IEEE C802.16maint-08/286
Project
IEEE 802.16 Broadband Wireless Access Working Group
<http://ieee802.org/16>
Title
PCINR Formulas for MIMO Mode
Date
Submitted
2008-07-16
Source(s)
Itay Lusky, Altair Semiconductor
Dave Pechner, Arvind Raghavan,
Arraycomm
Voice: +33 1 41 02 82 99
E-mail:
sylvain@sequans.com
Amir Francos, Alvarion
Djordje Tujkovic, Louay Jalloul,
Beceem
Rotem Avivi, Dov Andelman Intel
Ji-Yun Seol Samsung
Sylvain Labonte, SEQUANS
Re:
LB#26d comment 4182
Abstract
This paper presents the formulas MSs can use to determine PCINR in MIMO mode.
Purpose
This is my reply to the proposed remedy of LB#26d-4182. Please incorporate the
text of this contribution in IEEE P802.16 Rev2 Draft 6. instead of the one proposed
in LB#26d-4182.
Notice
Release
Patent
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Formulas for PCINR in MIMO Mode
Itay Lusky, Altair Semiconductor
Dave Pechner, Arvind Raghavan, Arraycomm
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IEEE C802.16maint-08/286
Amir Francos, Alvarion
Djordje Tujkovic, Louay Jalloul, Beceem
Rotem Avivi, Dov Andelman Intel
Ji-Yun Seol Samsung
Sylvain Labonte SEQUANS
Proposed Text Changes
P.839, line 21: change the text as follows: “
8.4.5.4.10.1 Fast DL measurement feedback
MIMO-capable MS shall measure post-processing CINR for each individual layers as shown in Figure
244. When the FFSH's Feedback Type field is 00, the MS shall report the post-processing average CINR
(Avg_CINR) as defined in Equation (62). When BS requests MS feedback through CQICH_Alloc_IE() or
CQICH_Enhanced_Alloc_IE() with feedback_type field = 00, MS shall report Avg_CINR or individual
layer CINR as described in 8.4.5.4.12 and 8.4.5.4.16 as described below.
(Note to editor: Remove all following text in red )
For a vertically encoded MIMO system, the averaged CINR (Avg_CINR) is defined as shown in
Equation (62).
Avg _ CINR  eC ( d
2
, y |H )
1
(62)
IEEE C802.16maint-08/286
Where C (d , y | H ) is the receiver-constrained mutual information conditioned on knowing the
channel knowledge. Note that d is the transmitted signal, y is the post-processing receive signal, and
H is the channel matrix between Tx and Rx antennas. For an LMMSE receiver, the individual postdetector-processing signal-to-noise ratios are given as CINR1, ...,CINRN, as shown in Figure 244 and
in Equation (63).
C (d , y | H ) 
1
N
N
 log(1  CINR )
(63)
n
n 1
“In this case,
1/ N
 N

Avg _ CINR    1  CINRn  
 n1

1
(64)
When the individual post-detector processing CINR is high, the average CINR is
Avg_CINR 
1
N
N
 CINR
n 1
n
(65)
(in dB)
For ML MIMO detectors case,
C (d , y H ) 
1
log det  I N  H H R 1H p 
N
(66)
Where
I N is an N x N identity matrix
R is the correlation matrix of interference plus noise measured at MS
For a single layer MIMO system (Matrix A and Matrix B) denote p as the index for a pair of pilots,
 p2 is the average noise plus interference variance over MS’s receive antennas and pair of pilots.
Further denote C  d , y | H  as the receiver-constrained mutual information conditioned on the
channel knowledge, wherein d is the transmitted signal, y is the post-processing receive signal and
H is the channel matrix between Tx and Rx antennas.
For Matrix B the average CINR is given by:
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IEEE C802.16maint-08/286

Avg _ CINRdB  10 log10 e
C (d , y | H ) 

C (d , y H )

1
1 P
Cp d p , yp | H p 
P p 1
Cp d p , yp H p


H pH H p
1
 log det  I N 

N
 p2

(62)



where N is the number of streams, i.e. N = 2 is this case.
For Matrix A the average CINR is given by:

Avg _ CINRdB  10 log10 e
C (d , y | H ) 
C (d , y H )

1
1 P
Cp d p , yp | H p 
P p 1

1
C p (d p , y p H p )  log 1  2 H p
 p

2
where ||  ||F denotes the Frobenius norm of a matrix.
(63)


F 

2
(Note to editor: Add the following after section 8.4.5.4.10.1)
8.4.5.4.10.1.1 Standard Compliant Approximations
Standard-compliant approximations of Equations (62) and (63) are shown below.
Referring to Figure xxx, the following are defined:





1 k  K




l is the index of an OFDMA symbol, 1  l  L ,
j is the index of a “column”, and has resolution of two OFDMA symbols, 1  j  J ,
sub-carrier block is a set of physically adjacent sub-carriers,
m is the index of sub-carrier block, 1  m  M ,
k is the index of a pair of pilots within one sub-carrier block within one column,
∆ is a subset of the columns in the zone,   1, 2,
, J,
 is the cardinality of ∆, where 2    J ,
Λ is a subset of the OFDMA symbols in the zone,   1, 2,
, L ,
 is the cardinality of Λ, 2    L .
Note that the number of sub-carrier blocks is implementation-dependent with the only constraint that
M  1 . Also note that when working in segmented PUSC, only the active pilots in the sub-carrier
block should be considered.
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IEEE C802.16maint-08/286
j=1
j=J
l=1
l=L
k=1
k=2
m=1
k=K
m= M
STC Zone
Figure xxx: PUSC STC zone illustration. The white and black circles indicate the pilot tones.
The average CINR over a zone can be given by

C d,y H 
Avg _ CINRdB  10 log10 e 
q

where q=0 or q=1 depending on the MS specific implementation. This is to say that MS specific
implementation can drop the “1” inside the log term.
The capacity can be averaged over a zone as follows:
C d, y H  
Cm 
1

C
j
1
M
M
C
m 1
m
m, j
For Matrix B, we have
Cm , j
1

2K

H m, j ,k H H m, j ,k
log det  zI 


 m2
k 1

K
and for Matrix A we have
Cm, j
1

K

H
 z  m, j ,k
log


 m2
k 1

2
K
5
F

,



 ,

IEEE C802.16maint-08/286
where z=0 or z=1 depending on the MS specific implementation. This is to say that the MS specific
implementation can drop the “I” inside the determinant for the capacity expression for Matrix B and
the “1” inside the log term for the capacity expression for Matrix A.
The noise can be averaged over the m-th sub-carrier block as follows:
K
1 1
 m2 
 l2,k

 K l k 1
where  l , k is the noise plus interference variance averaged over the MS's receive antennas on a single
pilot position (l,k).
2
6