OFDM Techniques

OFDM Techniques
OFDM technology was developed from multi-carrier CDMA techniques. Although bulk research on
OFDM has not been seen until the late 1990s, a primitive concept of OFDM first appeared in the
open literature in the mid-1960s, and many discussions on OFDM can be found from the discussions
given in [585–593, 814].
The major difference between OFDM and traditional FDM lies in the fact that OFDM uses multiple
carriers that are orthogonal to one another, such that the frequency space between two neighboring
subcarriers is equal to
f, where
f = 1
Ts
and Ts is the symbol duration. Two of the most important  modules used in any OFDM system are the inverse fast fourier transform (IFFT) and fast fourier transform
(FFT) algorithms, the former used in transmitters and the latter used in receivers. We will show
later in this section that IFFT and FFT can be used to replace multi-carrier modulation/demodulation
units in a multi-carrier system.
When compared with FDMA, TDMA, and CDMA, OFDM represents a different system design
approach. It can be thought of as a combination of modulation and multiple access techniques, which
divide a communication channel in such a way that multiple users can share it without much mutual
interference. FDMA, TDMA, and CDMA schemes segment the channel according to times, frequencies,
and codes, respectively. OFDM also segments the channel according to the frequency/tone. In
more specific words, it divides the spectrum into a number of equally spaced tones and carries a
portion of a user’s information on each tone. A tone can be thought of as a frequency, much in the
same way that each key on a piano represents a unique frequency. OFDM can be viewed as a form
of FDM. However, OFDM has an important special property that each tone is orthogonal with every
other tone. FDM typically requires some frequency guard bands between the frequencies so that they
do not interfere with each other. OFDM allows the spectrum of each tone to overlap because they
are orthogonal, and thus they do not interfere with each other. By allowing the tones to overlap, the
overall amount of spectrum required is reduced, as shown in Figure 7.12.
OFDM is a unique modulation technique that enables user data to be modulated onto the tones.
The information is modulated onto a tone by adjusting the tone’s phase, amplitude, or both. In
the most basic form, a tone may be present or disabled to indicate a one or zero bit of information.
Either phase-shift keying (PSK) or QAM is typically employed. An OFDM system takes
a data stream and splits it into M parallel data streams, each at a rate 1/M of the original rate.
Each stream is then mapped to a tone at a unique frequency and combined together using the
IFFT to yield the time-domain waveform to be transmitted. For example, if a 100-tone system were
used, a single data stream with a rate of 1 Mbps would be converted into 100 streams of 10 kbps.
By creating slower parallel data streams, the bandwidth of the modulation symbol is effectively
decreased by a factor of 100, or equivalently, the duration of the modulation symbol is increased
by a factor of 100. Proper selection of system parameters, such as the number of tones and tone
spacing, can greatly reduce, or even eliminate, ISI, because typical multipath delay spread represents
a much smaller proportion of the lengthened symbol time. Viewed in another way, the acceptable
coherence bandwidth of the channel can be much smaller, because the symbol bandwidth has been
reduced. OFDM can also be considered as a multiple access technique, because an individual tone or
groups of tones can be assigned to different users. Multiple users share a given bandwidth in this
manner, yielding the system called OFDMA. Each user can be assigned a predetermined number
of tones, or alternatively a user can be assigned a variable number of tones based on the amount
of information that they have to send. The assignments are controlled by the MAC layer, which
schedules the resource assignments based on user demand.
OFDM can be combined with frequency hopping to create an SS system, realizing the benefits
of frequency diversity and interference averaging previously used in CDMA, as discussed in
Section 2.2.2. In a FHSS system, each user’s set of tones change after each time period (usually
corresponding to a modulation symbol). By switching frequencies after each symbol time, the losses
due to frequency-selective fading are minimized.
7.5.1 From Multicarrier System to OFDM
Let us consider a simple multi-carrier system with a transmitter and a receiver, as shown in Figure 7.13,
where M subcarriers {f1, f2, . . . , fM} are shown. Each subcarrier signal can be written as
sm(t) = xm(t)ej2πfmt = xm(t)ejωmt, (m= 0, 2, . . . , M − 1) (7.1)
where xm(t) is a complex data symbol in the m-th subcarrier branch. If the input data stream is first
cut into frames, each of which has a length of M symbols, we will have the output signal from this
simple multi-carrier transmitter as follows:
s(t) =
1
M
M−1
m=0
xm(t)ejωmt , (7.2)
where ωm = 2πfm,ωm = ω0 + m
ω(m = 0, 2, . . . , M − 1) and 1
M is the normalized factor. Of
course, we can also let xm(t) = am(t)ejφm(t), such that
s(t) =
1
M
M−1
m=0
am(t)ej [ωmt+φm(t)], (7.3) where am(t ), φm(t), and ωm are amplitude, initial phase shift, and carrier frequency of the m-th
subcarrier, respectively.
Now we sample the above equation in the time domain with a sampling frequency of 1

t to have
am(t) = am, φm(t) = φm and the output multi-carrier signal as
s(n
t) =
1
M
M−1
m=0
amejφmej2π(m
f )(n
t), (n= 1, 2, . . . , M − 1) (7.4)
where we have assumed the carrier frequency ω0 = 0, if only a baseband equivalent model is considered
here; otherwise a complex carrier term ejω0t should be multiplied to both the sides of (7.4).
On the other hand, the M-point inverse discrete fourier transform (IDFT) between a time domain
discrete signal f (n
t) and its frequency domain discrete signal representation F(m
f) is defined
by
f (n
t) =
1
M
M−1
m=0
F(m
f)ej 2πnm
M , (n= 1, 2, . . . , M − 1) (7.5)
which will be equal to (7.4) if and only if
f = 1
M
t . Under this condition,
f is the frequency
spacing between two consecutive subcarriers, M
t is the frame length, and
t is the symbol duration.
We also have s(n
t) = f (n
t) (which is a time-domain signal) and amejφm = F(m
f ) (which is
a frequency-domain signal). Also note that the IFFT algorithm is only a fast computation method
for the IDFT. Therefore, a multi-carrier transmitter can be effectively implemented by an IFFT unit
cascaded by a complex carrier modulator (if ωo = 0), as shown in Figure 7.14. A reverse process can
be used to show that a FFT algorithm can be used at an OFDM receiver to implement a multi-carrier
receiver, as shown in Figure 7.13.
A MC-CDMA system can thus be implemented by an OFDM architecture. Figure 7.14 shows
an OFDM system, which functions as a multiplexed time-spreading MC-CDMA system shown in
Figure 7.10. Similarly, we can use some other suitable OFDM structures to implement other MCCDMA
schemes, which have been discussed in the previous section.
One of the most attractive features of an OFDM system is that it can use more flexible and
powerful baseband digital technologies to replace otherwise rigid and complicated analog multiple
carrier modulation units in a multi-carrier system. FFT and IFFT can also be implemented readily
by software, and thus a digital signal processor in an OFDM system is enough to replace all those
analog circuitries in a multi-carrier scheme. The complexity of implementing these carrier oscillators
is formidable, especially if a large number of subcarriers is needed. However, nothing is free. The simplicity of the baseband digital processing algorithms in an
OFDM scheme also produces some problems pertaining to their unique characteristics, such as peakto-
average-power-ratio, and so on, which will be discussed in the following subsections.
7.5.2 Cyclic Prefix
The sinusoidal waveforms making up the tones in OFDM have the very special property of being
the only Eigen-functions of a linear channel. This special property prevents adjacent tones in OFDM
systems from interfering with one another, in much the same way as the human ear can clearly
distinguish between each of the tones created by the adjacent keys of a piano. This property, and the
incorporation of a small amount of guard time to each symbol, enables the orthogonality between
tones to be preserved in the presence of MI. This is what enables OFDM to avoid the multiple access
interference that is present in CDMA systems.
Figure 7.15 illustrates how an OFDM transceiver works in terms of time and frequency domain
signaling, where M subcarriers are present and no cyclic prefix is added for simplicity of illustration.
The left side of Figure 7.15 shows the input and output signals of the IFFT unit at a transmitter;
while the right side shows those signals of the FFT unit at a receiver. The signal waveforms shown in
the input side of IFFT unit are sinc(f ) functions because of the square window truncated sinusoidal
waveforms at the output side of the IFFT unit.
The frequency-domain representation of a number of tones, shown in Figure 7.12 or Figure 7.15,
highlights the orthogonal nature of the tones used in the OFDM system. Notice that the peak of
each tone corresponds to a zero level, or null, of every other tone. The result of this is that there is
no interference between the tones. When the receiver samples at the center frequency of each tone,
the only energy present is that of the desired signal, plus whatever other noise happens to be in the
channel.
To maintain orthogonality between tones in an OFDM system, it is important to ensure that the
symbol time contains one or multiple cycles of each sinusoidal tone waveform. This is normally the
case, because the system numerology is constructed such that tone frequencies are integer multiples
of the symbol period, as is subsequently highlighted, where the tone spacing is 1/T. Viewed as
sinusoids, Figure 7.16 shows three tones over a single symbol period, where each tone has an integer
number of cycles during the symbol period.
In absolute terms, to generate a pure sinusoidal tone requires that the signal starts at time minus
infinity. This is important, because tones are the only waveform that can ensure orthogonality. Fortunately,
the channel response can be treated as finite, because multipath components decay over time
and the channel is effectively band-limited. By adding a guard time, called a cyclic prefix (CP), the
channel can be made to behave as if the transmitted waveforms were from time minus infinite, and thus ensure orthogonality, which essentially prevents one subcarrier from interfering with another
(called intercarrier interference, or (ICI)).
The CP is actually a copy of the last portion of the data symbol appended to the front of the symbol
during the guard interval, as shown in Figure 7.17. Multipath causes tones and delayed replicas of
tones to arrive at the receiver with some delay spread. This leads to misalignment between sinusoids, which need to be aligned as in Figure 7.17 to be orthogonal. The CP allows the tones to be realigned
at the receiver, thus regaining orthogonality.
The CP is sized appropriately to serve as a guard time to eliminate ISI. This is accomplished
because the amount of time dispersion from the channel is smaller than the duration of the CP. A
fundamental trade-off is that the CP must be long enough to account for the anticipated multipath
delay spread experienced by the system. However, the amount of overhead increases as the CP gets
longer. The sizing of the CP forces a trade-off between the amount of delay spread that is acceptable
and the amount of Doppler shift that is acceptable. In most practical application scenarios, the length
of the CP is made about one fourth of the symbol duration.
7.5.3 PAPR Issues
As shown in Figure 7.14, an OFDM transmitter should finish all baseband signal processing before
the carrier modulation, which is a simple amplitude modulation (AM). Thus, all important data
information in an OFDM transmitter is carried on the amplitude of a carrier signal. An RF power
amplifier usually works in a saturated status to achieve a relatively high power efficiency, and thus
it will behave like a hard-limiter, which will cut off all useful data information if the dynamic range,
also called Peak-to-Average Power Ratio (PAPR), of the input signal exceeds a certain level. The
PAPR is a very important issue for any OFDM system.
It is seen from Figure 7.15 that the output from an IFFT unit is in fact the sum of all tones
corresponding to the presence of the subcarriers in the input side of the IFFT unit. In other words, if
only one of the M subcarriers exists at the input of the IFFT unit (or the input data symbol pattern is all
“0” but one “1”), then the output will consist of only single tone. On the other extreme, if the all-one
pattern appears at the input symbol, the output signal will be the sum of all tones, resulting in a very
high PAPR, which requires that an RF power amplifier with a very big dynamic range can be used.
Therefore, it is in our best interest to reduce the PAPR to avoid the appearance of all-one or
any other symbol patterns (which will generate high PAPR levels) at the input side of the IFFT unit.
Therefore, many real OFDM systems always use an interleaver at the input side of the IFFT unit to
make the symbol patterns appear more balanced in terms of zeros and ones.
7.5.4 OFDMA Technologies
To address the unique demands posed by mobile users of high-speed data applications, new air
interfaces must be designed and optimized across all the layers of the protocol stack, including the
networking layers. A prime example of this kind of optimization is found in OFDMA technology. As its name suggests, the system is based on OFDM, however, OFDMA is much more than just
a physical layer solution. It is a cross-layer-optimized technology that exploits the unique physical
properties of OFDM, enabling significant higher layer advantages that contribute to very efficient
packet data transmission in a cellular network.
Packet-switched air interface
The telephone network, designed basically for voice, is an example of circuit-switched systems.
Circuit-switched systems exist only at the physical layer that uses the channel resource to create an
end-to-end bit pipe. They are conceptually simple as the bit pipe is a dedicated resource, and the pipe
does not need to be controlled once it is created (some control may be required in setting up or tearing
down the pipe). Circuit-switched systems, however, are very inefficient for burst data traffic. Packetswitched
systems, on the other hand, are very efficient for data traffic but require that the upper layers
be controlled in addition to the physical layer that creates the bit pipe. The MAC layer is required for
the many data users to share the bit pipe. The data link layer is needed to take the error-prone pipe
and create a reliable link for the network layers to pass packet data flows over. The Internet is the best
example of a packet-switched network. Because all conventional cellular wireless systems, including
3G, were fundamentally designed for circuit-switched voice, they were designed and optimized primarily
at the physical layer. Some people suggested that the choice of CDMA as the physical layer
multiple access technology was also dictated by voice requirements. OFDMA, on the other hand, is a
packet-switched scheme designed for data and is optimized across the physical, MAC, data link, and
network layers. The choice of OFDM as the multiple access technology is based not only on physical
layer consideration, but also on the MAC layer, data link layer, and network layer requirements.
Physical layer advantages: OFDMA
As discussed earlier, most of the physical layer advantages of OFDM are well understood. Most
notably, OFDM creates a robust multiple access technology to deal with the impairments of the
wireless channel, such as multipath fading, delay spread, and Doppler shifts. Advanced OFDM-based
data systems typically divide the available spectrum into a number of equally spaced tones. For each
OFDM symbol duration, information carrying symbols (based on modulation such as QPSK, QAM,
etc.) are loaded on each tone.
The OFDMA can also use fast hopping across all tones in a predetermined pseudorandom pattern,
making it an SS technology.With fast hopping, a user that is assigned one tone does not transmit every
symbol on the same tone, but uses a hopping pattern to jump to a different tone for every symbol.
Different BSs use different hopping patterns, and each uses the entire available spectrum (thus to
realize frequency reuse of 1). In cellular deployment, this adds to the advantages of CDMA systems,
including frequency diversity and out of cell (intercell) interference averaging spectral efficiency
benefit that narrowband systems such as conventional TDMA do not have.
As discussed earlier, different users within the same cell use different resources (tones) and hence
do not interfere with each other. This is similar to TDMA, where different users in a cell transmit
at different time slots and do not interfere with one another. In contrast, CDMA users in a cell do
interfere with each other, increasing the total interference in the system. OFDMA therefore has the
physical layer benefits of both CDMA and TDMA and is at least three times (3times) more efficient
than CDMA. In other words, at the physical layer, OFDMA creates the biggest pipe of all cellular
technologies. Even though the 3times advantage at the physical layer is a huge advantage, the most
significant advantage of OFDMA for data is at the MAC and link layers.
MAC and link layer advantages
OFDMA exploits the granular nature of resources in OFDM to come up with extremely efficient
control layers. In OFDM, when designed appropriately, it is possible to send a very small amount (as little as one bit) of information from the transmitter to the receiver with virtually no overhead.
Therefore, a transmitter that is previously not transmitting can start transmitting as little as one bit of
information, and then stop, without causing any resource overhead. This is unlike CDMA or TDMA,
in which the granularity is much coarser, and merely initiating a transmission wastes a significant
resource. Hence, in TDMA, for example, there is a frame structure, and whenever a transmission
is initiated, a minimum of one frame (a few hundred bits) of information is transmitted. The frame
structure does not cause any significant inefficiency in user data transmission, as data traffic typically
consists of a large number of bits. However, for the transmission of control-layer information, the
frame structure is extremely inefficient, as the control information typically consists of one or two
bits but requires a whole frame. Not having a granular technology can therefore be very detrimental
from a MAC layer and link layer point of view.
OFDMA takes advantage of the granularity of OFDM in its control-layer design, enabling the
MAC layer to perform efficient packet switching over the air and at the same time provide all the
hooks to handle QoS. It also supports a data link layer that uses local (as opposed to end-to-end)
feedback to create a very reliable link from an unreliable wireless channel, with very low delays.
The network layer’s traffic therefore experiences small delays and no significant delay jitter. Hence,
interactive applications such as (packet) voice can be supported. Moreover, Internet protocols such
as TCP/IP run smoothly and efficiently over an OFDMA air link. As discussed in Chapter 3, TCP/IP
performance on 3G networks is very inefficient because the data link layer introduces significant delay
jitter so that channel errors are misinterpreted by TCP as network congestion and TCP responds by
backing off to the lowest rate.
Packet switching leads to efficient statistical multiplexing of data users and helps the wireless
operators to support a much greater number of users for a given user experience. This desirable feature
in OFDMA, together with QoS support and a three times bigger pipe, allows the operators to profitably
scale their wireless networks to meet the burgeoning data traffic demand in an all-you-can-eat pricing
environment