Full-Band CQI Feedback by Haar Compression in OFDMA Systems

Research Paper / Jan 2009

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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

3θ

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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[8]

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[10]

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