1

UNIT – 2
Orthogonal Frequency Division Multiplexing (OFDM)

Unit-0/Lecture-01
Introduction

OFDM is a method of encoding digital data on multiple carrier frequencies. OFDM has
developed into a popular scheme for wideband digital communication, used in applications
such as digital television and audio broadcasting, DSL Internet access, wireless networks,
powerline networks, and 4G mobile communications.

OFDM is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method. A large number of closely spaced orthogonal sub-carrier signals are
used to carry data on several parallel data streams or channels. Each sub-carrier is
modulated with a conventional modulation scheme (such as quadrature amplitude
modulation or phase-shift keying at a low symbol rate, maintaining total data rates similar
to conventional single-carrier modulation schemes in the same bandwidth.

The primary advantage of OFDM over single-carrier schemes is its ability to cope with
severe channel conditions (for example, attenuation of high frequencies in a long copper
wire, narrowband interference and frequency-selective fading due to multipath) without
complex equalization filters. Channel equalization is simplified because OFDM may be
viewed as using many slowly modulated narrow band signals rather than one rapidly
modulated wideband signal. The low symbol rate makes the use of a guard interval
between symbols affordable, making it possible to eliminate inter symbol interference
(ISI) and utilize echoes and time-spreading (on analogue TV these are visible as ghosting
and blurring, respectively) to achieve a diversity gain , i.e. a signal-to-noise ratio
improvement. This mechanism also facilitates the design of single frequency networks
(SFNs), where several adjacent transmitters send the same signal simultaneously at the
same frequency, as the signals from multiple distant transmitters may be combined
constructively, rather than interfering as would typically occur in a traditional single-carrier
system.

Unit 02/lecture 02
 2

Characteristics and principles of operation

Orthogonality

Conceptually, OFDM is a specialized FDM, the additional constraint being: all the carrier
signals are orthogonal to each other.

In OFDM, the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to
each other, meaning that cross-talk between the sub-channels is eliminated and inter-carrier
guard bands are not required. This greatly simplifies the design of both the transmitter and
the receiver; unlike conventional FDM, a separate filter for each sub-channel is not
required.

The orthogonality requires that the sub-carrier spacing is Hertz, where TU seconds
is the useful symbol duration (the receiver side window size), and k is a positive integer,
typically equal to 1. Therefore, with N sub-carriers, the total passband bandwidth will be B
≈ N·Δf (Hz).

The orthogonality also allows high spectral efficiency, with a total symbol rate near the
Nyquist rate for the equivalent baseband signal (i.e. near half the Nyquist rate for the
double-side band physical passband signal). Almost the whole available frequency band
can be utilized. OFDM generally has a nearly 'white' spectrum, giving it benign
electromagnetic interference properties with respect to other co-channel users.

A simple example: A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality. N =

1,000 sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz. For
this symbol time, the required bandwidth in theory according to Nyquist is N/2TU =
0.5 MHz (i.e., half of the achieved bandwidth required by our scheme). If a guard
interval is applied (see below), Nyquist bandwidth requirement would be even
lower. The FFT would result in N = 1,000 samples per symbol. If no guard interval
was applied, this would result in a base band complex valued signal with a sample
rate of 1 MHz, which would require a baseband bandwidth of 0.5 MHz according to
Nyquist. However, the passband RF signal is produced by multiplying the baseband
signal with a carrier waveform (i.e., double-sideband quadrature amplitude-
modulation) resulting in a passband bandwidth of 1 MHz. A single-side band (SSB)
 3

or vestigial sideband (VSB) modulation scheme would achieve almost half that
bandwidth for the same symbol rate (i.e., twice as high spectral efficiency for the
same symbol alphabet length). It is however more sensitive to multipath
interference.

OFDM requires very accurate frequency synchronization between the receiver and the
transmitter; with frequency deviation the sub-carriers will no longer be orthogonal, causing
inter-carrier interference (ICI) (i.e., cross-talk between the sub-carriers). Frequency offsets
are typically caused by mismatched transmitter and receiver oscillators, or by Doppler shift
due to movement. While Doppler shift alone may be compensated for by the receiver, the
situation is worsened when combined with multipath , as reflections will appear at various
frequency offsets, which is much harder to correct. This effect typically worsens as speed
increases, and is an important factor limiting the use of OFDM in high-speed vehicles. In
order to mitigate ICI in such scenarios, one can shape each sub-carrier in order to minimize
the interference resulting in a non-orthogonal subcarriers overlapping.For example, a low-
complexity scheme referred to as WCP-OFDM (Weighted Cyclic Prefix Orthogonal
Frequency-Division Multiplexing) consists in using short filters at the transmitter output in
order to perform a potentially non-rectangular pulse shaping and a near perfect
reconstruction using a single-tap per subcarrier equalization. Other ICI suppression
techniques usually increase drastically the receiver complexity.
 4

Unit 02/lecture 03

Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using
the FFT algorithm on the receiver side, and inverse FFT on the sender side. Although the
principles and some of the benefits have been known since the 1960s, OFDM is popular for
wideband communications today by way of low-cost digital signal processing components
that can efficiently calculate the FFT.

The time to compute the inverse-FFT or FFT transform has to take less than the time for
each symbol Which for example for DVB-T (FFT 8k) means the computation has to be
done in 896 µs or less.

For an 8192-point FFT this may be approximated to:

 MIPS = Million instructions per second

Implementation of Transceivers

Transmitter
 5

Fig 2.1: Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers, with baseband

data on each sub-carrier being independently modulated commonly using some type of
quadrature amplitude modulation (QAM) or phase-shift keying (PSK). This composite
baseband signal is typically used to modulate a main RF carrier.

is a serial stream of binary digits. By inverse multiplexing, these are first demultiplexed
into parallel streams, and each one mapped to a (possibly complex) symbol stream using
some modulation constellation (QAM, PSK, etc.). Note that the constellations may be
different, so some streams may carry a higher bit-rate than others.

An inverse FFT is computed on each set of symbols, giving a set of complex time-domain
samples. These samples are then quadrature-mixed to pass band in the standard way. The
real and imaginary components are first converted to the analogue domain using digital-to-
analogue converters (DACs); the analogue signals are then used to modulate cosine and
sine waves at the carrier frequency, , respectively. These signals are then summed to give
the transmission signal,

Receiver

Fig2.2: Receiver

The receiver picks up the signal , which is then quadrature-mixed down to baseband
using cosine and sine waves at the carrier frequency. This also creates signals centered on
 6

, so low-pass filters are used to reject these. The baseband signals are then sampled and
digitised using analog-to-digital converters (ADCs), and a forward FFT is used to convert
back to the frequency domain.

This returns parallel streams, each of which is converted to a binary stream using an
appropriate symbol detector. These streams are then re-combined into a serial stream, ,
which is an estimate of the original binary stream at the transmitter.
 7

Unit 02/Lecture 04

Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (i.e., where
the symbols are relatively long compared to the channel time characteristics) suffer less
from intersymbol interference caused by multipath propagation, it is advantageous to
transmit a number of low-rate streams in parallel instead of a single high-rate stream. Since
the duration of each symbol is long, it is feasible to insert a guard interval between the
OFDM symbols, thus eliminating the intersymbol interference.

The guard interval also eliminates the need for a pulse-shaping filter, and it reduces the
sensitivity to time synchronization problems.

A simple example: If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel, then the duration of each symbol would be one
microsecond or less. This imposes severe constraints on synchronization and necessitates
the removal of multipath interference. If the same million symbols per second are spread
among one thousand sub-channels, the duration of each symbol can be longer by a factor of
a thousand (i.e., one millisecond) for orthogonality with approximately the same
bandwidth. Assume that a guard interval of 1/8 of the symbol length is inserted between
each symbol. Intersymbol interference can be avoided if the multipath time-spreading (the
time between the reception of the first and the last echo) is shorter than the guard interval
(i.e., 125 microseconds). This corresponds to a maximum difference of 37.5 kilometers
between the lengths of the paths.

The cyclic prefix, which is transmitted during the guard interval, consists of the end of the
OFDM symbol copied into the guard interval, and the guard interval is transmitted
followed by the OFDM symbol. The reason that the guard interval consists of a copy of the
end of the OFDM symbol is so that the receiver will integrate over an integer number of
sinusoid cycles for each of the multipaths when it performs OFDM demodulation with the
 8

FFT. In some standards such as Ultrawideband, in the interest of transmitted power, cyclic
prefix is skipped and nothing is sent during the guard interval. The receiver will then have
to mimic the cyclic prefix functionality by copying the end part of the OFDM symbol and
adding it to the beginning portion.

Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction),
and almost always uses frequency and/or time interleaving.

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading. For example, when a part of the channel bandwidth fades,
frequency interleaving ensures that the bit errors that would result from those subcarriers in
the faded part of the bandwidth are spread out in the bit-stream rather than being
concentrated. Similarly, time interleaving ensures that bits that are originally close together
in the bit-stream are transmitted far apart in time, thus mitigating against severe fading as
would happen when travelling at high speed.

However, time interleaving is of little benefit in slowly fading channels, such as for
stationary reception, and frequency interleaving offers little to no benefit for narrowband
channels that suffer from flat-fading (where the whole channel bandwidth fades at the same
time).

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the
bit-stream that is presented to the error correction decoder, because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit
errors, and a burst of uncorrected errors occurs. A similar design of audio data encoding
makes compact disc (CD) playback robust.

A classical type of error correction coding used with OFDM-based systems is

convolutional coding, often concatenated with Reed-Solomon coding. Usually, additional
interleaving (on top of the time and frequency interleaving mentioned above) in between
the two layers of coding is implemented. The choice for Reed-Solomon coding as the outer
error correction code is based on the observation that the Viterbi decoder used for inner
convolutional decoding produces short error bursts when there is a high concentration of
errors, and Reed-Solomon codes are inherently well-suited to correcting bursts of
errors.Newer systems, however, usually now adopt near-optimal types of error correction
 9

codes that use the turbo decoding principle, where the decoder iterates towards the desired
solution. Examples of such error correction coding types include turbo codes and LDPC
codes, which perform close to the Shannon limit for the Additive White Gaussian Noise
(AWGN) channel. Some systems that have implemented these codes have concatenated
them with either Reed-Solomon (for example on the Media FLO system) or BCH codes
(on the DVB-S2 system) to improve upon an error floor inherent to these codes at high
signal-to-noise ratios.

Unit 02/ Lecture 05

Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about
the channel is sent over a return-channel. Based on this feedback information, adaptive
modulation, channel coding and power allocation may be applied across all sub-carriers, or
individually to each sub-carrier. In the latter case, if a particular range of frequencies
suffers from interference or attenuation, the carriers within that range can be disabled or
made to run slower by applying more robust modulation or error coding to those sub-
carriers.

The term discrete multitone modulation (DMT) denotes OFDM based communication
systems that adapt the transmission to the channel conditions individually for each sub-
carrier, by means of so-called bit-loading. Examples are ADSL and VDSL.

The upstream and downstream speeds can be varied by allocating either more or fewer
carriers for each purpose. Some forms of rate-adaptive DSL use this feature in real time, so
that the bitrate is adapted to the co-channel interference and bandwidth is allocated to
whichever subscriber needs it most.

OFDM extended with multiple access

 10

OFDM in its primary form is considered as a digital modulation technique, and not a multi-
user channel access method, since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols. However, OFDM can be
combined with multiple access using time, frequency or coding separation of the users.

In orthogonal frequency-division multiple access (OFDMA), frequency-division multiple

access is achieved by assigning different OFDM sub-channels to different users. OFDMA
supports differentiated quality of service by assigning different number of sub-carriers to
different users in a similar fashion as in CDMA, and thus complex packet scheduling or
Media Access Control schemes can be avoided. OFDMA is used in:

 the mobility mode of the IEEE 802.16 Wireless MAN standard, commonly referred
to as WiMAX,
 the IEEE 802.20 mobile Wireless MAN standard, commonly referred to as MBWA,
 the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink. The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA), now named Evolved UMTS Terrestrial Radio Access (E-UTRA).
 the now defunct Qualcomm/3GPP2 Ultra Mobile Broadband (UMB) project,
intended as a successor of CDMA2000, but replaced by LTE.

OFDMA is also a candidate access method for the IEEE 802.22 Wireless Regional Area
Networks (WRAN). The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum).

In Multi-carrier code division multiple access (MC-CDMA), also known as OFDM-

CDMA, OFDM is combined with CDMA spread spectrum communication for coding
separation of the users. Co-channel interference can be mitigated, meaning that manual
fixed channel allocation (FCA) frequency planning is simplified, or complex dynamic
channel allocation (DCA) schemes are avoided.

Channel Estimation

While evaluating OFDM system performance in previous sections, we assumed perfect

knowledge of the channel for equalization. While perfect channel knowledge can be used
to find the upper limit of OFDM system performance, such perfect channel knowledge is
not available in real-life and needs to be estimated. Channel estimation can be done in
 11

various ways: with or with the help of a parametric model, with the use of frequency and/or
time correlation properties of the wireless channel, blind or pilot (training) based, adaptive
or not. Non-parametric methods attempt to estimate the quantities of interest (for example
the frequency response) without relying on a specific channel model. Conversely,
parametric estimation assumes a certain channel model, determines the parameters of this
model and infers the quantities of interest. Spaced-time and spaced-frequency correlations
are specific properties of channel that can be incorporated in the estimation method,
improving the quality of estimate. Pilot based estimation methods are the most commonly
used methods which are applicable in systems where the sender emits some known signal.
Blind estimation, on the other hand, relies on some properties of the signal (e.g., cylco-
stationarity of the signal) and is rarely used in practical OFDM systems. Adaptive channel
estimation methods are typically used for rapidly time-varying channel.
we investigate pilot-based non-adaptive channel estimation methods. We do, however,
exploit channel correlation properties in one of the channel estimation methods. Figure
presents an OFDM system that utilizes pilot-based channel estimation method for
equalization at the receiver end. At the transmitter, binary data is mapped to a specific
modulation (QPSK, 16QAM,64QAM) and the modulated data undergoes serial-to-parallel
(S/P) conversion, forming a vector of (N − N pilot ) 0 symbols [12], [20]. 0 N is the
number of occupied sub-carriers and pilot N is the number of pilot sub-carriers. Known
pilot N pilot symbols are then inserted into the modulated data, forming frequency-domain
transmitted data k X of length o N . c N -point Inverse Fourier transform (IFFT) is
performed on zero-padded k X to generate time-domain vector x(n). Cyclic prefix of cp N
is then preappended to x(n) forming x (n) g vector of c cp N + N symbols. After parallel to
serial conversion (P/S),
 12

Fig: Pilot-based OFDM system model

Unit 02/Lecture 06

Simplified equalization

The effects of frequency-selective channel conditions, for example fading caused by

multipath propagation, can be considered as constant (flat) over an OFDM sub-channel if
the sub-channel is sufficiently narrow-banded (i.e., if the number of sub-channels is
sufficiently large). This makes frequency domain equalization possible at the receiver,
which is far simpler than the time-domain equalization used in conventional single-carrier
modulation. In OFDM, the equalizer only has to multiply each detected sub-carrier (each
Fourier coefficient) in each OFDM symbol by a constant complex number, or a rarely
 13

changed value.

Our example: The OFDM equalization in the above numerical example would require one

complex valued multiplication per subcarrier and symbol (i.e., complex

multiplications per OFDM symbol; i.e., one million multiplications per second, at the

receiver). The FFT algorithm requires [this is imprecise: over half of these
complex multiplications are trivial, i.e. = to 1 and are not implemented in software or HW].
complex-valued multiplications per OFDM symbol (i.e., 10 million multiplications per
second), at both the receiver and transmitter side. This should be compared with the
corresponding one million symbols/second single-carrier modulation case mentioned in the
example, where the equalization of 125 microseconds time-spreading using a FIR filter
would require, in a naive implementation, 125 multiplications per symbol (i.e., 125 million
multiplications per second). FFT techniques can be used to reduce the number of
multiplications for an FIR filter based time-domain equalizer to a number comparable with
OFDM, at the cost of delay between reception and decoding which also becomes
comparable with OFDM.

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier,

equalization can be completely omitted, since these non-coherent schemes are insensitive
to slowly changing amplitude and phase distortion.

In a sense, improvements in FIR equalization using FFTs or partial FFTs leads

mathematically closer to OFDM but the OFDM technique is easier to understand and
implement, and the sub-channels can be independently adapted in other ways than varying
equalization coefficients, such as switching between different QAM constellation patterns
and error-correction schemes to match individual sub-channel noise and interference
characteristics.

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for
measurement of the channel conditions (i.e., the equalizer gain and phase shift for each
sub-carrier). Pilot signals and training symbols (preambles) may also be used for time
synchronization (to avoid intersymbol interference, ISI) and frequency synchronization (to
avoid inter-carrier interference, ICI, caused by Doppler shift).
 14

OFDM was initially used for wired and stationary wireless communications. However,
with an increasing number of applications operating in highly mobile environments, the
effect of dispersive fading caused by a combination of multi-path propagation and doppler
shift is more significant. Over the last decade, research has been done on how to equalize
OFDM transmission over doubly selective channels.

Unit 02/Lecture 06

Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the
independent phases of the sub-carriers mean that they will often combine constructively.
Handling this high PAPR requires:

 a high-resolution digital-to-analogue converter (DAC) in the transmitter

 15

 a high-resolution analogue-to-digital converter (ADC) in the receiver

 a linear signal chain.

Any non-linearity in the signal chain will cause intermodulation distortion that

 raises the noise floor

 may cause inter-carrier interference
 generates out-of-band spurious radiation.

The linearity requirement is demanding, especially for transmitter RF output circuitry

where amplifiers are often designed to be non-linear in order to minimise power
consumption. In practical OFDM systems a small amount of peak clipping is allowed to
limit the PAPR in a judicious trade-off against the above consequences. However, the
transmitter output filter which is required to reduce out-of-band spurs to legal levels has the
effect of restoring peak levels that were clipped, so clipping is not an effective way to
reduce PAPR.

Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications, the high PAPR requirements have so far limited OFDM applications to
terrestrial systems.

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is

CF = 10 log ( n ) + CFc ...

Where CFc is the crest factor (in dB) for each sub-carrier. (CFc is 3.01 dB for the sine
waves used for BPSK and QPSK modulation).

For example, the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated, giving a crest factor of 35.32 Db.

Many crest factor reduction techniques have been developed.

The dynamic range required for an FM receiver is 120 dB while DAB only require about
90 dB. As a comparison, each extra bit per sample increases the dynamic range with 6 dB.
 16

Unit 02/Lecture 08

Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power
efficiency and bandwidth efficiency. The power efficiency describes the ability of
communication system to preserve bit error rate (BER) of the transmitted signal at low
 17

power levels. Bandwidth efficiency reflects how efficiently the allocated bandwidth is
utilized and is defined as the throughput data rate per Hertz in a given bandwidth. If the
large number of subcarriers are used, the bandwidth efficiency of multicarrier system such
as OFDM with using optical fiber channel is defined as

Factor 2 is because of two polarization states in the fiber.

where is the symbol rate in giga symbol per second (Gsps), and is the
bandwidth of OFDM signal.

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing . So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than
single carrier system.

M in Power at the
Transmission No. of Bit Fiber Bandwidth
S.No. M- receiver (at
Type Subcarriers rate length efficiency
QAM BER of 10−9)

10
1. single carrier 64 1 20 km -37.3 dBm 6.0000
Gbit/s
10
2. Multicarrier 64 128 20 km -36.3 dBm 10.6022
Gbit/s
There is only 1 dBm increase in receiver power, but we get 76.7% improvement in
bandwidth efficiency with using multicarrier transmission technique.

S.NO RGPV QUESTIONS Year Marks

Q.1 Discuss the working principle of OFDM. Jun 2014 7
 18

Q.2 How channel estimation is done in OFDM? Jun 2014 7

Q.3 What is inter carrier interference? How it can be June 2014 7

reduced?