This document provides an introduction and overview of orthogonal frequency division multiplexing (OFDM). It discusses the limitations of single-carrier transmission at high data rates due to inter-symbol interference (ISI) and the complexity of equalizers. OFDM is presented as a solution that divides the available bandwidth into multiple orthogonal subcarriers. The key concepts of OFDM covered include cyclic prefix, orthogonality of subcarriers, modulation and demodulation, and how the cyclic prefix mitigates ISI between symbols. Bit error rate simulation of an OFDM system is also demonstrated.
Design Ofdm System And Remove Nonlinear Distortion In OFDM Signal At Transmit...Rupesh Sharma
although OFDM seems to be a solution to keep up with
the demand of increasing data rates, it has some drawbacks.
Sensitivity to high PAPR is the most significant of these
drawbacks. The main objective of this paper was to investigate
and document the effects of PAPR on the performance of OFDM
based digital communications under different channel conditions.
A step-by-step approach was adopted in order to achieve the
objective of this paper. The first step is to provide a basic
background on the principles of OFDM. The reasons for the
PAPR and a theoretical analysis of these effects on OFDM
systems are documented. The OFDM system has a high peak-toaverage
power ratio (PAPR) that can cause unwanted saturation
in the power amplifiers, leading to in-band distortion and out-ofband
radiation. To be able to observe the system behavior, the
simulation results for different channel models are presented in
graphical form. Next, the simulation results obtained in this work
are compared to the simulation results reported in related studies
Design Ofdm System And Remove Nonlinear Distortion In OFDM Signal At Transmit...Rupesh Sharma
although OFDM seems to be a solution to keep up with
the demand of increasing data rates, it has some drawbacks.
Sensitivity to high PAPR is the most significant of these
drawbacks. The main objective of this paper was to investigate
and document the effects of PAPR on the performance of OFDM
based digital communications under different channel conditions.
A step-by-step approach was adopted in order to achieve the
objective of this paper. The first step is to provide a basic
background on the principles of OFDM. The reasons for the
PAPR and a theoretical analysis of these effects on OFDM
systems are documented. The OFDM system has a high peak-toaverage
power ratio (PAPR) that can cause unwanted saturation
in the power amplifiers, leading to in-band distortion and out-ofband
radiation. To be able to observe the system behavior, the
simulation results for different channel models are presented in
graphical form. Next, the simulation results obtained in this work
are compared to the simulation results reported in related studies
orthogonal frequency division multiplexing(OFDM)
its orthogonal frequency multiplexing topic basicallly in digital signal processing , network signal and system , it also helpful in engineering course either electrical or electronics and communication engineering.
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).
In this chapter we examine the capacity of a single-user wireless channel where transmitter and/or receiver have a single antenna. We will discuss capacity for channels that are both time invariant and time varying. We first look at the well-known formula for capacity of a time-invariant additive white Gaussian noise (AWGN) channel and then consider capacity of time-varying flat fading channels. We will first consider flat fading channel capacity where only the fading distribution is known at the transmitter and receiver. We will also treat capacity of frequency-selective fading channels. For time -invariant frequency-selective channels the capacity is known and is achieved with an optimal power allocation that water-fills over frequency instead of time. We will consider only discrete-time systems in this chapter.
orthogonal frequency division multiplexing(OFDM)
its orthogonal frequency multiplexing topic basicallly in digital signal processing , network signal and system , it also helpful in engineering course either electrical or electronics and communication engineering.
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).
In this chapter we examine the capacity of a single-user wireless channel where transmitter and/or receiver have a single antenna. We will discuss capacity for channels that are both time invariant and time varying. We first look at the well-known formula for capacity of a time-invariant additive white Gaussian noise (AWGN) channel and then consider capacity of time-varying flat fading channels. We will first consider flat fading channel capacity where only the fading distribution is known at the transmitter and receiver. We will also treat capacity of frequency-selective fading channels. For time -invariant frequency-selective channels the capacity is known and is achieved with an optimal power allocation that water-fills over frequency instead of time. We will consider only discrete-time systems in this chapter.
CS Based Channel Estimation for OFDM Systems under Long Delay Channels Using ...IJERA Editor
Orthogonal frequency division multiplexing (OFDM) is a technique which are used in the next-generation wireless communication. Channel estimation in the OFDM technique is one of the big challenges, ever since high-resolution channel estimation can significantly improve the equalization at the receiver and consequently enhance the communication performances. Channel computation using superimposed pilot sequences is also a fully new area, idea for using superimposed pilot sequences has been proposed by various authors for different applications. In this paper, we are introduced a high accurate, low complexity compressive sensing (CS) based channel estimation namely Auxiliary information based Subspace Pursuit (ASP) in TFT-OFDM systems. ASP based channel estimation in TFT-OFDM system is based on two steps. First is, by exploiting the signal structure of recently proposed TDM-OFDM scheme, the supporting channel information is obtained. Second is, we propose the supporting information based subspace pursuit (SP) algorithm to use a very small amount of frequency domain pilots embedded in the OFDM block used for the exact channel estimation. Moreover, the obtained auxiliary channel information is adopted to reduce the complexity of the conventional SP algorithm. Simulation results demonstrate a important reduction of the number of pilots relative to least-squares channel estimation and supporting high-order modulations like 256 QAM.
Multi-carrier Equalization by Restoration of RedundancY (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.
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.
A blind channel shortening for multiuser, multicarrier CDMA system over multi...TELKOMNIKA JOURNAL
In this paper we derive the Multicarrier Equalization by Restoration of Redundancy (MERRY) algorithm: A blind, adaptive channel shortening algorithm for updating a Time-domain Equalizer (TEQ) in a system employing MultiCarrier Code Division Multiple Access (MC-CDMA) modulation. We show that the MERRY algorithm applied to the MC-CDMA system converges considerably more rapidly than in the Orthogonal Frequency Division Multiplexing (OFDM) system [1]. Simulations results are provided to demonstrate the performance of the algorithm.
Distributed Architecture of Subspace Clustering and RelatedPei-Che Chang
Distributed Architecture of Subspace Clustering and Related
Sparse Subspace Clustering
Low-Rank Representation
Least Squares Regression
Multiview Subspace Clustering
Probabilistic Matrix Factorization (PMF)
Bayesian Probabilistic Matrix Factorization (BPMF) using
Markov Chain Monte Carlo (MCMC)
BPMF using MCMC – Overall Model
BPMF using MCMC – Gibbs Sampling
Deterministic MIMO Channel Capacity
• CSI is Known to the Transmitter Side
• CSI is Not Available at the Transmitter Side
Channel Capacity of Random MIMO Channels
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
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Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
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Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
2. 2
Single-Carrier vs. Multi-Carrier Transmission
Basic Principle of OFDM
Coded OFDM
OFDMA: Multiple Access Extensions of OFDM
Duplexing
Agenda
3. 3
Single-Carrier vs. Multi-Carrier Transmission
Basic Principle of OFDM
Coded OFDM
OFDMA: Multiple Access Extensions of OFDM
Duplexing
Agenda
4. 4
Single-Carrier Baseband Transmission: System Model
Fig. Single-carrier baseband communication system model
where z(t) is an additive noise and g(t) is the impulse response of overall end-to-end system given as
The equalizer is designed to compensate the effect of channel.
When the noise term is ignored, the sampled output signal of the equalizer can be expressed as:
Isolating the nth sample to detect an:
5. 5
Fig. Illustration: inter-symbol interference (ISI) and symbol period.
ISI
As illustrated here, the extent of ISI depends on the duration of a symbol period T: the shorter the symbol
period is, the larger the influence of the ISI may become.
ISI becomes significant as the data rate (R = 1/T) increases (i.e., decreasing T in Fig.) in a single-carrier system.
6. 6
ISI and Nyquist Criterion
ISI can be completely eliminated by fulfilling the following time-domain condition on the overall impulse response:
equivalent
Nyquist filter is an ideal LPF, which has a sinc function-type of impulse response or equivalently, rectangular pulse (or brick-wall)
type of frequency response as described by
Where W = R/2 = 1/(2T). R and W correspond to the Nyquist rate and Nyquist bandwidth, respectively.
Note that the Nyquist bandwidth W is the minimum possible bandwidth that is required to realize the date rate R without ISI.
Another well-known physically realizable Nyquist filter is the raised-cosine filter, which frequency response:
Ideal filter is not physically realizable.
where r is the roll-off factor, 0 ≤ r ≤ 1.
( ) 2 2 2
sin / cos /
/ 1 4 /
S S
RC
S S
t T t T
h t
t T t T
π απ
π α
= ⋅
−
https://gist.github.com/oklachumi/1359d9a4acb697c21b93c5bfb147cb6a
9. 9
Limitation of Single-Carrier Transmission for High Data Rate
In order to support the symbol rate of Rs symbols per second, the minimum required bandwidth is the Nyquist bandwidth, BW =
Rs/2 [Hz].
In a single-carrier transmission, higher data rate → need wider BW (assumed that channel is perfectly compensated by equalizer).
When the signal BW > coherence bandwidth in the wireless channel, the link suffers from multi-path fading, incurring ISI.
Adaptive equalizers are employed to deal with the ISI incurred by the time-varying multi-path fading channel.
The complexity of an equalizer increases with the data rate.
FIR filters with the adaptive tap coefficients that are adjusted so as to minimize the effect of ISI.
More equalizer taps are required as the ISI becomes significant.
The optimum detector for the multi-path fading channel is a maximum-likelihood sequence detector (MLSD), which bases on the
observation of a sequence of received symbols over successive symbol intervals, maximizing the posteriori probability.
(Complexity depends on the modulation order and the number of multi-paths).
Due to a memory of length L for the span of ISI, ML corresponding Euclidean distance path metrics must be evaluated to select the
best sequence in the MLSD.
6416 for L = 16 with 64-QAM at the data rate of 10 Mbps over the multi-path fading channel with a delay spread of 10 ms.
When M and L are too large, MMSE or LS equalizer, can be used.
The complexity of these suboptimum equalizers is still too enormous to be implemented as the ISI increases with the data rate.
A high data rate single-carrier transmission may not be feasible due to too much
complexity of the equalizer in the receiver.
10. 10
Basic Structure of a Multi-Carrier Transmission Scheme
Frequency-selective wideband channel can be approximated
by multiple frequency-flat narrowband channels.
Frequency-nonselectivity of narrowband channels reduces
the complexity of the equalizer for each subchannel.
As long as the orthogonality among the subchannels is
maintained, the ICI can be suppressed, leading to
distortionless transmission.
Fig. Structure and frequency characteristic of multichannel transmission system
11. 11
Fig. Structure and spectral characteristic of multicarrier transmission system.
FMT (Filtered Multi-Tone) transmission
FMT type of multicarrier transmission system can cope with the frequency selectivity of a wideband
channel.
But implementation becomes complex since it involves more encoders/decoders and oscillators,
and higher quality filters as # subcarriers increases.
12. 12
OFDM Transmission Scheme
OFDM scheme places a guard band at outer
subcarriers, called virtual carriers (VCs),
around the frequency band to reduce the
out of band radiation.
OFDM scheme also inserts a guard interval in
the time domain, called cyclic prefix (CP),
which mitigates the ISI between OFDM
symbols.
19. 19
% to plot several sinusoidal signals with different frequencies/phases and their DFT sequences to check their orthogonality
% {exp(j2π*fk*t)},0≤k≤N-1,fk=k/Tsym
clear,close,clc all
T = 1.6; % period = 1.6s in equations is Tsym
ND = 1000;
nn = 0:ND;
ts = 0.002;
tt = nn*ts; % time interval 0, 0.002, 0.004..., 2 [x-axis]
Ts =0.1; % Sampling period in continuous time
M = round(Ts/ts); % Sampling period in discrete time
nns = [1:M:ND+1]; % Sampling indices
tts = (nns-1)*ts; % Sampling times
ks = [1:4 3.9 4]; % Frequency indices
tds = [0 0 0.1 0.1 0 0.15]; %delay times
K = length(ks);
for i = 1:K
k = ks(i);
td = tds(i);
x(i,:) = exp(j*2*pi*k*(tt-td)/T); % [y-axis]
if i == K
x(K,:) = [x(K,[302:end]) x(K-3,[1:301])];
endif
title_string = sprintf('cos(2pi*%1.1f*(t-%4.2f)/%2.1f)',k,td,T);
subplot(K,2,2*i-1); % 6 x 2
plot(tt,real(x(i,:)),'LineWidth',1); title(title_string);
hold on;
plot(tt([1 end]),[0 0],'k'); % plot([xi xf],[yi yf])
set(gca,'fontsize',10);
axis([tt([1 end]) -1.2 1.2]); % axis([xi xf yi yf])
stem(tts,real(x(i,nns)),'.','markersize',7);
endfor
N = round(T/Ts);
xn = x(:,nns(1:N));
xn*xn'/N % check orthogonality
Xk = fft(xn.').';
kk = 0:N-1;
for i = 1:K
k = ks(i);
td = tds(i);
title_string = sprintf('DFT of cos(2pi*%1.1f*(t-%4.2f)/%2.1f), t=[0:%d]*%3.2f',k,td,T,N-1,Ts);
subplot(K,2,2*i); % 6 x 2
stem(kk,abs(Xk(i,:)),'.','markersize',7); title(title_string);
set(gca,'fontsize',10,'xtick',[k]);
axis([0 N 0 20]);
endfor
https://gist.github.com/oklachumi/f41c1f5af7e9f3c1684307d5575753b1
20. 20
OFDM Modulation and Demodulation: Tx
1. OFDM transmitter maps the message bits into a sequence of PSK or QAM symbols.
2. A sequence of PSK or QAM symbols will be subsequently converted into N parallel streams.
3. Each of N symbols from serial-to-parallel (S/P) conversion is carried out by the different subcarrier.
22. 22Fig. Illustrative block diagram of OFDM modulation and demodulation: N = 6.
continuous-time baseband OFDM signal
discrete-time OFDM symbol
The frequency-domain symbol X[k] modulates the subcarrier with a frequency of fk = k/Tsym.
Original symbol X[k] has simpling period Ts, but its length has been extended to Tsym = NTs by
transmitting N symbols in a parallel form.
23. 23
Fig. Block diagram of transmitter and receiver in an OFDM system.
(S/P)
Pulse
shaping
(S/P)
25. 25
The first received symbol (plotted in a solid line) is mixed up with the
second received symbol (plotted in a dotted line), which incurs the ISI.
It is obvious that all subcarriers are no longer orthogonal over the
duration of each OFDM symbol.
Fig. Effect of a multipath channel on the received
signal without guard interval.
26. 26
Cyclic Prefix (CP)
OFDM guard interval can be inserted in two different ways.
One is the zero padding (ZP) that pads the guard interval with zeros.
The other is the cyclic extension of the OFDM symbol (for some continuity) with CP (cyclic prefix) or CS (cyclic suffix).
27. 27
If the length of the guard interval (CP) is set ≥ the maximum
delay of a multipath channel, the ISI effect of an OFDM symbol
(plotted in a dotted line) on the next symbol is confined within
the guard interval so that it may not affect the FFT of the next
OFDM symbol, taken for the duration of Tsub.
Guard interval longer than the maximum delay of the
multipath channel allows for maintaining the orthogonality
among the subcarriers.
28. 28
Fig. ISI/ICI effect depending on the FFT window
start point.
Fig. ISI effect of a multipath channel on OFDM
symbols with CP length shorter than the
maximum delay of the channel.
29. 29
Suppose:
1. CP length is set ≥ the maximum delay of the channel.
2. The FFT window start point of an OFDM symbol is determined within its CP interval (i.e., unaffected by the previous symbol).
The OFDM receiver takes the FFT of the received samples:
Fig. Frequency-domain equivalent model of OFDM system.
circular convolution!!
Insertion CP in the transmitter makes the transmit samples
circularly-convolved with the channel samples, which yields
as desired in the receiver.[ ] [ ] [ ]l l lY k H k X k=
30. 30
Cyclic Suffix (CS)
The length of CP is set to cover the time dispersion of the channel.
The length of CS is set according to the difference between the upstream transmit time and downstream receive time.
Fig. shows the structure of the OFDM symbol used in Zipper-based VDSL systems, where the length of the guard interval is the
sum of CP length TCP and CS length TCS.
32. 32
Fig. Copying-and-adding the guard interval of the next symbol into the head part
of the current symbol to prevent ICI.
Fig. Power spectra of two OFDM symbols, one with ZP and one with CP.
:length of a rectangular window
sinc-type spectrum
Compare OFDM with or
has PSD with the smaller inband ripple and
the larger out-of-band power.
ZP
S
ZP
CP C
↓
↑
∴
33. 33
OFDM Guard Band
Each subcarrier component of an OFDM symbol with the effective duration Tsub = a single-tone signal x a rectangular window of
length Tsub, whose spectrum is a sinc function with zero-crossing bandwidth of 2/Tsub.
OFDM PSD is the sum of many frequency-shifted sinc functions has
• Large out-of-band power such that ACI (adjacent channel interference) is incurred.
• A guard band is required to reduce the effect of ACI in the OFDM system.
To reduce the out-of-band power of OFDM symbols:
• BPF can be used, but it may require enormous computation and high complexity to make performance acceptable.
• As an alternative, a time-domain shaping function like raised cosine (RC) windowing can be used.
35. 35
Fig. Raised cosine window for OFDM symbol.
roll-off factor , RC window becomes smoother
a longer effective guard interval ACI
β ↑
⇒ ⇒ ↓
Another ACI↓ is to employ the virtual carriers (VCs), which are the unused subcarriers at both ends of the transmission band.
The spectral BW efficiency is reduced by Nused/N times due to the unused subcarriers, where Nused is the number of subcarriers
used for data transmission.
The virtual carriers (VCs) + the (RC) windowing to reduce the out-of-band power and eventually to combat the ACI.
Fig. PSD of RC windows with different roll-off factors, where 54
out of the total 64 subcarriers (excluding 10 virtual subcarriers)
are used for data transmission.
44. 44
clear,close,clc all
N = 1000; % # of data
mlevel = 4; % QAM = 4, 16 QAM = 16 and so on
k = log2(mlevel); % # of bits per symbol
% signal generation in bit stream
x = randi([0 1],N,1); % 1000*1
% convert the bit stream into symbol stream
xsym = bi2de(reshape(x,k,length(x)/k).'); %500*1
% modulation
xmod = qammod(xsym,mlevel);
Tx_x = xmod;
% adding AWGN
SNR = 1;
Tx_awgn = awgn(Tx_x,SNR,'measured');
% Received signal
Rx_x = Tx_awgn;
%demodulation
Rx_x_demod = qamdemod(Rx_x,mlevel);
z = de2bi(Rx_x_demod); % Convert integers to bits.
% Convert z from a matrix to a vector.
Rx_x_BitStream = reshape(z.',prod(size(z)),1);
[number_of_errors, bit_error_rate] = biterr(x, Rx_x_BitStream)
%plot each steps
subplot(5,2,[1 2]); stem(x(1:200),'filled'); title('Transmitted Bit Stream');
subplot(5,2,[3 4]); stem(xsym(1:50),'filled'); title('Transmitted Symbol');
subplot(5,2,5); plot(real(Tx_x),imag(Tx_x),'go','MarkerFaceColor',[0,1,0]);
axis([-mlevel/2 mlevel/2 -mlevel/2 mlevel/2]);
subplot(5,2,6); plot(real(Rx_x),imag(Rx_x),'go','MarkerFaceColor',[0,1,0]);
axis([-mlevel/2 mlevel/2 -mlevel/2 mlevel/2]);
subplot(5,2,[7 8]); stem(Rx_x_demod(1:50),'filled'); title('Recieved Symbol');
subplot(5,2,[9 10]); stem(Rx_x_BitStream(1:200),'filled'); title('Recieved BitStream');
Review…BER Calculation
45. 45
clear,close,clc all
N=32; % # sub-carriers
x=randi([0 3],1,N); % data in sub-carriers
x1=qammod(x,4); % 4QAM
f=1:N; % sub-carriers freq
t=0:0.001:1-0.001; %synbol duration time
w=2*pi*f.'*t;
%w1=2*pi*(f+0.2).'*t; % sub-carriers
modulation
y1=x1*exp(j*w); % analog mod
x2=ifft(x1,N); % IFFT
plot(t,abs(y1));
hold on;
stem(0:1/N:1-1/N,abs(x2)*N,'-r')
legend('analog modulation','IDFT realization')
title('Compare between analog mod and IDFT')
%x3=fft(x2);
Review…OFDM signal modulation
46. 46
Review…QPSK in AWGN channel octave code
https://gist.github.com/oklachumi/884d36cfd0ef07a6a703b4a2e7bc30d4
52. 52
Water-Filling Algorithm for Frequency-Domain Link Adaptation
A data rate can be adaptively varied with the channel variation. Such link adaptation is a useful means of maximizing the system
bandwidth efficiency.
One particular example of link adaptation is time-domain AMC (Adaptive Modulation and Coding) technique. It has been widely
adopted for the packet data systems (e.g., cdma2000 1x EV-DO), in which a multiple number of time slots with different channel
gains are dynamically shared among the different users in an opportunistic manner which allows for increasing the average
system throughput.
In addition to time-domain link adaptation, the AMC technique can also be applied to the frequency domain in the OFDM system.
It allows for fully taking advantage of the time-varying characteristics of the subcarriers in the frequency-selective channel for link
adaptation.
The underlying key principle in the frequency-domain AMC technique is the waterfilling (or water pouring) algorithm that
allocates more (or less) bits and power to some subcarriers with larger (or smaller) SNR for maximizing the channel capacity.
53. 53
coherence BW
, [ ] .
subcarrier, SNR .
f
k H k const
const
∆
⇒ ∀ =
⇒ ∀ =
≪
solution implies that the sums of power and NSR (noise-to-signal ratio) for each subcarrier must be the same for all subcarriers
According to this algorithm, a subcarrier with larger SNR is allocated more transmission power.
54. 54
assigned no power
According to this algorithm, a subcarrier with larger SNR is allocated more transmission power.
Fig. Optimal power allocation with the
water-filling algorithm.
55. 55
Fig. Adaptive bit loading to subcarriers in an OFDM system.
If the transmission power and BER should be the same over all subcarriers, the number of bits that can be allocated to each
subcarrier is given by
Cons:
Water-filling algorithm requires a full knowledge of channel state information for each subcarrier on the transmitter side.
Channel quality information must be exchanged between the transmitter and receiver through a feedback loop. In general,
this is not straightforward, especially in mobile environments where the channel may be steadily time-varying.
56. 56
Single-Carrier vs. Multi-Carrier Transmission
Basic Principle of OFDM
Coded OFDM
OFDMA: Multiple Access Extensions of OFDM
Duplexing
Agenda
57. 57
Coded OFDM
Some consecutive subcarriers in OFDM system suffer from deep fading, in which the received SNR is below the required SNR level.
In order to deal with the burst symbol errors due to deep fading in this multi-carrier situation, it may be essential to employ FEC
(Forward Error Correction) codes.
The popular FEC codes associated with the coded OFDM systems include RS (Reed-Solomon) code, convolutional code, TCM
(Trellis-Coded Modulation), concatenated code, turbo code, and LDPC code.
The FEC codes can make error corrections only as far as the errors are within the error-correcting capability (that is defined as the
maximum number of guaranteed correctable errors per codeword), but they may fail with burst symbol errors.
In practice, interleaving is often employed to convert the burst errors into random errors. There are two types of interleaving:
block interleaving and convolutional interleaving.
Bit-wise, data symbol-wise, or OFDM symbol-wise interleavings can be used for block interleaving.
Interleaving type and size (depth) must be determined by the type of FEC code, degree of frequency and time fading, and delay
due to interleaving.
58. 58
Fig. Example of coded OFDM: Eureka-147-based DAB.
• Figure shows FEC codes and interleaving techniques used in Eureka-147-based DAB (digital audio broadcasting), which
is a typical example of the coded OFDM system.
• Here, concatenated coding is used for FEC.
• An RS code is used for the outer code while TCM is used for the inner code.
• The outer interleaver and inner interleaver are used to separate error bursts from inner coding and to interleave
bits/symbols in the time/frequency domain, respectively.
59. 59
OFDM (Orthogonal Frequency Division Multiplexing)
一種多載波調製技術
較強的抗多徑傳播, 抗頻率選擇性衰落
較高頻譜利用率
單載波單載波單載波單載波調製調製調製調製
將傳輸的data調製到單個載波上進行傳輸
前面介紹的ASK FSK PSK數字調製皆屬於單載波調製
|C(f)
|
t
f
f
B
TB
單單單單載波載波載波載波存在問題存在問題存在問題存在問題
高速data碼元持續時間TB短, 占用帶寬B大
信道特性|C(f)|不理想→碼間串擾ISI
TB < τmax(信道最大多徑延遲差) →產生頻率選擇性衰落, 需複雜的均衡
|C(f)
|
60. 60
NTB
t
f
B/N
多載波調製子多載波調製子多載波調製子多載波調製子信信信信道道道道
頻寬: Bi = B/N < 信道的相干帶寬
碼元持續時間: Ti = NTB > 信道最大多徑時延τmax
資料傳輸速率: Ri = RB/N
|C(f)
|
t
f
f
B
TB
B
TB
多載波多載波多載波多載波調製調製調製調製
將信道分成N個子信道
高速串/並N路低速子數據流
分別調製到各個子載波上並行傳輸
單載波調製單載波調製單載波調製單載波調製 多載波調製多載波調製多載波調製多載波調製
62. 62
表表表表達達達達式式式式表表表表達達達達式式式式
設OFDM系統中有N個子信道,每個子信道採用的子載波子載波子載波子載波為:
( ) cos(2 ) 0,1,2 , -1k k k kx t B f t k Nπ φ= + = ⋯
Where Bk 、fk、ϕk -分別為第k路子載波的振幅、頻率、初始相位;
Bk 受基帶碼元的調製。則此系統中的 N 路子信號之和為:
1 1
0 0
( ) ( ) cos(2 )
N N
k k k k
k k
e t x t B f tπ φ
− −
= =
= +∑ ∑=
可改寫成:
∑
−
=
+
=
1
0
2
B
N
k
tfj
k
kk
ete )(
)( ϕπ
Bk是一個複數, 為第k路子信道中的複輸入資料
63. 63
0
1
{cos[(2 ( ) ] cos[(2 ( ) ]} 0
2
BT
k i k i k i k if f t f f t dtπ φ φ π φ φ− + − + + + + =∫
即
正交條件正交條件正交條件正交條件正交條件正交條件正交條件正交條件
為了使這N路子信道信號在接收時能夠完全分離, 要求它們滿
足正交條件。在TB內, 任意兩個子載波都正交的條件是:
[ ] [ ]
( ) ( )
sin 2 ( ) sin 2 ( )
2 ( ) 2 ( )
sin sin
0
2 ( ) 2 ( )
k i B k i k i B k i
k i k i
k i k i
k i k i
f f T f f T
f f f f
f f f f
π φ φ π φ φ
π π
φ φ φ φ
π π
+ + + − + −
+ −
+ −
+ −
− =
+ −
積分結果為
0
cos(2 )cos(2 ) 0
BT
k k i if t f t dtπ ϕ π ϕ+ + =∫
64. 64
( ) and ( )k i B k i Bf f T m f f T n+ = − =
Where m = 整數和n = 整數;並且ϕk和ϕi可以取任意值
( ) / 2 , ( ) / 2k B i Bf m n T f m n T= + = −
上式等於0的條件:
這就是OFDM子載頻正交的條件子載頻正交的條件子載頻正交的條件子載頻正交的條件
即要求子載頻滿足 fk = k/2TB ,式中 k = 整數;且要求子載頻
間隔∆∆∆∆f = fk – fi = n/TB, 要求的最小子子子子載頻間隔為:
min 1/ Bf T∆ =
68. 68
直到1971年, S. Weinstein and P. Ebert這兩位老兄提出
• 採用Discrete Fourier Transform (IDFT/DFT)實現多載波調製/解調解決方案
• 取代複雜的硬體結構
• 由於VLSI + DSP, OFDM代表的多載波調製技術實用化!!
69. 69
OFDM的實現:以MQAM調製為例
複習DFT公式
設一個時間信號s(t)的抽樣函數為s(k),其中k = 0, 1, 2, … , K– 1,
則s(k)的Discrete Fourier Transform (DFT)定義為:
並且S(n)的Inverse Discrete Fourier Transform (IDFT)為:
1
(2 / )
0
1
( ) ( )
K
j K nk
k
S n s k e
K
π
−
−
=
= ∑ )1,,2,1,0( −= Kn ⋯
∑
−
=
=
1
0
)/2(
)(
1
)(
K
n
nkKj
en
K
ks π
S )1,,2,1,0( −= Kk ⋯
74. 74
用IDFT實現OFDM
1st 令OFDM的最低子載波頻率等於0,以滿足下式
右端第一項(即n = 0時)的指數因數等於1。
為了得到所需的已調信號最終頻位置,可以用上變頻的方法將所得OFDM信號的頻譜
向上搬移到指定的高頻上。
∑
−
=
=
1
0
)/2(
)(
1
)(
K
n
nkKj
en
K
ks π
S )1,,2,1,0( −= Kk ⋯
分幀
分組
串/並
變換
編碼
映射
.
.
.
.
.
.
IDFT .
.
.
並/串
變換
D/A
變換
上
變
頻
OFDM
信號
二進位
輸入信號
75. 75
2nd 我們令K = 2N,使IDFT的項數K等於子信道數目N的2倍,並用對稱性條件:
由N個並行複數碼元序列{Bi},(其中i = 0, 1, 2, …, N – 1),生成K=2N個等效的複數碼元序列
{B’n},(其中n = 0, 1, 2, …, 2N – 1),即令{B’n}中的元素等於:
這樣將生成的新碼元序列{B’n}作為S(n),代入IDFT公式,得到
*
( ) ( )K k k− =S S )1,,2,1,0( −= Kk ⋯
*
1
1 1
0 0
1 2 1 0
, 1, 2, , 1
, , 1, 2, , 2 2
Re( )
Im( )
K n n
K n K n
K N
n N
n N N N N
− −
− − − −
− −
′ = = −
′ = = + + −
′ =
′ ′= =
B B
B B
B B
B B B
⋯
⋯
1
(2 / )
0
1
( )
K
j K nk
n
n
e k e
K
π
−
=
′= ∑B )1,,2,1,0( −= Kk ⋯
分幀
分組
串/並
變換
編碼
映射
.
.
.
.
.
.
IDFT .
.
.
並/串
變換
D/A
變換
上
變
頻
OFDM
信號
二進位
輸入信號
1
(2 / )
0
1
IDFT : ( ) ( )
K
j K nk
n
s k n e
K
π
−
=
= ∑S
76. 76
式中
相當於OFDM信號e(t)的抽樣值。
故e(t)可以表示為
子載波頻率fk = n/TB,(n = 0, 1, 2, … , N - 1)。
離散抽樣信號e(k)經過D/A變換後就得到上式的OFDM信號e(t)。
3rd 進一步克服ISI, 在計算IDFT時加入CP, 在OFDM相鄰碼元間加入保護間隔(GI).
( ) ( / )Be k e kT K=
1
(2 / )
0
1
( )
K
j K nk
n
n
e k e
K
π
−
=
′= ∑B
1
(2 / )
0
1
( ) B
K
j T nt
n
n
e t e
K
π
−
=
′= ∑B (0 )Bt T≤ ≤
分幀
分組
串/並
變換
編碼
映射
.
.
.
.
.
.
IDFT .
.
.
並/串
變換
D/A
變換
上
變
頻
OFDM
信號
二進位
輸入信號