Comparative analysis of Wavelet Packet based MC-CDMA with the Conventional MC-CDMA using HHT tool

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GLOSSARY & KEYWORDS
Hilbert–Huang Transforms (HHT) : 1. The name of Hilbert–Huang transforms (HHT) was
designated by NASA and it was recommended by Huang et al. (1996, 1998, 1999, 2003, 2012).
It is the outcome of the empirical mode decomposition (EMD) and the Hilbert spectral analysis
(HSA). The decomposition of the signal in IMF is done by using the EMD technique and
immediate data related to frequency can be obtained by the HAS method. The HHT delivers a
novel technique of examining no stationary and non-linear time series data.
2. Hilbert–Huang Transform (HHT) is a way to decompose a signal into so-called intrinsic
mode functions (IMF), and obtain instantaneous frequency data. It is designed to work well for
data that are no stationary and nonlinear. In contrast to other common transforms like the Fourier
transform, the HHT is more like an algorithm (an empirical approach) that can be applied to a
data set, rather than a theoretical tool.
HHT Based MC-CDMA : A signal could be disintegrated into intrinsic mode functions (IMF)
by means of Hilbert–Huang transform (HHT) which can also be used to obtain immediate
frequency information. It is intended to do fine for information that is non-stationary as well as
non-linear. This transform is identical to a procedure (an experimental method) when compared
to other basic transforms for example, the Fourier transform. Furthermore it could be applied to a
data set too.
Orthogonal Frequency Division Multiplexing (OFDM) : The OFDM can be considered as a
multi-carrier modulation technique that is extensively accepted as well as maximum frequently
used now-a-days. In this, the modulation as well as demodulation is realized effortlessly by
Inverse DFT and DFT operators.
OFDM with Code Division Multiplexing (OFDM-CDM) : OFDM with Code Division
Multiplexing is a multiplexing system which is capable to use diversity in a superior way as
compared to traditional Orthogonal Frequency Division Multiplexing systems. For dissemination
of all the data symbols, numerous sub-carriers and/or numerous OFDM symbols are used. This is
how the system exploits extra time and/or frequency diversity.
Bit Error Rate (BER) : 1. This is the quantity of bit errors divided by the entire quantity of
transmitted bits through a considered time period. The BER of Binary Phase Shift Keying in
Additive White Gaussian Noise might be computed as BER= Error/ total number of bit .

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2. The bit error rate or bit error ratio (BER) is the number of bit errors divided by the total
number of transferred bits during a studied time interval. The bit error rate of BPSK in AWGN
can be calculated as BER= Error/ total number of bit .
Peak Signal To Noise Ratio (PSNR) : PSNR is the ratio between maximum possible pixel of
an image and the pixel of corrupting noise. PSNR is usually expressed in terms of the
logarithmic decibel.
Mean Square Error (MSE) : MSE is a difference between original image and noisy image
where, I(i,j) is an original image and Î(i,j) is an estimate of I(i,j) after Reconstruction.
Multiple Access Interference (MAI) : MC-CDMA system’s performance declines quickly with
the surge in amount of instantaneously active users because the capability of system having
modest processing gain is restricted by MAI.
Empirical Mode Decomposition (EMD) and Intrinsic Mode Functions (IMF) : The
fundamental part of the HHT is the empirical mode decomposition (EMD) method. Using the
EMD method, any complicated data set can be decomposed into a finite and often small number
of components, which is a collection of intrinsic mode functions (IMF). An IMF represents a
generally simple oscillatory mode as a counterpart to the simple harmonic function. By
definition, an IMF is any function with the same number of extrema and zero crossings, with its
envelopes being symmetric with respect to zero. The definition of an IMF guarantees a well-
behaved Hilbert transform of the IMF. This decomposition method operating in the time domain
is adaptive and highly efficient. Since the decomposition is based on the local characteristic time
scale of the data, it can be applied to nonlinear and no stationary processes.
Hilbert Spectral Analysis (HSA) : Having obtained the intrinsic mode function components,
the instantaneous frequency can be computed using the Hilbert Transform. After performing the
Hilbert transform on each IMF component, the original data can be expressed as the real part,
Real, in the following form:
The instant frequency could be calculated by making use of the Hilbert Transform once the
components of the IMF have been obtained. The primary data could be stated as the real part
after executing the transform on every IMF constituent in the subsequent system.

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Hilbert Spectral Analysis (HSA) : 1. The Hilbert spectral analysis (HSA) offers a technique
for investigating the Intrinsic Mode Function’s immediate data related to frequency as functions
of time which provides sharp IDs of embedded structures. The final outcome is an energy-
frequency-time spread that can be labeled as the Hilbert spectrum.
2. The Hilbert spectral analysis (HSA) provides a method for examining the IMF's instantaneous
frequency data as functions of time that give sharp identifications of embedded structures. The
final presentation of the results is an energy-frequency-time distribution, designated as the
Hilbert spectrum.
Additive White Gaussian Noise (AWGN) Channel : An AWGN channel is defined as additive
white Gaussian noise to the signal that goes through it. The components of signal incoming
through dissimilar propagation routes might add in a destructive way, leading to a phenomena
known as signal fading.
Binary Phase Shift Keying (BPSK) : The most straightforward type of PSK is called binary
phase shift keying (BPSK), where “binary” refers to the use of two phase offsets (one for logic
high, one for logic low).
We can intuitively recognize that the system will be more robust if there is greater separation
between these two phases—of course it would be difficult for a receiver to distinguish between a
symbol with a phase offset of 90° and a symbol with a phase offset of 91°. We only have 360° of
phase to work with, so the maximum difference between the logic-high and logic-low phases is
180°. But we know that shifting a sinusoid by 180° is the same as inverting it; thus, we can think
of BPSK as simply inverting the carrier in response to one logic state and leaving it alone in
response to the other logic state.
To take this a step further, we know that multiplying a sinusoid by negative one is the same as
inverting it. This leads to the possibility of implementing BPSK using the following basic
hardware configuration:
Diagram of Binary Phase Shift Keying (BPSK)

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Quadrature Phase Shift Keying (QPSK) : BPSK transfers one bit per symbol, which is what
we’re accustomed to so far. Everything we’ve discussed with regard to digital modulation has
assumed that the carrier signal is modified according to whether a digital voltage is logic low or
logic high, and the receiver constructs digital data by interpreting each symbol as either a 0 or a1.
Before we discuss quadrature phase shift keying (QPSK), we need to introduce the following
important concept: There is no reason why one symbol can transfer only one bit. It’s true that the
world of digital electronics is built around circuitry in which the voltage is at one extreme or the
other, such that the voltage always represents one digital bit. But RF is not digital; rather, we’re
using analog waveforms to transfer digital data, and it is perfectly acceptable to design a system
in which the analog waveforms are encoded and interpreted in a way that allows one symbol to
represent two (or more) bits.
QPSK is a modulation scheme that allows one symbol to transfer two bits of data. There are four
possible two-bit numbers (00, 01, 10, 11), and consequently we need four phase offsets. Again,
we want maximum separation between the phase options, which in this case is 90°.
Diagram of Quadrature Phase Shift Keying (QPSK)