International Journal of Engineering Trends and Technology (IJETT) – Volume 13 Number 1 – Jul 2014
Compressive Modulation in Digital
Communication Using OFDM
Lokendra Singh1, Anuj Sharma2
1Post Grad. Scholar, ECE, DIT University, Dehradun, India
2Associate Professor,ECE, DIT University, Dehradun, India
Abstract- In digital communication, the bandwidth efficiency is one of the most important parameter to measure
different modulation schemes, while the separation of waveforms in time domain of existing modulation schemes make it
difficult to improve their bandwidth efficiency. Hence, in past decade researchers and engineers continuously try to find
out the way to solve out this biggest problem in the field of communication. Finally they were able to proposed such a
scheme that is able to reconstruct the original signal in aliasing measurement, named as Compressive Sensing (CS). In
this paper, we are using proposed scheme Compressive Modulation (CM) by combining Compressive Sensing (CS) with
traditional OFDM in order to improve its bandwidth efficiency. Theoretical analysis and experimental results shows that
bandwidth efficiency of OFDM is somewhat improved by using the proposed scheme (CS).
Keywords: Compressive Sensing, Compressive Modulation, OFDM.
I. INTRODUCTION
In digital communication, every researcher is trying
to attained high bandwidth efficiency during the
modulation process of most commonly used
modulation schemes i.e. BPSK, OFDM etc. While,
due to separation of waveform in time domain of all
modulation technique makes it difficult to increase
their bandwidth in the large era of higher bandwidth.
idea of increasing bandwidth efficiency, which early
combines CS theory with traditional BPSK to make
later one more bandwidth efficient. The main
principle of CM is that, a transmitting signal can be
aliased at modulation and original signal is
reconstructed at the receiving end by using
optimization algorithm at the during demodulation.
In this paper, section II describe OFDM and CM
scheme with in detail.
The bandwidth efficiency of OFDM is given as:
II. COMPRESSIVE MODULATION
η =(
×
)
=
(1)
for, reliable transmission ⁄ ≥ 1or η≤ 1. While
it is desirable that, for OFDM η should be equal to 1.
Thus latest work in this field leads to a technique
named as Compressive Sensing (CS) which states
that it is possible to reconstruct a original signal from
the few number of samples of that signal. By the help
of CS theory compressible signals can capture and
represented at the rate lower than nyquist rate. CS
theory also able to deal with sparse signal as well as
with under sampled signal containing noise. This also
says that OFDM code element that carries
information is aliased in time domain at transmitter
end during modulation. The aliasing process can be
achieved by first multiplying the code elements by a
sinusoidal carrier wave, then adding the current
elementary modulated code element with the next
shifted code (in forward) for a portion of the carrier
wave period. Compressing and adding all the code
elements provides a time domain aliasing modulated
signal. Compressive Modulation (CM) is the core
ISSN: 2231-5381
In order to make OFDM more bandwidth efficient we
combine it with Compressive Sensing and hence
leads to new technique called Compressive
Modulation.
A. OFDM (Orthogonal
Multiplexing)
Frequency
Division
In Orthogonal Frequency Division Multiplexing
(OFDM) the whole channel is divided into many sub
channels which have narrow bandwidth and are used
in parallel transmission, which leads to increment in
symbol duration with reduction in ISI (Inter Symbol
Interference). Due to this, OFDM becomes a
effective technique which able to combat multipath
fading and have high-bit-rate transmission for mobile
wireless channels. OFDM is based on the wellknown technique of Frequency Division Multiplexing
(FDM). In FDM different streams of information are
mapped onto separate parallel frequency channels
and each channel is separated by a frequency guard
band to reduce interference among the adjacent
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International Journal of Engineering Trends and Technology (IJETT) – Volume 13 Number 1 – Jul 2014
channels. While OFDM is minutely differ from FDM
in following ways i.e.:



Multiple carriers are used to carry the
information data streams.
All the subcarriers are orthogonal to each
other.
A guard time is added to each symbol to
reduce the time delay spread and inter
symbol interferences.
one signal by using optimization algorithm. So, in
this theory we make the aliased modulated signal in
time domain in order to make it easy for improving
its bandwidth.
An OFDM signal that is to be transmitted is represent
as: let consider that N symbols ( ) have to transmit
in the
OFDM symbol period through N sub
channels
of
subcarriers
spacing
1/(N ),
x (t ) 
Ts
NT f

j
N 1

s n ( i ) v ( t  iNT ) e
N 1 

2  n 
 ( t  iNT )
2 

NT f
i   n  0
(2)
Where, T is the symbol period of data, NT is the
OFDM symbol period, 1/
is approx. the total
bandwidth of OFDM signal, and v(t) is the OFDM
symbol pulse shaping filter.
The bandwidth efficiency of OFDM is given as:
η =(
Fig.1. Compressive Sensing Acquisition Process
×
)
=
where, T is symbol period and
bandwidth of OFDM.
is approx.
Acquisition of CS based signal is more efficient than
simple sampling for sparse or compressible signal.
Let us consider that x(t) is a analog signal that
sampled at nyqist rate and processed with N samples
in frames. Each frame is N× vector, x is given as
x= ΨX, where Ψ is an N×N matrix whose columns
are the similarly sampled basis function
given by = , where Ψ is an
matrix whose
Ψ ( ), and X is the vector that chooses the linear
combination of the basis function, X is thought as
that x is in domain of Ψ, X is considered as sparse
signal for CS for its well performance.
is
considered as -sparse if it contains only nonzero
elements.
In OFDM system, ICI (Inter Carrier Interference) and
ISI have very important place because without these
interference, the computational efficient FFT (Fast
Fourier Transform) is applied for decoupling of subchannels and their equalization is obtained simply by
complex scalar. Major drawback of OFDM system
without ISI and ICI are: First, a guard band should be
used which is longer than channel delay in each
OFDM symbol, which results in loss of bandwidth
efficiency utilization. Second, demodulation method
based on FFT is simple and do not use sufficient
statistics for equalization of channel due to which
performance degrades. In this paper, this problem of
bandwidth efficiency is combat by using CM scheme.
B. COMPRESSIVE MODULATION
Fig.2. parallel segmented compressed sensing.
1). Modulation scheme
The basic principle of CS theory is that, if a signal is
sparse in a time domain, it will be treated as aliased
and then that aliased signal is converted into original
ISSN: 2231-5381
According to CS theory x can be reconstructed
successfully from M measurements, where M≪ The measurement is achieved by projecting x over
another random basis Ф that is incoherent with Ψ.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 13 Number 1 – Jul 2014
Thus representation of measurement is by M×1
vector given by
= Φ = ΦΨ
(3)
This is right CS signal for signal reconstruction, CS
theory also employs convex optimization algorithm.
The time delay between adjacent element is
determined by sampling at the receiving end.
The equation (3) can also written as,
=∑
Component Analysis (PCA) theory dictionary of Φ
is,
Φ can be represented approximately by the linear
component of first k principle component of it. i. e.
B=
2). Optimization and Reconstruction of original
code element
(5)
=Φ
(6)
=Φ
In this way the problem is becomes convex and can
be solved via existing algorithms. Let consider that
channel is AWGN (Additive White Gaussian Noise)
channel, and the received signal is expressed as,
= y+z
(7)
Where, z is noise in channel, following the normal
distribution z ~ N(0, ). Incoherence of Φ is,
‖
−
‖ + ‖ ‖
(8)
Where is a weight factor. Optimization result is
only obtained when is,
=
(11)
,
2 log
(9)
Where, n refers to the length of x, and
can be
determined by the noise signal received when no
signal is sent in the transmitter.
To reduce the influence of noise in received signals
on reconstructive results and to reduce the scale of
this problem we use SVD. According to the Principle
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−
∑
(12)
Where, and
are total energy of the modulated
signal and noise. The speed of reconstruction
algorithm is improved by reducing the scale of
Φ, and respectively the length of measurement vector
y can be shortened, as follows:
=
While, the equation (5) is non-convex optimization
problem. According to CS theory if dictionary Φ is
incoherent, the model of norm is,
=
,
∑
=
The process of attaining the original code element
stream is as follows,
^
Λ
,
(4)
Where x(i) is projection of measurement vector
in the dictionary Φ. If the period of original code
element signal is T, then the bandwidth of CM will
be ⁄ times that of OFDM modulation.
‖ ‖ s. t.
(10)
The parameter can be calculated as
()
‖ ‖ s. t.
Ʌ
Φ=
,
,
y
(13)
Where, is a low noise estimation of y since the first
k principle component in
have fewer noises than
original received signal y has. The optimization
model in equation (8) is expressed as,
^
=
‖ −
‖ + ‖ ‖
(14)
A good estimation of x which have position
information of code elements “1”s can be obtained
faster and accurately. Hence, the original code
element stream is reconstructed by using 3 -rule.
3). Spectral Analysis of Compressive Modulated
Signal
In communication system, the bandwidth is very
important parameter, which often means higher cost
communication.
Let us consider that (t) = (1,2 . . . . n) is carrier
wave form sequence correspond to
(1,2 . . . . n),
in Φ. it is all zeros but a period of code element with
different amounts of shift in time domain, then the
modulated signal can be formulated as,
( ) (t)
(15)
(t) = ∑
Where, ( ) is representing code element stream in
time domain and n is number of wave atoms in Φ.
Length of (t) and
(t) is
L = (n-1)
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+T
(16)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 13 Number 1 – Jul 2014
Where, is set of T and L is equal to Nt and
(t)
is same as OFDM modulated signal, which is given
as
η =(
×
)
where, T is symbol period and
bandwidth of OFDM.
=
(17)
is approx.
According to Linear Theorem of Fourier Transform,
spectral characteristics of
(t) and OFDM
modulated signal are similar. The above process
shows that CM will not broadened the bandwidth due
to which it is able to improve the bandwidth. Let the
bandwidth of CM is
and of OFDM is
then the
relationship between
and is,
=
(18)
Fig.3. simulation of OFDM using Compressive Modulation
III. SIMULATION AND EXPERIMENT
This section, tells about the estimation that we made
which is that, the maximum possible bandwidth
efficiency under exactly same channel between CM
and OFDM under certain BER values in same
additive white Gaussian noise channel. The channel
attenuation rate is set to 0.8 and the SNR of
modulated signal at the receiving end is varies in
between 5dB-20dB. The baseband frequency is set to
16 kHz and sample rate is 145 . “0”and ”1” are
input code elements having equal probability. The
solver that is being used in reconstruction process in
CM is cvx, and other parameters are considered as
default. Generally, BER in the order of 10e-4 is
considered as the valid condition of a communication
process.
In fact, the BER of OFDM can be calculated by this
formula
=
(19)
⁄
⁄
{
Where,
is maximum Doppler frequency,
is
Bessel function and x is rician parameter.
Approximate equation of calculating BER is given at
(0)=0 i.e.
⁄
=
(
⁄
ISSN: 2231-5381
)
exp(−
⁄
) (20)
From the above experiment it is obtained that
is 10 times of
at most and 3 times at least of
under the precondition which ensures the
reliability of communications.
While traditional OFDM performance is very fine
only when the SNR of received signal is higher than
7 dB, but CM can perform very well when SNR is as
low as 4dB. Hence the channel bandwidth of OFDM
should be increased with increase in transmission rate
of code element, while CM will not occupy more
channel bandwidth, which obey that CM scheme
highly improved the bandwidth efficiency.
CM have good performance in bandwidth efficiency.
But it also face some problem which needs to be
improved in future works. 1st, the optimization
algorithm used in the reconstruction need to spend lot
of time and this is one of the main drawback in CS
applications. 2nd, the sampling rate at receiving end of
CM is much higher than OFDM. 3rd, the SNR level of
CM can be improved by using effective error control
coding to ensures the reliability of communication.
IV. CONCLUSION
In this paper, the inspiration of CS theory and
amelioration of OFDM is helpful to proposed a new
modulation scheme called Compressive Modulation
which is able to highly improve the bandwidth in
digital communication system with good robustness
in terms of error even in the image processing.. By
the effectiveness of this method it can be applied to
various modulation scheme i.e. 4-PSK, 8-PSK etc. so
on in the future works.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 13 Number 1 – Jul 2014
ACKNOWLEDGMENT
It was my great pleasure in extending special
thanks to Miss. Vandana and my family under whose
guidance and help, I was able to propose my work in
the form of this research paper. I’ am deeply
inhibited to themselves for their training and
guidance throughout my work. They was always
been a source of constant inspiration and
encouragement for me.
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AUTHOR
Lokendra singh presently lives in Dehradun and
completed his Graduation as a B. Tech. graduate in
the field of Electronics and communication from
Uttar Pradesh Technical University, Lucknow, UP,
India in 2012. He is a post-graduate scholar in the
field of Wireless & Mobile Communications from
Dehradun Institute of Technology, Dehradun,
Uttarakhand, India in 2013. Presently he is working
on “OFDM using Compressive Modulation”.
ISSN: 2231-5381
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