The Vault

Haar Compression for Efficient CQI Feedback Signaling in 3GPP LTE Systems
Research Paper / Jan 2008


Haar Compression for Efficient CQI Feedback
Signaling in 3GPP LTE Systems

Afshin Haghighat, Zinan Lin and Guodong Zhang
afshin.haghighat, zinan.lin, guodong.zhang@interdigital.com

InterDigital Communications


Abstract— Frequency selective scheduling is an attractive

feature in the 3GPP LTE system that allows optimum usage of
the allocated spectrum. 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. Several CQI feedback scheme have been proposed
for 3GPP LTE systems. We propose to apply Haar compression
to distributed subband groups to reduce the CQI feedback
overhead. The simulation results indicate that the distributed-
Haar scheme achieves the best trade-off between the
throughput performance and overhead reduction compared
with other CQI feedback schemes. We also observe that the
sensitivity in sector throughput performance to user mobility is
approximately the same for all feedback methods considered in
the paper.

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



I. INTRODUCTION
The 3GPP Long Term Evolution (LTE) technology

improves the capacity, coverage and flexibility of the
cellular system significantly beyond the existing 2G and 3G
cellular system technologies [1]. In order to realize such
enhancements, there have been several fundamental changes
in the system definitions and requirements in all layers of
the system [2]. One striking difference in the physical layer
of the system is the use of OFDMA as air interface instead
of WCDMA in the 3G UMTS systems. OFDMA offers
higher capacity and robust performance in a multipath
frequency selective mobile channel.

In 3G WCDMA HSDPA systems, since WCDMA is a
single-carrier system, only a single CQI is reported for each
H-ARQ process. Hence, the overhead associated with CQI
reporting is relatively small. On the other hand, in LTE
systems frequency selective scheduling is used to achieve
efficient usage of the spectrum. 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
report a set of CQI values, one for each sub-band. However,
this will lead to overwhelming large CQI feedback
overhead. In the current LTE standards, a budget of
approximately 10 bits per Transmission Time Interval (TTI)
for CQI feedback is being considered. Although this number

may be refined in the future, it provides an insight on the
range of the allowed feedback overhead for the CQI
feedback.




This challenge of designing a CQI feedback scheme that
achieves efficient usage of spectrum with reasonably low
overhead has spurred some research interests. Numerous
CQI reporting and compression schemes have been
proposed with different levels of compression and system
performance [3]-[5]. The proposed schemes can be divided
into two categories. The schemes in the first category
compress the CQI information of all the sub-bands in the
entire cell bandwidth and report the compressed CQI
information to the base station. An example of the schemes
in this category is DCT significant-M feedback scheme [3].
The second category includes techniques that are based on
reporting of only limited number of the highest CQIs among
all subbands, 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. Descriptions of other CQI feedback
reporting schemes that are referenced and compared to in the
simulations can be found in [3]-[5].

The techniques discussed in this paper hinges on the
principle of the latter category. We propose to further reduce
signaling overhead for the CQI feedback by applying Haar
compression to distributed groups of sub-bands. The
proposed distributed-Haar CQI feedback scheme supports a
flexible trade-off between system performance and CQI
feedback signaling overhead.

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 the Best-M Haar CQI
reporting scheme is provided in Sections III and IV. Then, in
order to further reduce the overhead feedback, the
distributed-Haar CQI reporting scheme is introduced in
Section V. The performance of the distributed-Haar CQI
reporting scheme is simulated and compared with other
methods such as Best-M, DCT significant, and DCT
Partitioning in Section VI. Finally, the paper is concluded in
section VII.

II. SYSTEM DESCRIPTION
The diagram of the downlink OFDMA air interface in the

LTE system is shown in Figure 1. In the OFDMA system,
modulated bits are converted from serial to parallel first, and
then mapped to different subcarriers. After IFFT, the output






signals are converted back to serial signals called an OFDM
symbol. Cyclic prefix (CP) is attached to the beginning of
the OFDM symbol before transmission. Subcarrier spacing
of 15 kHz is used in the 3GPP LTE system. The time in the
3GPP LTE system is divided into radio frames. 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
uplink and downlink. Therefore, a sub-frame is also called a
TTI.



Figure 1: OFDMA air interface in 3GPP LTE systems.


The basic concept of frequency selective scheduling in the

3GPP LTE systems is depicted in Figure 2. Each UE needs
to estimate the channel quality and report the CQI of
downlink sub-bands to the base station. Then, the base
station schedules and allocates sub-bands for mobile users
based on reported CQI. The modulation and coding set
(MCS) of each scheduled user is also adapted according to
the reported CQI.



Figure 2: Frequency selective scheduling in the LTE

systems.

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

Detailed description of the Haar compression method can be
found in [6]-[7]. Haar compression encodes an input stream
in multiple steps according to the level of the detail of the
input sequence. Haar compression belongs to the class of
lossy compression methods, and it 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. The
process can be explained by an example as follows. Let the
input vector y be:

[ ]921151428312=y (1)

Since the vector has 23 elements, the transformation takes
3 steps of sum and difference operations as follows: first,
group the elements of the vector y in groups of 2’s. Find the
sum and the difference terms for each group and divide the
results by two. The results are now in a new vector y1.

[ ]
[ ]
[ ]3.5374.51.256.25.75y

3.5374.51.256.75y
3.5374.5y

−−−=
−−−=
−−=

35.10
75.625.14

5.58215.7

3

2

1

(2)

The first four elements of the vector y1 are called
“Approximate” and the last four elements, in Bold, are
called “Detail” coefficients. Steps 2 and 3 are similar to step
1, with the only difference being that they apply only on the
“Approximate” coefficients, while the “Detail” coefficients
are maintained to the end. As shown in Equation 2, the final
compressed vector is comprised of one “Approximate”
coefficient along with seven “Detail” coefficients.

In an abstract form, for a vector length equal to 8, the
successive averaging and differencing steps involved in the
compression process can be mathematically expressed as

( ) ( ) ( )[ ] 83333 178 yWy == yyy L (3)
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

(4)

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

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

Therefore, the decompression can be easily implemented by

83Fyy = , (5)

⎥⎥
⎥⎥
⎥⎥
⎥⎥
⎥⎥






⎢⎢
⎢⎢
⎢⎢
⎢⎢
⎢⎢












−−

−−−−
−−

== −

1100
0011
0000
0000

0000
0000
1100
0011

1111
0000
1111

1111

0000
1111

1111
1111

1
88 WF . (6)






It is worth mentioning that due to the particular value of
the coefficients for the compression and the decompression,
all the required multiplications can be performed by simple
shift-add functions in binary domain. Also, half of the
matrix elements are zeros. The two features result in a very
low complexity for compression and decompression
functions.

IV. BEST-M HAAR CQI FEEDBACK SCHEME
In [8], we proposed the best-M Haar CQI feedback

scheme for the 3GPP LTE systems. For a system with Nsb
sub-bands, the procedure for the proposed Haar-based
compression of the best M sub-bands’s CQI is as follows:
1. Select the M largest CQIs among all sub-bands.
2. Calculate the average CQI of remaining sub-bands

( ). AvgCQI
3. Create a vector comprising the M CQI values and

the . Hence, the total number of CQIs to be
reported in steps 1 and 2 is M+1. The Best-M CQI
values are reported in the same order as their relevant
sub-bands. The length of the input vector for Haar
compression is 2

AvgCQI

m, where m is the smallest integer to
satisfy (M+1) ≤ 2m. However, assuming a common
implementation structure, m could be larger than what is
specified earlier. The vector y will have 2m-(M+1) zeros
at predefined locations. For example, given an input
vector with a fixed length of 8,
For M = 3:

[ ]0000 321 AvgCQICQICQICQI=y ; (7)
For M = 4:

[ ]000 4321 AvgCQICQICQICQICQI=y ; (8)
For M = 5:

[ ]005421 AvgCQICQICQICQICQI L=y ; (9)
For M = 7:

[ ]AvgCQICQICQICQICQI 7621 L=y . (10)
If 5 bits are used to represent one CQI value in the
feedback, the vector will contain 5(M+1) bits of
information.


4. Apply the Haar transform as in Equation 3.

5. In step 3, if (M+1)<2m then zero insertion will be
implemented. However, after the compression,
according to the position of the inserted zeros, certain
elements of the compressed vector can be dropped
without any loss of information. For example, the last
four, three and two elements of the compressed vector
y3 become irrelevant for transmission and can be
dropped, for M=3, 4 and 5 respectively.

6. Quantize and send the remaining elements of the vector.

7. Send the location information of the Best-M sub-bands.
The number of bits required for the location information
is determined by

⎟⎟⎠


⎜⎜⎝


⎟⎟⎠


⎜⎜⎝
⎛=

M
N

N sbLocation 2log (11)

Each element of the compressed vector has a statistical
distribution that can be exploited to optimize the
quantization process and overhead. Assuming 5 bits of
dynamic range for each CQI value, extensive simulations of
channel variations suggest certain distributions for each
element of the compressed vector.

Table 1 shows the predefined offset values and the
required number of quantization bits for each element of the
compressed vector. Each element of the compressed vector
is represented by a fixed offset value and a Q-bit binary
word (0Æ2Q-1). As shown in the Table 1, a higher number
of bits is only required for the first two elements of the
vector that carry more information than the others. The
remaining elements can be represented by a fewer number of
bits.

The total number of required feedback bits is given by

LocationHaar NNN += . (12)
In Table 2, the total number of required bits for different

values of M is shown. In comparison to Best-M individual
CQI reporting scheme, Haar compression results in 25%,
26% and 32% saving for M=4, 5 and 7, respectively. Similar
comparison reveals considerable savings over DCT-based
schemes as well.

Elements of
compressed

vector

Offset
value

Range Quant bits
per

element

Number

of bits

y3(8) 3 3 Æ 16 4
y3(7) -1 -1 Æ 2 3
y3(6) -1 -1 Æ 1 2



M=3

y3(5) 0 0 Æ 2.5 2



NHaar=11

y3(8) 5 5 Æ 24 4
y3(7) 2 2Æ 9 4
y3(6) -1 -1 Æ 1 3
y3(5) 0 0 Æ 2.5 3
y3(4) -2 -2 Æ 2 2





M=5

y3(3) -2 -2 Æ 2 2





NHaar=18


Table 1 - Quantization information for different M values.


CQI feedback

scheme Nsb=25

M=3 M=4 M=5 M=7

Full Feedback 125 bits 125 bits 125 bits 125 bits

Best-M Average 22 bits 24 bits 26 bits 29 bits
Best-M
Individual

32 bits 39 bits 46 bits 59 bits

Haar Best-M
Individual

<20 bits 29 bits 34 bits 40 bits

Best-M DM 28 bits 32 bits 36 bits 43 bits






DCT
Significant-M

24 bits 31 bits 39 bits 53 bits

DCT
Partitioning NA

N1=3,N2=1,
34 bits

N1=4,N2=1,

43 bits

N1=6,N2=1,

57 bits

Table 2 - Overhead comparison of CQI feedback schemes.

V. DISTRIBUTED-HAAR CQI FEEDBACK SCHEME
Although the multipath channel is time-varying, in many

cases it preserves most of its frequency spectrum
characteristics over a finite period of time (i.e., the channel
coherence time). Therefore, the update interval of the full
channel does not need to be every sub-frame. In this paper,
we proposed a new CQI feedback scheme called distributed-
Haar to reduce the overhead feedback by exploiting this
characteristic.

The flow of the reporting mechanism can be summarized
as follows:
1. Divide the sub-bands into NG groups. Locations of the

groups are known in advance to both mobile users and
base station. The groups can be defined in any manner.
However, partitioning sub-bands into equal-distant
groups is a simple and efficient way to do the grouping.

2. At each Reporting Interval (RI), apply a best-M Haar
compression to the CQI values of one of the
groups.

Gsb NN /

3. Perform step 2 on the remaining groups in subsequent
reporting intervals to cover the whole cell bandwidth.

As a result of this approach, in every reporting interval, the
number of sub-bands is reduced from to .
Hence, this allows the mobile user to use a smaller M for
CQI reporting at each reporting interval. Figure 3 shows an
example of distributed-Haar compression for CQI feedback
for N

sbN Gsb NN /

sb=8 and NG=2.



Figure 3: An example of Distributed-Haar CQI Feedback.

For the purpose of illustration, we consider a system with
Nsb = 25, M = 5. For such a system, the Best-M individual
CQI reporting scheme with and without Haar compression
requires 46 bits and 34 bits overheads, respectively.
However, using the distributed-Haar scheme with NG =2, the
sub-bands can be divided into two groups (even and odd) of
12 and 13 sub-bands. Then, Haar compression is applied
with a smaller M of 3 to each group. Therefore, for CQI
reporting of odd and even sub-band groups we have

bits19811
bits20911

=+=+=
=+=+=

LocationHaareven

LocationHaarodd

NNN
NNN

(13)

Hence, the number of information bits in each partial
feedback is much lower than other schemes listed in Table 2.

In each partial feedback, the M best sub-bands and an
average CQI is reported to the base station. Given a lower
number of bits per report, the base station will have more
frequent updates of CQI than other reporting schemes.

VI. PERFORMANCE RESULTS

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

sectors per site
Inter-site distance (ISD) 500m
Number of transmit antennas at NB 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
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 reporting interval (RI) 2, 4, 6 and 8 TTIs
Target BLER 10%

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

scheduler was performed to evaluate the aforementioned
CQI reporting schemes in a system with a 10 MHz
bandwidth. In the downlink transmission Resource Block
(RB) grouping is assumed, where one CQI sub-band
contains
2 RBs. 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 [4] and [8]. The simulation
parameters are listed in Table 3.

Table 3 – Simulation parameters

B. Simulation Results
The performance metric of evaluating CQI feedback

schemes is the average sector throughput. For different CQI
reporting schemes including Best-M individual, distributed-
Haar, DCT Significant-M and DCT partitioning, the average
sector throughput performance is measured and compared
under different CQI reporting intervals via simulations.

The average sector throughputs for mobile user speeds of
3km/h and 15km/h are shown in Figure 3 and Figure 4,

1 2 3 4 5 6 7 8

1

2

3

4

5

6

7

8 t=i

t=i+1

Haar

Haar

Feedback t=i


Feedback t=i+1






respectively. Each graph demonstrates the performance of
various schemes against the required number of bits per
report. The required number of bits per report is evaluated
by dividing the corresponding number from Table 2 and
Equation (13) by the RI. As observed, the distributed-Haar
scheme outperforms other schemes around 10 bits per TTI
range for both cases (3 km/h and 15 km/h). At the speed of
15 km/hr, DCT-Significant has the best performance when
the number of overhead bits per TTI is small (< 7 bits per
TTI). However, around the range of 10 bits per TTI, the
distributed-Haar scheme yields the best performance and
outperforms Best-M individual, DCT partitioning and DCT
significant-M by 15.4%, 14.2% and 5%, respectively. At the
speed of 3km/h, distributed-Haar consistently provides the
best performance among all schemes over the whole range
of overhead bits per TTI. For example, the distributed-Haar
CQI reporting scheme provides 1.2%, 5.8%, 14.3%
throughput gains over Best-M individual, DCT partitioning
and DCT significant-M, respectively, at around 10 bits per
TTI.

For the same value of M, at low mobile user speed, e.g.
3km/h, the average sector throughput is insensitive to the
value of reporting intervals. This is because the CQI
reporting intervals of interest (2, 4, 6 and 8 TTIs) are much
smaller than the channel coherence time, which means that

0 5 10 15 20 25
12

13

14

15

16

17

18

number of overhead bits per TTI

A
ve

ra
ge

S
ec

to
r T

hr
ou

gh
pu

t (
M

bp
s)

3km/h





Best-5 Individual
DCT Partitioning (5-4-1)
DCT Significant(M=5)
Distributed-Haar(M=3)

RI=2msRI=4ms
RI=6msRI=8ms

RI=2msRI=4ms

RI=6ms

RI=8ms

RI=4ms

RI=2ms

RI=6msRI=8ms

RI=2msRI=4msRI=6msRI=8ms



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

0 5 10 15 20 25
6

7

8

9

10

11

12

13

14

15

number of overhead bits per TTI

A
ve

ra
ge

S
ec

to
r T

hr
ou

gh
pu

t (
M

bp
s)

15km/h





Best-5 Individual
DCT Partitioning (5-4-1)
DCT Significant(M=5)
Distributed-Haar(M=3)

RI=2ms

RI=4ms

RI=6ms

RI=8ms

RI=8ms

RI=4ms

RI=6ms

RI=2ms
RI=2ms

RI=4ms

RI=6ms

RI=8ms

RI=2ms

RI=4ms

RI=6ms

RI=8ms

Figure 4 –Average sector throughput vs. the number of overhead bits per
TTI at a mobile user speed of 15 km/h.

the multipath channel is static during the reporting interval.
However, at higher mobile user speed, e.g. 15km/h, the
average sector throughput decreases remarkably with
increasing CQI reporting interval. This is because the CQI
reporting 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 reporting
interval. Large reporting intervals introduce inaccuracy to
the reported CQI and corresponding base station’s
scheduling, which in turns degrades the average sector
throughput.

VII. CONCLUSIONS AND DISCUSSIONS
In this paper we have addressed the CQI feedback

overhead issue by applying best-M Haar compression to
distributed groups of sub-bands. Simulation results show
that the distributed-Haar scheme achieves a more flexible
trade-off between the throughput performance and feedback
overhead compared with other CQI compression techniques
(e.g., Best-M individual, DCT-Partitioning and DCT
significant-M). At a reasonable CQI feedback payload (e.g.,
around 10 bits per TTI), the distributed-Haar scheme
provides throughput gains up 15.4%, 14.2% and 5% over
Best-M individual, DCT-Partitioning and DCT significant-M
feedback schemes, respectively. Excluding the significant-M
method that has the poorest performance at the low speed,
all the other investigated methods exhibit similar sensitivity
in sector throughput performance to the mobile speed.

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