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International Journal of Engineering and Technology Volume 6 No.7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 217
Design Four Transmit Antennas STBC-MC-DS-CDMA System Based On
DWPT In Flat Fading Channel
Nader Abdullah Khadam1, 2, Laith Ali Abdul-Rahaim1; Arash Ahmadi2
1 Electrical Engineering Department, College of Engineering, University of Babylon, Babylon, Iraq 2 Electrical Engineering Department, College of Engineering, Razi University, Kermanshah, Iran
ABSTRACT
This paper provides the detail about the two main applications of multicarrier direct sequence code division multiple access (MC-DS-
CDMA) which are fixed MC-DS-CDMA and Mobile MC-DS-CDMA. Fixed MC-DS-CDMA delivers point to multipoint broadband
wireless access to our homes and offices. Mobile MC-DS-CDMA gives full mobility of cellular networks at high broadband speeds.
The design of space time block coding STBC-MC-DS-CDMA systems based on Discrete Fast Fourier transform (FFT) or Discrete
Wavelets packet transform DWPT, evaluation tests, and simulations results of these proposed systems were done. The Bit Error Rate
(BERs) and the operating range of these systems are obtained using frequency domain baseband simulations. All systems that simulated
in this work, are compared with each other STBC types designed using FFT and DWPT using 1,2,3 and 4 antennas in transmitter. The
simulation results of these systems are examined in AWGN and flat fading channel for different Doppler frequencies (fd ) and subcarrier
size and compared with each other. The proposed structures for the STBC-MC-DS-CDMA system based on (DWPT) batter than based
on (FFT) in varies Doppler frequencies and subcarrier size. Also proposed system with STBC based on 4 transmitters better than other
systems based on 1 or 2 or 3 transmitters in all Doppler frequencies and subcarrier size in all simulation results. These MC-DS-CDMA
systems were modeled using MATLAB V7.10 to allow various parameters of the system to be varied and tested.
Keywords: MC-DS-CDMA, Flat Fading Channels, FFT, DWPT, OFDM.
1. INTRODUCTION
The experienced growth in the use of digital networks has led to
the need for the design of new communication networks with
higher capacity and high reliability broadband wireless
telecommunication systems. MC-DS-CDMA is one of the most
promising techniques which have changed the scenario of the
industry completely. MC-DS-CDMA, the Worldwide
Interoperability for Microwave Access, is based on the IEEE
802.11 standard, which is also called Wireless MAN. Compared
with other wireless networks, MC-DS-CDMA has the virtues of
higher transmission speed and larger transmission coverage. Its
transmission rate and distance can reach up to 75 Mbps and 50
km [1]. The MC-DS-CDMA physical layer is based on
orthogonal frequency division multiplexing. One of the main
reasons to use OFDM is to increase robustness against
frequency-selective fading or narrowband interference. OFDM
belongs to a family of transmission schemes called multicarrier
modulation, which is based on the idea of dividing a given high-
bit-rate data stream into several parallel lower bit-rate streams
and modulating each stream on separate carriers often called
subcarriers (SCs), or tones. Because the symbol duration
increases for the lower rate parallel subcarriers, the relative
amount of dispersion in time caused by multipath delay spread
is decreased [2, 3].
The fixed and mobile versions of MC-DS-CDMA have slightly
different implementations of the OFDM physical layer. Fixed
MC-DS-CDMA, which is based on IEEE 802.11, uses a 256
FFT-based OFDM physical layer. Mobile MC-DS-CDMA,
which is based on the IEEE 802.16e-2005 standard, uses a
scalable OFDMA-based physical layer. In the case of mobile
MC-DS-CDMA, the FFT sizes can vary from 128 bits to 2,048
bits. Fixed MC-DS-CDMA, OFDM-PHY: For this version the
FFT size is fixed at 256, which 192 subcarriers used for carrying
data, 8 used as pilot subcarriers for channel estimation and
synchronization purposes, and the rest used as guard band
subcarriers.6 Since the FFT size is fixed, the subcarrier spacing
varies with channel bandwidth. When larger bandwidths are
used, the subcarrier spacing increases, and the symbol time
decreases. Decreasing symbol time implies that a larger fraction
needs to be allocated as guard time to overcome delay spread.
Mobile MC-DS-CDMA OFDMA-PHY: In Mobile MC-DS-
CDMA, the FFT size is scalable from 128 to 2,048. Here, when
the available bandwidth increases, the FFT size is also increased
such that the subcarrier spacing is always 10.94kHz. This keeps
the OFDM symbol duration, which is the basic resource unit,
fixed and therefore makes scaling have minimal impact on
higher layers. A scalable design also keeps the costs low. The
subcarrier spacing of 10.94kHz was chosen as a good balance
between satisfying the delay spread and Doppler spread
requirements for operating in mixed fixed and mobile
environments. This subcarrier spacing can support delay-spread
values up to 20 μs and vehicular mobility up to 125 kmph when
operating in 5.8GHz [2, 4].
2. MOTIVATION TOWARD A NEW
STRUCTURE FOR MC-DS-CDMA
The Fourier based MC-DS-CDMA uses the complex
exponential bases functions and it’s replaced by orthonormal
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 218
wavelets in order to reduce the level of interference. It is found
that the Haar-based orthonormal wavelets are capable of
reducing the ISI and ICI, which are caused by the loss in
orthogonality between the carriers [4]. In [5, 6, 7], the simulation
results show the BER performance of OFDM system with
different orthogonal bases which is the Fourier based OFDM and
wavelet based OFDM. The simulations have found a great deal
of channel dependence in the performance of wavelet and
Fourier filters [7]. A main motivation for using wavelet-based
MC-DS-CDMA is the superior spectral containment properties
of wavelet filters over Fourier filters. It has been found that
under certain channel conditions. Wavelet MC-DS-CDMA does
indeed outperform Fourier MC-DS-CDMA. However, under
other channels the situation is reversed as in the selective fading
channel. Further performance gains can be made by looking at
alternative orthogonal basis functions and found a better
transform rather than Fourier and wavelet transform. The
implementations in practice of MC-DS-CDMA today have been
done by using FFT and its inverse operation IFFT (or DWPT and
its inverse operation IDWPT) to represent data modulation and
demodulation. Intersymbol interference (ISI) is eliminated
almost completely by introducing a guard time in every OFDM
symbol and this will take nearly about 25%-40% and this is one
of the disadvantage of FFT-OFDM ,therefor we will use two
systems the first is DWPT to increase the orthogonality of the
system and this will be better to combat the narrowband
interference and the second is STBC to combat the effect of
multipath frequency selective fading channel .In this paper we
will designing a wireless communication system with least bit
error rate for high data rate to stationary and mobile users by
improving the performance of MC-DS-CDMA based on STBC
and DWPT under flat fading channel. OFDM is multicarrier
modulation (MCM) technique which provides an efficient means
to handle high speed data streams on a multipath fading
environment that causes ISI. Normally OFDM is implemented
using FFT and IFFT’s [8]. To decrease the BW waste brought by
adding cyclic prefix, wavelet based OFDM is employed. Due to
use of wavelet transform the transmission power is reduced. One
type of wavelet transform is Discrete Wavelet transforms have
been considered as alternative platforms for replacing IFFT and
FFT, which employs Low Pass Filter (LPF) and High Pass Filter
(HPF). These filters operate as Quadrature Mirror Filters
satisfying perfect reconstruction and orthonormal bases
properties [9]. The transceiver of DWPT- MC-DS-CDMA is
shown in Fig. (1).
2.1. A Fast Computation Method of DWPT Algorithms
Under the reconstruction condition 0 dtt , the
continuously labeled basis functions (wavelets), tkj, behave
in the wavelet analysis and synthesis just like an orthonormal
basis [10].
By appropriately discretizing the time-scale parameters, , s,
and choosing the right mother wavelet, t , it is possible to
obtain a true orthonormal basis. The natural way is to discretize
the scaling variable s in a logarithmic manner jss
0 and to
use Nyquist sampling rule, based on the spectrum of function x
(t), to discretize t at any given scale Tskj 0
. The
resultant wavelet functions are then as follows:
002
0, ktsstjj
kj … (1)
If s0 is close enough to one and if T is small enough, then the
wavelet functions are over-complete and signal reconstruction
takes place within non-restrictive conditions on t . On the
other hand, if the sampling is sparse, e.g., the computation is
done octave by octave (s0 = 0), a true orthonormal basis will be
obtained only for very special choices of t . Based on the
assumption that wavelet functions are orthonormal:
otherwise
nkandmjifdttt nmkj
0
1,, (2)
For discrete time cases in eq (1) is generally used with s0 = 2, the
computation is done octave by octave. In this case, the basis for
a wavelet expansion system is generated from simple scaling and
translation. The generating wavelet or mother wavelet,
represented by t , results in the following 2D
parameterization of tkj, [11].
22 2, ktt jjkj … (3)
The 22 j factor in (2) normalizes each wavelet to maintain a
constant norm independent of scale j. In this case, the
discretizing period in is normalized to one and is assumed that
it is the same as the sampling period of the discrete signal
-j2 k . All useful wavelet systems satisfy the multiresolution
conditions. In this case, the lower resolution coefficients can be
calculated from the higher resolution coefficients by a tree-
structured algorithm called filter-bank [12]. In wavelet transform
literatures; this approach is referred to as discrete wavelet packet
transform (DWPT)[13].
2.1.1. The Scaling Function
Fig.(1) Block Diagram of a STBC- MC-DS-CDMA system
based on DWPT
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 219
The multiresolution idea is better understood by using a function
represented by t and referred to as scaling function. A 2-D
family of functions is generated, similar to (3), from the basic
scaling function by [14]:
ktt jjkj 2 2 2
, (4)
Any continuous function, f(t), can be represented, at a given
resolution or scale j0, by a sequence of coefficients given by the
expansion:
k
kjjj tkftf ,000 (5)
In other words, the sequence kx j0 is the set of samples of the
continuous function x(t) at resolution j0. Higher values of j
correspond to higher resolution. Discrete signals are assumed
samples of continuous signals at known scales or resolutions. In
this case, it is not possible to obtain information about higher
resolution components of that signal. It is however, desired to
use the given samples to obtain the lower resolution
representation of the same signal. This can be achieved by
imposing some properties on the scaling functions. The main
required property is the nesting of the spanned spaces by the
scaling functions. In other words, for any integer j, the functional
space spanned by [15]:
,2,1 ; , kfortkj … (6)
Should be a subspace of the functional space spanned by:
,2,1 ; ,1 kfortkj … (7)
The nesting of the space spanned by ktj 2 is achieved by
requiring that t be represented by the space spanned by t2
. In this case, the lower resolution function, t , can be
expressed by a weighted sum of shifted version of the same
scaling function at the next higher resolution, t2 , as follows:
2 2 ktkhtk
… (8)
The set of coefficients kh being the scaling function
coefficients and 2 maintains the norm of the scaling function
with scale of two, and t being the scaling function which
satisfies this equation which is sometimes called the refinement
equation, the dilation equation, or the multiresolution analysis
equation (MRA) [16-18].
2.1.2 The Wavelet Functions
The important features of a signal can better be described or
parameterized, not by using tkj, and increasing j to increase
the size of the subspace spanned by the scaling functions, but by
defining a slightly different set of functions tkj, that span the
differences between the spaces spanned by the various scales of
the scaling function [19, 20].
It is shown that these functions are the same wavelet functions
discussed earlier. Since it is assumed that these wavelets reside
in the space spanned by the next narrower scaling function, they
can be represented by a weighted sum of shifted version of the
scaling function t2 as follows:
2 2 ktkgtk
… (9)
The set of coefficients kg ’s is called the wavelet function
coefficients (or the wavelet filter). It is shown that the wavelet
coefficients are required by orthogonality to be related to the
scaling function coefficients by [19,21]:
khkgn
11 … (10)
One example for a finite even Length-N kh
kNhkgk
11 … (11)
The function generated by (9) gives the prototype or mother
wavelet t for a class of expansion functions of the form
shown in (3). Any function tf could be written as a series
expansion in terms of the scaling function and wavelets by:
0
,,00jj k
kjjk
kjj tkbtkatf (12)
In this expansion, the first summation gives a function that is a
low resolution or coarse approximation of f(t) at scale j0 . For
each increasing j in the second summation, a higher or finer
resolution function is added, which adds increasing details. The
choice of j0 sets the coarsest scale whose space is spanned by
tkj .0 . The rest of the function is spanned by the wavelets
providing the high-resolution details of the function. The set of
coefficients in the wavelet expansion represented by (12) is
called the discrete wavelet packet transform (DWPT) of the
function f(t) [10].
These wavelet coefficients, under certain conditions, can
completely describe the original function, and in a way similar
to Fourier series coefficients, can be used for analysis,
description, approximation, and filtering. If the scaling function
is well behaved, then at a high scale, samples of the signal are
very close to the scaling coefficients. In order to work directly
with the wavelet, transform coefficients, one should present the
relationship between the expansion coefficients at a given scale
in terms of those at one scale higher. This relationship is
especially practical by noting the fact that the original signal is
usually unknown and only a sampled version of the signal at a
given resolution is available. As mentioned before, for well-
behaved scaling or wavelet functions, the samples of a discrete
signal can approximate the highest achievable scaling
coefficients [22]. It is shown that the scaling and wavelet
coefficients at scale j are related to the scaling coefficients at
scale (j + 1) by the following two relations.
m
jj makmhka 1 2 … (13)
m
jj mbkmgkb 1 2 … (14)
The implementation of equations (13) and (14) is illustrated in
Fig. (2). In this figure, two levels of decomposition are depicted.
h and g are low-pass and high-pass filters corresponding to the
coefficients nh and ng respectively. The down-pointing
arrows denote a decimation or down-sampling by 2. This
splitting, filtering and decimation can be repeated on the scaling
coefficients to give the two-scale structure. The first stage of two
banks divides the spectrum of kja ,1 into a low-pass and high-
pass band, resulting in the scaling coefficients and wavelet
coefficients at lower scale kja , and kjb , . The second stage then
divides that low-pass band into another lower low-pass band and
a band-pass band [22].
For computing fast discrete wavelet transform (DWPT) consider
the following transformation matrix for length-4:
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 220
1000000032
3210000000
0000321000
00003210
1000000032
0000321000
0000003210
gggg
gggg
gggg
gggg
hhhh
hhhh
hhhh
T
(15)
Here blank entries signify zeros. By examining the transform
matrices of the scalar wavelet as shown in equations (13) and
(14) respectively, one can see that, the first row generates one
component of the data convolved with the low-pass filter
coefficients ( 0h , 1h , …). Likewise, the second, third, and
other upper half rows. The lower half rows perform a different
convolution, with high pass filter coefficients ( 0g , 1g , …).
The action of the matrix is thus to perform two related
convolutions, then to decimate each of them by half (throw away
half the values), and interleave the remaining halves [23].
By using (11), the transform matrices become:
2300000001
0123000000
0000012300
00000123
1000000032
0000321000
0000003210
hhhh
hhhh
hhhh
hhhh
hhhh
hhhh
hhhh
T
(16)
It is useful to think of the filter ( 0h , 1h , 2h , 3h …) as
being a smoothing filter, H, something like a moving average of
four points. Then, because of the minus signs, the filter ( 3h ,
2h , 1h , 0h , …), G, is not a smoothing filter. In signal
processing contexts, H and G are called Quadrature mirror
filters. In fact, the nh ’s are chosen so as to make G yield,
insofar as possible, a zero response to a sufficiently smooth data
vector. This results in the output of H, decimated by half
accurately representing the data’s “smooth” information. The
output of G, also decimated, is referred to as the data’s “detail”
information [24]. For such characterization to be useful, it must
be possible to reconstruct the original data vector of length N
from its N/2 smooth and its N/2 detail. That is affected by
requiring the matrices to be orthogonal, so that its inverse is just
the transposed matrix:
20130000
31020000
0210
0300
000
000000300
001000200
002000130
003100020
000200013
000310002
000023001
100032000
2
hhhh
hhhh
hh
hh
hh
hh
hhhh
hhhh
hhhh
hhhh
hhhh
hhhh
T
(17)
For the length-4 coefficients sequence, there is one degree of
freedom or one parameter that gives all the coefficients that
satisfies the required conditions [14-18]:
03 1 2 0
13210
23 2 1 0
2222
hhhh
hhhh
hhhh
(18)
Letting the parameter be the angle , the coefficients become
22sincos13
22sincos12
22sincos11
22sincos10
h
h
h
h
(19)
These equations give length-4 Daubechies coefficients for
3 . These Daubechies-4 coefficients have a particularly
clean form:
24
31,
24
33,
24
33,
24
314Dh (20)
The structure of a one-dimensional DWPT is shown in
Fig. (3). nX is the1-D input signal. nh and ng are the
analysis lowpass and highpass filters which, split the input signal
into two subbands: lowpass and highpass. The lowpass and
highpass subbands are then down sampled generating nXL and
nXH respectively.
Fig. (2): The filter bank for calculating the wavelet
coefficients.
Fig. (3): Analysis and Synthesis stages
of a 1-D single level DWT.
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 221
The up sampled signals are filtered by the corresponding
synthesis lowpass nh~
and highpass ng~ filters and then added
to reconstruct the original signal. Note that the filters in the
synthesis stage, are not necessary the same as those in the
analysis stage. For an orthogonal filter bank, nh~
and ng~ are
just the time reversals of nh and ng respectively [23].
To compute a single level DWPT for 1-D signal the next
step should be followed:
1. Checking input dimensions: Input vector should be of
length N, where N must be power of two.
2. Construct a transformation matrix: using transformation
matrices given in (16) and (17).
3. Transformations of input vector, which can be done by
apply matrix multiplication to the N×N constructed
transformation matrix by the N×1 input vector.
2.1.3- Computation of IDWPT for 1-D Signal:
To compute a single level IDWPT for 1-D signal the next step
should be followed:
1. Let X be the N×1 wavelet transformed vector.
2. Construct N×N reconstruction matrix, T2, using
transformation matrices given in (18).
3. Reconstruction of input vector, which can be done by apply
matrix multiplication to the N×N reconstruction matrix, T2,
by the N×1 wavelet transformed vector.
2.2 Space Time block coding with four Antennas:
The second proposed idea to MC-DS-CDMA system is adding
space-time blocks coding (STBC) to the system. The STBC
reduce the effect of multipath frequency selective Multipath
fading channel. The aims this paper are designing a wireless
communication system with least bit error rate (BER) for high
data rate to fix stationary nodes and mobile users under
multichannel models. These ideas will be implemented in MC-
DS-CDMA system by adding STBC with more than two
antennas and using DFT or DWPT [1, 16,17]. The proposed
STBC- MC-DS-CDMA transceiver is shown in Fig. (1). All the
type of space-time block codes with three transmitters or more
has a coding rate of 1/2, to satisfy orthogonality condition. The
space-time block code for four transmits antennas N = 4, with
input symbols (S1, S2, S3, S4), the output will be over T = 8
symbol periods, thus the coding rate R =1/2 [18, 19]. At a given
symbol period, four antennas transmitted four signals
simultaneously. At time slot T0, transmitted signal from first
transmitter (Tx1) is denoted by S1, the signal from second
transmitter (Tx2) by S2 and the signal from third transmitter (Tx3)
by S3and the signal from fourth transmitter (Tx4) by S4. This
process will go on in the same manner for each time slot until
transmitting the last row of Table (1). This table has a rate of
(1/2) and is used as STBC encoder to transmit any complex
signal constellations [20,21]. For the four transmit and one
receive antenna system, the channel coefficients are modeled by
some complex multiplicative distortions, h1 for the first transmit
antenna, h2 for the second transmit antenna and h3 for the third
transmit antenna and h4 for the fourth transmit antenna [22].
Since some models used in this work are time varying and
frequency selective for wide band mobile communication
systems, so a dynamic estimation of channel is necessary to
compensate MC-DS-CDMA signal [24].
Table(1 ): STBC mapping for four transmit antennas
using complex signals Four transmit antennas
Time slot Three transmit antennas
𝑻𝒙𝟒 𝑻𝒙𝟑 𝑻𝒙𝟐 𝑻𝒙𝟏
𝑺𝟒 𝑺𝟑 𝑺𝟐 𝑺𝟏 Slot T0 𝑺𝟑 −𝑺𝟒 𝑺𝟏 −𝑺𝟐 Slot T1 −𝑺𝟐 𝑺𝟏 𝑺𝟒 −𝑺𝟑 Slot T2 𝑺𝟏 𝑺𝟐 −𝑺𝟑 −𝑺𝟒 Slot T3 𝑺𝟒∗ 𝑺𝟑
∗ 𝑺𝟐∗ 𝑺𝟏
∗ Slot T4 𝑺𝟑∗ 𝑺𝟒
∗ 𝑺𝟏∗ −𝑺𝟐
∗ Slot T5 −𝑺𝟐
∗ 𝑺𝟏∗ 𝑺𝟒
∗ −𝑺𝟑∗ Slot T6
𝑺𝟏∗ 𝑺𝟐
∗ −𝑺𝟑∗ −𝑺𝟒
∗ Slot T7
The channel transfer function estimation, and the inverse of it
are applied to each MC-DS-CDMA packet to reduce the channel
effects, much like equalization [25]. There are two types of
channel estimations, block type and comb-type pilot channel
estimation as shown in [26]. After pilot-carrier (training
sequence) is generated as a bipolar sequence {±1}, the receiver
previously knows this sequence. So the system can estimate the
channel transfer function h1(t) ,h2(t) ,h3(t) and h4(t). The
inverse of these channels can be calculated. Using channels and
there inverse to compensate the received packet and reduce the
errors.
2.3 Spreading Codes (Gold codes):
Various spreading codes exist which can be distinguished with
respect to orthogonality, correlation properties, implementation
complexity and peak-to-average power ratio (PAPR). The
selection of the spreading code depends on the scenario. In the
synchronous downlink, orthogonal spreading codes are of
advantage, since they reduce the multiple access interference
compared to non-orthogonal sequences. However, in the uplink,
the orthogonality between spreading codes gets lost due to
different distortions of the individual codes. Thus, simple PN
sequences can be chosen for spreading in the uplink. If the
transmission is synchronous, Gold codes have good cross-
correlation properties. In cases where pre-equalization is applied
in the uplink, orthogonality can be achieved at the receiver
antenna, such that in the uplink orthogonal spreading codes can
also be of advantage. PN sequences with better cross-correlation
properties than m-sequences are the so-called Gold sequences
[13,17]. A set of n Gold sequences is derived from preferred pair
of m-sequences of length L=2n
-1 by taking the modulo-2 sum of
the first preferred m-sequence with the n cyclically shifted
versions of the second preferred m-sequence [20]. By including
the two preferred m-sequences, a family of n+2 Gold codes is
obtained. Gold codes have a three-valued cross correlation
function with values {-1, -t(m), t(m)-2} where
𝑡(𝑚) = {2(𝑚+1)
2 + 1 𝑓𝑜𝑟 𝑚 𝑜𝑑𝑑
2(𝑚+2)
2 + 1 𝑓𝑜𝑟 𝑚 𝑒𝑣𝑒𝑛 (21)
2.4. Signal model
Multiple accesses are created by assigning a different spreading
code to every user in the system (similar to multicarrier CDMA).
Like in multiband OFDM, DWPT symbols duration consider of
T, bandwidth 20MHz, spanning Ns =180 samples (equivalent to
180 sub-carriers of OFDM) to be transmitted in different sub-
bands [18].
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 222
y(k, n) = ∑ H𝑀(k)s𝑀(k, n) + z(k, n)4
𝑀=1, (22)
where z(k, n) (2 × 1) is a complex-valued additive white
Gaussian noise vector with entities of zero mean and variance 2Z ; H(k) (4 × 1) denotes the channel frequency response
according to the ITU channel model [18]. The channel assumed
that certain frequency band keeps constant within the time
interval of N OFDM symbols. The (i, j )th element of H(k) is
given by
0 0
),.
,(2,
,,)]([l m
jilm
jil
Tfkjjilmji eXkH
(23)
where ∆f is the frequency separation between two adjacent
subcarriers; jilm
,,
is the multipath gain for cluster l and ray m
between the jth transmit antenna and the ith receive antenna; the
lth cluster arrives at ji
lT
, and its kth ray arrives at
jilm
,,
; X
represents the Rayleigh's distributed random variable for
shadowing, i.e., 20 log10 X ∝ N(0, 2X ), while the total energy
contained in the terms jilm
,,
, ∀m, l for each couple (i, j ), is
normalized to unity for each channel realization. For simplicity
of notation, the indices of k and n, and denote hi,j = [H(k)]i,j and
ci,j =
0 0
),.
,(2,
,l m
jilm
jil
Tfkjjilme
, respectively. Thus, it
shows that
ℎ𝑖,𝑗 = 𝑋𝑐𝑖,𝑗 (24)
When the Alamouti coding is applied, the system is equivalent
to independent single-input single-output systems defined as
[15, 17]
jjj du (25
Where 21
21
2
,i j jih , dj denote original symbols before
dispreading and ςj is an equivalent complex Gaussian random
variable with zero mean and variance ф2
Z From (23), it can
rewrite 21
21
2
,i j jic . Therefore, the output signal to
noise ratio (SNR) in (25) can be expressed as
2
2X
z
s (26)
Where 21
21
2
,i j jic and ρs denotes the averaged power
of transmitted symbols.
Therefore, the SNR, (S/N), at the output of receiver, can be
written as
(𝑆𝑁𝑅 =𝐸{𝑋𝐼|𝛼𝐼
(1)}2
𝑉𝐴𝑅{𝑋𝐼|𝛼𝐼(1)}) ≡ 𝑁2𝐸𝐶𝛾 (27)
For BPSK signaling, the evaluation of average BER for different
scenarios can be approximately achieved by [26]:
𝑃𝐵𝐸𝑅𝑠𝑢 = ∫ 𝑄 {
𝐸(𝜉𝑈)
√𝑉𝐴𝑅(𝜉𝑈)}
∞
0
𝑓(𝛼(1)) 𝑑𝛼1(1)…𝑑𝛼𝑀
(1)⏞ 𝑀 𝑓𝑜𝑙𝑑𝑠
=∫ 𝑄(√𝑁2𝐸𝐶𝛾𝑠𝑢)∞
0𝑓𝛾(𝛾𝑠𝑢)𝑑(𝛿𝑠𝑢) (28)
The Q(x) in (28) is the Gaussian Q-function. Hereafter, the
average BER of an MC-DS-CDMA system over fading channel
can be calculated from (28).
3.SIMULATION RESULTS OF THE PROPOSED
MC-DS-CDMA SYSTEMS:
In this section the simulation of the proposed STBC DWT-MC-DS-CDMA system in MATLAB version 7.10 is achieved, beside the BER performance of the MC-DS-CDMA system considered in different channel models, the AWGN channel, the flat fading channel, and the selective fading channel. We used the carrier frequency of 5.8 GH for fixed and mobile MC-DS-CDMA system with three values of MDS (10.7Hz with speed 2km/hr ,241.7Hz with speed 45 km/hr, and537Hz with speed 100 km/hr). Also we used ITU Path Loss Models (indoor office, outdoor to indoor , vehicular ) that we mentioned in section (2.4.1)for selective fading channel . Table (1) shows the parameters of the system used in the simulation.
Table (.1): Simulation Parameter
Parameter Fixed
MC-
DS-
CDMA
Mobile MC-DS-CDMA
Scalable
FFT or DWT size 256 128 512 102
4
204
8
Number of used
data subcarriers 96 64 180 360 720
Modulation types BPSK
Cyclic prefix or
guard time (Tg/Tb) 1/16
Channel bandwidth
(MHz) 20 20 20 20 20
Channel type Rayleigh Flat Fading
Carrier frequency fc 5.8GHz
3.1 Performance of STBC DWT-MC-DS-CDMA in AWGN
channel
According to the table (1) we only used the size of 256-(FFT or
DWT) for fixed MC-DS-CDMA. Figure (5) for BER=10-5
shows that in FFT system the SNR of 1 antenna is about 38 dB
and this ratio decreasing to 34dB in 4 antenna and in DWT
system the SNR is about 14dB in 1 antenna and decreasing to
10dB in 4 antenna, therefore a gain of 4dB for the STBC because
the use of multiple antennas at the transmitter enhances the
system spectral efficiency and supports better error rate and
these benefits come at no extra cost of bandwidth and power. It
is shown clearly that the proposed STBC DWT-MC-DS-CDMA
is much better than the traditional system of STBC FFT-MC-
DS-CDMA this is a reflection of the fact that the orthogonal base
of the DWT-MC-DS-CDMA is more significant than the
orthogonal bases used in FFT-MC-DS-CDMA.
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 223
For mobile MC-DS-CDMA, we used the size of
(128,512,1024,2048) -(FFT or DWT) according to the table (4.1).
Generally, the dB power losses increase when the size of subcarriers
increase as shown in fig. (6), fig. (7), fig. (8) and fig. (9)
3.2 Performance of STBC DWT-MC-DS-CDMA in Flat
Fading Channel
In this type of channel, the signal will be affected by the flat
fading in addition to AWGN; in this case all the frequency
components in the signal will be affected by a constant
attenuation and linear phase distortion of the channel, which has
been chosen to have a Rayleigh's distribution. For fixed system
the proposed MC-DS-CDMA it still performs better than the
traditional MC-DS-CDMA using FFT as shown in fig.(10) and
we can see that the SNR increases about 5dB as a compare with
the AWGN channel due to the Rayleigh's distribution.
Three values of the Doppler frequencies (fd) are considered in
the simulation of mobile system, these are 10.7Hz, 241.7Hz and
537Hz.In all sizes of subcarriers we can see that the smaller
effect appears in fd=10.7Hz and the larger effect appears in
fd=537Hz as shown in figures.
Fig. (6) BER performance of STBC DWT-Mobile MC-
DS-CDMA in AWGN channel model-128 subcarriers
Fig. (7) BER performance of STBC DWT-Mobile MC-
DS-CDMA in AWGN channel model-512 subcarriers
Fig. (9) BER performance of STBC DWT-Mobile MC-DS-
CDMA in AWGN channel model-2048 subcarriers
Fig. (10) BER performance of STBC DWT-Fixed MC-DS-
CDMA in flat fading Channel model -256 subcarriers
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 224
Fig. (12) BER performance of STBC DWT- Mobile MC-
DS-CDMA in flat fading Channel model -128 subcarriers-
MDS=241.7Hz
Fig. (13) BER performance of STBC DWT- Mobile MC-
DS-CDMA in flat fading Channel model -128
subcarriers- MDS=537Hz
Fig. (14) BER performance of STBC DWT-Mobile MC-
DS-CDMA in flat fading Channel model -512
subcarriers- MDS=10.7Hz
Fig. (16) BER performance of STBC DWT-Mobile MC-DS-
CDMA in flat fading Channel model -512 subcarriers-
MDS=537Hz
Fig. (17) BER performance of STBC DWT-Mobile MC-DS-
CDMA in flat fading Channel model -1024 subcarriers-
MDS=10.7Hz
Fig. (18) BER performance of STBC DWT-Mobile MC-DS-
CDMA in flat fading Channel model -1024 subcarriers-
MDS=241.7Hz
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 225
The important results present in this work under flat fading
channel are shown in figures above. These figures were
computed after testing the proposed systems by transmits over
10M symbols through channel at each SNR point, so massive
computations had been done in these simulations. All simulation
results in figures above shows that the worst scenario in all
proposed STBC-MC-DS-CDMA systems with FFT and DWPT,
in terms of BER performance, occurs when Doppler frequency
(fd) increased to high values. It can be concluded from the
comparison of the performance results of STBC-MC-DS-
CDMA based on DWPT with the same model based on FFT
given a robust implementation and perform better BER
performance in all values of the Doppler frequencies and the
BER and losses increase as the Doppler frequency increases in
both models with FFT and DWPT. The STBC still performs
higher spectral efficiency and supports better BER performance
with respect to FFT and DWPT systems in three values of (fd)
and in different no. of transmit antennas. This improvement in
the proposed systems are due to the reflection of the fact that the
orthogonal base of the wavelets transform is stronger and
immunity than the orthogonal bases used in FFT to the fading of
the channel. The orthogonal multiple copies of data due use of
STBC also given the System more option to get properly receive
data. The simulation results of these systems are examined in flat
fading channel at different Doppler frequencies (fd) (10.7, 241.7
and 537 Hz) and subcarrier sizes (128,512,1024 and 2048) and
compared with each other. The proposed structures of STBC-
MC-DS-CDMA system based on (DWPT) are better than based
on (FFT) in all different Doppler frequencies and subcarrier
sizes. Also proposed system with STBC based on 4 transmitters
better than other systems based on 1 or 2 or 3 transmitters in all
Doppler frequencies and subcarrier size in all simulation results.
The simulation results and table (2) show that Fixed STBC-MC-
DS-CDMA based on DWPT have again 17dB over based on
FFT with 1 antenna and about 21dB with 4 antennas. The same
notes can be observed for mobile STBC-MC-DS-CDMA with
different multicarrier size, and different Doppler frequencies. So
for high data rate the designer needed bigger multicarrier size
like 1024 or 2048, but the system will be complex and need high
power consumption and then will be more expansive and used
for short distance wireless communication. The long distance
wireless can use less multicarrier size like (128 and 512) for
different Doppler frequencies.
4. CONCLUSION
This paper presents a simulation of the proposed MC-DS-
CDMA system base FFT then improved its BER performance
and diversity by using space time block coding with two, three
and forth antennas. Then DWPT have been replacing FFT also
to improve BER performance and spectrum Efficiency. So the
combination STBC and DWPT are given better results
especially with four antennas in transmitter this is a reflection of
the fact that the orthogonal base of the wavelets is more
significant than the orthogonal bases used in FFT and the
orthogonal multiple copies of data due use of STBC. Also this
paper focuses on using different multicarrier size (128, 512,
1024 and 2048) for mobile wireless communications and 256 for
fixed wireless communications. From simulation results when
multicarrier size increase BER performance decreased. Also this
paper shows the effect of change Doppler frequencies for
different value from walking speed (10.7 Hz) to speed of car in
high way (537 Hz) in mobile wireless communications for the
proposed systems and also found that when increase Doppler
frequency the BER performance of proposed systems will
decreased. So from all simulation results it’s clear that the
proposed STBC-MC-DS-CDMA based on DWPT was the better
system among all system in flat fading channel models at all
Fig. (20) BER performance of STBC DWT-Mobile MC-DS-
CDMA in flat fading Channel model -2048 subcarriers-
MDS=10.7Hz
Fig. (21) BER performance of STBC DWT-Mobile MC-DS-
CDMA in flat fading Channel model -2048 subcarriers-
MDS=241.7Hz
Fig. (22) BER performance of STBC DWT-Mobile MC-DS-
CDMA in flat fading Channel model -2048 subcarriers-
MDS=537Hz
International Journal of Engineering and Technology (IJET) – Volume 6 No. 7, July, 2016
ISSN: 2049-3444 © 2016 – IJET Publications UK. All rights reserved. 226
Doppler frequencies and multicarrier size in fixed and mobile
wireless application.
REFERENCES
Baig S. and Mughal M. J., “A Frequency Domain Equalizer in Discrete Wavelet Packet Multitone Transceiver for In-Home PLC LANS”, IEEE International Symposium on Power Line Communications and its Applications, PISA, Italy, March 2007.
Fazelk and S. Kaiser-2002, “Multi-Carrier and Spread Spectrum
Systems”. 1st Edition, John Wiley & Sons.
Xiangbin Yu; TingTing Zhou; YanFeng Li, "Uplink performance of
multiband complex wavelet based multicarrier DS-CDMA system in
fading channel," in Wireless Communications & Signal Processing,
2009. WCSP 2009. International Conference on , vol., no., pp.1-5,
13-15 Nov. 2009.
Koga H., N. Kodama, and T. Konishi-, "High-speed power line
communication system based on wavelet OFDM," in Proc. IEEE
ISPLC 2003, Kyoto, Japan, May, pp. 226-231,2003.
Keita I., Daisuke U., and Satoshi D., “Performance Evaluation of
Wavelet OFDM Using ASCET” IEEE, 2007.
You-L. C. and Shiao-L. T., “A Low-Latency Scanning with
Association Mechanism for Real-Time Communication in Mobile
WiMAX”, IEEE Transactions On Wireless Communications, 2012.
Qinghua Shi, Yong Liang Guan, Yi Gong and Choi Look Law,
“Receiver Design for Multicarrier CDMA Using Frequency-Domain
Oversampling”, IEEE Transactions on Wireless Communications,
Vol. 8, No. 5, 2009.
Jia Shi; Lie-Liang Yang, "Novel Subcarrier-Allocation Schemes for
Downlink MC DS-CDMA Systems," in Wireless Communications,
IEEE Transactions on, vol.13, no.10, pp.5716-5728, Oct. 2014.
Sobia B., Gohar N.D., Fazal R., “An efficient wavelet based MC-
CDMA transceiver for wireless communications”, IBCAST, 2005
Laith Abdul-Rahaim., "DWT based WIMAX system with four STBC transmit antennas in Multipath Fading LTE Channels models," International Journal of Advancements in Computing Technology 7 (6), 1., pp.1-12, Nov. 2015.
Ali, A.A.; Abdul-Rahaim, L.A., "Discrete wavelets transform based
space time block code multicarrier direct sequence CDMA," in
Systems, Signals and Devices, 2008. IEEE SSD 2008. 5th
International Multi-Conference on , vol., no., pp.1-4, 20-22 July
2008.
Chitra, S.; Kumaratharan, N., "Performance improvement of MC-
DS-CDMA system through ICI cancellation and modified duobinary
coding scheme," in Computing Communication & Networking
Technologies (ICCCNT), 2012 Third International Conference on ,
vol., no., pp.1-7, 26-28 July 2012.
Yeen, Linnartz J-P and Fettweis G., “Multicarrier CDMA in Indoor
Wireless Radio Networks”. Proc. of IEEE PIMRC 1993, Yokohama,
Japan, Sept., pp.109-13
Jia Shi; Lie-Liang Yang, "Novel Transmission Schemes for Multicell
Downlink MC/DS-CDMA Systems Employing Time- and
Frequency-Domain Spreading," in Vehicular Technology
Conference (VTC Spring), 2013 IEEE 77th , vol., no., pp.1-5, 2-5
June 2013
Yuan D., Zhang H., Jiang M. and Dalei Wu- “Research of DFT-
OFDM and DWT-OFDM on Different Transmission Scenarios.”
Proceedings of the 2nd International Conference on Information
Technology for Application (ICITA), pp. 31–33, 2004.
Zhang H., D. Yuan, M. Jiang and Dalei Wu-2004 “Research of DFT-
OFDM and DWT-OFDM on Different Transmission Scenarios.”
Proceedings of the 2nd International Conference on Information
Technology for Application (ICITA).
Medhi, M.R.; Sarma, K.K., "DWT based multi carrier CDMA
system using ANN-aided channel estimation," in Signal Processing
and Integrated Networks (SPIN), 2015 2nd International
Conference on , vol., no., pp.248-252, 19-20 Feb. 2015.
H. Zarrinkoub “Understanding LTE with MATLAB: from
mathematical foundation to simulation, performance evaluation and
implementation” John Wiley & Sons, Ltd,2014
P. Tong, R. C. de Lamare, and A. Schmeink, “Adaptive distributed
space-time coding based on adjustable code matrices for cooperative
MIMO relaying systems,” IEEE Trans. Commun., vol. 61, no. 7, pp.
2692–2703, Jul. 2013.
Third Generation Partnership Project (3GPP), “Evolved Universal
Terrestrial Radio Access (E-UTRA); Physical Channels and
Modulation,” standard specifications TS 36.211, 2009, available on
www.3gpp.org,
M. Suryanegara, and M.Asvial, “In Searching for 4G Mobile Service
Applications: The Case of Indonesia Market,” Telecommunications
Journal of Australia, Vol.63, No.2, 2013.
His-LuChao, Chia-kai Chang, Chia-Iung Liu, "A novel channel-
aware frequency-domain scheduling in LTE uplink", IEEE Wireless
Communication and Networking Conference (WCNC),2013
Matolak, D.W.; Sen, I.; Wenhui Xiong, "Multicarrier multiuser
modulation performance in severely fading channels," in Mobile
Future, 2006 and the Symposium on Trends in Communications.
SympoTIC '06. Joint IST Workshop on , vol., no., pp.88-91, 24-27
June 2006
Chen, Joy Iong-Zong; Hsieh, Tai Wen, "Another view point on the
performance evaluation of an MC-DS-CDMA system," in
Communications and Networks, Journal of , vol.11, no.3, pp.240-
247, June 2009.
Xiangbin Yu; Dazhuan Xu; GuangguoBi, "Performance analysis of
complex wavelet packet function based MC-DS-CDMA in Rayleigh
fading channel," in Communications, Circuits and Systems, 2005.
Proceedings. 2005 International Conference on, vol.1, no., pp.115-
119 Vol. 1, 27-30 May 2005.
Akho-Zahieh, M.M.; Ugweje, O.C., "Diversity Performance of a
Wavelet-Packet-Based Multicarrier Multicode CDMA
Communication System," in Vehicular Technology, IEEE
Transactions on , vol.57, no.2, pp.787-797, March 2008.