Journal of Engineering and technology Design Four Transmit...

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


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



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:



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.



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].



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.



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


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



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


DS-CDMA in flat fading Channel model -512

subcarriers- MDS=10.7Hz


CDMA in flat fading Channel model -512 subcarriers-

MDS=537Hz



MDS=10.7Hz



MDS=241.7Hz



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



MDS=10.7Hz



MDS=241.7Hz



MDS=537Hz



Doppler frequencies and multicarrier size in fixed and mobile

wireless application.

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