An Integrated Sub Channel Scheduling Algorithm for Adaptive Modulation and AMC in MIMO OFDM Wirelss Systems

8/3/2019 An Integrated Sub Channel Scheduling Algorithm for Adaptive Modulation and AMC in MIMO OFDM Wirelss Systems

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An Integrated Subchannel Scheduling Algorithm for Adaptive Modulation and

Coding (AMC) MIMO-OFDM Wireless Systems

Lei Li , Zhisheng Niu

Department of Electronic Engineering

Tsinghua University, 100084, Beijing, P. R. China

[email protected]

Abstract— In this paper, we develop an integrated subchannelscheduling algorithm to maximize the system throughput whileguarantee minimum data rate requirements for multimedia usersin multiuser MIMO-OFDM systems downlink transmission uti-lizing adaptive modulation and coding (AMC) with limited chan-nel state information feedback. By integrated subchannel schedul-

ing, we apply the mathematical equivalence between antennas andsubcarriers in the analysis, getting multiple parallel transmit sub-channels, and then evaluate the channel state from the viewpointof receivers. Joint space-frequency diversity as well as multiuserdiversity is exploited simultaneously by the subchannel allocationalgorithm. A modified proportional fair scheduling is proposedand a fast algorithm for more practical implementation is also pro-posed. By numerical examples, system throughput and fairnesssuperiority of the our scheduling scheme are verified.

I. INTRODUCTION

In recent years, two powerful technologies in physical layer

design: OFDM (Orthogonal Frequency Division Multiplexing)

and MIMO (Multiple Input Multiple Output) provide additional

dimension of freedom for radio resource management in spec-

tral resource and spatial resource. We call it multi-dimensional

radio resource management.

OFDM has been emerging as a promising technology due to

its ability in combating frequency selective fading. In OFDM

systems, a broadband signal is divided and modulated on mul-

tiple narrowband subcarriers. Since the frequency-domain fad-

ing deteriorates the SNR of certain subcarriers, but improves

others’ above the average SNR value, the potential loss of

throughput due to the exclusion of faded subcarriers can be

mitigated by employing higher order modulation and coding

modes on the subcarriers exhibiting high SNR values [1], whichis called Adaptive Modulation and Coding (AMC). In a mul-

tiuser OFDM system, multiuser diversity and frequency diver-

sity may be exploited by assigning subcarriers to the users with

best channel gain [2]. Ref. [3] proposed joint subcarrier and bit

allocation algorithm with minimum total transmission power

for real-time services with fixed data rate. In [4], Generalized

Processor Sharing (GPS) scheduling is integrated in power and

subcarrier allocation to achieve maximum system throughput

and provide fairness to heterogeneous traffic as well.

MIMO have also been attracting much attention because they

have the potential of providing enormous increase in spectral

efficiency of wireless systems [5], [6], [7]. By employing mul-

tiple transmit and/or receive antennas, multiple spatial subchan-

nels are created, and it is unlikely all the subchannels fade si-

multaneously, thus providing space diversity over fading envi-

ronments. In multiuser environments, channel state dependent

scheduling schemes are examined in [8] to increase the systemcapacity by multiuser diversity. For fairness consideration, ref.

[9] applies round robin scheduling in the selection of scheduled

user group, then maps the selected users to the spatial chan-

nels one-by-one. In MIMO environments, however, scheduling

alone is hard to satisfy user’s diverse QoS requirements.

From the perspective of radio resource management, the

combined MIMO-OFDM system is more desirable to allocate

the channel’s degrees of freedom in space and frequency in

a flexible way. Current studies on radio resource manage-

ment in MIMO-OFDM systems mainly focus on OFDM sub-

carrier management under MIMO transmission environments

[10], instead of joint space and frequency resource optimiza-

tion. It is suboptimum because the inherent space diversity of

the MIMO channels is not exploited. In [11], the authors es-

tablished a basic mathematical analogy between antennas and

subcarriers and explained how this similarity can be used for

space-time-frequency (STF) coding to exploit the inherent di-

versity among both the required subcarriers and antennas si-

multaneously. However, their analogy between antennas and

subcarriers is only valid from the viewpoint of transmit diver-

sity and without concerning multiuser diversity property. In the

latter environment, users have to evaluate the channel state and

feedback the evaluation information to the transmitter. The ev-

ident difference between MIMO channels and OFDM channels

is that for different antennas crosstalk always exists, which con-stitutes receive diversity contributing greatly to the performance

in MIMO systems, while there is no crosstalk across OFDM

subcarriers.

In this paper, we apply the mathematical analogy between

antennas and subcarriers to radio resource scheduling and get

multiple parallel transmit subchannels. We evaluate these sub-

channels from the viewpoint of receivers by taking into con-

sideration of the receive diversity combination. Based on this

parallel subchannels model, we propose an optimal resource

scheduling problem across all the subcarriers and antennas by

GPS to guarantee minimum tolerant data rate for QoS users.



AMC scheme is utilized, which supplies multiple supportable

data rates based on the Channel State Information (CSI) at the

receiver. In our scheme AMC mode ID on each subchannel

needs to be fed back to the transmitter only. For practical imple-

mentation, a modified proportional fair scheduling is proposed

and for efficiency application a more practical algorithm is also

proposed. Simulation results show that the proposed algorithmachieves better performance in terms of system throughput and

the similar fairness performance under the GPS scheme as well.

The rest of this paper is organized as follows. In Section

II, the system model of joint MIMO-OFDM cellular system is

described. Mathematical analogy between antennas and sub-

carriers and the way of subchannel evaluation are analyzed in

Section III. The optimized multi-dimensional resource schedul-

ing problem is formulated in Section IV. In Section V, the prac-

tical proportional fair scheduling algorithm as well as a simple

implementation is proposed. Simulation results are shown in

Section VI and conclusions are given in Section VII.

II . SYSTEM MODEL

Consider a single cell downlink environment withÆ

Ì

¢ Æ

Ê

MIMO antennas andÄ

OFDM subcarriers. The resource

scheduling algorithms are carried out at the base station. In

order to keep the scheduling complexity low, we divide theÄ

subcarriers intoÃ

subbands made up of Ä Ã

neighboring sub-

carriers, which are the minimum resource units to be allocated.

This is reasonable, since adjacent subcarriers usually experi-

ence similar fading. Suppose that the base station communi-

cates withÅ

users simultaneously, and the

th user has the QoS

requirement of minimum tolerant data rateÊ

.

We use the multiple antennas to multiplex independent datastreams, namely spatial multiplexing, which can be easily ap-

plied in BLAST schemes [7]. In order for spatial multiplexing

recovery,Æ

Ì

andÆ

Ê

should satisfyÆ

Ì

Æ

Ê

. Therefore,Æ

Ì

transmit antennas and Ã OFDM subbands construct the trans-

mitted symbol vector by multiplexingÆ

Ì

Ã

independent data

streams. Suppose the transmit power is equally allocated to the

transmit antennas and subcarriers and normalized to 1.

Let theÆ

Ì

Ã

dimension column vector× ́ Ø µ

denote the trans-

mission symbol in time slotØ

. The corresponding received sym-

bol vector recovered by user

is

Ü

́ µ

́ Ø µ À

́ µ

́ Ø µ × ́ Ø µ · Ò

́ µ

́ Ø µ

(1)

whereÒ

́ µ

́ Ø µ

is additive noise vector andÀ

́ µ

́ Ø µ

is the channel

matrix from the transmit array to the receive array for user

,

which is anÆ

Ì

Ã ¢ Æ

Ì

Ã

matrix written as

À

́ µ

́ Ø µ

¾

́ µ

½ ½

́ Ø µ

́ µ

½ ¾

́ Ø µ ¡ ¡ ¡

́ µ

½ Æ

Ì

́ Ø µ

́ µ

¾ ½

́ Ø µ

́ µ

¾ ¾

́ Ø µ ¡ ¡ ¡

́ µ

¾ Æ

Ì

́ Ø µ

¡ ¡ ¡ ¡ ¡ ¡

. . .¡ ¡ ¡

́ µ

Æ

Ê

½

́ Ø µ

́ µ

Æ

Ê

¾

́ Ø µ ¡ ¡ ¡

́ µ

Æ

Ê

Æ

Ì

́ Ø µ

¿

(2)

where each entry block

́ µ

Ô Õ

́ Ø µ

is aÃ ¢ Ã

matrix, denoting

the channel matrix by receive antenna Ô

on user

from trans-

mit antennaÕ

withinÃ

OFDM subbands. For example, ele-

ment

́ µ ́ Ô Õ µ

Ð Ñ

́ Ø µ of

́ µ

Ô Õ

́ Ø µ is distinguished by receive subband

Ð from receive antenna Ô and transmit subband Ñ on trans-

mit antenna Õ ́ Ô ½ ¾ ¡ ¡ ¡ Æ

Ê

Õ ½ ¾ ¡ ¡ ¡ Æ

Ì

Ð Ñ

½ ¾ ¡ ¡ ¡ Ã µ . If a perfect cyclic prefix is used in OFDM, no

intercarrier interference occurs.

́ µ

Ô Õ

́ Ø µ

becomes a diagonal

matrix. We will hold this assumption in the following discus-

sion and denote the diagonal elements of

́ µ

Ô Õ

́ Ø µ

as

́ µ ́ Ô Õ µ

́ Ø µ

́ ½ ¾ ¡ ¡ ¡ Ã µ

.

Throughout this paper, we assume that the bandwidth of each

subband is less than the channel coherence bandwidth so that it

undergoes flat fading. Hence

́ µ ́ Ô Õ µ

́ Ø µ

can be modeled as an

i.i.d. complex Gaussian variable. Additionally, we suppose that

the channel is constant over one time slot but varies from time

slot to time slot. The radio resource scheduling algorithm is

carried out at the very beginning of each time slot. In the anal-

ysis below, we will focus on a specific time slot only, therefore,

there is no harm to neglect the time noteØ

.

AMC is utilized on each OFDM subcarrier based on the CSIfeedback. Fig.1 depicts the integrated MIMO-OFDM system

structure and resource management scheduler with AMC.

Antenna NT

Antenna 1IFFT

Joint

antenna

&

subcarrier

scheduler

User 2

User M

User 1

IFFT

Adaptive modulator & coder on f 1

Adaptive modulator & coder on f k



Adaptive modulator & coder on f k


Fig. 1. Integrated MIMO-OFDM system structure and scheduler with AMC

III. EQUIVALENT SUBCHANNEL EVALUATION

We start with the basic mathematical analogy between an-

tennas and subbands in a MIMO-OFDM system where the sub-

carriers and antennas are widely spaced to exhibit independent

fading.

In MIMO systems, Æ

Ê receive antennas receive Æ

Ê copiesof signals from one transmit antenna simultaneously, which is

inherent advantage for MIMO system called receive diversity,

whereas in OFDM systems, such kind of crosstalk is eliminated

by carrier orthogonality and also by the use of cyclic prefix.

Therefore, it is not enough to evaluate channel gains of the

Æ

Ì

Ã

parallel subchannels from the perspective of receivers by

use of the channel matrixÀ

́ µ , because it merely defines the

channel gain fromÒ

Ì

th transmit antenna toÒ

Ê

th receive an-

tenna on

th subband for

th user. Since the users concern the

channel states of the transmit subchannels available only, re-

ceive diversity combination must be taken into consideration to



define the channel gain fromÒ

Ì

th transmit antenna to user

on

th subband. Here we characterize the channel gains by use of

the post-processing SNR from receivers.

In a practical system, the receiver tracks the CSI by use of

pilot symbols and feedbacks the CSI to the transmitter. To

simplify the notations, we denote the subscript

as the sub-

band index when calculate the joint space and frequency chan-nel gains then deduce the calculation on a specific subband

.

LetÆ

Ê

¢ Æ

Ì

matrixÀ

́ µ

denote the MIMO channel matrix

for user

on subband

. The ́ Ô Õ µ

element of À

́ µ

is

́ µ ́ Ô Õ µ

in (2). Then (1) can be written as

Ü

́ µ

À

́ µ

×

· Ò

́ µ

(3)

whereÜ

́ µ

,Ò

́ µ

, areÆ

Ê

dimension column vector andÒ

́ µ

is

an i.i.d. complex Gaussian variable with mean¼

and variance

Æ

¼

. The transmit power on each antenna and subband Ô

Ø

has

been normalized.

In order to recover the transmitted symbols, anÆ

Ì

Ã ¢ Æ

Ì

Ã

matrix

́ µ

is applied as follows

Ý

́ µ

́ µ

Ü

́ µ

́ µ

À

́ µ

×

·

́ µ

Ò

́ µ

(4)

The post-processing SNR of the multiplexed streams is then

given by

Ë Æ Ê

́ µ

Ò

Ì

£ ́ µ

Ò

Ì

́ µ

Ò

Ì

¾

Æ

¼

£ ́ µ

Ò

Ì

¾

·

È

Ò

Ì

£ ́ µ

Ò

Ì

́ µ

¾

(5)

whereÒ

Ì

is the transmit antenna index,

£ ́ µ

Ò

Ì

denotes theÒ

Ì

row of

́ µ

, and

́ µ

Ò

Ì

denotes theÒ

Ì

th column of À

́ µ

. Ex-pression (5) can be viewed as the spectral dimension extension

of the conclusion in [12].

Like the description in [11], we can also view theÆ

Ì

Ã

in-

dependent data streams asÆ

Ì

Ã

parallel transmit subchannels

in multi-dimensional resource rescheduling. We evaluate these

subchannels from the perspective of the receivers by use of

post-processingSNR. For intuitive comprehension, such equiv-

alent is obtained by either viewing the antennas as additional

subbands or viewing the subbands as additional antennas. It

does not matter whether they are distinguishedby different sub-

bands or by different antennas. We might as well denote the

channel on

th subband andÒ

Ì

th transmit antenna as a sub-

channel with a general index . User evaluates these Æ

Ì

Ã

transmit subchannels by use of SNR ́ µ

s.

When AMC is utilized in each subchannel based on the CSI,

improved capacity can be obtained. An example of such an

AMC transmission scheme with 1024 OFDM subcarriers is

shown in Table I (extracted from [13]). We denote the capacity

values for the corresponding SNRs as Supportable Data Rates

(SDRs). In such circumstances, an AMC scheme table such as

Table I is maintained in both receivers and transmitters. The

receiver determines the AMC mode based on the receive SNR,

then feeds back the selected AMC mode ID to the transmit-

ter. And accordingly the transmitter adjusts the modulation and

Mode ID SNR Modulation Code rate Capacity

(dB) (bps/Hz)

1 -3.4 BPSK 1/4 0.25

2 -0.4 BPSK 1/2 0.5

3 2.2 QPSK 1/2 1

4 5.2 QPSK 3/4 1.5

5 7.6 8PSK 2/3 2

6 10.9 16QAM 3/4 3

7 14.5 64QAM 2/3 4

TABLE I

ADAPTIVE TRANSMISSION SCHEME

coding mode. Only AMC mode ID needs to be fed back as

the channel state evaluation, instead of the full CSI matrix with

complex Gaussian variables.

IV. OPTIMAL RESOURCE MANAGEMENT SCHEME

Based on the analysis above, we formulate a Generalized

Processor Sharing (GPS) approach for joint spectral and spa-

tial resource management. GPS is a flow-based ideally fair

scheduling discipline. It assumes that multiple users can be

served simultaneously according to the preestablished weights.

Theparallel character in fact is quite suitable forMIMO-OFDM

systems where multiple users can be served simultaneously us-

ing different space and frequency subchannels. That was our

motivation to study a GPS-type scheduling in MIMO-OFDM

systems. Ref. [4] integrated GPS scheduling in OFDM sub-

carrier allocation, while our scheme is more general as it joints

both spectral and spatial resource management.Likewise, in order to apply the GPS scheduling, we first as-

sume that the number of subbandsÃ

is large enough such that

the subchannel allocation can be carried out at any small fre-

quency band. Therefore the subchannel distribution can be de-

fined as continuous functions. We introduce

́ × µ

as the time

sharing factor for the×

th subchannel, which is a binary value

indicating whether user

occupies the×

th subchannel or not,

× ¾ ¼ Æ

Ì

Ï µ

, whereÏ

is the total bandwidth of each OFDM

modulation block and the total system available bandwidth is

Æ

Ì

Ï

.

́ × µ

can be written as

́ × µ

½

if ×

th subchannel is occupied by the

th user¼

otherwise (6)

By the conclusion in [2],sharing a subchannel by differentusers

is not allowed, that is, one subchannel should be allocated to

one user only at one time, i.e.,

¾

́ × µ ½ for all × ¾ ¼ Æ

Ì

Ï µ (7)

where

is the set of backlogged users. At a GPS node, Call

Admission Control (CAC) interprets the

th user’s minimum

tolerant data rate requirementÊ

as the corresponding weight



. Our objective is to maximize the total system throughput

, subjecting to the predefined weights. The optimal resource

management is described as

Ñ Ü

́ × µ

Ñ Ü

́ × µ

È

¾

Ê

Æ

Ì

Ï

¼

Ë Ê

́ µ

×

́ × µ ×

subject to:Ê

Æ

Ì

Ï

¼

Ë Ê

́ µ

×

́ × µ ×

Ê

Æ

Ì

Ï

¼

Ë Ê

́ µ

×

́ × µ ×

¾

È

¾

́ × µ ½

for all× ¾ ¼ Æ

Ì

Ï µ

(8)

This optimization is an ideal GPS scheduling. Although the

parallel transmission property makes the joint MIMO-OFDM

more fit for an ideal GPS scheduling, the real joint MIMO-

OFDM system still transmit symbols as entities. Neither the

total bandwidth nor the transmission symbol is infinitely divis-

ible. In the follows, we will propose a modified proportional

fair scheduling to fit for the parallel channel scheduling envi-

ronment in the real joint MIMO-OFDM systems.

V. WEIGHTED PROPORTIONAL FAIR SCHEDULING

By the modified proportional fair scheduling, the transmitter

checks theË Ê

́ µ

based on the feedback of AMC mode ID

from each user on each subchannel. It is the data rate that the

th channel for

th user can currently support. The scheduler

also keeps the track of the average throughput Ì

of each user

in a past window with lengthØ

. When the scheduler is ready to

transmit the next packet, the scheduling algorithm simply picks

the user with the largest

Ë Ê

́ µ

Ì

(9)

among all active users in the system. Then allocate the sub-

channel to user . Unlike the traditional proportional fair al-

gorithms, the user’s weight

is concluded. We call it Weighed

Proportional Fair (WPF). The average throughputs Ì

can be

updated using an exponentially weighted low-pass filter as fol-

lowing after each scheduling interval Ð until all the subchannels

are allocated. There are two definitions about the scheduling

interval, which will be discussed later.

Ì

́ Ð µ

½

½

Ø

Ì

́ Ð ½ µ

·

½

Ø

Ë Ê

́ µ

user

is scheduled

½

½

Ø

Ì

́ Ð ½ µ

user

is not scheduled

(10)

The traditional proportional fair scheduling algorithms sched-

ule one user only at one scheduling slot. Our scheme, however,

is a parallel transmission system, where multiple subchannels

need to be allocated one by one at each scheduling slot. Multi-

ple users can be served simultaneously and one user may obtain

more than one subchannel at one time.

Such a circumstance introduces two ways in updating the

average throughputÌ

for each user. One way is that all the

users compete one subchannel firstly then update their average

throughputÌ

immediately before competing the next subchan-

nel until all the subchannels are allocated at a scheduling slot.

The other way is that users use a constant average throughput

Ì

at one scheduling slot then update their average throughput

Ì

until all the subchannels are allocated.

Obviously, first way is more deliberate in fairness guarantee

with the cost of computational complexity. The simulation re-sults in the next section will show the latter way maybe a better

choice with little performance deterioration.

VI. NUMERICAL RESULTS

In this section we evaluate the proposed WPF scheduling al-

gorithm by computer simulation. In the simulation, we group

the subcarriers into 16 subbands for the OFDM system and use

4 transmit antennas and 4 receive antennas for the MIMO sys-

tem. If ZF (Zero Forcing) detection is employed at the re-

ceivers for spatial signal recuperation, the corresponding re-

ceive weight matrix

́ µ

is given by

́ µ

À

́ µ

À

À

́ µ

À

́ µ

À

½

(11)

where ́ ¡ µ

À denotes the conjugate transpose. For MMSE (Min-

imum Mean-Square Error) receiver, the corresponding receive

weight matrix

́ µ

is

́ µ

À

́ µ

À

À

́ µ

À

́ µ

À

· Æ

¼

×

Á

Æ

Ê

½

(12)

whereÆ

¼

and

×

are the total noise power and signal power

respectively. With ZF receiver, computational complexity re-

duces significantly. The post-processing SNR values are com-

puted by (5) to evaluate the channel states. We apply the AMC

scheme as in Table I.

Fig.2 and Fig.3 depict the average throughput normalized by

system bandwidth as a function of the user number from 2 to 24

under the condition that all the users have equal weights, when

mean receive SNR is 10dB. In Fig.2 ZF receiver is applied and

in Fig.3 MMSE receiver is utilized. For comparison, the ca-

pacity with fixed subchannel allocation and optimal multiuser

diversity allocation without fairness considerations are also in-

cluded for benchmarks. These figures show that the system

throughput for the WPF algorithms increase with the increas-

ing in user number, while for the fixed allocation there is no

increment with user number. Compared with the optimal mul-tiuser diversity allocation, the WPF algorithms have slight de-

crease in system throughput due to the fairness constraint. For

comparison, antenna-assistant RoundRobinschedulingin [9] is

also simulated (marked AA-RRS). For the AA-RRS algorithm

the throughput increase is not significant after the user num-

ber reaches to 5. The performance improvement in our WPF

algorithms show the frequency diversity gain of joint space-

frequency scheduling over spatial scheduling only. With either

receiver, the WPF with immediate update and WPF with late

update almost have identical performance. These figures verify

the conclusion in the above section.



Fig.3 shows fairness comparison, which demonstrates the

fairness property of the WPF with late update algorithm in

terms of the throughput for each user over a scheduling slot.

We set four persistently backlogged users with weights

½

¾

½

and

¿

¾

. The average throughput for each

user over a past window with the length of Ø

scheduling slots

are calculated (here Ø

is set to 200). As the figure depicts,the throughput for each user is proportional to its weight, ex-

cept small fluctuations due to the channel station fluctuating.

Therefore, the our WPF algorithm can achieve the fairness per-

formance as that under GPS scheduling.

5 10 15 20 25

7

8

9

10

11

12

13

14

15

16

S y s t e m t h

r o u g h p u t

( b p s / H z )

User number

Optimal multiuser allocation

WPF-late updateWPF-immediate update

AA-RRS

Fixed allocation

Fig. 2. Average throughput versus number of users with ZF receiver

5 10 15 20 25

9

10

11

12

13

14

15

16

S y s t e m t h

r o u g h p u t ( b p s / H z )

User number

Optimal multiuser allocation

WPF-immediate updateWPF-late update

Fixed allocation

Fig. 3. Average throughput versus number of users with MMSE receiver

VII. CONCLUSIONS

In this paper, we have developed a resource allocation

method to maximize the system throughput for multiuser

MIMO-OFDM systems downlink transmission with limited

CSI feedback. It has been shown that the proposed GPS-type

schemecanguaranteeminimum data rate requirements for mul-

timedia users, and at the same time make ef ficient resource uti-

lization by exploiting joint space-frequency diversity as well

10 20 30 40 50

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

T h r o u g h p u t a l l o c a t e

d ( b p s )

Time (tc

scheduling slots)

User 1User 2

User 3User 4

Fig. 4. Throughput allocation comparison

as multiuser diversity simultaneously. We have also proposed

a modified proportional fair scheduling algorithm to avoid thecomputational burden. By numerical examples, we have veri-

fied the superiority of the proposed scheme in system through-

put and fairness for QoS users.

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Documents

An Integrated Sub Channel Scheduling Algorithm for Adaptive Modulation and AMC in MIMO OFDM Wirelss Systems