Hopping for Multiuser OFDM
Lawrey, Cornelis Jan Kikkert
Electrical and Computer Engineering
James Cook University, Douglas Campus, Townsville, Queensland,
International Conference on Information, Communications
& Signal Processing,
ICICS’99, Singapore, 7-10 December, 1999,
Organised by the School of Electrical & Electronic
Engineering, Nanyang Technological University
This paper presents adaptive frequency hopping
as a new user allocation scheme for multiuser OFDM. Users
are allocated carriers that have the highest SNR of available
system carriers. This process is updated regularly to track
channel fading. Adaptive frequency hopping greatly reduces
frequency selective fading, improves interference rejection,
and consequently improves the received SNR. Additionally Doppler
spread is minimised due to the avoidance of nulls in the spectrum.
These effects improve the system capacity and user access
reliability. Improvements in system capacity out weigh the
overhead required for implementation of adaptive frequency
hopping for applications that have a user data rate of greater
than 20 kbps at 100 km/hr and 5 kbps for fixed transmissions.
Multiuser OFDM is a promising new modulation
technique for wireless communications . It includes many
of the advantages of broadcast OFDM that is used for Digital
Audio Broadcasting (DAB)  and for Digital Video Broadcasting
(DVB) in Europe and Australia. OFDM was selected for these
systems primarily because of its high spectral efficiency
and multipath tolerance.
In a multiuser OFDM system, data is transmitted
as a set of parallel low bandwidth (1 kHz - 50 kHz) carriers.
The frequency spacing between these carriers is chosen to
be the reciprocal of the useful symbol period. The resulting
carriers are orthogonal to each other at the receiver provided
correct time windowing is used. Transmitted carriers are independent
of each other even though their spectra overlap. OFDM signals
can be easily generated and received using a Fast Fourier
Transform (FFT). For a multiuser OFDM system each user is
allocated a fraction of the system carriers.
Wahlqvist  presented one implementation
of a multiuser OFDM system. A user allocation scheme using
random frequency hopping scheme was presented. This paper
presents a new user carrier allocation scheme where each user
is allocated carriers that have the highest Signal to Noise
Ratio (SNR). Adaptive frequency hopping involves characterising
the radio channels of each link, and allocating carriers appropriately.
2 User allocation
There are several methods for allocating
carriers to users in a multiuser OFDM system. The main four
schemes are to use a group of carriers with a fixed frequency,
randomly hopped group of carriers, spread out carriers in
a comb pattern and adaptive frequency hopping.
Due to the overlapping nature of OFDM any
loss of orthogonality can result in high levels of inter-carrier
interference. Frequency and time synchronisation errors result
in loss of orthogonality between carriers. A frequency offset
error of 1-2% of the carrier spacing results a carrier power
to interference ratio of 20dB. In the forward link all
user carriers are transmitted from the base station, and thus
all carriers can be transmitted with perfect frequency and
time synchronisation with respect to each other.However in
the reverse link, carriers from each user are transmitted
from different sources, leading to possible inter-user interference.
Distortion products can result in inter-user interference,
particularly if the received power from one user is significantly
larger than neighbouring user carriers.
2.1 Fixed frequency grouped carriers
The simplest user carrier allocation scheme
is to assign each user a group of fixed frequency carriers.
Grouping the carriers minimises inter-user interference due
to distortion, power level variation and frequency errors.
However, having a fixed group of carriers makes the transmission
susceptible to fading, as the whole group of carriers can
be lost in a null in the spectrum. Time interleaving with
forward error correction can improve fading performance of
a moving station. However for stationary applications, static
nulls can greatly degrade performance.
2.2 Grouped carriers with random frequency hopping
The problem of static fading can be partly
overcome by randomly frequency hopping the carriers. In the
user allocation scheme described by , groups of carriers
are transmitted in short time blocks. These blocks are randomly
frequency hopped to ensure that the time period spent in a
null would is relatively short, approximately 11 symbols.
To recover data lost during a null, time interleaving and
forward error correction is used. These come at the cost of
reduced system data capacity and increased delay.
2.3 Comb Spread Carriers
Static nulls can occur for fixed wireless
applications causing problems if the transmission uses a single
group of carriers with a fixed frequency. Instead carriers
can be allocated in a fixed comb pattern, spreading them over
the entire system bandwidth. This improves the frequency diversity,
preventing all the carriers used by a user being lost in a
single null in the spectrum.
Using a comb pattern reduces the probability
that all carriers will be lost in a null, however it increases
the chance that some of the carriers will be in a null due
to the increased frequency span of the carrier comb pattern.
It is therefore essential that forward error correction be
used in order to recover data lost in null carriers.
Additionally this allocation scheme may
be susceptible to inter-user interference due to the overlapping
nature of OFDM carriers. Transmitting as a comb pattern requires
user carriers to be interleaved with one another, resulting
in a large amount of overlapping energy between the users.
Any slight loss of orthogonality due to frequency or timing
errors can result in significant inter-user interference.
By comparison grouping the user carriers reduces the energy
overlap between users, thus reducing inter-user interference.
Despite these problems this type of user allocation is useful
in applications that can not use adaptive hopping or random
hopping, due to the added complexity.
2.4 Adaptive Frequency Hopping
A new adaptive frequency hopping technique
is proposed for multiuser OFDM such that blocks of carriers
are hopped based on the current channel conditions. After
the radio channel has been characterised each user is allocated
carriers which have the highest SNR ratio for that user. Since
each user will be in a different location the fading pattern
will be different for each remote station. The strongest carriers
for one user are likely to be different from other users.
Thus most users can be allocated carriers with a high SNR,
allowing the entire system bandwidth to be used without any
All users must be frequency and time synchronised
to each other in order to use this technique. This technique
is suited to low velocity applications that suffer from frequency
selective fading, and those that have a moderate user data
Two implementations of AFH are presented,
single group AFH and multi-group AFH. With single group AFH
all user carriers are allocated as a single group of consecutive
carriers. With multi-group AFH carriers are allocated in independent
small blocks (2-10) of carriers.
3 Advantages of Adaptive Frequency Hopping
3.1 Frequency Selective Fading Minimisation
Adaptive frequency hopping achieves large
performance gains by avoiding nulls in the channel frequency
response caused by frequency selective fading. Provided that
the system bandwidth is significantly greater than the coherence
bandwidth of the channel, there is a high probability that
there will be at least one peak in the frequency response
of the channel available to the user. The larger the system
bandwidth the more chance there is of finding a group of carriers
with a high SNR.
Figure 1. Single user Adaptive Frequency
Hopping Note: The bright regions are the strongest received
Figure 2. Received power verses distance
travelled for Adaptive Frequency Hopping and for a fixed frequency
Figures 1 and 2 show results for a single
user adaptive frequency hopping system. The radio channel
model used for this experiment was measured for a link between
two rooms in the Electrical and Computer Engineering building
at JCU. The transmitter and receiver were spaced 24 m apart.
This radio link is short resulting in a large coherence bandwidth.
As a result a large system bandwidth was used. These measurements
were obtained using a sweeping tone transmitter and a spectrum
analyser as the receiver. The receiver was moved along a guide
tack after each frequency response measurement was made.
Figure 1 shows simulated adaptive frequency
hopping for the measured radio channel. For this experiment
the bandwidth allocated to the user was 5 % of the system
bandwidth and 50 % of the channel coherence bandwidth. The
frequency allocations used for AFH were updated every 2cm.
It was assumed that the time required for updating the frequency
re-allocations was negligible. This is a reasonable assumption
for systems where the AFH overhead is low. The frequency groups
used are shown as an outline.
Figure 2 shows for the same measured channel,
the received power verses the distance travelled. The received
power for the worst user carrier at each point in space is
shown. The adaptive hopping receiver suffers much less fading
and has a much greater average power level than when no hopping
is used. A comb user allocation pattern results in a high
probability of at least one of the carriers being in a null,
thus giving a poor performance.
Effect of User Bandwidth
Increasing the user bandwidth increases
the chance that some of the carriers being used will be in
a null. Figure 3 shows the effect of increasing the user bandwidth
while having a fixed system bandwidth. The results were obtained
using the measured data shown in figure 1. At a low user bandwidth
both single and multi group AFH perform the same. This is
because the user bandwidth is much lower than the coherence
bandwidth of the radio channel. As the user bandwidth increases
the effectiveness of single group AFH falls off significantly,
due to the user carriers spaning a bandwidth approaching or
greater than the coherence bandwidth of the channel. Since
the carriers are allocated as a single group, carriers at
the edges of the group will tend to be in a null. Multi-group
AFH doesn’t suffer the same problems as user bandwidth is
Figure 3. Average (with respect to distance)
minimum user carrier power verses user bandwidth for a fixed
When no frequency hopping was used there
was a variation in the performance depending on the particular
centre frequency used. The error bars shown on figure 3 show
one standard deviation in the performance variation.
Multi-group AFH performs much better than
single group AFH when then user bandwidth approaches or exceeds
the channel coherence bandwidth.
Effect of System Bandwidth
The effect of changing the system bandwidth
is shown in figure 4. This plot shows the average (over distance)
minimum carrier power for a low bandwidth user as the system
bandwidth is increased. Both single and multi group AFH perform
similarly as the user bandwidth is small. As the system bandwidth
is increased it improves the chance of finding stronger carriers,
thus the performance of AFH improves with an increase in the
system bandwidth. The system bandwidth has no effect of a
fixed group of carriers, as the system carriers are not used
as a resource. When using a comb pattern increasing the system
bandwidth spreads the carriers over a wider number of nulls
in the spectrum. This increases the chance of having at least
one carrier in a deep fade. However the average power for
a comb pattern would remain constant as the system bandwidth
Effect of AFH update rate
The frequency response of a radio channel
changes with movement of the transmitter or receiver. It is
therefore important that in any AFH system that it tracks
these changes in the channel. The more often the AFH is updated
the better the performance will be. However, the information
overhead required will be approximately proportional to the
update rate thus it is important minimise the update rate
without loosing the effectiveness of the AFH. Figure 5 shows
the effect of changing the hop update rate on performance
of AFH. The update rate has been specified as a distance.
The update rate can be calculated from the velocity of movement.
Figure 4. Average (with respect to distance)
minimum user carrier power verses system bandwidth
Figure 5 shows that increasing the distance
between updates of AFH decreases the performance as would
be expected. Using a hop distance of 7 cm results in about
1 dB loss in performance, 12 cm gives about a 2dB loss. Thus
a hop distance of less than one third the RF wavelength would
be sufficient (10 cm at 1GHz). The frequency hopping distance
will be proportional to the wavelength of the RF signal used.
Results shown here are for an RF frequency of 1GHz.
Performance improvement by AFH
The addition of the AFH reduces the fast
fading. This reduction in signal power variation allows the
fading margin used to be decreased when designing an RF link.
This allows the average transmission power to be reduced or
a higher modulation used with the same transmission power.
The results shown in figures 3-5 are distance
averaged minimum user carrier power. This measure smooths
out deep fades. However during deep fades data is nearly always
lost, thus the depth of the fade in not important. Forward
error correction must be used to recover this information.
However using AFH greatly reduces deep fading (as can be seen
in figure 2), reducing the need for forward error correction.
As less forward error correction is required, a higher user
data rate can be used.
AFH improves the average received power
by 6-8dB and reduces the worst case carrier fading by 15-25dB.
AFH allows the system capacity to be increased by reducing
the forward error correction required and allowing a higher
modulation to be used. The average power gain of 6-8dB allows
the modulation to be increased by 1 bits/Hz/sec, while the
reduced fading should allow the forward error correction to
be reduced by 50%. This will result in an overall system capacity
gain of 75-300%.
3.2 Doppler Spread Minimisation
An additional advantage of adaptive hopping
is that it reduces Doppler spread. Doppler spread causes frequency
spreading of the transmitted signal resulting in a reduction
in the orthogonality of the carriers for a multiuser OFDM
system. In a multipath channel, delayed reflected signals
will each have a different Doppler shift due to the direction
of the reflection. As the transmitter or receiver moves the
relative strength of the reflected components will change
resulting in a fast fluctuation of the Doppler shift. This
fluctuation is referred to as Doppler spread. It can be calculated
from the rate of change of the phase response of the radio
As a receiver passes through or near a null
in the spectrum, the signal will shift from one dominant multipath
component to another, resulting in a change in the Doppler
shift. The level of Doppler shift can become many times (>10)
greater than the average Doppler shift. In regions where the
signal is strong the Doppler shift is approximately constant
and equal to the average Doppler shift, thus resulting in
minimal Doppler spread. Using adaptive frequency hopping minimises
transmission near nulls and thus also minimises Doppler spread.
3.3 Interference Rejection
Adaptive frequency hopping will provide
strong interference rejection. Carriers that are interfered
with will have a low SNR, and thus will not be used for transmission.
Since the frequency hopping is regularly updated any changes
in frequency of the interferer will be compensated for very
quickly (<10ms). Interference rejection will be limited
by the overlapping nature of the carriers in multiuser OFDM.
An interferer who is one carrier spacing away will only be
attenuated by 13 dB. After ten carrier spacings the attenuation
will only be 28dB.
4 Overhead Requirements for Adaptive frequency hopping
4.1 Adaptive Frequency Hopping Update Rate
In a multipath environment the frequency
response of the radio channel will change significantly in
half a wavelength as can be seen in figure 1. For a 1 GHz
transmission it is therefore important that the frequency
update rate is faster than every 15 cm moved. The faster the
frequency hopping is updated the better the performance. Updating
faster than 0.1 x wavelength only gives minimal further improvements.
Typically an update distance of 10 cm is sufficient for a
1 GHz transmission. At a velocity of 60 km/Hr this results
in a required update rate of 160 times per sec.
4.2 Information Overhead
Full Duplex System
Most two-way communication systems use a
full duplex transmission, in which the forward and reverse
links use a different transmission frequency. In order to
implement an AFH system for this type of system each of the
forward and reverse links must be characterised before frequency
allocations can be made. The number of radio channels that
must be characterised is 2N, where N is the number of users.
In a multiuser OFDM system each link can be characterised
by transmitting a reference symbol in which the transmitted
data is known. The receiver can then compare the received
signal with the ideal signal allowing the phase and amplitude
noise of each carrier to be measured, and consequently an
estimate of the carrier SNR. The number of reference symbols
that must be transmitted is N+1, i.e. one from the base station
in the forward link and one from each user. Transmitting a
comb pattern of pilot carriers can reduce the number of reference
symbols required. Multiple users can transmit interleaved
comb pilot carriers, allowing the reverse link of up to 20
users to be characterised per reference symbol. This reduces
the number of reference symbols to N/M+1 where M is the number
of carriers between pilot carriers in the comb pattern.
Table 1. Information overhead required for
implementation of AFH.
Table 1. shows an estimate of the information
overhead that would be required for implementing AFH in difference
applications. AFH is less suitable for applications where
the user data rate is low and the velocity is high as can
be seen by the large overhead required for the mobile phone
application. This level of overhead outweighs the benefits
obtained by using AFH. However in high data rate applications
the overhead can be very low.
Half Duplex System
For systems that have a lower user data
rate the overhead can be reduced by using a time division
half-duplex system. In such a system both the forward and
reverse links use the same frequency, and two way communication
is achieved by time interleaving the forward and reverse channel
transmissions. A single reference symbol transmitted by the
base station is received by all remote stations, allowing
characterisation of all forward links. Due to the reciprocal
nature of radio channels the transfer function of the reverse
link will be the same as the forward link. The number of reference
symbols needed is reduced from N/M+1 to only 1. Although the
number of reference symbols need is reduced to one the number
of frequency re-allocations will still be proportional to
the number of users. Using a half duplex system reduces the
overhead by 2-3 times.
5 Multiple User Adaptive Frequency Hopping
When there are multiple users, each will
have a different frequency selective fading pattern. As each
user is allocated carriers, the number available to other
users will be diminished. This will start to prevent users
from being allocated the strongest carriers. If the base station
has complete knowledge of all links then an optimal combination
of carrier allocations could be made. However the information
overhead in obtaining the complete knowledge could outweigh
the performance gains. It is therefore important to establish
the minimum amount of information needed by the base station
in order to make suitable carrier allocations. Further work
is to be done on this area to resolve some of these issues.
Adaptive frequency hopping for multiuser
OFDM has been presented and shown to be a powerful technique
for reducing the effects of frequency selective fading. Fading
in a multipath channel can be reduced from typically 25 dB
to less than 7 dB, improving the received power by up to 18
dB. This gain in received power can be used to double the
system capacity and provide an additional 6dB link margin.
For full duplex mobile systems with velocities up to 60 km/hr,
the overhead required to implement adaptive frequency hopping
can be kept low (15-25%), provided the user data rate is moderately
high (>100 kbps). The amount of overhead can be reduced by
2-3 times by using a half-duplex system where the transmission
and reception use the same frequency band. For fixed wireless
systems the overheads for adaptive frequency hopping would
be minimal. This paper has presented a new user allocation
technique for multiuser OFDM that will enhance system performance.
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