The Vault

Full-Band CQI Feedback by Haar Compression in OFDMA Systems
Research Paper / Jan 2009






Abstract— Implementation of an efficient CQI feedback
mechanism is the focus of the study presented in this paper.
OFDMA-based systems such as 3GPP Long Term Evolution
(LTE) downlink and WiMax require an accurate CQI feedback
to allow effective operation of the adaptive modulation and
coding. Besides accuracy, such mechanism should impose only
a low overhead when using uplink resources for conveying the
CQI information. Unlike the Best-M CQI feedback algorithms
where only the M highest CQI’s and their locations are
reported, a full-band feedback method compresses the whole
CQI vector and transmits the compressed vector in the uplink
channel. In this paper, application of the Haar transform for a
full-band CQI report is investigated and its performance is
compared against DCT-based compression schemes. Full-band
Haar CQI feedback offers a flexible process for CQI feedback
that can be easily adapted to different operating scenarios. Key
features of Haar compression are incremental update and very
low complexity for compression and decompression. Simulation
results indicate that the full-band Haar scheme achieves
significantly higher throughput than the DCT-based schemes at
low speeds and about the same performance at higher speeds.

Index Terms—Haar, CQI, feedback, frequency selective
scheduling.


I. INTRODUCTION
Frequency selective scheduling is an attractive feature in

OFDMA-based systems such as LTE downlink and WiMax.
It allows optimum usage of the allocated spectrum by
assigning proper modulation and coding to each user
according to their channel conditions. In order to support
frequency selective scheduling in the downlink, the mobile
user needs to feedback channel quality indication (CQI) of
the downlink channel to the base station.

In OFDMA systems, the unit used for frequency selective
scheduling is a sub-band, which includes a number of
consecutive subcarriers. To fully support the frequency
selective scheduling, ideally each mobile user needs to
feedback a set of CQI values, one for each sub-band.
However, this will lead to overwhelmingly large CQI
feedback overhead.

The challenge of designing low overhead CQI feedback
schemes has spurred many research initiatives in recent
years. A summary of the state of the art in academia can be
found in [1]. Also, numerous CQI feedback and compression

schemes have been proposed with different levels of
compression and system performance [2]-[4] for LTE.

In general, most of the proposed CQI feedback schemes
fall under either full-band or Best-M categories [2]-[4]. In
full-band schemes, the CQI information of all the sub-bands
in the entire cell bandwidth is compressed and then the
compressed CQI information is reported to the base station.
An example of the schemes in this category is DCT
significant-M feedback [4]. The second category includes
techniques that are based on feedback of only a limited
number of the highest CQIs among all sub-bands, such as
Best-M individual, DCT-partitioning. The effectiveness of
these methods varies and each has its own inherent trade-off
in terms of performance and feedback overhead [2]-[4], [7]-
[9].

In [7], application of Haar compression in Best-M CQI
feedback was investigated. In this paper, we investigate the
application of the Haar transformation to full-band CQI
feedback and we compare its performance against DCT-
based compression schemes. Full-band Haar CQI feedback
offers a flexible process for CQI feedback that can be easily
adapted to different operating conditions. Important features
of Haar are incremental update and very low complexity for
compression and decompression.


The rest of the paper is organized as follows: At first in
Section II, the 3GPP LTE system is briefly described. Then,
a review of Haar compression and its applications for full-
band CQI feedback are provided in Sections III and IV,
respectively. In section V, the throughput performance and
the feedback overhead requirement of the proposed approach
are compared against other compression based CQI feedback
schemes. Final conclusion and remarks are provided in
Section VI.

II. SYSTEM DESCRIPTION
In this section, we present the Full-band CQI feedback

and Haar compression in the context of a general OFDMA
system. Without any loss of generality, for a better
presentation of its impact in a real system, the downlink of
the LTE system is considered. The time in the 3GPP LTE
system is divided into radio frames [5]-[6]. Each radio frame
(10 ms) is divided into 10 sub-frames of 1 ms each. A sub-
frame is the minimum time unit for transmission in both



Full-Band CQI Feedback by Haar Compression in
OFDMA Systems

Afshin Haghighat, Guodong Zhang and Zinan Lin

afshin.haghighat, guodong.zhang, zinan.lin@interdigital.com
InterDigital Communications LLC.






uplink and downlink. Therefore, a sub-frame is also called a
transmission time interval (TTI).

The basic concept of frequency selective scheduling in the
3GPP LTE systems is depicted in Figure 1. Each handset
needs to estimate the channel quality and report the CQI of
downlink sub-bands to the base station. The network
schedules and allocates sub-bands for mobile users based on
the reported CQI. Then, the modulation and coding set
(MCS) of each scheduled user is adapted according to the
reported CQI.








Figure 1 - Frequency selective scheduling in LTE

III. HAAR COMPRESSION
Haar compression is based on the Haar wavelet transform.

A detailed description of the Haar compression method can
be found in [10]-[11]. Haar compression encodes an input
stream in multiple steps according to the level of detail of
the input sequence. It belongs to the class of lossy
compression methods, and is recognized as an effective and
low complexity compression/decompression means for
processing 1- or 2-dimensional data.

The main idea of using the Haar transform to compress a
data vector is to shift the weight and importance of the
vector elements to the first element of the vector.

Assuming a vector with 2i elements, the transformation
consumes i steps of sum and difference operations [10]-[11].
The elements of the vector are grouped in groups of 2’s, and
then the sum and the difference terms for each group are
computed and the results are divided by two. In the
following steps, the same procedure is applied only on the
first half of the compressed vector and the second half is left
untouched. Hence, the process continues in i consequent
steps resulting a compressed vector,

[ ]ii iiiiiii yyyyyy 2)12(5432 −= Li1yy (1)
The first element of the vector, in Bold, is called

“Approximate” and the remaining elements are called
“Detail” coefficients.

In an abstract form, the successive averaging and
differencing steps can be mathematically expressed by a
compression matrix W2i. For example, for a vector with a
length of 8,

( ) ( ) ( )[ ] 83333 178 yWy == yyy L (2)
where

.

































=





−−

−−













2
1

2
1

2
1

2
1

4
1

8
1

8
1

4
1

8
1

8
1

4
1

8
1

8
1

4
1

8
1

8
1

2
1

2
1

2
1

2
1

4
1

8
1

8
1

4
1

8
1

8
1

4
1

8
1

8
1

4
1

8
1

8
1

8

000
000

000
000

0
0
0
0

000
000
000
000

0
0
0
0

W (3)

As such, the decompression can be easily implemented by

83Fyy = , (4)









































−−

−−−−

−−

==


1100
0011
0000
0000

0000
0000
1100
0011

1111
0000
1111

1111

0000
1111

1111
1111

1
88 WF . (5)

IV. FULL-BAND HAAR CQI FEEDBACK SCHEME
The general mechanism for uplink CQI feedback can be

summarized as follows: The handset performs several
measurements, computes CQI values and performs
compression on the whole CQI vector. According to the
channel condition, handset mobility and the CQI feedback
granularity requested by the network, the handset sends all
or some of the elements of the compressed vector. At the
network, the received vector is decompressed using always
the same matrix F. Hence, the total number of bits
transmitted is:


=

=

cN

i
iTotal bN

1
(6)

where cN and ib are the number of elements of the
compressed vector sent and the number of bits per
compressed vector element, respectively.

The size of the compression/decompression matrices is
determined from the number of Nsb sub-bands. For a system
with Nsb=25 sub-bands, the size of the
compression/decompression matrices will be 32×32. The
remaining 7 unused places in the input vector are filled by
zeros. The locations of the zeros are arbitrary, however it is
more reasonable to spread them across the vector to balance
the weight of the vector. Hence, the following locations in
the input CQI vector are filled with zeros.

y(6) = 0, y(10) = 0, y(14) = 0,
y(18) = 0, y(22) = 0, y(26) = 0, y(28) = 0 (7)

It should be noted that the zero insertion does not increase
the overhead. After the compression the following 7

1- Schedule the user and allocate sub-bands
2- Assign the proper MCS

1- Estimate the channel quality
2- Report CQIs of sub-bands






5 10 15 20 25

5

10

15

20

25

Subband Index

CQ
I V

al
ue





Measured CQI at UE
Estimated CQI at NB



5 10 15 20 25

5

10

15

20

25

Subband Index

CQ
I V

al
ue





Measured CQI at UE
Estimated CQI at NB



5 10 15 20 25

5

10

15

20

25

Subband Index

CQ
I V

al
ue





Measured CQI at UE
Estimated CQI at NB



5 10 15 20 25

5

10

15

20

25

Subband Index

CQ
I V

al
ue





Measured CQI at UE
Estimated CQI at NB



Figure 2 - Incremental update using Full-band Haar





elements are dropped as they are not relevant in
decompressing the compressed vector. Let y5 be the
compressed vector, then the elements

y5(19), y5(21), y5(23) , y5(25), y5(27), y5(29), y5(30) (8)
can be dropped without any loss of information. This can be
simply explained by noting that the decompression
mechanism is aware of the locations of the inserted zeros as
stated in Equation (7). Therefore, they have no effect on sum
and difference terms, and can be ignored for decompression
without any penalty [11].

Assuming 5 bits per CQI value, the first element of the
compressed vector that is equal to the mean of the vector
expects 5 bits of resolution. However, the remaining
elements that are basically differential information can be
represented by 4 bits. Thus,

If 4=cN coefficients � 17435 =×+=TotalN bits
If 8=cN coefficients � 33475 =×+=TotalN bits

Therefore for 8=cN and assuming a Reporting Interval
(RI) of 4 TTIs, the average CQI budget will be,

25.84
33

= bits/TTI
Coefficient bits can be reduced or expanded to result in an
integer number of bits per message, alternatively rate-
matching can be used.

Figure 2 shows incremental update of the full-band Haar
compression/decompression process. As shown,
decompression with two coefficients yields only information
about the average of the lower and upper bands. However,
by transmitting more coefficients, a higher accuracy in the
reconstruction of the original CQI vector is attained.


A. Main Features
There are several benefits using the proposed full-band Haar
CQI.

Compared to Best-M methods [2], there is a significant
saving in feedback overhead by not requiring sending the
label and average information.

Gradual update is possible. In other words, it is not
necessary to receive the whole set of coefficients at the
network to start updating the scheduler. The network can
update the scheduler per reception of each element. Thus,
the update rate could be every TTI.

By using incremental update, the system can be easily
adapted to various channel, mobility conditions and/or a
given CQI budget.

In comparison against other full-band compression
methods, full-band Haar is significantly less complex. For a
given dimension, Haar (de)compression matrices need a
significantly smaller number of computations. The matrix
calculations rely only on basic shift and addition/subtraction
operations. Also it is important to note that a significant
number of matrix elements are zero resulting in more
savings in computations. For example, for vector lengths of
4, 8, 16 and 32, the number of elements of the
compression/decompression matrices that are zero are ¼, ½,
¾ and 192⁄1024, respectively.


Nc=2


































Nc=4
































Nc=8
































Nc=16







B. Updating Strategies
For a given update interval, two strategies might be

considered for CQI feedback using full-band Haar
compression, namely: One-shot and Incremental. Assuming
an update rate of 4 TTI, here are the steps taken in one-shot
update:

1. Handset takes a snapshot once every 4 TTIs,
2. In every TTI, handset sends ¼NTotal bits available

from the step-1,
3. Upon complete reception of NTotal bits, the network

decompresses the receive vector.

The steps for the incremental update can be summarized as
follows:

1. Take a snapshot once every TTI,
2. In every ith TTI, send the ith ¼NTotal bits of the total

NTotal bits,
3. Upon receiving each ¼NTotal bits, the network

updates only that portion of the NTotal and then
decompresses the available partially updated vector.





Figure 3 – a) One-shot update, b) Incremental update

V. PERFORMANCE RESULTS

A. Simulation Methodology and Parameters
A system-level simulation using a proportional fair

scheduler was performed to evaluate the performance of the
Haar-based full-band CQI feedback against similar
competitive schemes in a 10 MHz system. In the downlink
transmission RB grouping is assumed, where one CQI sub-
band contains 2RBs. In the simulation a CQI granularity of
20 MCS levels is used. The impact of CQI measurement
delay and errors are considered as suggested in [3] and [9].
The simulation parameters are listed in Table 1.


B. Simulation Results
The average sector throughput performance of full-band

Haar, DCT Significant-M [4] and DCT Partitioning [4] is
evaluated under different CQI feedback intervals. The
update mechanism for decompression is based on the
incremental approach. Figures 4 and 5 show the average
sector throughput performance of the system for handset
speeds of 3km/h and 15km/h, respectively.

For each case, there are three curves for the full-band
Haar, each corresponding to a particular feedback
interval(RI). Each feedback interval also implies the number
of the coefficients sent to the network for decompression. As
demonstrated in both figures, increasing RI from 2 to 8 ms
improves the performance. The fundamental reason for this

behavior is that by extending the RI, the network receives a
higher number of coefficients and therefore will be able to
decompress the CQI information with more accuracy (see
figure 2).

Since the uplink control channel for CQI feedback is
designed to support about 10 information bits per TTI, the
reference point of interest for the CQI budget in this paper is
assumed 10 bits/TTI. It is worthwhile to note that at handset
speed of 3 km/h, the full-band Haar scheme offers
significantly better performance than other schemes over a
wide range of bits/TTI. At speed of 15 km/h, the full-band
Haar with RI=4 and RI=8 performs about the same as the
DCT schemes at 10 bits/TTI. For RI=4 and RI=8, it is
important to mention that such performance is achieved by
requiring only 8.25 and 8.125 bits/TTI that is 10% less than
the assumed budget. This could result in higher coding gain
to improve cell edge performance.

At higher mobile user speed, e.g. 15km/h, the average
sector throughput decreases remarkably. This is because the
CQI feedback intervals of interest (4, 6, 8 and 10 TTIs) are
comparable to the channel coherence time, which means that
the multipath channel fluctuates during the feedback
interval. Hence, large feedback intervals introduce
inaccuracy to the reported CQI and corresponding base
station’s scheduling, which in turns degrades the average
sector throughput.



Parameter Assumption
Cellular Layout Hexagonal grid, 19 cell sites, 3

sectors per site
Inter-site distance (ISD) 500m
Number of Tx antennas at network 1
Number of receive antennas 2
Distance-dependent path loss L=I + 37.6log10(.R), R in kilometers

I=128.1 – 2GHz
Lognormal Shadowing Similar to UMTS 30.03, B 1.41.4
Shadowing standard deviation 8 dB
Penetration Loss 20dB
Channel model Typical Urban (TU)
Antenna pattern (horizontal)
(For 3-sec. cell sites with fixed ant.
patterns)

( )






















−= m

dB

AA ,12min
2


θθ

dB3θ = 70 degrees, Am = 20 dB
BS Antenna Gain plus cable loss 15 dBi
Carrier Frequency 2.0 GHz
System Bandwidth 10 MHz
RB bandwidth 180 KHz
Number of mobile users per Sector 10
Mobile user speeds of interest 3km/h, 15 km/h
Maximum Node B transmission
power

35 dBm

Mobile user Traffic Model Full Buffer
Noise Figure 9dB
Thermal noise density -174 dBm/Hz
Scheduler Proportional Fair
HARQ Asynchronous (Chase combining)
CQI measurement error Gaussian zero-mean error model
CQI averaging window 4 TTIs
CQI feedback delay 2 TTIs
CQI feedback interval (RI) 2, 4, 6 and 8 TTIs
Target BLER 10%



Table 1 – Simulation parameters







4 6 8 10 12 14 16 18 20 22
11

12

13

14

15

16

17

18

19

number of overhead bits per TTI

Av
er

ag
e


Se

ct
o

r
Th

ro
u

gh
pu

t (M
bp

s)

3km/h





Full Band Haar (RI = 2ms)
Full Band Haar (RI = 4ms)
Full Band Haar (RI = 8ms)
DCT Partitioning (5-4-1)
DCT Significant(M=5)



Figure 4 - Average sector throughput vs. the number of overhead bits
per TTI at a mobile user speed of 3 km/h.

4 6 8 10 12 14 16 18 20 22
6

7

8

9

10

11

12

13

14

number of overhead bits per TTI

Av
er

ag
e

Se
ct

or


Th
ro

u
gh

pu
t (M

bp
s)

15km/h





Full Band Haar (RI = 2ms)
Full Band Haar (RI = 4ms)
Full Band Haar (RI = 8ms)
DCT Partitioning (5-4-1)
DCT Significant-5





Figure 5 - Average sector throughput vs. the number of overhead bits
per TTI at a mobile user speed of 15 km/h.



VI. CONCLUSIONS AND DISCUSSIONS
In this paper, we propose the application of Haar

compression to full-band CQI feedback for OFDMA based
systems. Full-band Haar CQI feedback offers a flexible
mechanism for CQI feedback that can be easily adapted to
different operating scenarios. Key features are incremental
update and very low complexity for compression and
decompression. Simulation results show that under the
constraint of a low overhead budget per TTI, i.e., ~10
bits/TTI, the full-band Haar scheme achieves significantly
higher performance than the DCT schemes at a low speed of
3 km/h and about the same performance at a higher speed of
15 km/h. The above mentioned performance for RI=4 and
RI=8 are achieved at CQI budgets of only 8.25 and 8.125
bits/TTI that are 10% less than the initially assumed
10bits/TTI budget.



ACKNOWLEDGMENT
The authors would like to thank Donald Grieco, Robert

Olesen and Joseph Levy for their valuable feedback during
the course of this work.


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