OFDM is a digital multi-carrier modulation technique that divides the available spectrum into multiple orthogonal subcarriers. It allows high spectral efficiency by spacing the carriers to maintain orthogonality even when their spectra overlap. The document provides an intuitive explanation of OFDM using analogies like a shower head vs faucet and multiple smaller trucks vs one large truck. It explains how OFDM provides resistance to interference by spreading data across orthogonal subcarriers rather than a single carrier. The key concept of orthogonality allows the subcarriers to overlap without interference by ensuring the area under one subcarrier's frequency multiplied by another is always zero.
Wireless Communication Networks and Systems 1st Edition Beard Solutions Manualpuriryrap
Full download : http://alibabadownload.com/product/wireless-communication-networks-and-systems-1st-edition-beard-solutions-manual/
Wireless Communication Networks and Systems 1st Edition Beard Solutions Manual
Orthogonal Frequency Division Multiplexing, OFDM uses a large number of narrow sub-carriers for multi-carrier transmission to overcome the effect of multi path fading problem. LTE uses OFDM for the downlink, from base station to terminal to transmit the data over many narrow band careers of 180 KHz each instead of spreading one signal over the complete 5MHz career bandwidth. OFDM meets the LTE requirement for spectrum flexibility and enables cost-efficient solutions for very wide carriers with high peak rates.
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions. Channel equalization is simplified. The low symbol rate makes the use of a guard interval between symbols affordable, making it possible to eliminate inter symbol interference (ISI).
Performance and Analysis of OFDM Signal Using Matlab SimulinkIJMER
Multi-carrier modulation is an attractive technique for fourth generation .OFDM is based on
multicarrier modulation technique. In OFDM system the bit stream is divided into many different sub
channels. An efficient and distortionless scheme for peak power reduction in OFDM is proposed. In this
paper, a set of mapping where the actual transmit signal is selected. From this set of signal reduced
PAPR. Simulation results are shown. The lowest PAPR is compared with conventional work. It is also
compared BER to SNR and best result is achieved.
Wireless Communication Networks and Systems 1st Edition Beard Solutions Manualpuriryrap
Full download : http://alibabadownload.com/product/wireless-communication-networks-and-systems-1st-edition-beard-solutions-manual/
Wireless Communication Networks and Systems 1st Edition Beard Solutions Manual
Orthogonal Frequency Division Multiplexing, OFDM uses a large number of narrow sub-carriers for multi-carrier transmission to overcome the effect of multi path fading problem. LTE uses OFDM for the downlink, from base station to terminal to transmit the data over many narrow band careers of 180 KHz each instead of spreading one signal over the complete 5MHz career bandwidth. OFDM meets the LTE requirement for spectrum flexibility and enables cost-efficient solutions for very wide carriers with high peak rates.
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions. Channel equalization is simplified. The low symbol rate makes the use of a guard interval between symbols affordable, making it possible to eliminate inter symbol interference (ISI).
Performance and Analysis of OFDM Signal Using Matlab SimulinkIJMER
Multi-carrier modulation is an attractive technique for fourth generation .OFDM is based on
multicarrier modulation technique. In OFDM system the bit stream is divided into many different sub
channels. An efficient and distortionless scheme for peak power reduction in OFDM is proposed. In this
paper, a set of mapping where the actual transmit signal is selected. From this set of signal reduced
PAPR. Simulation results are shown. The lowest PAPR is compared with conventional work. It is also
compared BER to SNR and best result is achieved.
Multiplexing generally refers to independent signals, those produced by different sources. SO it is a question of how to share the spectrum with these users. In OFDM the question of multiplexing is applied to independent signals but these independent signals are a sub-set of the one main signal.
In OFDM the signal itself is first split into independent channels, modulated by data and then re-multiplexed to create the OFDM carrier.
OFDM is a combination of modulation and multiplexing.
Simulation Study and Performance Comparison of OFDM System with QPSK and BPSKpaperpublications3
Abstract: FDMA, TDMA and CDMA are the well-known multiplexing techniques used in wireless communication systems. While working with the wireless systems using these techniques various problems are encountered especially when a typical transmitted signal arrives at the receiver using various paths of different lengths. Since multiple versions of the signal interfere with each other, it becomes difficult to extract the original information. The use of orthogonal frequency division multiplexing (OFDM) technique provides better solution for the above mentioned problem. OFDM technique distributes the data over a large number of carriers that are spaced apart at precise frequencies. This spacing provides the "orthogonality", which prevents the demodulator from seeing frequencies other than their own. The benefits of OFDM are high spectral efficiency, resiliency of RF interference, and lower multi-path distortion. OFDM is a powerful modulation technique that is capable of high data rate and is able to eliminate ISI. Using MATLAB, simulation of OFDM was done with different modulation techniques using different transform techniques. The digital modulation schemes such as BPSK and QPSK were selected to assess the performance of the designed OFDM system.
SIDELOBE SUPPRESSION AND PAPR REDUCTION FOR COGNITIVE RADIO MIMO-OFDM SYSTEMS...ijistjournal
Orthogonal Frequency Division Multiplexing (OFDM) is deployed to overcome the interference. However, OFDM has a relatively large OOB emissions. In spectrum sharing approaches such as dynamic spectrum access networks, the OOB power levels of secondary transmissions should be kept below a certain level, in order not to interfere with primary transmissions. . The difficulties such as sidelobes and PAPR caused by OFDM is reduced by convex optimization and PTS technique respectively. In this technique each OFDM subcarrier is multiplied with a real-valued weight that is determined in order not to interfere with adjacent users. The problem with the SW technique is involving a very complex optimization. We propose a heuristic approach called convex optimization. It can achieve considerable sidelobe suppression while requiring significantly less computational resources than the optimal solution. Implementation results prove that it can be introduced for real-time transmissions. Optimizing the subcarrier weights and SINR is complex, for which we use the technique of convex optimization. For reducing the PAPR we use Partial Transmit Sequence (PTS) technique.
Orthogonal Frequency Division Multiplexing (OFDM) is deployed to overcome the interference. However,
OFDM has a relatively large OOB emissions. In spectrum sharing approaches such as dynamic spectrum
access networks, the OOB power levels of secondary transmissions should be kept below a certain level, in
order not to interfere with primary transmissions. . The difficulties such as sidelobes and PAPR caused by
OFDM is reduced by convex optimization and PTS technique respectively. In this technique each OFDM
subcarrier is multiplied with a real-valued weight that is determined in order not to interfere with adjacent
users. The problem with the SW technique is involving a very complex optimization. We propose a heuristic
approach called convex optimization. It can achieve considerable sidelobe suppression while requiring
significantly less computational resources than the optimal solution. Implementation results prove that it
can be introduced for real-time transmissions. Optimizing the subcarrier weights and SINR is complex, for
which we use the technique of convex optimization. For reducing the PAPR we use Partial Transmit
Sequence (PTS) technique.
Index terms : OFDM (Orthogonal Frequency Division Multiplexing), PAPR (Peak Average Power
Ratio), OOB (Out Of Band), IFFT (Inverse Fast Fourier Transform).
Comparative evaluation of bit error rate for different ofdm subcarriers in ra...ijmnct
In the present situation, the expectation about the quality of signals in wireless communication is as high as possible. This quality issue is dependent upon the different communication parameters. One of the most important issues is to reduce the bit error rate (BER) to enhance the performance of the system. This paper provides a comparative analysis on the basis of this bit error rate. I have compared the BER for different number of subcarriers in OFDM system for BPSK modulation scheme. I have taken 6 varieties of data subcarriers to analyze this comparison. Here my target is to reach at the lowest level of BER for BPSK modulation. That is achieved at 2048 number of subcarriers.
Design and Fabrication of a Two Axis Parabolic Solar Dish CollectorIJERA Editor
The work consists of the design of the chain drive system and the fabrication of the two axis parabolic solar dish.
It is a model study of the two axis parabolic dish which worked by the automatic circuit that was developed. Ready
made parabolic solar dish is taken and fabricated. The circular iron ring provides the two axis motion of the dish.
A compound chain drive system was developed for the smooth movement of the dish. An electromechanical
system which tracks the sun on both axes and which is controlled via a programmable logic control (PLC) was
designed and implemented. In this a theoretical study was done. A C program was made which gave the required
result for the graphical representation of the recorded radiation. Programmable Logic Controls (PLC) was used
instead of photo sensors, which are widely used for tracking the sun. The azimuthal angle of the sun from sunrise
to sunset times was calculated for each day of the year at 23.59 Lat & 72.38Longitude in the Northern hemisphere,
the location of the city Mehsana. According to this azimuth angle, the required analog signal was taken from the
PLC analog module and sent to the power window motor, which controlled the position of the panel to ensure that
the rays fall vertically on the panel. After the mechanical control of the system was started, the performance
measurements of the solar panel were carried out. The values obtained from the measurements were compared and
the necessary evaluations were conducted.
Multi carrier equalization by restoration of redundanc y (merry) for adaptive...IJNSA Journal
This paper proposes a new blind adaptive channel shortening approach for multi-carrier systems. The
performance of the discrete Fourier transform-DMT (DFT-DMT) system is investigated with the proposed
DST-DMT system over the standard carrier serving area (CSA) loop1. Enhanced bit rates demonstrated
and less complexity also involved by the simulation of the DST-DMT system.
Performance evaluation on the basis of bit error rate for different order of ...ijmnct
Today, we have required to accommodate a large number of users under a single base station. This can be
possible only if we have some flexibility over the spectrum. Previously we have lots of multiplexing methods
to accommodate large number of signals in time and frequency domain. But now we have required to
accommodate a large number of users in the same bandwidth, without any fading over the received signal.
So, orthogonality can be maintained over the frequency response. This technology is now more popular in
the mobile communication domain, called Orthogonal Frequency Division Multiplexing (OFDM). Actually
user data can be converted into the parallel form and then they are modulated using digital modulation
techniques. Finally, they have followed by OFDM Modulator and cyclic prefix can be inserted into the
OFDM symbols. Here, I have worked on the measurement of Bit error rate for different modulation
techniques in OFDM technology. It has been considered that subchannel size is not constant. According to
that I have concluded the overall idea regarding the performance under OFDM technology.
PAPR Reduction in OFDM using Active and Non-Active ChannelsIOSR Journals
Abstract : According to the request of advance communication field there should be high data rate in addition to both power efficiency and lower bit error rate. This request of high data rate can be achieved by the multi carrier modulation scheme using the OFDM technique. But the great drawback of the OFDM technique is its high peak to average power ratio (PAPR). High PAPR reduces OFDM signals by driving the analog amplifier to work in the nonlinear region, changing this way the signal and making the amplifier to consume more power. To reduce the PAPR methods exist which adjust or present new signals to battle large signal peaks. The methods which use data carrying channels are called active channel methods and which use redundant channel are called non active channel methods. This work deals with reduction of the PAPR of OFDM signal using both Active and Non Active Channels. Clipping technique has been applied to active channels and Tone reservation has been applied to Non Active Channels. By using both channels we can get considerable reduction in PAPR. Keywords:Orthogonal Frequency Division Multiplexing (OFDM), Peak to Average Power Ratio (PAPR), Power Amplifier (PA).
This presentation include the basic concept of communication, modulation techniques in analog and digital. ADC (Analog to Digital Conversion) and Demodulation schemes
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
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After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
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Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
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Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
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As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
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1. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 1
Intuitive Guide to Principles of Communications
www.complextoreal.com
Orthogonal Frequency Division Multiplexing (OFDM)
Modulation - a mapping of the information on changes in the carrier phase, frequency or
amplitude or combination.
Multiplexing - method of sharing a bandwidth with other independent data channels.
OFDM is a combination of modulation and multiplexing. Multiplexing generally refers to
independent signals, those produced by different sources. So it is a question of how to share the
spectrum with these users. In OFDM the question of multiplexing is applied to independent
signals but these independent signals are a sub-set of the one main signal. In OFDM the signal
itself is first split into independent channels, modulated by data and then re-multiplexed to create
the OFDM carrier.
OFDM is a special case of Frequency Division Multiplex (FDM). As an analogy, a FDM channel
is like water flow out of a faucet, in contrast the OFDM signal is like a shower. In a faucet all
water comes in one big stream and cannot be sub-divided. OFDM shower is made up of a lot of
little streams.
(a) (b)
Fig. 1 – (a) A Regular-FDM single carrier – A whole bunch of water coming all in one stream. (b)
Orthogonal-FDM – Same amount of water coming from a lot of small streams.
Think about what the advantage might be of one over the other? One obvious one is that if I put
my thumb over the faucet hole, I can stop the water flow but I cannot do the same for the shower.
So although both do the same thing, they respond differently to interference.
Fig. 2 – All cargo on one truck vs. splitting the shipment into more than one.
Another way to see this intuitively is to use the analogy of making a shipment via a truck.
We have two options, one hire a big truck or a bunch of smaller ones. Both methods carry the
exact same amount of data. But in case of an accident, only 1/4 of data on the OFDM trucking
will suffer.
Copyright 2004 Charan Langton www.complextoreal.com
2. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 2
These four smaller trucks when seen as signals are called the sub-carriers in an OFDM system
and they must be orthogonal for this idea to work. The independent sub-channels can be
multiplexed by frequency division multiplexing (FDM), called multi-carrier transmission or it can
be based on a code division multiplex (CDM), in this case it is called multi-code transmission.
In this tutorial we will only talk about the multi-carrier FDM or OFDM.
Fig. 3 – Multi-carrier FDM and Multi-code division multiplex
The importance of being orthogonal
The main concept in OFDM is orthogonality of the sub-carriers. Since the carriers are all
sine/cosine wave, we know that area under one period of a sine or a cosine wave is zero. This is
easily shown.
Positive and
negative area
cancel.
Positive and
negative area
cancel. +Area
+Area
+Area
-
-
Fig. 4 - The area under a sine and a cosine wave over one period is always zero.
Let's take a sine wave of frequency m and multiply it by a sinusoid (sine or a cosine) of a
frequency n, where both m and n are integers. The integral or the area under this product is given
by
Copyright 2004 Charan Langton www.complextoreal.com
3. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 3
( ) sin sinf t mwt n= × wt (1)
f t wt nwt( ) sin *sin=
Sine wave multiplied by
another of a different
harmonic
Figure 5 - The area under a sine wave multiplied by its own harmonic is always
zero.
By the simple trigonometric relationship, this is equal to a sum of two sinusoids of frequencies
(n-m) and (n+m)
1 1
cos( ) cos( )
2 2
m n m n= − − +
These two components are each a sinusoid, so the integral is equal to zero over one period.
2 2
0 0
1 1
cos( ) cos( )
2 2
0 0
m n t m n t
π π
ω ω= − − +
= −
∫ ∫
We conclude that when we multiply a sinusoid of frequency n by a sinusoid of frequency m/n, the
area under the product is zero. In general for all integers n and m, si
are all orthogonal to each other. These frequencies are called harmonics.
n ,cos ,cos ,sinmx mx nx nx
This idea is key to understanding OFDM. The orthogonality allows simultaneous transmission on
a lot of sub-carriers in a tight frequency space without interference from each other. In essence
this is similar to CDMA, where codes are used to make data sequences independent (also
orthogonal) which allows many independent users to transmit in same space successfully.
OFDM is a special case of FDM (just as it says in its name, OFDM)
Let’s first look at what a Frequency Division Multiplexing FDM is. If I have a bandwidth that
goes from frequency a to b, I can subdivide this into a frequency space of four equal spaces. In
frequency space the modulated carriers would look like this.
Copyright 2004 Charan Langton www.complextoreal.com
4. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 4
ba
c1 c2 c3 c4
Fig. 6 – FDM carriers are placed to next to each other.
The frequencies a and b can be anything, integer or non-integer since no relationship is implied
between a and b. Same is true of the carrier center frequencies which are based on frequencies
that do not have any special relationship to each other.
But, what if frequency c1 and cn were such that for any n, an integer, the following holds.
(2)1nc n c= ×
So that
2 1
3 1
4 1
2
3
4
c c
c c
c c
=
=
=
All three of these frequencies are harmonic to c1. In this case, since these carriers are
orthogonal to each other, when added together, they do not interfere with each other. In
FDM, since we do not generally have frequencies that follow the above relationship, we
get interference from neighbor carriers. To provide adjacent channel interference
protection, signals are moved further apart.
The symbols rate that can be carried by a PSK carrier of bandwidth b, is given by
2s l pR B B= =
where Bl is lowpass bandwidth and Bp, the passband bandwidth. This relationship assumes a
perfect Nyquist filtering with rolloff = 0.0. Since this is unachievable, we use root raised cosine
filtering which for a roll-off of α gives the following relationship.
1
p
s
B
R
α
=
+
So if we need three carriers, each of data rate = 20 Mbps, then we might place our BPSK carriers
as shown below. With Rs = 20 and B = 20 x 1.25 = 25 MHz. Each carrier may be placed (25 +
2.5) 27.5 MHz apart allowing for a 10% guard band. The frequencies would not be orthogonal
but in FDM we don’t care about this. It’s the guard band that helps keep interference under
control.
An example of OFDM using 4 sub-carriers
Copyright 2004 Charan Langton www.complextoreal.com
5. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 5
In OFDM we have N carriers, N can be anywhere from 16 to 1024 in present technology and
depends on the environment in which the system will be used.
Let’s examine the following bit sequence we wish to transmit and show the development of the
ODFM signal using 4 sub-carriers. The signal has a symbol rate of 1 and sampling frequency is 1
sample per symbol, so each transition is a bit.
Fig. 7 – A bit stream that will be modulated using a 4 carrier OFDM.
First few bits are 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1,…
Let’s now write these bits in rows of fours, since this demonstration will use only four sub-
carriers. We have effectively done a serial to parallel conversion.
Table I – Serial to parallel conversion of data bits.
c1 c2 c3 c4
1 1 -1 -1
1 1 1 -1
1 -1 -1 -1
-1 1 -1 -1
-1 1 1 -1
-1 -1 1 1
Each column represents the bits that will be carried by one sub-carrier. Let’s start with the first
carrier, c1. What should be its frequency? From the Nyquist sampling Theorem, we know that
smallest frequency that can convey information has to be twice the information rate. In this case,
the information rate per carrier will be 1/4 or 1 symbol per second total for all 4 carriers. So the
smallest frequency that can carry a bit rate of 1/4 is 1/2 Hz. But we picked 1 Hz for convenience.
Had I picked 1/2 Hz as my starting frequency, then my harmonics would have been 1, 3/2 and 2
Hz. I could have chosen 7/8 Hz to start with and in which the harmonics would be 7/4, 7/2, 21/2
Hz.
We pick BPSK as our modulation scheme for this example. (For QPSK, just imagine the same
thing going on in the Q channel, and then double the bit rate while keeping the symbol rate the
same.) Note that I can pick any other modulation method, QPSK, 8PSK 32-QAM or whatever.
No limit here on what modulation to use. I can even use TCM which provides coding in addition
to modulation.
Carrier 1 - We need to transmit 1, 1, 1 -1, -1, -1 which I show below superimposed on the BPSK
carrier of frequency 1 Hz. First three bits are 1 and last three -1. If I had shown the Q channel of
this carrier (which would be a cosine) then this would be a QPSK modulation.
Copyright 2004 Charan Langton www.complextoreal.com
6. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 6
Fig. 8 – Sub-carrier 1 and the bits it is modulating (the first column of Table I)
Carrier 2 - The next carrier is of frequency 2 Hz. It is the next orthogonal/harmonic to frequency
of the first carrier of 1 Hz. Now take the bits in the second column, marked c2, 1, 1, -1, 1, 1, -1
and modulate this carrier with these bits as shown in Fig.
Fig. 9 – Sub-carrier 2 and the bits that it is modulating (the 2nd column of Table I)
Carrier 3 – Carrier 3 frequency is equal to 3 Hz and fourth carrier has a frequency of 4 Hz. The
third carrier is modulated with -1, 1, 1, -1, -1, 1 and the fourth with -1, -1, -1, -1, -1, -1, 1 from
Table I.
Fig. 10 – Sub-carrier 3 and 4 and the bits that they modulating (the 3rd
and 4th columns of Table I)
Copyright 2004 Charan Langton www.complextoreal.com
7. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 7
Now we have modulated all the bits using four independent carriers of orthogonal frequencies 1
to 4 Hz. What we have done is taken the bit stream, distributed the bits, one bit at a time to the
four sub-carriers as shown in figure below.
Time
C1
C2
C3
C4
Fig. 11 – OFDM signal in time and frequency domain.
Now add all four of these modulated carriers to create the OFDM signal, often produced by a
block called the IFFT.
Fig. 12 – Functional diagram of an OFDM signal creation. The outlined part is often called an IFFT
block.
Copyright 2004 Charan Langton www.complextoreal.com
8. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 8
Fig. 13 – The generated OFDM signal. Note how much it varies compared to the underlying
constant amplitude sub-carriers.
In short-hand, we can write the process above as
1
( ) ( )sin(2 )
N
n
n
c t m t ntπ
=
= ∑ (4)
Eq. 4 is basically an equation of an Inverse FFT.
Using Inverse FFT to create the OFDM symbol
The equation 4 is essentially an inverse FFT. The IFFT block in the OFDM chain confuses
people. So let’s examine briefly what an FFT/IFFT does.
Copyright 2004 Charan Langton www.complextoreal.com
9. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 9
(a) Time domain view (b) Frequency domain view
Fig. 14 - The two views of a signal
Forward FFT takes a random signal, multiplies it successively by complex exponentials over the
range of frequencies, sums each product and plots the results as a coefficient of that frequency.
The coefficients are called a spectrum and represent “how much” of that frequency is present in
the input signal. The results of the FFT in common understanding is a frequency domain signal.
We can write FFT in sinusoids as
∑ ∑
−
=
−
=
⎟
⎠
⎞
⎜
⎝
⎛
+⎟
⎠
⎞
⎜
⎝
⎛
=
1
0
1
0
2
cos)(
2
sin)()(
N
n
N
n
N
kn
nxj
N
kn
nxkx
ππ
(5)
Here x(n) are the coeffcients of the sines and cosines of frequency 2 /k Nπ , where k is
the index of the frequencies over the N frequencies, and n is the time index. x(k) is the
value of the spectrum for the kth frequeny and x(n) is the value of the signal at time n.
In Fig. 14 (b), the x(k =1) = 1.0 is one such value.
The inverse FFT takes this spectrum and converts the whole thing back to time domain signal by
again successively multiplying it by a range of sinusoids.
The equation for IFFT is
∑ ∑
−
=
−
=
⎟
⎠
⎞
⎜
⎝
⎛
−⎟
⎠
⎞
⎜
⎝
⎛
=
1
0
1
0
2
cos)(
2
sin)()(
N
n
N
n
N
kn
kxj
N
kn
kxnX
ππ
(6)
The difference between Eq. 5 and 6 is the type of coefficients the sinusoids are taking, and the
minus sign, and that’s all. The coefficients by convention are defined as time domain samples
x(k) for the FFT and X(n) frequency bin values for the IFFT.
The two processes are a linear pair. Using both in sequence will give the original result back.
Copyright 2004 Charan Langton www.complextoreal.com
10. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 10
(a) a time domain signal comes out as a spectrum out of a FFT and IFFT. They both do the same thing.
(b) A frequency domain signal comes out as a time domain signal out of a IFFT.
c) The pair return back the original input.
(d) The pair return back the input no matter what it is.
(e) the pair is commutable so they can be reversed and they will still return the original input.
Fig 15 – FFT and IFFT are a matched linear pair.
Copyright 2004 Charan Langton www.complextoreal.com
11. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 11
Column 1 of Table I the signal bits, can be considered the amplitudes of a certain range of
sinusoids. So we can use the IFFT to produce a time domain signal. You say, they are already in
time domain, how can we process a time domain signal to produce an another time domain
signal? The answer is that we pretend that the input bits are not time domain representations but
are frequency amplitudes which if you are thinking clearly, will see that that is what they are. In
this way, we can take these bits and by using the IFFT, we can create an output signal which is
actually a time-domain OFDM signal.
The IFFT is a mathematical concept and does not really care what goes in and what goes out. As
long as what goes in is amplitudes of some sinusoids, the IFFT will crunch these numbers to
produce a correct time domain result. Both FFT and IFFT will produce identical results on the
same input. But most of us are not used to thinking of FFT/IFFT this way. We insist that only
spectrums go inside the IFFT.
Keeping with that mindset, each row of Table I can be considered a spectrum as plotted below.
These rows aren’t actually spectrums, but that does not matter. Each row spectrum has only 4
frequencies which are 1, 2, 3 and 4 Hz . Each of these spectrums can be converted to produce a
time-domain signal which is exactly what an IFFT does. Only in this case, the input is really a
time domain signal disguising as a spectrum..
Spectrum 1
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4
Frequency
Amplitude
Spectrum 2
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4
Frequency
Amplitude
Spectrum 3
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4
Frequency
Amplitude
Spectrum 4
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4
Frequency
Amplitude
Fig. 16 – The incoming block of bits can be seen as a four bin spectrum, The IFFT converts this
“spectrum” to a time domain OFDM signal for one symbol, which actually has four bits in it.
IFFT quickly computes the time-domain signal instead of having to do it one carrier at time and
then adding. Calling this functionality IFFT may be more satisfying because we are producing a
time domain signal, but it is also very confusing. Because FFT and IFFT are linear processes and
completely reversible, it should be called a FFT instead of a IFFT. The results are the same
whether you do FFT or IFFT. In literature you will see it listed as IFFT everywhere. You can
show you cleverness by recognizing that this block can also be a FFT as long as on the receive
side, you do the reverse.
Copyright 2004 Charan Langton www.complextoreal.com
12. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 12
The functional block diagram of how the signal is modulated/demodulated is given below.
Fig 17 – The OFDM link functions
Defining fading
If the path from the transmitter to the receiver either has reflections or obstructions, we can get
fading effects. In this case, the signal reaches the receiver from many different routes, each a
copy of the original. Each of these rays has a slightly different delay and slightly different gain.
The time delays result in phase shifts which added to main signal component (assuming there is
one.) causes the signal to be degraded.
Tree0
0
Line of sight path gain
Pathdelay
α
τ
=
=
1
1
Secondary path gain
Secondary pathdelay
α
τ
=
=
k
k
Secondary path gain
Secondary pathdelay
α
τ
=
=
Faded path
Reflected multipath
1
0
0
0
( ) ( )
ex p
K
c k k
k
k
k k
h t t
Compl ath gain
Normalized path delay relativeto LOS
difference in pathtime
α δ τ
α
τ
τ τ
−
=
= −
=
=
∆ = −
∑
Fig. 18 – Fading is big problem for signals. The signal is lost and demodulation must have a way of
dealing with it. Fading is particular problem when the link path is changing, such as for a moving car
or inside a building or in a populated urban area with tall building.
If we draw the interferences as impulses, they look like this
Copyright 2004 Charan Langton www.complextoreal.com
13. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 13
0α
1α kα
1∆
k∆0∆
Fig. 19 – Reflected signals arrive at a delayed time period and interfere with the main line of sight
signal, if there is one. In pure Raleigh fading, we have no main signal, all components are reflected.
In fading, the reflected signals that are delayed add to the main signal and cause either gains in
the signal strength or deep fades. And by deep fades, we mean that the signal is nearly wiped out.
The signal level is so small that the receiver can not decide what was there.
The maximum time delay that occurs is called the delay spread of the signal in that environment.
This delay spread can be short so that it is less than symbol time or larger. Both cases, cause
different types of degradations to the signal. The delay spread of a signal changes as the
environment is changing as all cell phone users know.
Fig. 19 shows the spectrum of the signal, the dark line shows the response we wish the channel to
have. It is like a door through which the signal has to pass. The door is large enough that it allows
the signal to go through without bending or distortion. A fading response of the channels is
something like shown in Fig.20 b, we note that at some frequencies in the band, the channel does
not allow any information to go through, so called deep fades frequencies. This form of channel
frequency response is called frequency selective fading because it does not occur uniformly
across the band. It occurs at selected frequencies. And who selects these frequencies.
Environment. If the environment is changing such as for a moving car, then this response is also
changing and the receiver must have some way of dealing with it.
Rayleigh fading is a term used when there is no direct component and all signals reaching the
receiver are reflected. This type of environment is called Rayleigh fading.
In general when the delay spread is less than one symbol, we get what is called flat fading. When
delay spread is much larger than one symbol that it is called frequency-selective fading.
Copyright 2004 Charan Langton www.complextoreal.com
14. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 14
Fig. 20 – (a) The signal we want to send and the channel frequency response are well matched. (b) A
fading channel has frequencies that do not allow anything to pass. Data is lost sporadically. (c) With
OFDM, where we have many little sub-carriers, only a small sub-set of the data is lost due to fading.
An OFDM signal offers an advantage in a channel that has a frequency selective fading response.
As we can see, when we lay an OFDM signal spectrum against the frequency-selective response
of the channel, only two sub-carriers are affected, all the others are perfectly OK. Instead of the
whole symbol being knocked out, we lose just a small subset of the (1/N) bits. With proper
coding, this can be recovered.
The BER performance of an OFDM signal in a fading channel is much better than the
performance of QPSK/FDM which is a single carrier wideband signal. Although the underlying
BER of a OFDM signal is exactly the same as the underlying modulation, that is if 8PSK is used
to modulate the sub-carriers, then the BER of the OFDM signal is same as the BER of 8PSK
signal in Gaussian channel. But in channels that are fading, the OFDM offers far better BER than
a wide band signal of exactly the same modulation. The advantage here is coming from the
diversity of the multi-carrier such that the fading applies only to a small subset.
In FDM carriers, often the signal is shaped with a Root Raised Cosine shape to reduce its
bandwidth, in OFDM since the spacing of the carriers is optimal, there is a natural bandwidth
advantage and use of RRC does not buy us as much.
Copyright 2004 Charan Langton www.complextoreal.com
15. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 15
Delay spread and the use of cyclic prefix to mitigate it
You are driving in rain, and the car in front splashes a bunch of water on you. What do you do?
You move further back, you put a little distance between you and the front car, far enough so that
the splash won’t reach you. If we equate the reach of splash to delay spread of a splashed signal
then we have a better picture of the phenomena and how to avoid it.
Delayed splash from front symbol
Symbol 1 Symbol 2
Fig. 21 – Delay spread is like the undesired splash you might get from the car ahead of you. In
fading, the front symbol similarly throws a splash backwards which we wish to avoid.
Increase distance from car in front to avoid splash. The reach of splash is same as the delay
spread of a signal. Fig. 22a shows the symbol and its splash. In composite, these splashes become
noise and affect the beginning of the next symbol as shown in (b).
Fig. 21 – The PSK symbol and its delayed version.
(a) The delayed, attenuated signal and (b) composite interference.
To mitigate this noise at the front of the symbol, we will move our symbol further away from the
region of delay spread as shown below. A little bit of blank space has been added between
symbols to catch the delay spread.
Fig 22 – Move the symbol back so the arriving delayed signal peters out in the gray region. No
interference to the next symbol!
But we can not have blank spaces in signals. This is won’t work for the hardware which likes to
crank out signals continuously. So it’s clear we need to have something there. Why don’t we just
let the symbol run longer as a first choice?
Copyright 2004 Charan Langton www.complextoreal.com
16. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 16
Fig. 23 – If we just extend the symbol, then the front of the symbol which is important to us since
it allows figuring out what the phase of this symbol is, is now corrupted by the “splash”.
We extend the symbol into the empty space, so the actual symbol is more than one cycle.
But now the start of the symbol is still in the danger zone, and this start is the most important
thing about our symbol since the slicer needs it in order to make a decision about the bit. We do
not want the start of the symbol to fall in this region, so lets just slide the symbol backwards, so
that the start of the original symbol lands at the outside of this zone. And then fill this area with
something.
Fig. 24 – If we move the symbol back and just put in convenient filler in this area, then not only we
have a continuous signal but one that can get corrupted and we don’t care since we will just cut it out
anyway before demodulating.
Slide the symbol to start at the edge of the delay spread time and then fill the guard space with a
copy of what turns out to be tail end of the symbol.
1. We want the start of the symbol to be out of the delay spread zone so it is not corrupted and
2. We start the signal at the new boundary such that the actual symbol edge falls out side this
zone.
We will be extending the symbol so it is 1.25 times as long, to do this, copy the back of the
symbol and glue it in the front. In reality, the symbol source is continuous, so all we are doing is
adjusting the starting phase and making the symbol period longer. But nearly all books talk about
it as a copy of the tail end. And the reason is that in digital signal processing, we do it this way.
Copyright 2004 Charan Langton www.complextoreal.com
17. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 17
Original symbol
Portion added in
the front
Copy this part at front
Symbol 1 Symbol 2 Copy this part at front
Original symbolExtension
Fig. 25 – Cyclic prefix is this superfluous bit of signal we add to the front of our precious cargo, the
symbol.
This procedure is called adding a cyclic prefix. Since OFDM, has a lot of carriers, we would do
this to each and every carrier. But that’s only in theory. In reality since the OFDM signal is a
linear combination, we can add cyclic prefix just once to the composite OFDM signal. The prefix
is any where from 10% to 25% of the symbol time.
Here is an OFDM signal with period equal to 32 samples. We want to add a 25% cyclic shift to
this signal.
1. First we cut pieces that are 32 samples long.
2. Then we take the last .25 (32) = 8 samples, copy and append them to the front as shown.
Fig. 26 – The whole process can be done only once to the OFDM signal, rather than doing it to each
and every sub-carrier.
We add the prefix after doing the IFFT just once to the composite signal. After the signal has
arrived at the receiver, first remove this prefix, to get back the perfectly periodic signal so it can
be FFT’d to get back the symbols on each carrier.
However, the addition of cyclic prefix which mitigates the effects of link fading and inter symbol
interference, increases the bandwidth.
Copyright 2004 Charan Langton www.complextoreal.com
18. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 18
Fig 27 – Addition of Cyclic prefix to the OFDM signal further improves its ability to deal with fading
and interference.
Properties of OFDM
Spectrum and performance
0 Rs 2Rs 3Rs 4Rs 5Rs-4Rs -3Rs -2Rs -Rs
0 Rs 2Rs 3Rs 4Rs 5Rs-4Rs -3Rs -2Rs -Rs
Fig. 28 – The spectrum of an OFDM signal (without addition of cyclic prefix) is much more
bandwidth efficient than QPSK.
Unshaped QPSK signal produces a spectrum such that its bandwidth is equal to (1+ α )Rs. In
OFDM, the adjacent carriers can overlap in the manner shown here. The addition of two carriers,
now allows transmitting 3Rs over a bandwidth of -2Rs to 2Rs or total of 4Ts. This gives a
bandwidth efficiency of 4/3 Hz per symbol for 3 carriers and 6/5 for 5 carriers.
As more and more carriers are added, the bandwidth approaches,
1N
N
+
bits per Hz.
So the larger the number of carriers, the better. Here is a spectrum of an OFDM signal. Note that
the out of band signal is down by 50 dB without any pulse shaping.
Copyright 2004 Charan Langton www.complextoreal.com
19. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 19
Fig. 29 – the spectrum of an OFDM signal with 1024 sub-carriers
Compare this to the spectrum of a QPSK signal, not how much lower the sidebands are for
OFDM and how much less is the variance.
Fig. 30 – the spectrum of a QPSK signal
Bit Error Rate performance
The BER of an OFDM is only exemplary in a fading environment. We would not use OFDM is a
straight line of sight link such as a satellite link. OFDM signal due to its amplitude variation does
not behave well in a non-linear channel such as created by high power amplifiers on board
satellites. Using OFDM for a satellite would require a fairly large backoff, on the order of 3 dB,
so there must be some other compelling reason for its use such as when the signal is to be used
for a moving user.
Peak to average power ratio (PAPR)
If a signal is a sum of N signals each of max amplitude equal to 1 v, then it is conceivable that we
could get a max amplitude of N that is all N signals add at a moment at their max points. The
PAPR is defined as
Copyright 2004 Charan Langton www.complextoreal.com
20. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 20
2
( )
avg
x t
R
P
=
Fig. 31 – AN OFDM signal is very noise like. It looks just like a composite multi-FDM signal.
For an OFDM signal that has 128 carriers, each with normalized power of 1 w, then the max
PAPR can be as large as log (128) or 21 dB. This is at the instant when all 128 carriers combine
at their maximum point, unlikely but possible. The RMS PAPR will be around half this number
or 10-12 dB. This same PAPR is seen in CDMA signals as well.
The large amplitude variation we see in Fig. 12 increases in-band noise and increases the BER
when the signal has to go through amplifier non-linearities. Large back off is required in such
cases. This makes use of OFDM just as problematic as Multi-carrier FDM in high power
amplifier applications such as satellite links.
What can be done about the large PAPR? Several ideas are used to mitigate it.
1. Clipping
We can just clip the signal at a desired power level. This reduces the PAPR but
introduces other distortions and ICI.
2. Selective Mapping
Multiply the data signal by a set of codes, do the IFFT on each and then pick the one with
the least PAPR. This is essentially doing the process many times using a CDMA like code.
3. Partial IFFT
Divide the signal in clusters, do IFFT on each and then combine these. So that if we
subdivide 128 carrier in to a group of four 32 carriers, each, the max PAPR of each will be 12 dB
instead of 21 for the full. Combine these four sequences to create the transmit signal.
These are some of the things that people are doing to keep the effect of the non-linearity
manageable.
Synchronization.
The other problem is that tight synchronization is needed. Often pilot tones are served in the sub-
carrier space. These are used to lock on phase and to equalize the channel.
Coding
The sub-carriers are typically coded with Convolutional coding prior to going through IFFT. The
coded version of OFDM is called COFDM or Coded OFDM.
Parameters of real OFDM
Copyright 2004 Charan Langton www.complextoreal.com
21. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 21
The OFDM use has increased greatly in the last 10 years. It is now proposed for radio
broadcasting such as in Eureka 147 standard and Digital Radio Mondiale (DRM). OFDM is used
for modem/ADSL application where it coexists with phone line. For ADSL use, the channel, the
phone line, is filtered to provide a high SNR. OFDM here is called Discrete Multi Tone (DMT.)
(Remember the special filters on you phone line if you have cable modem.) OFDM is also in use
in your wireless internet modem and this usage is called 802.11a. Let’s take a look at some
parameters of this application of OFDM. The summary of these are given below.
Data rates
6 Mbps to 48 Mbps
Modulation
BPSK, QPSK, 16 QAM and 64 QAM
Coding
Convolutional concatenated with Reed Solomon
FFT size
64 with 52 sub-carriers uses, 48 for data and 4 for pilots.
Subcarrier frequency spacing
20 MHz divided by 64 carriers or .3125 MHz
FFT period
Also called symbol period, 3.2 µsec = 1/∆f
Guard duration
One quarter of symbol time, 0.8 µsec
Symbol time
4 µsec
http://www.csee.wvu.edu/wcrl/public/jianofdm.pdf
http://www.drm.org/indexdeuz.htm
__________________________________________
This tutorial by
Charan Langton
www.complextoreal.com
Copyright 2004
All Rights reserved
Copyright 2004 Charan Langton www.complextoreal.com
22. Orthogonal Frequency Division Multiplex (OFDM) Tutorial 22
Copyright 1998, 2002 Charan Langton
I can be contacted at
mntcastle@earthlink.net
Other tutorials at
www.complextoreal.com
Copyright 2004 Charan Langton www.complextoreal.com