IEEE C802.16maint-07/060
Project
IEEE 802.16 Broadband Wireless Access Working Group <http://ieee802.org/16>
Title
Calculating CINR for Handoff
Date
Submitted
2007-11-01
Source(s)
Djordje Tujkovic, Louay Jalloul, Anupama
Lakshmanan, Anuj Puri, Frank Zhou
Beceem Communications
dtujkovic@beceem.com
jalloul@beceem.com
apuri@beceem.com
Re:
IEEE 802.16Rev2/D0b – proposal to calculate CINR for Handoff
Abstract
We propose a method to calculate CINR for Handoff.
Purpose
Notice
Release
Patent
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Calculating CINR for Handoff
Djordje Tujkovic, Louay Jalloul, Anupama Lakshmanan, Anuj Puri, Frank Zhou
Beceem Communications
1.
Introduction
The serving BS can through MOB_SCN-RSP message request any subset of report metrics including BS mean
CINR, BS mean RSSI, Relative delay and BS RTD. Apart from BS RTD, which shall be only measured on
serving BS, all other metrics should be measured on each and every BS from the requested subset of BSs in the
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IEEE C802.16maint-07/060
MOB_NBR-ADV message.
This contribution addresses preferred averaging method for HO reports (RSSI and CINR).
2.
Mean HO CINR report
There are two main classes of CINR reports in standard, Link Adaptation (LA) CINR and Handoff (HO) CINR,
which have categorically different requirements in terms of both amount and type of averaging.
The LA is supposed to adapt scheduling and MCS level selection to instantaneous variations in fast fading.
Therefore, time constants for mean LA CINR are typically small (on the order of a several frames), with IIR
filter default value in standard being alpha=1/4.
The HO should be triggered on differences in path losses and shadowing between serving and candidate BSs.
Therefore, the fast fading variation needs to be averaged out in the mean HO CINR reports. Apart from larger
time constants for averaging, the actual type of averaging of HO CINR plays a crucial role as we will see from
the following section.
a. Ramifications of obtaining mean HO CINR as average value of instantaneous
CINRs
Section 8.4.11.3 of 802.16e standard specifies that mean CINR shall be derived from the multiplicity of single
messages using the equation in which the mean CINR is obtained as the IIR average of instantaneous CINRs.
While this is proper for mean CINR in Link Adaptation, this type of averaging may result in erroneous HO
decisions if applied directly to mean HO CINR reports.
For large time constants, which are desirable for HO, the sample mean can be replaced by expectation (E{∙}).
Therefore, equation (146) in Section 8.4.11.3 suggests that mean CINR should be derived as the expectation of
instantaneous ratios of signal and interference powers (expectation of ratios, EOR). This type of averaging over
fading channels deviates from the true signal-to-noise ratio defined as the mean (expectation) of signal divided
by the mean (expectation) of interference power (ratio of expectations, ROE). While the exact derivation can be
found in the Appendix, here we summarize the main difference between EOR and ROE
CINR 
ES 
EI 
(1)
S 
 1  ES 
EOR  E    ES E   
I 
 I  EI 
EOR  CINR
M
M 2
(2)
(3)
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IEEE C802.16maint-07/060
 M 
EOR[ dB]  CINR[ dB]  10 log 10

 M 2
(4)
As seen from equation (4), calculating the mean CINR for HO by EOR results in the deviation from the true
CINR, ie, bias in dB CINR value. The bias is proportional to the number of degrees of freedom M in the fading
channel, which is again directly related to power delay profile and frequency selectivity of the channel.
Therefore, in HO situation, where links between SS and different candidate BSs in general have different
frequency selectivity, the bias caused by improper averaging can result not only in the wrong mean CINR report
but can also alter the order of BS CINRs and consequently result in erroneous HO decision.
To illustrate the problem, without loss of generality, we have simulated a typical reuse 3 HO scenario with four
BSs. Segment 0 contains serving BS and one interfering BS with CIR0=1dB. Segment 1 contains two BSs with
CIR1 = 3dB. Segment 2 does not contain any BSs with significant power. Without loss of generality, the
channel between SS and two BSs on Segment 0 is assumed to be Frequency flat while the channel between SS
and two BSs on Segment 1 is modeled as Veh A. The SS is assumed to move with 60Kmph. The system is
assumed to be interference limited.
As seen from Fig. 1, reported mean HO CINRs for both Segment 0 and Segment 1 have the large bias. The
amount of bias depends on the type of channel. The lack of degrees of freedom over flat fading channel has
resulted in as much as 6-7dB error in HO CINR on Segment 0. Likewise, large number of degrees of freedom
for Veh A channel has created an error of around 2dB in reported CINR on Segment 1. Consequently, the order
of CINRs on two segments will appear altered, ie, the Segment 0 would appear to have larger CINR than
Segment 1 although the actual CINR on Segment 0 is 2dB lower then CINR on Segment 1. Notice that the SS
typically does not have information about degrees of freedom for channels towards individual BSs in active set,
hence it can not compensate for bias in HO CINR. For typical CINR HO trigger threshold of 2dB, instead of
triggering HO to stronger of two BSs on Segment 1, the SS would in this situation remain connected with its
serving BS on Segment 0 and with further drop in serving BS CINR lose the connection to the NW. Therefore,
the coverage of the system will be affected with erroneous EOR HO averaging. Likewise, from Figure 2,
reporting the mean CINR as the ROE will result in the true CINR without any bias and will trigger HO as
planned.
From Figs. 3 and 4 we further conclude that ROE results in much lower variance of reported mean CINR as
compared to EOR. This is very important as large variance in reported CINR will result in ping-pong effect
whenever two candidate CINRs are not sufficiently apart. This will in turn create large overhead to the NW and
potentially result in decreased coverage. From Fig. 3 we further conclude that even setting alpha to much lower
value (1/256) does not fully alleviate the problem of increased variance. From Fig. 4, the ROE on contrary has
very smooth behavior.
Although simulations assumed intra-FA, introduced problems from using EOR for mean HO CINR readily
apply to Inter-FA.
b. Recommended mean CINR for HO
From Section 8.4.11.3, the measurement for HO CINR and RSSI is implementation specific. We suggest adding
the following equation to the standard for handoff CINR calculation:
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IEEE C802.16maint-07/060
The mean CINR for HO should be calculated as a dB value of the IIR averaged received Signal power divided
by the IIR averaged Noise plus Interference power as seen by a given MS-BS pair. Whenever measurement is
missing in a given frame, average values of received Signal power and Noise plus Interference power are
repeated from the previous frame. The RSSI for HO and IIR averaged received signal and IIR averaged Noise
plus interference power for calculating mean CINR for HO for a given MS-BS pair should be calculated from
multiplicity of single messages as

 RSSI [k ]  
k 0
RSSI [0],
 RSSI [k  1]   avg RSSI [k ]   RSSI [k  1]g[k ], k  0
(145)
where
RSSI measured in frame k
1,
g[ k ]  
0, RSSI not measured in frame k
c. Implementation aspects
Apart form above mentioned bias problems with EOR, defining mean HO CINR as ROE has also significant
implementation advantages. The number of divisions in creating mean HO CINR reports is considerably
reduced from once every frame in EOR to once every report periodicity number of frames (typically 50) in ROE.
Furthermore, the SS can independently track and keep averaging individual BS RSSIs from MOB_NBR-ADV
message in which case reporting either mean RSSI or mean CINR becomes just a matter of post-processing.
Instead, if CINR is defined as EOR, SS needs to run separate IIR filters for RSSI and CINR (reuse 1 and reuse 3
separately) in parallel to be able to promptly respond with required HO metric form MOB_SCN-RSP message.
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EOR, alpha=1/64
16
Seg0 Flat 60Kmph SIR=1dB
Seg1 Veh A 60Kmph SIR=3dB
14
12
HO CINR
10
8
6
4
2
0
0
500
1000
1500
# frames
Figure 1: Mean HO CINR as IIR average value of instantaneous frame by frame CINRs, alpha=1/64
ROE, alpha=1/64
10
Seg1 Veh A 60Kmph SIR=3dB
Seg0 Flat 60Kmph SIR=1dB
8
HO CINR
6
4
2
0
-2
0
500
1000
1500
# frames
Figure 2: Mean HO CINR as the ratio of IIR averaged signal over IIR averaged Interference power, alpha=1/64
5
IEEE C802.16maint-07/060
EOR, alpha=1/256
12
Seg1 Veh A 60Kmph SIR=3dB
Seg0 Flat 60Kmph SIR=1dB
10
HO CINR
8
6
4
2
0
0
500
1000
1500
# frames
Figure 3: Mean HO CINR as IIR average value of instantaneous frame by frame CINRs, alpha=1/256
ROE, alpha=1/256
10
Seg0 Flat 60Kmph SIR=1dB
Seg1 Veh A 60Kmph SIR=3dB
8
HO CINR
6
4
2
0
-2
0
500
1000
1500
# frames
Figure 4: Mean HO CINR as the ratio of IIR averaged signal over IIR averaged Interference power, alpha=1/256
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IEEE C802.16maint-07/060
d. Ramifications of the alternative proposal for mean HO CINR based on dB IIR
averaging
In their comments to [3] (a previous version of this document), Motorola in [2] acknowledged the fundamental
issue with EOR filtering of HO CINR raised in section 3. As an alternative method to ROE filtering introduced
in 3.b, it was further suggested that bias in mean CINR can be avoided by passing the dB instead of linear value
of instantaneous CINR measurement through IIR filter in section 8.4.11.3. Let us denote this approach as
expectation of dB ratio (EOdBR)
  S 
EOdBR  E log  
  I 
(5)
Without loss of generality, let us assume that instantaneous signal and inference powers can be represented as
the product of constant representing the mean power and the random chi-square variable with unit power with
given number of degrees of freedom. That is
S  S 0  M2 s
(6)
I  I 0  M2 I
with
S 0  E{S }
I 0  E{I }
(7)
E (  M2 s )  1
E (  M2 I )  1
where MS and MI denote the number of degrees of freedom in signal and interference channels, respectively. Let
us zoom into EOdBR from (5)
EOdBR  Elog( S )  Elog( I )




 Elog( S 0 )  E log(  M2 S )  Elog( I 0 )  E log(  M2 I )
 S
 E log  0
  I0
S
 log  0
 I0

  E log(  M2 S )  E log(  M2 I )


 

(8)

  M S , M I 

With assumptions in (6) and (7), the dB value of true CINR (ROE), denoted hereafter by ROEdB, is given by
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IEEE C802.16maint-07/060
 ES  

ROEdB  log 
 EI  
S
 log  0
 I0
(9)



Comparing (8) and (9), it is apparent that in general EOdBR has bias compared to true CINR (ROEdB). The
sign and value of bias depends on the number of degrees of freedom in signal and interference channel. Only in
the special case when MS and MI are equal, the bias term is equal to zero. In deed, in simulation results in [2], it
was assumed that both signal and interfering channel have the same Veh A profile.
In many practical scenarios, it is quite unlikely that propagation channel between SS and different candidate BSs
in HO will have the same power delay profile. Hence, in Fig 5, the dB values of ROE and EOR are further
compared to EOdBR but with assumption that signal and interference channels have different power delay
profiles. It was assumed that there are two BSs on a given segment with equal average received powers
(SIR=0dB). Without loss of generality, the channel from SS to the first BS was assumed to have Veh A power
delay profile while the channel to the second BS was assumed to be frequency flat. The SS is assumed to move
with 60Kmph. The system is assumed to be interference limited. As seen from Fig. 5, although EOdBR results
in more accurate mean HO CINR then EOR, it still suffers form 2dB bias in measurement which can again
result in erroneous HO triggers and consequently decrease the coverage in the system.
SIR=0dB, BS1 Veh A, BS2 Flat, 60 Kmph
14
EOR[dB]
ROE[dB]
EO[dB]R
12
10
HO CINR
8
6
4
2
0
-2
0
500
1000
1500
# frames
Figure 5: Comparison of Mean HO CINRs based on EOR, ROE and IIR averaged dB values on instantaneous
CINRs (EOdBR), alpha=1/128
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3. Appendix
Expectation of ratios vs ratio of expectations
The ratio of the expected signal and expected interference power (ROE) and expectation of instantaneous ratios
of signal and interference powers (EOR) are given as
ROE  CINR 
ES 
EI 
(4)
S 
EOR  E  
I 
(5)
The ROE in (4) is also marked as the true CINR since the mean CINR for HO should average out fast fading
variations without changing the relative ratio of individual mean BS powers. Let us zoom into EOR:
 
EOR 
s
i p
S ,I
( s, i )dsdi
  




  sp S ( s )ds 
 ES 



1
p I (i )di
i
(6)
1
p I (i )di
i
where the last two steps stem from fact that signal and interference power are independent. The interference
power is a chi-squared random variable with M degrees of freedom. Hence, the probability density function
(PDF) p I (i) of the inverse of interference power is given by the so called inverse chi-squared distribution
2  M / 2  M / 21 1 /(2i )
p I (i; M ) 
i
e
( M / 2)
(7)
whose mean is given by



1
1
M
p I (i, M )di 
i
EI  M  2
9
(8)
IEEE C802.16maint-07/060
We finaly write the EOR as
ES  M
EI  M  2
M
 CINR
M 2
EOR 
(9)
Notice that for flat fading channel, where the number of degrees of freedom is equal to M=2, the EOR grows to
infinity
EOR
M 2

(10)
Applying the IIR filter, which acts as a moving average filter will to some extent, bound the bias in EOR mean
CINR. Nevertheless, the impact from bias will be still rather dramatic in practice.
4. Proposed text changes to the 802.16Rev2 draft
From Section 8.4.11.3, the measurement for HO CINR and RSSI is implementation specific. We suggest adding
the following equation to the standard for handoff CINR calculation:
The mean CINR for HO should be calculated as a dB value of the IIR averaged received Signal power divided
by the IIR averaged Noise plus Interference power as seen by a given MS-BS pair. Whenever measurement is
missing in a given frame, average values of received Signal power and Noise plus Interference power are
repeated from the previous frame. The RSSI for HO and IIR averaged received signal and IIR averaged Noise
plus interference power for calculating mean CINR for HO for a given MS-BS pair should be calculated from
multiplicity of single messages as

 RSSI [k ]  
k 0
RSSI [0],
 RSSI [k  1]   avg RSSI [k ]   RSSI [k  1]g[k ], k  0
where
RSSI measured in frame k
1,
g[ k ]  
0, RSSI not measured in frame k
1
0
IEEE C802.16maint-07/060
References
[1] 2005-802.16e
[2] Rob Nikides, Motorola, “Comments on HO RPD Scanning and Measurement”, WiMax Forum
[3] Beceem Contribution on HO RPD Scanning and Measurement, WiMax Forum
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