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A study of impact of inband signaling and

realistic channel knowledge for an

example dynamic OFDM-FDMA system

James Gross, Stefan Valentin, Holger Karl, Adam Wolisz

TU Berlin

Einsteinufer 25, 10587 Berlin, Germany

{gross|valentin|wolisz}@tkn.tu-berlin.de, hkarl@ieee.org

fon: +49.30.31423830, fax: +49.30.31423818

Abstract—Dynamically assigning sub-carriers of

OFDM systems to multiple different terminals in

a cell has been shown to be beneficial in terms of

different transmission metrics. The success of such

a scheme, however, depends on the ability of the

access point to inform terminals of their newest sub-

carrier assignments as well as on the accuracy of

the channel state information used to generate new

assignments. It is not clear whether the overhead

required to implement these two functions consumes

all of the potential performance increase possible by

dynamically assigning sub-carriers.

In this paper, a specific MAC structure is selected

enabling the operation of a dynamic OFDM system,

incorporating a signaling scheme for dynamically

assigned sub-carriers. Based on this structure, we

study the overhead required for a dynamic sub-

carrier scheme; a static variant serves as a compar-

ison case. We investigate the performance difference

of these two schemes for various scenarios where at

first signaling and then realistic channel knowledge

is added to the system model. Average throughput

and goodput per terminal serve as figures of merit;

the number of terminals in the cell, the transmission

power per sub-carrier, the delay spread and the

movement speed of the terminals are varied. We

find that a realistic overhead model decreases the

performance of both static and dynamic schemes

such that the overall ratio favors in all cases except

for higher speeds the dynamic rather than the static

scheme especially in realistic system environments.

This work has been partially supported by the German

research funding agency ’Deutsche Forschungsgemeinschaft

(DFG)’ under the program ”Adaptability in Heterogeneous

Communication Networks with Wireless Access” (AKOM)

I. INTRODUCTION

Recently, theoretical studies have proven that

dynamically assigning sub-carriers of Orthogonal

Frequency Division Multiplexing (OFDM) sys-

tems can be advantageous for the downlink of a

single cell in terms of several transmission met-

rics, e.g. required power or achieved throughput

[1–4]. These approaches all exploit the combina-

tion of two aspects regarding wireless channels

in multi-user communication scenarios: First, for

a given sub-carrier, its attenuation values with

respect to different sub-carriers are statistically

independent random variables. Second, the at-

tenuation of sub-carriers changes over time and

frequency as a consequence of terminal mobility

and the multi-path propagationenvironment.Thus,

also regarding a single terminal, the attenuation

varies from sub-carrier to sub-carrier; dynami-

cally assigning “good” sub-carriers to terminals

promises to improve performance.

When evaluating this potential of dynamic

OFDM-FDMA systems, all these studies are based

on two common, simplifying assumptions. First,

it is assumed that at the access point, prior to the

computation of sub-carrier assignments, all sub-

carrier attenuations (also referred to as “states”)

to each terminal are known. Second, it is as-

sumed that after the generation of assignments

wireless terminals somehow “know” which sub-

carriers they have been assigned by the dynamic

algorithm. In some studies the authors mention

European Transactions on Telecommunications, 2005

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an existing out-of-band signaling system, but no

investigation has been conducted highlighting the

cost of such a signaling system (in effect repre-

senting an unfair advantage for dynamic systems

as a potential performance disadvantage is not

considered). Interestingly, in reality the success of

dynamically assigning sub-carriers to terminals is

directly related to the provided channel knowledge

of the access point and to a working signaling

system.

It is obvious that fulfilling these two require-

ments costs system performance. An important

question is if this “administrative” overhead re-

quired for dynamic schemes might eliminate all

the performance advantages that these schemes

achieve compared to schemes which do not as-

sign sub-carriers dynamically, like static FDMA

schemes or TDMA schemes. In this study we

investigate this question regarding an example

system that is set up quite similar to IEEE 802.11a.

Especially, we investigate the variation of four

different parameters: the number of terminals in

the cell, the transmit power per sub-carrier, the

delay spread of the propagation environment and

the maximum speed of objects in the propagation

environment. A preliminary version of this study

has been published in [5]. We extend on this work

by incorporating the investigation regarding the

delay spread variation and the maximum speed

variation. In addition, we present more analysis

explaining the observed result differences.

In order to study the two aspects decreasing the

achieved performance we constrain ourselves to a

simple Medium Access Control (MAC) protocol,

described in Section III, which provides a timing

structure for channel state acquisition, signaling

the assignment information and transmitting data

either in downlink or uplink direction. We thus

assume an inband signaling system. As dynamic

assignment algorithm we choose a heuristic one

described in Section II, which generates near-

optimal assignments in a short amount of time.

Based on this, we then study the behavior of the

dynamic algorithm and the behavior of a static

comparison scheme for different parameter sets of

the transmission scenario in Section IV. Finally,

we conclude the paper in Section V.

II. SYSTEM MODEL

We consider a single cell of a wireless system.

Any data transmission within this cell is managed

by an access point. There are J wireless terminals

located within this cell. For data transmission a

radio frequency band of bandwidth B is available

at center frequency fc. The transmission scheme

used in the cell is OFDM, which splits the band-

width into S overlapping sub-carriers. In order to

avoid Inter-carrier Interference (ICI) of the over-

lapping sub-carriers, the used symbol length per

sub-carrier and the frequency spacing of any two

adjacent sub-carriers have to be chosen carefully,

the relation is given by the equation Ts =

We only consider the downlink data transmission

direction.

The terminals move constantly within the cell,

which has a radius of R, with a certain maxi-

mum speed vmax. Therefore, the attenuation of

the sub-carriers varies constantly due to path loss,

shadowing and fading. The attenuation differs for

multiple sub-carriers regarding the same termi-

nal; also the attenuation of the same sub-carrier

varies regarding different terminals. The matrix

A(t) = (aj,s(t)) describes the attenuation values

of all S sub-carriers regarding all J terminals.

Given the attenuation aj,s(t), the Signal to Noise

Ratio (SNR) xj,s(t) of sub-carrier s with respect to

terminal j is given by Equation 1, where Ptx,s(t)

denotes the transmission power for sub-carrier s

at time t and n2(t) denotes the noise power.

1

∆f.

xs(t) =a2

j,s(t)

n2(t)· Ptx,s(t)

(1)

To exploit the varying nature of these sub-

carrier states, in the downlink the system em-

ploys dynamic Frequency Division Multiplexing

(FDM) for data transmission. Due to this, multiple

downlink transmissions of data can be supported

simultaneously by assigning different sets of sub-

carriers to different terminals. Prior to each down-

link transmission the access point can dynami-

cally allocate (i.e. decide about the number of

sub-carriers given to each terminal) and assign

(i.e. decide about which sub-carriers are given to

each terminal according to the allocation) sub-

carriers to terminals, based on information of all

sub-carrier states regarding each terminal. Then,

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still prior to the downlink transmission itself, the

assignments of sub-carriers have to be signaled

to the terminals. Both, the acquisition of chan-

nel knowledge and the signaling of assignments

are discussed in detail in Section III where the

Medium Access Control (MAC) layer, enabling

these functions, is described.

As dynamic assignment algorithm we choose

here the nearly optimal heuristic one referred to as

advanced Dynamic Algorithm (aDA) , introduced

in [6]. It requires as input the sub-carrier states

and the sub-carrier allocations for each terminal.

Based upon this input, aDA can generate quite

good sub-carrier assignments within 0.5 ms on

standard computers. This delay caused by the

computational complexity of the algorithm has not

been considered any further.1

In order to transmit data on each sub-carrier,

adaptive modulation is used with the following

modulation types: BPSK, QPSK, 16-QAM, 64-

QAM and 256-QAM. During one downlink trans-

mission the sub-carrier assignments as well as

the modulation types are not changed. Out of

the available modulation types the system always

chooses the one with the highest throughput that

still provides a symbol error rate lower than Ps;

the choice is based on the individual sub-carrier’s

SNR. Transmission power is equally distributed

over all sub-carriers; we do not assume an adap-

tive power distribution here due to the additional

computational complexity associated with it. For

forward error control we use block codes due to

their easy handling in simulations.

Each terminal in the cell receives a stream of

packets from a source outside of the cell. These

packets arrive at the access point and are queued

separately for each terminal until they are trans-

mitted to the respective terminal. For simplicity

we assume that the access point has always data

to transmit to the terminals, therefore the queues

are never empty.

III. CHANNEL KNOWLEDGE AND SIGNALING

SYSTEM

Successfully assigning sub-carriers to wireless

terminals, depending on the sub-carrier states for

1This simplification is justifiable since the computation of

allocations and assignments can be pipelined and overlapped

with the last half of a MAC frame.

each terminal, requires of course that the access

point has sufficient knowledge of these states. If

the sub-carriers can be assumed to be reciprocal

in terms of attenuation, then the access point

might obtain the required knowledge by observing

the attenuation during uplink transmissions. But

since this is not the case in general, an alternative

is to obtain this knowledge explicitly via the

uplink transmissions themselves: The terminals

measure the attenuation of each sub-carrier during

the previous downlink transmission and transmit

these measured values to the access point in the

following uplink transmission.

Once the access point generated the assign-

ments based on this channel knowledge, the wire-

less terminals have to be informed prior to the

downlink transmission which sub-carriers are as-

signed to them. In addition, since we consider a

system with adaptive modulation, the used modu-

lation type also has to be signaled to the terminals.

In the following we present and discuss a

framing structure that enables such a system to

acquire channel knowledge as well as to signal

assignments realistically: By paying a price in

terms of system performance. This structure is

then used for the further study.

A. General frame structure

We divide time into a continuous stream of

frames. Denote the length of one frame by Tf. For

each frame, the access point computes the sub-

carrier assignments for this frame (using channel

knowledge acquired in the previous frame), signals

these assignments to the terminals, conducts the

actual downlink data transmission, and, at the end

of the uplink, receives channel information from

each terminal to be used for the next frame’s

channel assignments.

Figure 1 shows the basic elements of a frame. A

frame starts with a phase during which signaling

information is sent to the terminals. This takes

a time of Tsig. Then follows a downlink phase,

which lasts for Td. The last element of a frame is

the uplink phase, which has a length of Tu.

B. Inband signaling system

Instead of considering a separate control chan-

nel, we suggest the usage of an inband signaling

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MAC Frame MAC Frame

Tsig

Td

Tu

Tf

Uplink

...

MAC Frame

SIG Phase

Downlink

Fig. 1.Elements of a frame

S

F

D

E

F

D

SAF SYNC

Uplink

SIG Phase

Downlink

Fig. 2. Elements of the signaling field

system. The signaling information is therefore

conveyed using the system bandwidth which is

also used to transmit payload. The advantage of

such a method is that it does not require additional

bandwidth (and thus allows a fair comparison

between static and dynamic schemes, unlike out-

of-band signaling approaches). The downside of

this inband signaling is that a certain time has

to be reserved for transmitting the signaling in-

formation, which therefore reduces the system’s

performance.

The signaling field within each frame consists

again of multiple elements, shown in Figure 2.

At the beginning of the signaling field, a syn-

chronization field is transmitted, analog to the

one used in IEEE 802.11a [7] with a length of

12 symbols (signal acquisition, synchronization

and training of the receiver). Then, a start frame

delimiter is transmitted to indicate the start of

the signaling information. Next, the Sub-carrier

Assignment Field (SAF) is transmitted completely,

which holds all assignments and also includes

error coding. Finally, an end frame delimiter is

sent, which is the last element of the signaling

field. The signaling field is shown in Figure 2.

The transmission of the signaling information

within this field is done as broadcast. Every ter-

minal in the cell receives this information, even if

1

... ...

FEC

1

m

m

WT

S

WT

S

CRC

Fig. 3.Structure of the Sub-carrier Assignment Field (SAF)

a terminal will not receive data during this frame

and therefore will not be assigned a sub-carrier.

The signaling field is always transmitted with the

same modulation type (BPSK) and is sent via all

available S sub-carriers.

The signaling information itself is transmitted

with a fixed structure (Figure 3). For each frame

all S sub-carriers are assigned a terminal and a

modulation type. This results in a pair of numbers

which have to be transmitted for each sub-carrier:

The terminal’s address that has been assigned

this sub-carrier and the modulation type to be

used for downlink transmission. This information

is transmitted pairwise for each sub-carrier, then

follows a CRC code for error detection. This

complete field is also protected by a strong error

correction code.

By broadcasting this information during the sig-

naling phase, all terminals receive all assignments.

The advantage of this method is that it gives full

flexibility to the assignment algorithm within the

access point. The structure of the signaling field

does not change, even if only a few terminals

are assigned sub-carriers. This is not the case

if the signaling information is not broadcasted

but rather transmitted individually (“piggyback-

ing”the signaling information for example). Then,

terminals are excluded from the system whenever

they do not receive a sub-carrier for a frame. As

a consequence these terminals would have to go

through the admission process again.

If the signaling information is received com-

pletely and it is correct, the terminals only process

the data received on their specific sub-carriers

during the following downlink phase, all other

data, although received, is ignored. If the signaling

information is not received correctly, all received

data during the downlink phase is discarded and

during the following uplink phase the loss is indi-

cated by the terminal. Then, the data transmission

is repeated during the next frame.

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Measured values

are transmitted

to the access point

Values serve as subcarrier

estimates for the next

downlink phase

Downlink

Uplink

Downlink

Uplink

Subcarrier SNR

subcarrier’s SNR

Terminals measure

Time

SIG SIG

Frame xFrame x+1

Fig. 4.Process of acquiring sub-carrier gain knowledge

C. Acquisition of channel knowledge

In an ideal case a system would have the

following properties: While the attenuation of sub-

carriers does not change for the time span of

one frame, the access point would “know” about

these sub-carrier states in advance of each frame.

Obviously, this cannot be the case in reality. First,

the attenuation of sub-carriers changes constantly

during one frame, depending on the fading rate

[8, 9]. Second, sub-carrier states cannot be known

in advance.

One approach for a working system in real-

ity could be like this: During the signaling or

downlink phase of frame x each wireless terminal

measures the attenuation of all sub-carriers. In the

following uplink phase this information is then

conveyed to the access point. The complete sub-

carrier state information is then available at the

access point at the end of frame x. Note that it

reflects the sub-carrier states as they were at the

end of the downlink phase of this frame (in the

most optimistic case). This information is now

used as an estimate of the sub-carrier states for

the next frame x + 1. So the access point gen-

erates new assignments based on these estimates,

signals these assignments to the terminals and then

starts the downlink payload transmission. Figure 4

illustrates this process.

The quality of this estimate depends of course

on the fading rate of the sub-carriers. Note that

we do not assume any sophisticated estimation

techniques to be present at the access point. The

sub-carrier state information is obtained at the end

of the downlink phase of frame x, and is used

as estimate until the end of the downlink phase

of frame x + 1. Therefore, Tf should be short

enough so that matrix A(t) and matrix A(t+Tf)

do not differ significantly. Since the speed of ob-

jects within the propagation environment directly

influences the fading process of the sub-carriers

(together with the center frequency of the system)

[8], which is characterized by the coherence time,

the length of a frame should be lower than this

value. Even in this case, however, the channel

estimates will vary from the real values since

the coherence time is a statistical measure which

cannot guarantee channel stability over some time

span. Note that an estimation error as such does

not have to harm the system, only if the next

sub-carrier state has been overestimated a certain

performance decrease will be observed (resulting

in an increase of bit errors).

IV. PERFORMANCE STUDY

The focus of this study is to highlight the per-

formance of dynamic OFDM-FDM systems con-

sidering realistic costs for signaling and channel

knowledge acquisition. In this section we first dis-

cuss our metrics and comparison schemes, then we

introduce the chosen scenario and at last present

our results. For further details on any aspect of

this investigation, refer to [10].

A. Metrics and comparison schemes

Two primary metrics are chosen in this study.

The first one is the average throughputper wireless

terminal in bits per second. The second metric

is the average goodput per wireless terminal in

packets per second. Both metrics consider the data

received at the terminals. For the throughput this

received data amount is always equal to the trans-

mitted data amount at the access point. However,

for the goodput this is not true in general. Here

the amount of successfully received packets per

terminal is relevant, which depends on the length

of the packets considered as well as on the used

forward error correction code.

We investigate the behavior of the dynamic

OFDM-FDM system in three different scenarios.

The first one is the ideal scenario: signaling does

not cost bandwidth, is not subject to transmission

errors and the access point has perfect knowledge

of the sub-carrier states in advance of each frame.

For the second scenario we assume the signaling

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system to be present as described in Section III-

B but the access point has still perfect channel

knowledge. This one is called the half-realistic

scenario. Finally, in the third one, the realistic

scenario, the access point generates assignments

based on outdated channel information. These

assignments then have to be signaled through the

discussed inband signaling system.

For all three scenarios the performance in terms

of throughputand goodput of the dynamic OFDM-

FDM system is obtained and compared with the

performance of a static scheme. In the static

scheme each terminal receives the same set of sub-

carriers during all downlink phases. Nevertheless,

adaptive modulation is still applied for data trans-

mission on these sub-carrier sets. Therefore, the

static scheme also depends on signaling as well as

channel knowledge acquisition, but the influence

of dynamically assigning sub-carriers is taken out

of the system.

The performance of both schemes, the dynamic

as well as the static one, are obtained for the three

different scenarios. Then, for both metrics the ratio

between the dynamic and static system setup is

computed and considered as the figure of merit in

the following. This ratio precisely expresses the

gain (or loss) in performance one has to expect

if the dynamic scheme is applied instead of a

static one for the corresponding scenario. Hence,

this ratio is the result of investing into a certain

additional computational power at the access point

and at the terminal.

B. Simulation parameterization

We consider the following simulation scenario.

We choose a system with a bandwidth equivalent

to IEEE 802.11a [7, 11], thus the available band-

width is B = 16.25 MHz, which is split into 52

sub-carriers, each with a bandwidth of 312.5 kHz,

from which S = 48 sub-carriers are available

for data transmission. Corresponding to this, each

OFDM symbol has a length of Ts= 4 µs, from

which Tg = 0.8 µs belong to the guard interval.

As center frequency we choose a channel from the

U-NII lower band, located at 5.2 GHz.

The sub-carrier states change constantly due

to the movement of the terminals and the multi-

path propagation environment. Wireless terminals

move within the cell with a random velocity,

initially the maximum speed is given by vmax=

1 m/s. The considered cell has a radius of R =

100 m. The effects influencing the sub-carrier

attenuation states are path loss, shadowing and

fading. Path loss is determined by the formula

P0

Ptx

= K ·

between received and transmitted power, d denotes

the distance between transmitter and receiver, K

denotes the reference loss for the distance unit

d is measured in and α is the path loss ex-

ponent. We parameterize the reference loss with

10 log(K) = 46.7 dB and the path loss exponent

with α = 2.4. The shadowing is assumed to be

log-normal distributed with a standard deviation

of σ = 5.8 dB and a mean of 0 dB while

no correlational behavior was incorporated in the

model. For the fading the power spectral density

is chosen to have a Jakes-like shape [9] with a

Doppler frequency depending on vmax. The multi-

path propagation environment is characterized by

a delay spread, initially set to ∆σ = 0.15 µs,

with an exponential power delay profile according

to the large open space model of ETSI C [12].

An example environment corresponding to such a

setting would be a large airport or exposition hall.

We set the frame length to Tf = 2 ms which

corresponds to the frame length of HIPERLAN/2

systems [13]. The uplink is not considered any

further; the time reserved for Tu equals 1 ms,

which leaves a time span of 1 ms for the downlink

and signaling phase. We consider a maximum of

J = 48 terminals to be within the cell. Since

five modulation types have to be considered in the

signaling also, a total of ?log248?+?log25? = 6+

3 = 9 bits has to be transmitted as pure signaling

information per sub-carrier. Together with a 12

Bit CRC code and a (498,444,13)-BCH code, the

length of the whole signaling field results finally

in 498 bits. Using all sub-carriers for conveying

this information with a BPSK modulation type

results in the usage of 11 OFDM symbols for

the transmission. Considering the frame delimiters

and the synchronizationfield results in the require-

ment of 19 OFDM symbols or a time length of

Tsig = 0.076 ms for the complete initial phase.

The remaining 0.924 ms are spent on the downlink

phase.

If a bit error occurs within the signaling data

and cannot be corrected by FEC, the terminal has

1

dα , where

P0

Ptxdenotes the ratio

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to discard all data transmitted to it during the

following downlink phase. Then, it has to indicate

the loss of the data during the uplink phase while

also passing the measured attenuation values of

the sub-carriers to the access point (assuming that

each terminal has a slot during the uplink phase).

Therefore, it simply waits for the next frame to

continue the reception of data.

For illustration purposes, each terminal is al-

located the same amount of sub-carriers, which

corresponds to the ratioS

whereS

number of sub-carrier could be distributed un-

equally such that over a larger time span (multiple

frame times) all terminals receive the same num-

ber of sub-carriers. Such a scheme would yield

the data points in the case of 20 or 5 terminals

in the cell. However, in a running system also

different policies could be implemented using an

allocation algorithm which determines the amount

of sub-carriers each terminal receives, for example

according to the amount of data queued for each

terminal at the access point [14].

J. We only consider cases

Jresults in an integer number. If not, the

The noisepowerisassumed to equal

−117 dBm per sub-carrier. Initially the transmit

power is set to −7 dBm per sub-carrier, according

to the maximal allowed transmit power in the

U-NII lower band. From the attenuation values of

each sub-carrier, an instantaneous Signal to Noise

Ratio (SNR) is obtained. After the assignment

of sub-carriers a modulation type is chosen to

be employed during the downlink phase. As

maximum acceptable symbol error probability we

choose the value 10−2. Depending on the SNR

of the sub-carrier, the modulation type with the

highest rate is chosen that still has a symbol error

probability lower than 10−2. These decisions

(sub-carrier and modulation) are then signaled to

each terminal, after which the downlink phase

starts. The data transmitted in the downlink phase

is grouped into packets with a size of 1 kByte.

Error coding in form of BCH block codes protects

the transmission of data in the downlink. For this

a (711,631,17) code has been chosen, which has

been selected according to the maximum symbol

error probability and a target bit error probability

of 10−5.

C. Results

All results are obtained via simulation. We

simulated the movement of all wireless termi-

nals within the cell for 300 s. During this time

span the terminals moved in the cell following

a rather simple movement pattern [10]. Every

2 ms samples for each sub-carrier attenuation

were generated regarding each wireless terminal,

providing a significant oversampling (depending

on the maximum speed of the terminals) of each

sub-carrier during the down-link phase of a frame.

Due to space limitations not all investigated

parameters of the study can be presented here. For

the complete study and further information refer

to [10]. Out of the study, four parameter variations

of the presented system setup are going to be

presented in the following. First, we varied the

number of terminals in the system. Next, we varied

the transmit power per sub-carrier. Finally, we

varied two parameters influencing the correlational

behavior of the fading: the delay spread and the

maximum speed of objects, both related to the

propagation environment of the wireless cell.

1) Variation of the number of terminals: First

we present results where the number of wireless

terminals in the cell varies between 1 and 48. The

maximum speed was set to vmax= 1 m/s while

the delay spread was ∆σ = 0.15 µs. The transmit

power equaled −7 dBm per sub-carrier.

In Figure 5 the absolute throughput per terminal

is shown for a varying number of terminals in

the cell for the ideal scenario (dynamic and static

scheme). The higher the number of terminals is,

the lower is the throughput per terminal. Between

the performance of the static and dynamic scheme

is a varying gap. Note that this general behavior

is the same for the remaining absolute throughput

and goodput curve pairs for all scenarios.2Conse-

quently, we only discuss the ratios between each

curve pair in the following.

Figure 6 shows the ratio of the dynamic versus

the static scheme for all three scenarios. In gen-

eral, the throughput ratio increases for a higher

number of terminals in the system due to an

increase in diversity that can only be exploited

by the dynamic mechanisms (multi-user diversity).

2For all presented absolute plots the 0.95-confidence inter-

vals have been removed, due to their very small size compared

to the curve behaviors.

Page 8

0

Number of Terminals in the Cell

Absolute Throughput per Terminal [MBit/s]

12

10

8

6

4

2

45 40 35 30 25 20 15 10 5

Dynamic

Static

Fig. 5.

scenario for a varying number of terminals in the cell

Average absolute throughput in the case of the ideal

Throughput Ratio

Number of Terminals in the Cell

Half Realistic

Realistic

Ideal

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

5 10 15 20 25 30 35 40 45

Fig. 6.

terminals in the cell

Average throughput ratio for a varying number of

For about 16 or more terminals, dynamic schemes

outperform static schemes by about 50 %, even

when taking signaling cost into account. Com-

pared to the ratio of the ideal scenario, the other

two ratios are slightly smaller, reduced absolutely

by 0.04. This offset is clearly due to the addi-

tional signaling cost that is taken into account

for these scenarios. Furthermore, the half-realistic

scenario and the realistic scenario do not differ

in the ratios. Therefore, using actual or slightly

outdated channel knowledge does not change the

throughput performance of the schemes. Note that

by using outdated channel knowledge the statistics

of the channel do not change, therefore throughput

should indeed not change, in contrast to goodput.

In Figure 7 the ratios are given for the good-

put. Comparing this with the behavior of the

throughput ratios the general behavior is the same:

Number of Terminals in the Cell

Goodput Ratio

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

5 10 15 20 25 30 35 40 45

Half Realistic

Realistic

Ideal

Fig. 7.

terminals in the cell

Average goodput ratio for a varying number of

The higher the number of terminals in the cell,

the higher is the ratio. However, while for the

throughput the ideal scenario has the highest ratio,

in the case of the goodput the realistic scenario

does achieve the highest ratio. Therefore, in this

case the dynamic scheme outperforms the static

scheme even more, almost doubling the goodput in

a highly loaded cell. Note that in terms of absolute

goodput (not shown here) the dynamic scheme in

the realistic scenario evidently has a lower good-

put than in the ideal scenario (differing by at most

30%). But also the goodput of the static scheme

is reduced for the realistic scenario compared to

the ideal scenario. Since the goodput of the static

scheme suffers more from the condition of using

realistic channel knowledge than the goodput of

the dynamic scheme, the ratio between dynamic

and static increases stronger than in the case of

the ideal scenario.

Why does the goodput of the static scheme

with adaptive modulation suffer more in the case

of realistic channel knowledge than the dynamic

scheme with adaptive modulation? Two possi-

ble reasons were further investigated. One reason

could be that the probability of overestimating a

certain modulation type is higher in the static case

than in the dynamic case. A second reason could

be that the average overestimation error for each

modulation type is higher for the static scheme

than for the dynamic scheme.

Out of these two reasons, the first one has no

effect. For all modulation types beside BPSK the

probability of an overestimation is higher for the

Page 9

0.3

0.25

0.2

0.15

0.1

0.05

P(Assigned modulation type per subcarrier)

0

Dynamic

Static

N/ABPSKQPSK16QAM64QAM 256QAM

Fig. 8.

modulation type (average for 16 terminals in the cell, a transmit

power of −7 dBm per sub-carrier and low maximum speed

within the environment of 1 m/s)

Probability of assigning a sub-carrier with a specific

dynamic scheme than the static scheme (figure

not shown here). However, the main source of

bit errors that cannot be corrected by the error

coding is the average overestimation error of the

modulation types.

Consider first the probability of scheduling a

certain modulation type: According to Figure 8,

for 16 terminals in the cell on average the static

scheme assigns a sub-carrier with BPSK or with

QPSK with a probability of 0.46 while assign-

ing a sub-carrier with a 16-, 64- or 256-QAM

modulation type has a probability of 0.41 (in the

remaining cases no data is scheduled on the sub-

carrier due to a too bad SNR, even for BPSK). In

contrast, the dynamic scheme assigns a sub-carrier

with BPSK or with QPSK only with a probability

of 0.29 while assigning a sub-carrier with a QAM

modulation type has a probability of 0.7 (almost

never is a sub-carrier scheduled with a very bad

SNR). Higher modulation types (the QAM types)

are therefore much more often utilized in the case

of the dynamic scheme, lower modulation types

(the phase shift keying modulation types) are uti-

lized much more often by the static scheme. This

directly explains the difference in the throughput.

Now consider the average overestimation error

at a maximum speed of 1 m/s, shown in Fig-

ure 19. It is higher for both schemes for lower

modulation types. Therefore, a higher number of

symbols is erroneous in the case of the static

scheme (Figure 19) overall. In addition, a single

symbol error has a higher impact on the bit error

Transmission Power [dBm]

2.5

3

2

1.5

1

0.5

0

−14 −12 −16−10−2 0 2−6 −4 −8

Absolute Throughput per Terminal [MBit/s]

Dynamic

Static

Fig. 9.

the ideal scenario for a varying transmit power

Average absolute throughput behavior in the case of

probability for lower modulation types than for

higher ones, if the overestimation is not too high

(as long as the SNR is not very low for each

modulation type, most symbol errors map into a

single bit error, assuming the usage of Gray codes

for coding adjacent symbols [8, page 273]).

We conclude from this, that as long as the aver-

age estimation error is not too high, the probability

of overestimating a certain modulation type does

not have a significant impact (as the caused bit

errors can be corrected by the BCH codes). In

contrast, the average overestimation error together

with the probability of scheduling a certain mod-

ulation type is the major source for bit errors, that

remain in the bit stream after error correction. This

leads to the behavior of the goodput ratio in the

realistic case.

2) Variation of the transmit power: Next we

varied the transmission power in the cell where the

number of wireless terminals was fixed at J = 16.

The power (per sub-carrier) was varied between

−16 dBm and 3 dBm in steps of 1 dBm. The

maximum speed was still set to vmax = 1 m/s

while the delay spread was set to ∆σ = 0.15 µs.

In Figure 9 the absolute throughput per terminal

for the static and dynamic scheme is shown for the

ideal scenario. The higher the transmission power,

the higher is the throughput for both schemes; the

dynamic scheme outperforms the static one. Again

this general behavior also applies to all other curve

pairs of the scenarios as well as to the absolute

goodput behavior, such that we only discuss the

ratios next.

Page 10

1.2

1.3

1.4

1.5

1.6

1.7

1.8

−16

Transmission Power [dBm]

−14−12−10 −8−6 −4−2 0 2

1.9

Throughput Ratio

Ideal

Realistic

Half Realistic

Fig. 10. Average throughput ratio for a varying transmit power

per sub-carrier in the cell

In Figure 10 the throughput ratios are given for

varying transmission power. Clearly, the higher

the transmit power per sub-carrier, the smaller

is the throughput ratio. Note that for a higher

transmission power the average sub-carrier SNR is

higher in general. Therefore, a dynamic algorithm

will achieve only a smaller throughput advantage

over the static scheme, since choosing sub-carriers

with a state well above the average becomes less

and less likely (all sub-carriers are in a better

state due to the higher transmit power). Again

there is a difference between the ideal scenario’s

ratio and the ones of the half-realistic and realistic

scenario ratios, caused by the required signaling.

This has already been observed when varying

the number of terminals. The half-realistic and

realistic scenario have again the same ratio.

In Figure 11, the goodput ratio is given. Here

again the goodput ratios have the same behavior

as the throughput ratios (decreasing ratio for an

increasing transmit power). In this case it can be

seen that for a quite low transmit power the real-

istic scenario ratio is significantly higher than the

ratios of the ideal and the half-realistic scenarios.

The higher the transmit power is, though, the more

similar do all three ratios become.

3) Variation of the delay spread: For any prop-

agation environment the delay spread has a strong

impact on the frequency-selectivity of the fading

process (experienced in the time domain as ISI).

If the delay spread is high, the attenuation due

to fading is less correlated for two adjacent sub-

carriers. Over the course of all sub-carriers a

Transmission Power [dBm]

−14−12−16−10−2 0 2 −6 −4−8

Goodput Ratio

Realistic

Half Realistic

Ideal

2

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

2.3

2.2

2.1

Fig. 11.

per sub-carrier in the cell

Average goodput ratio for a varying transmit power

high delay spread leads to a higher frequency

diversity of the sub-carriers, the variability of the

attenuation values per sub-carrier is increased.

In order to study the impact of this higher

variability on the system metrics, we varied the

delay spread from 0.05 µs up to 0.3 µs in steps

of 0.05 µs. Note that these values are all much

smaller than the guard interval of 0.8 µs such that

the small change of the delay spread did not lead

to any consequences for the intersymbol interfer-

ence per sub-carrier. However, the variability of

the attenuation per terminal over all sub-carriers

did change. According to [9] the corresponding

coherence bandwidth changed from 3.1 MHz to

0.5 MHz (and therefore was still a lot higher than

the bandwidth of each single sub-carrier). For this

investigation the number of terminals in the cell

was chosen to be 16, the transmit power equaled

−7 dBm per sub-carrier. The maximum speed in

the environment was set to vmax= 1 m/s.

Figure 12 shows the absolute throughput behav-

ior for the static and dynamic scheme in the ideal

scenario. Clearly, with an increasing delay spread

we can observe an increasing throughput for the

dynamic scheme while the throughput of the static

scheme stays constant. The reason for this is that

the dynamic scheme can exploit the increasing

frequency diversity caused by the increasing delay

spread. In contrast, since the static scheme only

applies adaptive modulation but has no means

to choose from different sub-carriers, the static

scheme does not benefit from an increasing delay

spread.

Page 11

Absolute Throughput per Terminal [MBit/s]

Dynamic

Static

1.1

1

1.2

1.3

1.4

1.5

1.6

1.7

Delay Spread [ns]

300

250 200 150 100 50

Fig. 12.

the ideal scenario for a varying delay spread

Average absolute throughput behavior in the case of

Throughput Ratio

Delay Spread [ns]

300

250 200 150 100 50

1.4

1.45

1.5

1.55

1.6

Half Realistic

Realistic

Ideal

1.35

Fig. 13.

per sub-carrier in the cell

Average throughput ratio for a varying delay spread

Accordingly, the ratio of the throughput, shown

in Figure 13, increases roughly from 1.4 for the

smallest value of the delay spread, up to 1.6 for

the highest value of the delay spread. Including the

signaling cost reduces this figure by 0.04 while

the usage of realistic channel knowledge has no

significant effect on the throughput ratio.

However, the usage of realistic channel knowl-

edge has a significant effect on the goodput ratio,

as shown in Figure 14. The qualitative behavior

of the goodput ratio equals the behavior for the

throughput ratio. However, especially in the real-

istic channel knowledge case, the resulting ratio

is significantly higher than in the case with the

varying transmit power and the varying number

of terminals. The quantitative ratios vary between

1.5 and 1.9 for the goodput. The explanation

for this is again the average estimation error (as

Goodput Ratio

Delay Spread [ns]

300

250 200 150 100 50

Half Realistic

Realistic

Ideal

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

1.9

Fig. 14.

the propagation environment of the cell

Average goodput ratio for a varying delay spread in

shown in Figure 19). The throughput gain of the

dynamic scheme is achieved by scheduling higher

modulation types more often. These modulation

types have a lower average estimation error than

the lower ones. Thus, the goodput ratio increases

with an increasing delay spread. Note that the

absolute goodput decreases for each scheme as

realistic channel knowledge is included in the

investigation.

4) Variation of the maximum speed: At last,

we present an investigation where the maximum

speed of objects within the propagation environ-

ment was varied, from vmax = 1 m/s up to

vmax = 50 m/s. Note that a speed of vmax =

50 m/s would not match the propagation envi-

ronment any more, since nothing within a large

open space environment would have such a speed.

However, since the speed of the objects influences

the variability in time of the attenuation of the

sub-carriers, this high speed could correspond

to a different scenario, where the speed is only

increased modestly, but the length of a frame

is considerably increased. In this investigation,

though, the speed was varied while the frame

length was kept constant at Tf= 2 ms. Note that

the coherence time, resulting from the maximum

speed of the propagation environment and the

center frequency of the radio system [9], varies for

the chosen values from 12 ms down to 0.25 ms

for the highest speed. Thus, the coherence time of

the sub-carriers was longer than the frame length

for a speed larger than 6 m/s. The number of

wireless terminals was kept constant at 16, while

Page 12

Absolute Throughput per Terminal [MBit/s]

5 10 15 20 25 30 35 40 45 50

Maximum Terminal Speed [m/s]

1

Dynamic

Static

1.1

1

1.2

1.3

1.5

1.6

1.7

1.8

1.4

Fig. 15.

the ideal scenario for a varying maximum speed

Average absolute throughput behavior in the case of

the transmit power equaled −7 dBm per sub-

carrier. The delay spread was set to ∆σ = 0.15 µs.

In Figure 15 the absolute throughput behavior

is shown for the ideal scenario in the case of the

dynamic and static scheme. As the speed increases

in the system, the average throughput per terminal

for both schemes remains the same. Note that

with an increasing speed the statistics only change

in the time domain. This cannot be exploited by

this dynamic scheme; therefore, the throughput

stays constant (in contrast to the increasing delay

spread, where the dynamic scheme was able to

exploit the changed statistics in the frequency

domain).

In Figure 16 the corresponding ratios are shown

for all three scenarios. As it is with the ideal

scenario, the ratios stay constant roughly at a

value of 1.5 for the other two scenarios. Including

realistic channel knowledge leads to no effect

for the throughput ratio, including the signaling

impact leads to an absolute loss of 0.04 for both

ratios.

As we turn now to the results for the goodput,

the qualitative and quantitative behavior does not

match the throughput anymore, in contrast to the

previous parameter investigations. In Figure 17 we

first show the absolute goodput behavior for the

ideal scenario of the dynamic and static scheme.

As the speed increases, the goodput for both

schemes drops. Up to a speed of 10 m/s there is

still a significant performance difference between

the static and dynamic scheme, however for higher

speeds the goodput of the dynamic scheme drops

Throughput Ratio

5 10 15 20 25 30 35 40 45 50

Maximum Terminal Speed [m/s]

1

Half Realistic

Realistic

Ideal

1.48

1.49

1.5

1.51

1.52

1.53

1.54

1.55

Fig. 16.

speed in the cell

Average throughput ratio for a varying maximum

5 10 15 20 25 30 35 40 45 50

Maximum Terminal Speed [m/s]

1

Dynamic

Static

0

120

100

80

60

40

20

140

160

Absolute Goodput per Terminal [Packets/s]

Fig. 17.

the ideal scenario for a varying maximum speed

Average absolute goodput behavior in the case of

below the one of the static scheme. At these speeds

the absolute goodput is very low, less than 10

packets are correctly received by the terminal on

average for both schemes, the packet error rate

is therefore unacceptable high (for the dynamic

scheme on average 170 packets are transmitted

per second, for the static scheme on average 130

packets are transmitted).

Considering the ratio for this scenario, in Fig-

ure 18, we observe at first an increase of the

ratio up to a maximum ratio point for a speed

of 5 m/s, for a higher velocity the ratio drops

sharply. Interestingly, at very high speeds the ratio

is below 1 – the static scheme has a higher

goodput than the dynamic scheme. However, at

these speed values the absolute goodput is very

low (< 10 Pakets/s) in either case anyway.

Switching to realistic channel knowledge leads

Page 13

Goodput Ratio

5 10 15 20 25 30 35 40 45 50

Maximum Terminal Speed [m/s]

1

Half Realistic

Realistic

Ideal

0.4

0.6

0.8

1

1.2

1.6

1.4

1.8

2

2.2

Fig. 18. Average goodput ratio for a varying maximum speed

in the cell

Maximum Terminal Speed [m/s]

1

5

25

QPSK

BPSK

16QAM

64QAM

256QAM

0

1

2

3

4

6

5

Mean Overestimation Error [dB]

Dynamic

Static

Fig. 19.

each modulation type at three different maximum speeds

(1 m/s, 5 m/s and 25 m/s) of the terminals (16 terminals,

transmit power of −7 dBm per sub-carrier and a delay spread

of ∆σ = 0.15 µs)

Mean overestimation error (realistic scenario) for

to a much faster decrease of the ratio. Here, the

ratio peaks at a speed of 2 m/s, for a speed higher

than 6 m/s the ratio drops below 1 (at 6 m/s

the coherence time of the channel is 2 ms). For

this speed and higher ones, the absolute goodput

(graph not shown here) is very low, resulting again

in a very high packet error probability.

This behavior of the performance ratios can

be explained by the average estimation error in

case that the channel is overestimated for each

modulation type. For low speeds the estimation

error is higher for low modulation types in case

of the realistic channel knowledge (Figure 19). If

the speed increases now, and thus the variability

in time of the channel is increased, this imbal-

ance in the average estimation error is reversed.

First of all, for all modulation types the absolute

estimation error increases quite a lot from around

1.5 dB on average to 5 dB on average (Figure 19).

In addition, the absolute estimation error is now

as high for the high modulation types as it is for

the low modulation types, which leads to quite a

strong performance loss considering the goodput

for both schemes. Therefore, a more sophisticated

estimation algorithm should reduce the average

estimation error with a positive impact for the

goodput performance of both schemes.

V. CONCLUSIONS AND FUTURE WORK

This paper studied the question whether or not

it pays off to dynamically assign sub-carriers in

an OFDM system when the requirements of a

realistic system structure – costs for signaling and

outdated channel knowledge – are taken into ac-

count. We answer this question in the affirmative,

both for throughput and goodput.

In terms of throughput we find that consider-

ing realistic channel knowledge does not change

the throughput behavior of the static or dynamic

schemes at all. However, by introducing the sig-

naling system, the throughput of the dynamic

set up is slightly more reduced (versus the ideal

scenario’s values) while the one of the static

scheme is not so much reduced. This performance

reduction is moderate, though.

In terms of goodput the picture changes. While

the performance decreasing influence of the sig-

naling system is still present, we actually find

that the benefit of using dynamic sub-carrier as-

signments is significantly increased if realistic

channel knowledge is taken into consideration for

low speeds of the terminals. The more realistic

assumptions result in a bigger performance loss

for the static scheme than for the dynamic one.

The resulting improvement over the static scheme

is actually larger than with less realistic assump-

tions, making the case for dynamic sub-carrier

assignments even stronger. This effect becomes

significant for a high number of terminals in the

cell as well as for a low transmit power or for

a relatively high delay spread. However, as the

speed of the terminals increases, the goodput for

both schemes decreases drastically due to severe

estimation errors, calling for a more sophisticated

channel estimation scheme, if such a system is

Page 14

going to be applied in equivalent propagationenvi-

ronments. This area remains as an issue for future

work, together with analytical characterizations of

the issues raised in this paper.

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