
9
4
P
3
1
P
2
0
0
28
26
4
27
25
25
14
12
29
13
11
11
39
37
10
38
36
36
20
P
35
24
P
22
6
23
21
5
22
36
39
37
35
38
8
31
9
7
30
8
3
1
4
2
0
38
33
17
34
32
16
33
7
P
7
7
P
7
6
9
7
5
8
19
P
15
18
P
19
P
8
8
P
8
8
14
12
10
13
11
P
37
35
P
36
39
8
9
9
8
9
9
17
15
18
16
19
39
23
21
38
22
20
9
10
10
9
10
10
20
23
21
24
22
20
9
7
24
8
6
10
11
11
10
11
11
28
26
29
27
25
6
34
32
5
33
31
11
12
P
11
12
P
31
34
32
30
33
31
15
P
30
19
P
12
13
12
12
13
12
39
37
35
38
36
17
1
18
16
0
17
13
14
13
13
14
13
3
26
4
2
25
3
1
4
2
0
3
14
15
14
14
15
14
28
12
29
27
11
28
15
P
15
15
P
15
14
P
10
13
P
14
P
16
16
P
16
16
P
32
30
P
31
34
34
18
16
33
17
15
15
4
2
19
3
1
1
29
27
0
28
26
26
10
P
25
14
P
12
35
13
11
39
12
16
17
17
16
17
17
17
18
18
17
18
18
18
19
19
18
19
19
20
20
P
19
20
P
21
20
20
21
20
21
22
21
21
22
21
22
23
22
22
23
22
23
P
23
23
P
P
24
24
P
24
25
25
25
26
26
26
27
27
28
Intra-row
permutation
for 2-nd
symbol
9
7
5
8
6
12
10
13
11
14
15
18
16
19
17
23
21
24
22
20
26
29
27
25
28
19
Intra-row
permutation
for 3-rd
symbol
34
32
30
33
31
37
35
38
36
39
Same Intra-column
permutation pattern
applied for all
symbols
4
2
0
3
1
37
21
38
36
20
37
7
5
8
6
9
23
7
24
22
6
23
23
10
13
11
14
12
9
P
5
8
P
9
24
24
18
16
19
17
15
P
27
25
P
26
29
24
25
25
21
24
22
20
23
29
13
11
28
12
10
25
26
26
29
27
25
28
26
10
38
36
14
37
35
27
26
27
27
32
30
33
31
34
35
24
22
39
23
21
28
P
27
28
P
35
38
36
39
37
21
5
P
20
9
P
29
28
28
29
28
7
30
8
6
34
7
2
0
3
1
4
32
16
33
31
15
32
18
2
19
17
1
18
4
P
0
3
P
4
P
22
20
P
21
24
29
30
29
29
30
29
30
31
30
30
31
30
31
P
31
31
P
31
P
32
32
P
32
32
32
33
33
32
33
33
33
34
34
33
34
34
34
35
35
34
35
35
35
36
P
35
36
P
36
37
36
36
37
36
37
38
37
37
38
37
38
39
38
38
39
39
P
39
39
P
Intra-row
permutation
for 4-th
symbol
Intra-row
permutation
for 5-th
symbol
5
8
6
9
7
13
11
14
12
10
16
19
17
15
18
24
22
20
23
21
27
25
28
26
29
30
33
31
34
32
38
36
39
37
35
0
3
1
4
2
8
6
9
7
5
38
11
14
12
10
13
39
19
17
15
18
16
22
20
23
21
24
25
28
26
29
27
33
31
34
32
30
36
39
37
35
38
Each distributed
LRU(subchannel)
contains all the
pair indices from
0 to Npair, (=39)
which maximizes
frequency
diversity gain
and minimizes
hits between
cells
24
8
6
23
7
5
5
33
31
9
32
30
30
19
17
34
18
16
16
0
P
15
4
P
2
25
3
1
29
2
27
11
28
26
10
27
13
36
14
12
35
13
38
P
39
37
P
38
Subchannel # 1
P
Subchannel # 2
0
Column-wise index
reading (each
column maps to
each subchannel)
Subchannel # 3
0
Intra-column
permutation
for 0-th
0
symbol
25
Subchannel # 4
P
Intra-row
permutation
for 0-th
0
symbol
8
Subchannel # 5
Row-wise
index writing
for each
symbol
NDRU=5
Inner Permutation for DL

The inner permutation equation for DL, which performs
the block interleaving shown previously, is given by
npair (s, k, l) = n1·NDRU + PInner[s ; n1+l], l = 0, 1, …, Nsym,TTI
where
npair (s, k, l) : pair index of the k-th pair of s-th distributed
LRU (subchannel) in l-th symbol
n1= (5k+7s) mod Npair,PRU
Nsym,TTI : the number of OFDMA symbols during the TTI
PInner [i ; j] : the i-th element of the series obtained by
rotating the basic permutation sequence
PInner [i ; 0] cyclically to the left j times.
Inner Permutation for UL


The same method as DL can be applied to UL with
some modifications on permutation unit from pair to tile
The inner permutation equation for UL is given by
ntile (s, k, l) = n2·NDRU + PInner[s ; n2+l], l = 0, 1, …, NSF,TTI
where
ntile (s, k, l) : tile index of the k-th tile of s-th distributed
LRU (subchannel) in l-th subframe
n2= (5k+7s) mod Ntile,PRU where Ntile,PRU =3
NSF,TTI : the number of subframes during the TTI
PInner [i ; j] : the i-th element of the series obtained by
rotating the basic permutation sequence
PInner [i ; 0] cyclically to the left j times.
Inner Permutation for UL
NDRU=5
Tile
0
0
0
0
3
1
1
1
1
11
14
12
2
2
2
8
6
9
3
3
3
6
9
7
3
1
4
14
12
10
UL inner
permutation
4
4
4
5
5
5
6
6
6
12
10
13
7
7
7
9
7
5
8
8
8
1
4
2
9
9
9
4
2
0
10
10
10
10
13
11
11
11
11
7
5
8
12
12
12
5
8
6
13
13
13
2
0
3
14
14
14
13
11
14
#1
#2
SF #0
NSF,TTI=2
Subchannel # 1
Subchannel # 2
Subchannel # 3
Subchannel # 4
Subchannel # 5
Each distributed
LRU(subchannel)
contains different
tile colors per
subframe and
also minimizes to
have the same
tile colors through
the TTI, which
maximizes
frequency
diversity gain and
minimizes hits
between cells