I. J. Communications, Network and System Sciences. 2008; 1: 1-103
Published Online February 2008 in SciRes (http://www.SRPublishing.org/journal/ijcns/).
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
Adaptive Throughput Optimization in Downlink
Wireless OFDM System
Youssef FAKHRI1, Benayad NSIRI2, Driss ABOUTAJDINE1, Josep VIDAL3
1University Mohamed V-Agdal Faculty of Sciences, UFR Informatics and Telecommunication B.P. 1014 Rabat, Maroc.
2Faculty Ain Chok ,UFR Signal Processing ,University Hassan II, B.P. 5366 Casablanca, Maroc.
3University of Catalonia Dept. of Signal Theory and Communications Campus Nord,
Modul D5, C/ Jordi Girona 1-3, Espagne.
Abstract
This paper presents a scheduling scheme for packet transmission in OFDM wireless system with adaptive techniques.
The concept of efficient transmission capacity is introduced to make scheduling decisions based on channel conditions.
We present a mathematical technique for determining the optimum transmission rate, packet size, Forward Error
Correction and constellation size in wireless system that have multi-carriers for OFDM modulation in downlink
transmission. The throughput is defined as the number of bits per second correctly received. Trade-offs between the
throughput and the operation range are observed, and equations are derived for the optimal choice of the design
variables. These parameters are SNR dependent and can be adapted dynamically in response to the mobility of a
wireless data terminal. We also look at the joint optimization problem involving all the design parameters together. In
the low SNR region it is achieved by adapting the symbol rate so that the received SNR per symbol stays at some
preferred value. Finally, we give a characterization of the optimal parameter values as functions of received SNR
Simulation results are given to demonstrate efficiency of the scheme.
Keywords: Rate, Packet Lenght, FEC, Throughput, QoS, SISO-OFDM
1. Introduction
Orthogonal frequency division multiplexing (OFDM)
is a promising technique for the next generation of
wireless communication systems [1] [2]. OFDM divides
the available bandwidth into N orthogonal sub-channels.
By adding a cyclic prefix (CP) to each OFDM symbol,
the channel appears to be circular if the CP length is
longer than the channel length. Each sub-channel thus can
be modelled as a time-varying gain plus additive white
Gaussian noise (AWGN). Following the success of
cellular telephone services in the 1990s, the technical
community has turned its attention to data transmission.
Throughput is a key measure of the quality of a wireless
data link. It is defined as the number of information bits
received without error per second and we would naturally
like this quantity as to be high as possible. This paper
looks at the problem of optimizing throughput for a
packet based wireless data transmission scheme from a
general point of view. The purpose of this work is to
show the very nature of throughput and how it can be
maximized by observing its response to certain changing
parameters. There has been little previous work on the
topic of optimizing throughput in general. Some things
that have been investigated include choosing an optimal
power level to maximize throughput [4][5]. Maximizing
throughput in a direct sequence spread spectrum network
by way of a link layer protocol termed the Transmission
Parameter Selection Algorithm (TPSA) has also been
discussed [3]. This provides real time distributed control
of transmission parameters such as power level, data rate,
and forward error correction rate. An analysis of
throughput as a function of the data rate in a CDMA
system has also been presented [6]. Most of the previous
work found has taken a very specific look at throughput
in different wireless voice systems such as TDMA,
CDMA, GSM, etc. by taking into account many different
system parameters in the analysis such as Parameter
Optimization of CDMA Data Systems [7]. We have taken
a more general look at throughput by considering its
definition for a packet-based scheme and how it can be
maximized based on the channel model being used.
Unlike most of the work done on this topic, our research
is focused on the transmission of data as opposed to that
of voice. Most of the work done on data throughput
analysis has been in wired networks (i.e. Ethernet,
SONET, etc.). Even in this work, however, the analysis is
mostly done with system specific parameters. Many

ADAPTIVE THROUGHPUT OPTIMIZATION IN DOWNLINK WIRELESS OFDM SYSTEM 11
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
variables affect the throughput of a wireless data system
including the packet size, the transmission rate, and the
number of overhead bits in each packet, the received
signal power, the received noise power spectral density,
the modulation technique, and the channel conditions.
From these variables, we can calculate other important
quantities such as the signal-to-noise ratio
γ
, the binary
error rate)(
γ
e
P, and the packet success rate)(
γ
f.
Throughput depends on all of these quantities. The rest of
this paper is organized as follows. In Section 2, our
system model is introduced. In Section 3 and 4, we derive
an optimal adaptation of individual design parameters in
constant and varying receiver power. In Section 5, we
conclude by describing future areas of research in multi-
user throughput optimization.
2. Problem Formulation
Consider a communication link which consists of a
transmitter, a receiver, and a communication channel with
bandwidth W. The transmitter constructs packets of K
bits and transmits the packets in a continuous stream. To
ensure that bits received in error are detected, the
transmitter attaches a C bit CRC to each data packet,
making the total packet length K + C = L bits. This packet
is then transmitted through the air and processed by the
receiver. The CRC decoder at the receiver is assumed to
be able to detect all the errors in the received packet. (In
practice some errors are not detectable, but this
probability is small for reasonable value of C and
reasonable SNRs.) Upon decoding the packet, the
receiver sends an acknowledgment, either positive (ACK)
or negative (NACK), back to the transmitter. For ease of
analysis we assume this feedback packet goes through a
separate control channel, and arrives at the transmitter
instantaneously and without error. If the CRC decoder
detects any error and issues a NACK, the transmitter uses
a selective repeat protocol to resend the packet. It repeats
the process until the packet is successfully delivered. A
packet is transmitted symbol by symbol through the
channel, where each MQAM symbol has b bits in it and is
modulated using fixed power MQAM. Thus, each packet
corresponds to L/b = Ls MQAM symbols. We assume
additive white Gaussian noise (AWGN) at the receiver
front end, and no interference from other signals. The
channel is narrowband (flat fading), so the power spectra
of both the received signal and the noise have no
frequency dependence, i.e., the channel is characterized
by a single path gain variable.
2.1. SISO-OFDM Systems
This is the conventional system that is used
everywhere. Assume that for a given channel, whose
bandwidth is B, and a given transmitter power of P the
signal at the receiver has an average signal-to-noise ratio
of SNR0. Then, an estimate for the Shannon limit on
channel capacity, Cp, is:
)1(log 02 SNRBC p
+
≈
(1)
It is clear from the formula that increasing the SNR,
the channel capacity only increases following a
logarithmic law (that is 1 more bit for a 3 dB increase of
SNR), and the SNR cannot be increased as much as
wished. This happens to be a big limitation, due to the
strict power regulations, to the achievable throughput in
wireless communication systems. In this paper we
consider an OFDM system with only one antenna at the
transmitter and the receiver, i.e., a Single-Input- Single-
Output (SISO) channel. A N-carriers modulation is
assumed, where:
)(tSk, 0 ≤ t < N. are the information symbols
transmitted during the tth time-block, the mean energy of
which is normalized:
E (|Sk(t)|2) = 1. and k is the carrier index. The OFDM
modulation technique is generated through the use of
complex signal processing approaches such as fast
Fourier transforms (FFTs) and inverse FFTs in the
transmitter and receiver sections of the radio. One of the
benefits of OFDM is its strength in fighting the adverse
effects of multipath propagation with respect to
intersymbol interference in a channel. OFDM is also
spectrally efficient because the channels are overlapped
and contiguous. The basic principle of OFDM is to split a
high-rate datastream into a number of lower rate streams
that are transmitted simultaneously over a number of
subcarriers. The relative amount of dispersion in time
caused by multipath delay spread is decreased because the
symbol duration increases for lower rate parallel
subcarriers. The other problem to solve is the intersymbol
interference, which is eliminated almost completely by
introducing a guard time in every OFDM symbol. This
means that in the guard time, the OFDM symbol is
cyclically extended to avoid intercarrier interference. An
OFDM signal is a sum of subcarriers that are individually
modulated by using phase shift keying (PSK) or
quadrature amplitude modulation (QAM). The symbol
can be written as:
• If ts ≤ t < ts +T
))))(
5.0
(2exp(Re()(
1
2
2
2
∑
−
=+−
+
−=
Ns
N
i
scNs
i
tt
T
i
fjdtS π
(2)
• else
S(t)=0 (3)
Ns is the number of subcarriers T is the symbol duration
fc is the carrier frequency.
The use of channel estimation is a very interesting

12 Y. FAKHRI ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
function to be added to the receiver to make the system
more resistant to fading and Doppler effects, over all, if it
is going to be used aboard of cars in a highway. Wireless
LAN is a very important application for OFDM and the
development of the standard promises to have not only a
big market but also application in many different
environments.
2.2. Throughput Analysis
The total throughput of the system, T, is the sum of the
individual throughputs of the sub-carriers i operating
simultaneously in the system.
Since we are considering a OFDM system with N sub-
carriers.
With the above simplifying assumptions, we define the
throughput of a system as the number of payload bits per
second received correctly [8],[9]:
)(**
1
ii
N
i
fR
L
CL
T
γ
∑
=
−
= (4)
where i R is the symbol rate assigned to sub-carriers i,
)( i f
γ
is the packet success rate (PSR) defined as the
probability of receiving a packet correctly, and i
γ
is the
SNR given by:
i
i
iRN
P
*
0
= γ (5)
where N0 the one-sided noise power spectral density, and
i
P the received power in sub-carriers i.
3. Throughput Optimization
3.1. Optimal Symbol Rate
To find the symbol rate is R that maximizes
throughput, we differentiate (4) with respect to is Rand
set it to zero to obtain the following condition.
i
i
idR
d
d
df
R
L
CL
f
L
CL
dR
dT
γ
γ
γ
γ
)(
)( − +
−
= (6)
))(
)(
)((2
0i
i
i
iRN
P
d
df
Rf
L
CL
dR
dT −
+
−
=
γ
γ
γ (7)
Next we set the derivative to zero
0
)(
)()(
0
=−
γ
γ
γ
d
df
RN
P
f
i
i (8)
γ
γ
γγ
d
df
f)( )( = (9)
We adopt the notation * γγ = for a signal to noise
ration that satisfies equation (9). Since any symbol error
in the packet results in a loss of the packet, the PSR f is
given in terms of the symbol error rate e
Pby:
b
L
e
Pf )](1[)(* γγ −= (10)
Combining these two, we arrive at an equation for
obtaining the preferred SNR per symbol*
γ :
bL
P
d
dP ee
/
)](1[)( *
*
*
γ
γ
γ
γγγ
−
−=
= (11)
where Pe of MQAM in AWGN channels is
(approximately) given by [8]:
)
12
3
()21(4)(2 γγ
−
−=−
b
b
eQP (12)
Once * γ is determined, the optimal symbol rate is
obtained from (5).
0
*
*
N
P
Ri
i
γ
= (13)
Note that the solution * γ in equations (10) and (11)
depends on only design parameters b and L, but is
independent of the received power level. In essence, the
adaptive system monitors
γ
, and upon deviation from its
internally preset value
γ
, changes its symbol rate such
that * γγ =. Figure 1 shows the spectral efficiency T/W
versus received SNR for different symbol rates. Where W
the bandwidth required for transmission of
)2(log2
b
b= information bits. We see that the system
can support high symbol rates at high SNR, but its
throughput rapidly decreases at a certain SNR value
below which the system should switch to a lower symbol
rate to maintain the optimal throughput. The optimal
curve is obtained by adapting Ri to keep
γ
=* γ .

ADAPTIVE THROUGHPUT OPTIMIZATION IN DOWNLINK WIRELESS OFDM SYSTEM 13
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
−10−50510 15 20 25 30
0
5
10
15
20
25
Received SNR(db)
Spectral efficiency(bps/Hz)
R=1MHz
R=500KHz
R=250KHz
R=125KHz
Optimal curve
Figure 1. Throughput vs SNR with variable R,L=100,b=2
and N=50
3.2. Optimal Packet Length
To find an analytic solution for the optimal packet
length L, we assume L to take continuous values.
Differentiating (4) with respect to L and using (10)
produce:
))(1ln()()1()(
2
γγγ
eii PfR
L
C
fR
L
C
dL
dT −−+= (15)
Setting this to zero produces a quadratic equation in L
with the positive root:
))(1ln(
4
2
1
2
2*
γ
e
P
bC
C
C
L− −+= (16)
Thus, the optimal packet length L depends on the
constellation size 2b, the SNR per symbol
γ
, and the
probability of symbol error Pe. Fortunately, we observe in
(4) that at high
γ
, 1)(
≈
γ
fand the throughput is
proportional to 1-C/L. Therefore, the throughput gain
becomes negligible if we increase L beyond a certain
point. In Rayleigh fading channels, * L is much smaller
and in fact asymptotically proportional to
γ .
Figure 2 shows the spectral efficiency of systems with
various packet lengths under a fixed symbol rate and
constellation size.
We see that large packet size gives high throughput at
high SNR, whereas small packet size gives a better
performance at low SNR. Thus, by adaptively changing
the packet length, we can achieve both higher throughput
and a wider operation range than using a fixed packet
length. However, this doesn’t necessarily mean that the
packet length should always be variable. For example, if
we adapt the symbol rate and the packet length
simultaneously, there is a single )(**
γ Lthat is optimal
regardless of the received SNR value, because the symbol
rate is adapted first to maintain* γγ =, eliminating the
effect of any SNR change. In this case, one degree of
adaptation (i.e., symbol rate) would be enough for the 2-
D optimization problem [11].
−10−50510 15 20 25 30
0
5
10
15
20
25
Received SNR (db)
Spectral efficiency (bps/Hz)
L=64
L=128
L=256
Optimal curve
Figure 2. Throughput vs SNR with variable L,R=1MHz,b=2
and N=50
3.3. Optimal Constellation Size
Constellation size 2b is another degree of freedom that
can be adapted to variations in received SNR, to allow
packing more bits per symbol when the channel gain is
high By differentiating (4) with respect to b and setting it
to zero, we obtain an equation for the optimal number of
bits per MQAM symbol b* as:
L
bP
db
bdPe
bb
e)],(1[),(*
*
γγ −
−=
= (17)
050100 150 200 250 300 350 400 450 500
0
10
20
30
40
50
60
70
80
Disance from transmitter[meters]
Spectral efficiency [bps/hz]
b=2
b=3
b=4
Optimal curve
Figure 3. Throughput vs Distance from transmitter with
variable b, L=64, R=1Msps

14 Y. FAKHRI ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
Figure 3 shows the spectral efficiency of systems with
various constellation sizes under fixed symbol rate and
packet length in AWGN channels. Higher level
modulations using MQAM mainly increase the
throughput at high low distance, but have shorter
communication ranges. By adapting the constellation size,
therefore, we can boost the throughput at low distance
while maintaining the same performance at high distance.
4. Throughput Optimization using Forward
Error Correction
4.1. Forward Error Correction Throughput
Equations
We will denote the number of information bits in the
packet as K, and the number of CRC bits as C. L is
defined as K+C. Now instead of transmitting those L bits
with no error correction capability, we will now add B
error correcting bits and transmit a total of L+B bits.
Using a block code forward error correction scheme, the
minimum number of bits B required to correct t errors is
given by [12]:
Bkt
k
n
BL
n
≤
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=∑
=
+
0
2
logmax (18)
Now that we can correct t errors, our packet success
rate, )(
γ
f should be larger than its previous value with
no error correction. Recall that )(
γ
f with t=0 is given
by:
b
L
ie
Pf )](1[)( γγ −= (19)
where )(
γ
e
P is the probability of a bit error as a
function of the SNR. Now, with error correction
capability, the packet success rate for some arbitrary
value of t is [13]:
()
nBL
ie
t
n
i
n
e
BL
n
PPf −+
=
+
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=∑)](1[ )(
0
γγγ (20)
Our new equation for the throughput as a function of
the signal to noise ratio is:
)(*
/
*0
1
it
i
N
i
f
NP
BL
CL
T γ
γ
∑
=+
−
= (21)
4.2. Optimum Error Correction
If we plot equation (21) for different values of t using
MQAM in AWGN channels we get a very interesting
result. Figure (4) shows the throughput for t=0, 20,
60,100. In each of these plots, P/N0 is fixed at 5*106 and
C at 16 bits, N=50, b=1. Perhaps the most important thing
to note in this graph is that there is an optimum value for t
at which higher values of t will not produce higher
throughput. From this graph the throughput appears to
reach an optimum value somewhere around t=20.
0 1 2 3 4 5 6 7 8 910
0
2
4
6
8
10
12
14
16
18 x 107
SNR(db)
Throughput[bits per second]
t=100
t=60
t=20
t=0
Figure 4. Throughput vs SNR (L=216,N=50)
5. Conclusion
Maximizing throughput in a wireless channel is a very
important aspect in the quality of a voice or data
transmission.
In this paper, we have shown that factors such as the
optimum packet length and optimum transmission rate are
all functions of the signal to noise ratio. These equations
can be used to find the optimum signal to noise ratio that
the system should be operated at to achieve the maximum
throughput. The key concept behind this research is that
for each particular channel (AWGN or Rayleigh) and
transmission scheme))((
γ
e
P, there exists a specific
value for the signal to noise ratio to maximize the
throughput. Once the probability of error, )(
γ
e
Pis
known, this optimal SNR value can be obtained. The
optimal values depend on the received signal strength. At
low SNR, the throughput is maximized by adapting the
symbol rate while using the smallest constellation size
and some fixed packet length. Finally, we have
characterized the optimal adaptation of the parameters in
AWGN under restrictions on the values that the
parameters can take. Our optimization framework is very
general and can be applied to any systems where the
combination of FEC, adaptive modulation, and packet
length can be adapted to maximize throughput. The
analysis and intuition in this paper, however, apply to
single user systems. Typical multi-user systems are
interference-limited and should be dealt with differently.
For example, schemes that enable orthogonal channel
sharing among users through frequency (variable symbol
rate), time (time division multiplexing), or code division

ADAPTIVE THROUGHPUT OPTIMIZATION IN DOWNLINK WIRELESS OFDM SYSTEM 15
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
(spread spectrum modulation) may have an advantage
over the other schemes (variable packet length and/or
adaptive FEC).
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