A study of impact of inband signalling and realistic channel knowledge for an example dynamic OFDMFDMA system.
ABSTRACT Dynamically assigning subcarriers of orthogonal frequency division multiplexing (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 subcarrier 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 subcarriers. In this paper, a specific MAC structure is selected enabling the operation of a dynamic OFDM system, incorporating a signalling scheme for dynamically assigned subcarriers. Based on this structure, we study the overhead required for a dynamic subcarrier scheme; a static variant that serves as a comparison case. We investigate the performance difference of these two schemes for various scenarios where at first signalling 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 subcarrier, 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 favours in all cases except for higher speeds the dynamic rather than the static scheme especially in realistic system environments. Copyright © 2005 AEIT.

Conference Paper: Enhanced IEEE 802.11 by integrating multiuser dynamic OFDMA
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ABSTRACT: In this paper, we discuss the problems associated with the present contention resolution mechanism of IEEE 802.11 DCF and present a new, dynamic and robust approach to improve it. Our new MAC, using OFDMA in the physical layer, can incorporate multiple concurrent transmissions or receptions in a dynamic manner and can adjust the collision probability based on the traffic load when nodes are endowed with a single halfduplex radio only. Simulation results show that our system improves throughput by up to 40 percent, reduces collision in control messages by up to 80 percent and reduces the average delay for data transmission by up to 20 percent.Wireless Telecommunications Symposium (WTS), 2010; 05/2010  SourceAvailable from: James Gross
Article: Scheduling of heterogeneous data streams in the downlink of a dynamic OFDMFDMA wireless cell
 SourceAvailable from: Stefan Valentin
Conference Paper: Integrating Multiuser Dynamic OFDMA into IEEE 802.11 WLANs  LLC/MAC Extensions and System Performance
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ABSTRACT: Multiuser dynamic OFDMA for the downlink has been extensively studied, specifically, in terms of fast closeto optimal subcarrier allocation heuristics and the efficient representation of signaling information. Although these functions provide the fundament of dynamic OFDMA, a complete multiuser OFDMA system requires more functionality. Focusing on WLAN systems, we discuss such additional functionality required for enabling the IEEE 802.11 link and Medium Access Control (MAC) sublayer to leverage OFDMA advantages. We identify necessary extensions, study the resulting overhead, and introduce a lightweight design for a complete dynamic OFDMA IEEE 802.11a system. Studying its performance shows that with our lightweight integration dynamic OFDMA can improve IEEE 820.11a UDP throughput by up to 154% and UDP latency by up to 63% even if the full overhead is taken into account.Communications, 2008. ICC '08. IEEE International Conference on; 06/2008
Page 1
A study of impact of inband signaling and
realistic channel knowledge for an
example dynamic OFDMFDMA system
James Gross, Stefan Valentin, Holger Karl, Adam Wolisz
TU Berlin
Einsteinufer 25, 10587 Berlin, Germany
{grossvalentinwolisz}@tkn.tuberlin.de, hkarl@ieee.org
fon: +49.30.31423830, fax: +49.30.31423818
Abstract—Dynamically assigning subcarriers 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 subcarriers.
In this paper, a specific MAC structure is selected
enabling the operation of a dynamic OFDM system,
incorporating a signaling scheme for dynamically
assigned subcarriers. 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 subcarrier, 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 subcarriers 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 multiuser communication scenarios: First, for
a given subcarrier, its attenuation values with
respect to different subcarriers are statistically
independent random variables. Second, the at
tenuation of subcarriers changes over time and
frequency as a consequence of terminal mobility
and the multipath propagationenvironment.Thus,
also regarding a single terminal, the attenuation
varies from subcarrier to subcarrier; dynami
cally assigning “good” subcarriers to terminals
promises to improve performance.
When evaluating this potential of dynamic
OFDMFDMA 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 subcarrier 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
Page 2
an existing outofband 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 subcarriers 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 subcarriers 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 subcarrier, 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 subcarriers. In order to
avoid Intercarrier Interference (ICI) of the over
lapping subcarriers, the used symbol length per
subcarrier and the frequency spacing of any two
adjacent subcarriers 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 subcarriers varies constantly due to path loss,
shadowing and fading. The attenuation differs for
multiple subcarriers regarding the same termi
nal; also the attenuation of the same subcarrier
varies regarding different terminals. The matrix
A(t) = (aj,s(t)) describes the attenuation values
of all S subcarriers regarding all J terminals.
Given the attenuation aj,s(t), the Signal to Noise
Ratio (SNR) xj,s(t) of subcarrier s with respect to
terminal j is given by Equation 1, where Ptx,s(t)
denotes the transmission power for subcarrier 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
subcarriers given to each terminal) and assign
(i.e. decide about which subcarriers are given to
each terminal according to the allocation) sub
carriers to terminals, based on information of all
subcarrier states regarding each terminal. Then,
Page 3
still prior to the downlink transmission itself, the
assignments of subcarriers 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 subcarrier states
and the subcarrier allocations for each terminal.
Based upon this input, aDA can generate quite
good subcarrier 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 subcarrier,
adaptive modulation is used with the following
modulation types: BPSK, QPSK, 16QAM, 64
QAM and 256QAM. During one downlink trans
mission the subcarrier 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 subcarrier’s
SNR. Transmission power is equally distributed
over all subcarriers; 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 subcarriers to wireless
terminals, depending on the subcarrier 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 subcarriers 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 subcarrier 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 subcarriers 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
Page 4
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
ofband 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 Subcarrier
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 Subcarrier Assignment Field (SAF)
a terminal will not receive data during this frame
and therefore will not be assigned a subcarrier.
The signaling field is always transmitted with the
same modulation type (BPSK) and is sent via all
available S subcarriers.
The signaling information itself is transmitted
with a fixed structure (Figure 3). For each frame
all S subcarriers are assigned a terminal and a
modulation type. This results in a pair of numbers
which have to be transmitted for each subcarrier:
The terminal’s address that has been assigned
this subcarrier and the modulation type to be
used for downlink transmission. This information
is transmitted pairwise for each subcarrier, 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 subcarriers. 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 subcarrier 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 subcarriers
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.
Page 5
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 subcarrier 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 subcarrier states in advance of each frame.
Obviously, this cannot be the case in reality. First,
the attenuation of subcarriers changes constantly
during one frame, depending on the fading rate
[8, 9]. Second, subcarrier 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 subcarriers. 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 subcarrier 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 subcarrier 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 subcarriers. Note that
we do not assume any sophisticated estimation
techniques to be present at the access point. The
subcarrier 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 subcarriers
(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
subcarrier 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 OFDMFDM 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
OFDMFDM 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 subcarrier states in advance of each frame.
For the second scenario we assume the signaling
Page 6
system to be present as described in Section III
B but the access point has still perfect channel
knowledge. This one is called the halfrealistic
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 subcarrier sets. Therefore, the
static scheme also depends on signaling as well as
channel knowledge acquisition, but the influence
of dynamically assigning subcarriers 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
subcarriers, each with a bandwidth of 312.5 kHz,
from which S = 48 subcarriers 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
UNII lower band, located at 5.2 GHz.
The subcarrier 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 subcarrier
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
lognormal 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 Jakeslike 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 subcarrier. 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 subcarriers 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
Page 7
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 subcarriers 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 subcarriers, which
corresponds to the ratioS
whereS
number of subcarrier could be distributed un
equally such that over a larger time span (multiple
frame times) all terminals receive the same num
ber of subcarriers. 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 subcarriers 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 subcarrier. Initially the transmit
power is set to −7 dBm per subcarrier, according
to the maximal allowed transmit power in the
UNII lower band. From the attenuation values of
each subcarrier, an instantaneous Signal to Noise
Ratio (SNR) is obtained. After the assignment
of subcarriers 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 subcarrier, the modulation type with the
highest rate is chosen that still has a symbol error
probability lower than 10−2. These decisions
(subcarrier 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 subcarrier attenuation
were generated regarding each wireless terminal,
providing a significant oversampling (depending
on the maximum speed of the terminals) of each
subcarrier during the downlink 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 subcarrier. 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 subcarrier.
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 (multiuser diversity).
2For all presented absolute plots the 0.95confidence 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 halfrealistic
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 subcarrier and low maximum speed
within the environment of 1 m/s)
Probability of assigning a subcarrier 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 subcarrier with BPSK or with
QPSK with a probability of 0.46 while assign
ing a subcarrier with a 16, 64 or 256QAM
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 subcarrier
with BPSK or with QPSK only with a probability
of 0.29 while assigning a subcarrier with a QAM
modulation type has a probability of 0.7 (almost
never is a subcarrier 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 subcarrier) 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 subcarrier in the cell
In Figure 10 the throughput ratios are given for
varying transmission power. Clearly, the higher
the transmit power per subcarrier, the smaller
is the throughput ratio. Note that for a higher
transmission power the average subcarrier SNR is
higher in general. Therefore, a dynamic algorithm
will achieve only a smaller throughput advantage
over the static scheme, since choosing subcarriers
with a state well above the average becomes less
and less likely (all subcarriers 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 halfrealistic and realistic
scenario ratios, caused by the required signaling.
This has already been observed when varying
the number of terminals. The halfrealistic 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 halfrealistic 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 frequencyselectivity 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 subcarriers 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 subcarrier in the cell
Average goodput ratio for a varying transmit power
high delay spread leads to a higher frequency
diversity of the subcarriers, the variability of the
attenuation values per subcarrier 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 subcarrier. However, the variability of
the attenuation per terminal over all subcarriers
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 subcarrier). For this
investigation the number of terminals in the cell
was chosen to be 16, the transmit power equaled
−7 dBm per subcarrier. 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 subcarriers, 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 subcarrier 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
subcarriers, 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 subcarriers 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 subcarrier 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 subcarriers 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 subcarrier 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 subcarrier
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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