2007-11-12
IEEE C802.16m-07/309
Project
IEEE 802.16 Broadband Wireless Access Working Group <http://ieee802.org/16>
Title
RBIR MLD PHY Abstraction for HARQ IR/CC
Date
Submitted
2007-11-12
Source(s)
Hongming Zheng, Intel Corporation
hongming.zheng@intel.com
may.wu@intel.com
yang-seok.choi@intel.com
jingbao.zhang@intel.com
May Wu, Intel Corporation
Yang-seok Choi, Intel Corporation
Jingbao Zhang, Intel Corporation
Re:
IEEE 802.16m-07/031 – Call for Comments on Draft 802.16m Evaluation Methodology
Document
Abstract
This contribution provides a link abstraction methodology for HARQ IR with the symbol-level
ML receiver.
Purpose
For discussion and approval by TGm
Notice
Release
Patent
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contained herein.
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and any modifications thereof, in the creation of an IEEE Standards publication; to copyright in the IEEE’s name
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Further information is located at <http://standards.ieee.org/board/pat/pat-material.html> and
<http://standards.ieee.org/board/pat>.
RBIR MLD PHY Abstraction for HARQ IR/CC
Hongming Zheng, May Wu, Yang-seok Choi, Jingbao Zhang, Intel Corporation
1.0 Purpose
This contribution provides a detailed description of a link evaluation methodology for MIMO Maximum
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likelihood (ML) receivers when the HARQ IR/CC is used during the retransmission. The proposed phy
abstraction can be worked under the different HARQ cases, for example, full/partial IR and also with Chase
combining scheme when the receiver is used with ML detection in symbol-level.
2.0 Introduction
The more accurate phy abstraction mapping for HARQ IR/CC is important for the .16m performance evaluation
because there is no real decoding in the system-level simulation which can decide whether the decoding is
correct or not. So firstly we should guarantee our phy abstraction closer to the practical system which can
provide more accurate evaluation in system-level.
The current EVM document (section 4.7.3) on HARQ part includes IR and CC just defined the application over
SISO when the combining of retransmissions is considered for the calculation of phy metric. For MIMO
configuration the provided formula will not still be valid, for example, equation (92). The combined phy
abstraction metric over the repeated information bits between transmission and retransmission of HARQ IR/CC
should be defined more detail even if currently it is for general detection, for example, MMSE detection on
HARQ MIMO with multiple streams.
So based on above problem we proposed out the detailed definition for the combined phy metric between the
transmission and retransmission where the symbol-level ML receiver is used as the example to show how the
combined phy metric is calculated for MIMO HARQ IR/CC scheme over the repetition information part.
Also we presented the simulation result to show the accuracy on our combined RBIR metric. Finally we have
proposed the text to complement the shortcoming of current EVM definition on HARQ phy abstraction part.
3.0 PHY Abstraction Modelling for HARQ IR/CC
In this section we will give out the detailed phy abstraction calculation under the different HARQ combining
model.
3.1 Full IR (Incremental Redundancy)
As you know the Full IR will have the non-overlapped bits between the transmission and retransmission on the
systematic and redundant bits. It is the same case as without repetition of coded bits between the transmission
and retransmission as in current EVM document.
With no repetition of coded bits, the performance of the decoder at each stage is that corresponding to a binary
code with the modified equivalent code rate and code size as illustrated in Figure 1 for MI based approaches.
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X Information Bits
First Transmission
M I1
Second Retransmission
M I2
q-th Retransmission
M Iq
C2 Code Bits
Cq Code Bits
C1 Code Bits
Figure 1: MI-based parameter update after transmission
The required input parameters for AWGN mapping function are given below
Reff =
X
 C
= C
 CM

 C
q
i 1
Leff
i
q
i 1
(1)
i
q
M I IR ,q
i 1 i
q
i 1
where Reff , Leff
Ii
i
and M I IR ,q are the effective code rate, block size and mutual information after q
retransmissions, respectively.
So it is easy to figure out the phy abstraction modelling for this IR model. We can easily use the equation below
to get the whole IR metric no matter it is MMSE or MLD detection because here there is no combining
happened for the repetition information bits. We can then compute the updated mutual information metric after
this retransmission as follows
M Inew 
N pre  M Iold  N NR  I b
N pre  N NR
(2)
Where the averaged mutual information per bit from previous transmissions is M Iold . The averaged mutual
information per bit in this re-transmissions is I b . In addition here we consider a retransmission including a set
of N NR new coded bits and there are N pre coded bits that are not re-transmitted in this re-transmission.
3.2 Partial IR (Incremental Redundancy)
In practice, due to finite granularity in IR implementation, partial repetition of coded bits is possible. Depending
on the rate matching algorithm used, every H-ARQ transmission could have a set of new parity bits and other
bits that are repeated. Accumulating the mutual information is appropriate as long as new parity bits are
transmitted in every symbol. Otherwise, the receiver combines the demodulation symbols or, more typically, the
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LLRs. In this section, we consider a rate-matching approach that does pure IR transmissions and involves coded
bit repetitions once all the coded bits from a base code rate are exhausted.
To handle this general case, we consider a retransmission including a set of N NR new coded bits and a set of N R
coded bits repeated from pervious transmissions. Further, we assume that there are N pre coded bits that are not
re-transmitted in this re-transmission. The averaged mutual information per bit from previous transmissions is
M Iold . The averaged mutual information per bit in this re-transmissions is I b .
We can then compute an updated mutual information metric after this retransmission as follows
M Inew 
N pre  M Iold  N NR  I b  N R  I comb
N pre  N NR  N R
(3)
where I comb is the average mutual information per bit in this re-transmission after the IR combining. The
detailed definition for I comb will be described in section 4.0 and it can not be written simply as
 


I comb  f1 f11 M Iold  f11  Ib  which is defined in the current EVM document.
3.3 CC (Chase Combining)
Due to the repetition bit for the all transmission/retransmission duration there will need all combining on the
phy abstraction metric for the retransmission. So the average mutual information per bit in the retransmission
after the combining is as follows.
(4)
M Inew  I comb
In the next section we will figure out the detailed combining phy metric for the different retransmission under
the symbol-level ML receiver as example.
4.0 RBIR MLD Metric Definition for HARQ IR/CC
4.1
PHY Abstraction Definition for HARQ IR/CC
Figure 2 shows the general structure for the HARQ IR/CC scheme, and each of the retransmission can contain
the systematic bits S(x) and redundant bits R(x). There will have the corresponding definition for the different
HARQ retransmission mode as example below.
1) Chase Combining (CC): when S1=S2=…=Sq and R1=R2=…=Rq
2) Partial IR: when S1=S2=…=Sq and R1  R2  …  Rq
3) Full IR: when S2=…=Sq=0 and R1  R2  …  Rq
From the above definition corresponding to the different definition it is easily to see that Partial IR has the most
general representation for the different HARQ mode. So in the following we can study the phy abstraction
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model based on this HARQ mode.
X Information Bits
S1
R1
M Iold
First Transmission
S2
R2
Sq
Ib
Second Retransmission
Rq
q-th Retransmission
Combining
Length for the different information
R1
I comb
N pre
S2
NR
R2
N NR
Figure 2 PHY Abstraction Model for HARQ IR/CC
As defined in the previous section for partial IR the updated mutual information metric after the retransmission
can be gotten as
M Inew 
N pre  M Iold  N NR  I b  N R  I comb
N pre  N NR  N R
(5)
where I comb is the average mutual information per bit in this re-transmission after the IR combining. M I old is the
mutual information in last transmission but this part has not retransmitted in this retransmission; and I b is the
mutual information in this retransmission over the new coded bits.
M I old and I b can be easily be reached because they are not repeated between the transmission and
retransmission whose phy abstraction calculation is the same as the new information frame. The question here is
how to calculate the combined phy abstraction metric between the transmission and retransmission for the
repetitive information bits which is our focus for next section.
In this section we will focus the detailed derivation of the combined phy metric RBIRharq or I comb . In addition it
 


can not be written simply as I comb  f1 f11 M Iold  f11  Ib  which is defined in the current EVM document.
This contribution we use the symbol-level MLD receiver as the example to figure out the detailed combining
phy abstraction metric for HARQ IR/CC. All other phy abstraction under other receiver detection for HARQ
IR/CC can easily be derived like from the example demo.
4.2 Derivation of the PHY Abstraction with the IR/CC Combining when SL-MLD used
In the following all text related to ‘combined’ means the repetition information bits between the transmission
and retransmission.
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1) Distribution of the IR/CC Combined LLR (Theory Derivation)
From the link-level view the principle of HARQ combination is actually to do the combination over the soft
output bits (LLR) between the transmission and retransmission. The accumulated LLR on the i-th symbol over
the IR retransmission is to have
LLRi 
N HARQ

k 1
(6)
LLRik
As we have derived in our previous contribution (C802.16m-07/182r2) the LLR output for each
transmission/retransmission from symbol-level MLD can be approximated as Gaussian distribution.
(7)
LLRik ~ N ( AVEik ,VARik )
Thus the combined LLRi will have the distribution as
N HARQ
LLRi ~ N (

k 1
N HARQ
AVEik ,
 VAR
k 1
ik
(8)
)
We can easily testify the above distribution because of the sum of independent guassian variable can have the
new Gaussian distribution with the average of the sum of original average and the variance of the sum of
original variance.
2) HARQ IR/CC Combined LLR distribution (Simulation Results)
Taking transmitted symbol and one retransmitted symbol for example, we have simulated the combined LLR
distribution for the HARQ IR/CC over the repetition information part.
1
0.9
0.8
0.7
Prob
0.6
1st trans
retrans
combined
Gaussian for
1st trans
Gaussian for
retrans
Gaussian for
combined
SNR=5dB
0.5
0.4
0.3
0.2
0.1
0
-6
-5
-4
-3
-2
-1
0
1
SNR
Figure 3 LLR distribution for 1st transmission/retransmission/combined
(SISO, QPSK ½ Code Rate)
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0.35
1st trans
retrans
combined
Gaussian for
1st trans
Gaussian for
retrans
Gaussian for
combined
0.3
SNR=5dB
2nd stream
0.25
Prob
0.2
0.15
0.1
0.05
0
-10
-5
0
5
10
15
SNR
Figure 4 LLR distribution for 1st transmission/retransmission/combined
(2x2 MIMO, QPSK ½ Code Rate)
Figure 3 and 4 show the relationship of the combined LLR between simulation and theory derivation. In these
figures dash-line curve is from simulation and solid-line curve is from theory. ‘1st transmission’ mean the LLR
distribution from 1st transmission; ‘retransmission’ mean the LLR distribution from the retransmission but
without the combined with 1st transmission; ‘combined’ mean the LLR distribution from the retransmission
with the combined with 1st transmission.
From these figure we can see that SISO and 2x2 MIMO can have the small gap between the simulation and
theory.
3) Combined RBIR MLD PHY for HARQ IR/CC (Repetition Bits Parts)
As defined in the section 4.3.1.1 and the average mutual information over the ML receiver can be calculated
from the equation (45) and (50) in the EVM document as below.
SI harq ,i 
1
M
M
 
m 1 LLRm ,i
p  LLRm ,i  log 2
M
dLLRm ,i
1  exp( LLRm ,i )
(9)
Where SI harq ,i is the mutual information of the i-th symbol in the transmission or retransmission frame and m
denotes the constellation point index. Then the whole RBIR can be gotten from the division of total SI over the
total bits within the symbols.
Average mutual information for HARQ IR/CC can be averaged over the bit-level between the transmission and
retransmission on the corresponding IR/CC rate matching mode or position. In addition the mutual information
on the corresponding IR/CC bits can be gotten from the symbol-level RBIR on the corresponding symbol which
is the IR bit from.
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From the section 4.1 we know the key problem for HARQ IR/CC is to calculate the combined phy metric on the
repetition information bit between the transmission and retransmission for MIMO system. So in the following
we will give out the detailed combined phy metric for HARQ IR/CC based on symbol-level ML detection for
MIMO system. So the bit-level mutual information for the combined RBIR metric over repetition bits on HARQ
IR/CC can be converted to system-level RBIR due to the fixed rate match mode in the real system which can
guarantee the one-to-one mapping between the bit and symbol. The detailed formula for average mutual
information for HARQ IR/CC is shown as equation (92) in current EVM document but the combined metric
I comb over the repetition bits between the transmission and retransmission is derived as below for symbol-level
ML detection.
As derived and shown in the section of 4.3.1.1, the LLR distribution of the i-th symbol from symbol-level
MLD can be assumed as Gaussian distribution
(10)
p  LLRi   N ( AVEi ,VARi )
Thus
SI i 
 p  LLR  log
i
2
LLRi
M
dLLRi
1  exp( LLRi )
(11)
where for LLR distribution and SI calculation is based on one specific constellation point for phy abstraction.
Hence, we can skip the subscript m. For HARQ repetition combining (IR repetition part is the same as Chase
Combining on the calculation of SI metric on ML receiver) the combined LLR between the transmission and
retransmission also can be approximated as Gaussian but the combined average is equal to the sum of original
average and the combined variance is equal to the sum of original variance.
pharq ( LLRi )  N (
N HARQ

k 1
N HARQ
AVEik ,
 VAR
k 1
ik
)
(12)
where N HARQ is the HARQ combining number between the transmission and retransmission.
So the average combined SI phy metric between the transmission and retransmission over the repetition bits is
derived as
N HARQ
( LLRi 

LLRi
2
1
2
e
N HARQ
AVEik )2
k 1
N HARQ

SI harq ,i 


VARik
k 1
log 2
 VAR
k 1
M
dLLRi
1  e  LLRi
(13)
ik
If the channel will not change a lot due to the coherent time during these HARQ frames, then
pharq ( LLRi )  N ( N HARQ AVEi1 , N HARQVARi1 )
Where N HARQ is the maximum retransmission number for HARQ IR/CC.
Thus the combined RBIR phy metric on ML receiver can be calculated as
SI harq
I comb  RBIRharq 
Nbits
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1

Nbits
N symbols
 
i 1
LLRi
1
2 N HARQVARi1

( LLRi  N HARQ AVEi1 )2
2 N HARQVARi1
e
log 2
M
dLLRi
1  e LLRi
(15)
Here RBIRharq is equal to the average mutual information I comb per bit in the retransmission after the IR
combining in the equation (92) in the latter IR section; and N symbols is the symbol number per one block over the
IR combining, N bits is the bit number within the N symbols symbols.
4) Whole RBIR MLD PHY for HARQ IR/CC (Repetition Bits Parts + New Coded Bits + No Retrs Bits)
After getting the RBIR MLD phy metric for the repetition information bits part we can use the general partial IR
formula for the average whole RBIR value between the different transmission and retransmission as
N pre  M Iold  N NR  I b  N R  I comb
(16)
M Inew 
N pre  N NR  N R
Where I comb is equal to RBIRharq ,i defined in the previous section for repetition information part.
5) RBIR MLD PHY Abstraction Parameter Seaching for HARQ IR/CC
Different HARQ mode including IR/CC over the different transmission /retransmission can be seen as the
different increased MCS sets. Integrated with the combined phy metric defined as the above section we can use
the same procedure as defined in section 4.3.1.1 for the increase MCS sets from the HARQ IR/CC.
In summary HARQ IR/CC will add two additional tasks: 1) increased MCS sets that means we need more MCS
to be dealt with; 2) need to define the combined phy metric for the retransmission repetition information part
which is also our focus in this contribution.
5.0 Conclusions
In this contribution we proposed out the detailed definition for the combined phy metric between the
transmission and retransmission where the symbol-level ML receiver is used as the example to show how the
combined phy metric is calculated for HARQ IR/CC scheme over the repetition information part.
HARQ IR can be seen as the increased code rate due to the rate matching mode over the different retransmission
except the current defined MCS level in WiMAX I system. So the phy abstraction metric for each
transmission/retransmission over HARQ IR can be regarded as the phy abstraction calculation over the new
MCS (modulation and code rate).
The increased effort over HARQ IR will have two additional working: optimization parameter searching and the
calculation of combined phy metric. The first working on optimization parameter search is already defined in
the contribution of C802.16m-07/182r2; the second one is detailed introduced in this contribution. This
contribution also has considered the many HARQ mode over phy abstraction calculation which can also applied
in the different receiver implementation.
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Reference
[1] Intel, Link Performance Abstraction for ML Receivers based on RBIR Metrics, IEEE C802.16m-07/187r2
[2] Draft IEEE 802.16m Evaluation Methodology, IEEE 802.16m-07/037
[3] Ericsson, “System-level Evaluation of OFDM – Further Considerations”, R1-031303
[4] Lei Wan, “A Fading-Insensitive Performance Metric Unified Link Quality Model”, VTC paper, 2006
[5] Mot, “Link Performance Abstraction for ML Receivers based on MMIB Metrics”, IEEE C802.16m-07/142
[6] Mot, “”Link Performance Abstraction based on Mean Mutual Information per Bit (MMIB) of the LLR
Channel”, IEEE C802.16m-07/097
Proposed Text
1) Modify the line 9-14 page 84 of the document C80216m-07_037.doc as below
-----------------------------Begin Proposed Text ----------------------------------------------------------------------
M Inew 
N pre  M Iold  N NR  I b  N R  I comb
N pre  N NR  N R
where I comb is the average mutual information per bit in this re-transmission after the IR combining over the
repetition information bits. M I old is the mutual information in last transmission but this part has not
retransmitted in this retransmission; and I b is the mutual information in this retransmission over the new coded
bits. M I old and I b can be easily be reached because they are not repeated between the transmission and
retransmission whose phy abstraction calculation is the same as the new information bits.
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2) Include Section 4.7.3.1 HARQ Combined RBIR PHY Metric Calculation based on ML Detection
-----------------------------Begin Proposed Text ---------------------------------------------------------------------4.7.3.1 HARQ Combined RBIR PHY Metric Calculation based on ML Detection
As defined in the section 4.3.1.1 and the average mutual information per symbol (SI) over the ML receiver can
be calculated from the equation (45) and (50) in the EVM document as below.
SI harq ,i 
1
M
M
 
m 1 LLRm ,i
p  LLRm ,i  log 2
M
dLLRm ,i
1  exp( LLRm ,i )
Where SI harq ,i is the mutual information of the i-th symbol in the transmission or retransmission frame and m
denotes the constellation point index. Then the whole RBIR can be gotten from the division of total SI over the
total bits within the symbols.
Average mutual information for HARQ IR/CC can be averaged over the bit-level between the transmission and
retransmission on the corresponding IR/CC rate matching mode or position. In addition the mutual information
on the corresponding IR/CC bits can be gotten from the symbol-level RBIR on the corresponding symbol which
is the IR bit from.
Here the key problem for HARQ IR/CC is to calculate the combined phy metric on the repetition information bit
between the transmission and retransmission for MIMO system. So in the following we will give out the
detailed combined phy metric for HARQ IR/CC based on symbol-level ML detection for MIMO system. So the
bit-level mutual information for the combined RBIR metric over repetition bits on HARQ IR/CC can be
converted to system-level RBIR due to the fixed rate match mode in the real system which can guarantee the
one-to-one mapping between the bit and symbol. The detailed formula for average mutual information for
HARQ IR/CC is shown as equation (92) in current EVM document but the combined metric I comb over the
repetition bits between the transmission and retransmission is derived as below for symbol-level ML detection.
As derived in the section of 4.3.1.1 of current EVM document, the LLR distribution of the i-th symbol from
symbol-level MLD satisfied the Gaussian distribution as
p  LLRi   N ( AVEi ,VARi )
Thus
SI i 
 p  LLR  log
i
LLRi
2
M
dLLRi
1  exp( LLRi )
Here for LLR distribution and RBIR calculation is based on one specific constellation point for phy abstraction
so we can skip the subscript m. For HARQ repetition combining (IR repetition part is the same as Chase
Combining on the calculation of RBIR metric on ML receiver) the combined LLR between the transmission and
retransmission also can be approximated as Gaussian but the combined average is equal to the sum of original
average and the combined variance is equal to the sum of original variance.
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pharq ( LLRi )  N (
N HARQ

k 1
N HARQ
AVEik ,
 VAR
ik
k 1
)
where N HARQ is the HARQ combining number between the transmission and retransmission.
So the average combined SI phy metric between the transmission and retransmission over the repetition bits is
derived as
N HARQ
( LLRi 
2
1

SI harq ,i 
LLRi
2
AVEik )2

VARik
k 1
e
N HARQ

k 1
N HARQ

log 2
 VAR
M
dLLRi
1  e  LLRi
ik
k 1
If the channel will not change a lot due to the coherent time during these HARQ frames, then
pharq ( LLRi )  N ( N HARQ AVEi1 , N HARQVARi1 )
Where N HARQ is the maximum retransmission number for HARQ IR/CC.
Thus the combined RBIR phy metric on ML receiver can be calculated as
SI harq
I comb  RBIRharq 
Nbits

1
Nbits
N symbols
 
i 1
LLRi
1
2 N HARQVARi1

( LLRi  N HARQ AVEi1 )2
e
2 N HARQVARi1
log 2
M
dLLRi
1  e LLRi
Here RBIRharq is equal to the average mutual information I comb per bit in the retransmission after the IR
combining in the equation (92) in the latter IR section; and N symbols is the symbol number per one block over the
IR combining, N bits is the bit number within the N symbols symbols.
After getting the RBIR MLD phy metric for the repetition information bits part we can use the general partial IR
formula for the average whole RBIR value between the different transmission and retransmission as
N pre  M Iold  N NR  I b  N R  I comb
M Inew 
N pre  N NR  N R
Where I comb is equal to RBIRharq ,i defined in the previous section for repetition information part.
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