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Turk J Elec Eng & Comp Sci
() : 1 – 11
c
⃝T¨
UB˙
ITAK
doi:10.3906/elk-1303-202
Turkish Journal of Electrical Engineering & Computer Sciences
http://journals.tubitak.gov.tr/elektrik/
Researc h Article
GA based adaptive receiver for MC-CDMA system
Muhammad Adnan KHAN, Muhammad UMAIR∗, Muhammad Aamer Saleem CHOUDHRY
School of Engineering and Applied Sciences, Isra University, Islamabad, Pakistan
Received: 28.03.2013 •Accepted/Published Online: 18.06.2013 •Printed: ..201
Abstract: Multicarrier systems like the multicarrier code division multiple access (MC-CDMA) systems are designed
for maximum usability of available bandwidth. We use the MC-CDMA system with Alamouti’s space time coding in
this paper. We propose the genetic algorithm (GA) in order to calculate MC-CDMA receiver weights with two variation
schemes. The proposed schemes reduce receiver complexity. The bit error rate and convergence rate are also improved
by increasing the number of genes and chromosomes of the GA in both schemes as compared with conventional LMS
based receivers of the MC-CDMA system. This is verified via simulations.
Key words: Multiple input and multiple output, multicarrier code division multiple access, space time block coding,
genetic algorithm
1. Introduction
The single transmission path between a transmitter and a receiver minimizes the efficient utilization of available
bandwidth. The solution to this problem is multiple input and multiple output (MIMO) systems that use
more than one antenna at the transmitter and the receiver. This improves the effective utilization of available
bandwidth. These systems are effectively used due to a high data rate demand of future generation networks
[1].
Multicarrier schemes like multicarrier code division multiple access (MC-CDMA) and multicarrier direct
sequence code division multiple access (MC-DS-CDMA) provide an effective solution to high data rate demands
of future networks [2]. Alamouti’s scheme [3] is one of the plainest space time block coding (STBC) methods
that is recommended for attaining transmit diversity gain in future generation networks as in [4,5]. In this
paper, we used the MC-CDMA system with Alamouti’s STBC scheme.
One of the important causes of poor performance in MC-CDMA based systems is multiuser interference
(MI). The multiuser receivers are of two types: optimal and suboptimal receivers. The optimal receivers are
much more complex, and so they are not realistic. We used suboptimal receivers as they have low complexity as
compared with optimal receivers. The minimum mean square error (MMSE) is one of the well-known suboptimal
receivers. In this paper, the filter weights are intended to minimize the mean square error (MSE).
The batch processing system works on groups of data to minimize complications of the receiver in terms
of time. The batch processing systems are implemented along with STBC for MC-CDMA and DS-CDMA
effectively in [6–8]. The calculation of an inverse autocorrelation matrix on the receiver for each group of data
is one of the complications of batch processing systems. The reason is that an inverse autocorrelation matrix
∗Correspondence: umairbwp@gmail.com
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KHAN et al./Turk J Elec Eng & Comp Sci
changes with any change in the channel coefficients and user configuration settings. Another complication is a
large filter tap length. Thus, the solution to such problems is to implement the receiver adaptively. One of the
adaptive receivers is the least mean square (LMS) receiver. Its traditional version for MC-CDMA is proposed
in [9]. However, this receiver does not have a good bit error rate (BER) and convergence rate.
In this paper, we applied the genetic algorithm (GA) to a MC-CDMA receiver for adaptive MMSE weights
calculation. The GA is one of the famous optimization algorithms that are suitable for any natural evolution
process [10]. In the GA, a new population is produced through mutation. This technique is further compared
with a traditional LMS receiver. Our proposed receiver has a better convergence rate and BER by increasing
the number of genes and chromosomes in GA. This scheme also reduces the complexity of the receiver.
The paper is organized as follow: Section 2 describes the system model; the batch processing receiver is
given in Section 3; MMSE based improved cost function is given in Section 4; Section 5 explains the proposed
GA based MMSE weights calculation method; Section 6 explains the simulation results; and Section 7 concludes
the paper.
2. System model
We used two transmit and one receive antenna for simplicity as Alamouti’s STBC was to be applied to the
MC-CDMA system. The number of antennas can be increased as per future requirements.
Figure 1 shows the mth user uplink transmitter for a STBC based MC-CDMA system. Let the two
transmit antennas be X and Y, respectively. The two simultaneous symbols xm(2i−1) and xm(2i) are
transmitted from transmit antenna X and Y at the first symbol interval. In the next symbol interval, x∗
m(2i)
and x∗
m(2i−1) are transmitted from antennas X and Y. We used a spreading code pair (am,1am,2) of size
M×1 for frequency domain spreading from antennas X and Y. The am,n is given by the following:
am,n = [am,n,1, am,n,2, . . . , am,n,M ]T.(1)
STBC
[ (2 1), (2)]x i x i
k k
–
S p re a ding
S p re a ding
IFFT
IFFT
P/S &CP I
P/S &CP I
F re que nc y
Up
F re que nc y
Up
Figure 1. STBC based MC-CDMA transmitter.
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KHAN et al./Turk J Elec Eng & Comp Sci
The M-point inverse fast Fourier transform (IFFT) is performed where Mis the number of subcarriers. It is
also added in supposition that the number of subcarriers and that of the processing gain of the spreading code
are equal. The IFFT generated signal is further converted from parallel to serial, and then transmitted to the
channels. The Rayleigh flat fading channel is implemented using three paths. The fading gains are generated
by using complex Gaussian distributions that are normalized such that the average energy of the channel is
unity. In all cycles, the channel coefficients as well as the spreading code sequence are constant.
Figure 2 represents the receiver of the STBC based MC-CDMA system. First of all, the cyclic prefixes
are eliminated at the receiver. Further, the signal is converted from serial to parallel. The M-point fast Fourier
transform (FFT) is applied to this signal. As the multipath reflection results in a delay spread, we supposed
that the cyclic prefix length of all users is more than the maximum delay spread. The received signal vector in
a frequency domain is given by the following:
r(2i−1) =
K
m=1 {Hm,1am,1xm(2i−1) + Hm,2am,2xm(2i)}+z(2i−1) (2)
r(2i) =
K
m=1 {−Hm,1am,1x∗
m(2i) + Hm,2am,2x∗
m(2i−1)}+z(2i)
where Hm,n is the frequency domain channel response from the nth transmit antenna of the mth user:
Hm,n =diag (Hm,n,0, Hm,n,1, . . . , Hm,n,M−1) (3)
Furthermore, z(l) is additive white Gaussian noise with a mean of zero and a covariance matrix σ2
sI2Nwith an
identity matrix Iof size 2M×2M. The mth user’s nth information datum xm(n) is an identically distributed
random variable with a mean of zero and a unity variance.
Frequency
Down
CPR&
S /P FFT
Ada ptive
MUD
Ada ptive
MUD
( )
1
w i
( )
2
w i
1
^(2 1)x i –
2
^(2 1)x i –
Figure 2. STBC based MC-CDMA receiver.
Let the mth user’s useful spreading code for the nth transmit antenna be bk,m , then the received signal
is
r(2i−1) =
K
m=1 {bm,1xm(2i−1) + bm,2xm(2i)}+z(2i−1) (4)
r(2i) =
K
m=1 {−bm,1x∗
m(2i) + bm,2x∗
m(2i−1)}+z(2i)
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KHAN et al./Turk J Elec Eng & Comp Sci
3. Batch processing receiver
The extended received signal vector for two consecutive symbols is characterized by y(i) ;
y(i) = [rT(2i−1) rH(2i)]T=
K
m=1 {βm,1xm(2i−1) + βm,2xm(2i)}+η(i) (5)
where
βm,1=bm,1
b∗
m,2, βm,2=bm,2
−b∗
m,1, η (i) = z(2i−1)
z∗(2i)(6)
Suppose that the required user is 1. The extended signal y(i) in Eq. (5) is changed as follows:
r(i) = A1x1(i) + n(i) (7) (7)
where
A1= [β1,1β1,2]
and
x1(i) = [x1(2i−1) x1(2i)]T
with n(i) denoted by
n(i) =
K
m=2 {βm,1xm(2i−1) +βm,2xm(2i)}+n(i) (8)
By describing filter weight vectorsw1and w2of size2M×1, xm(2i−1) andxm(2i) are detected. Then, the
mean square error (MSE) at the filter output is as follows:
C(w1,w2) = E
WHr(i)−x1(i)
2
=E
wH
1r(i)−x1(2i−1)
2+E
wH
2r(i)−x1(2i)
2
=C1(w1) + C2(w2) (9)
where W= [w1w2] and
C1(w1) = E
wH
1r(i)−x1(2i−1)
2
C2(w2) = E
wH
2r(i)−x1(2i)
2(10)
The minimum mean square error (MMSE) receiver is attained by the minimization problem in [7]:
[wo,1,wo,2] = argC (w1,w2)
={C1(w1) + C2(w2) (11)
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KHAN et al./Turk J Elec Eng & Comp Sci
4. Improved cost function
A relationship between the optimum weights wo,1and wo,2is explained in this section. Let Qybe given
according to its dimensionsM×M:
Qy=Q1Q2
Q3Q4(12)
The Qyhas a unique relationship between diagonals [11,12]. It was shown that Q4=Q∗
1and Q3=−Q∗
2.We
used this relationship in the MMSE filter weight vectors in Eq. (10) to derive the improved cost function. The
optimal weights vectors wo,1and wo,2are as follows:
wo,1=w1,1
w1,2,wo,2=w2,3
w1,4(13)
The following relationship is fulfilled by these vectors as in [13,14]:
w1,2=w∗
2,3,w1,4=−w∗
1,1(14)
The relationship given in Eq. (14) is justifiable for the weights vectors given in Eq. (13). The convergence rate
is increased by only updating those weights vectors satisfying the relationship in Eq. (14). The MMSE cost
function in Eq. (11) can be altered as follows:
CN=CN1(wd,we) +CN2(wd,we) (15)
where
CN1(wd,we) = E[|wH
dr(2i−1) + wT
er∗(2i)−d1(2i−1) |2]
and
CN2(wd,we) = E[|wH
er(2i−1) + wT
dr∗(2i)−d1(2i)|2]
5. Genetic algorithm explanation
There are many algorithms that are being used in complex nonlinear systems. The GA works effectively in
nonlinear problems.
In the GA, the solution is represented as a chromosome. The new population is always generated by
breeding and mutation mechanisms [10]. The number of weights required for a solution is 2M. Each column
of the weight matrix is considered to be a gene. The total number of columns in this matrix is MT. The
qth element weight vector is given by:
wq= [wq,1wq,2. . . wq,MT]
In our proposed scheme, we have applied the GA in order to minimize the cost function given in Eq. (10).
Further, the GA is also applied to the improved cost function given in Eq. (15). The GA description is given
below in the Table.
Initially, a population of qindividuals W= [w1w2] is created randomly. The recursive execution process
mechanism is used in the GA after the initialization of the population. One generation is produced in each
recursive cycle. Two individuals are picked at random to be the parents of the next generation. These parents
give birth to two children. The fitness function is given in Eqs. (10) and (15) for calculating the fitness of
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KHAN et al./Turk J Elec Eng & Comp Sci
children. Furthermore, a new population is produced with genes that give the best answers with the fitness
function given in Eq. (10). We continue the process until a threshold value is achieved or a certain number of
cycles are completed.
Table. Genetic algorithm (GA) description.
GA algorithm
S. no. Steps
1. Start.
2. Initialization of weights wq.
3. Calculate the fitness function using the cost function given in Eq. (7).
4. Sort the weights in ascending order as per fitness values.
5. Select the best parents.
6. Generate the children using the crossover.
(The crossover ration is 3/4 and 1/4 of Parent No. 1 and Parent No. 2).
7. Mutation process is applied.
8. Calculate the fitness.
9. If (Number of cycles) go to step 10, else go to step 3.
10. Stop.
Let the two parents be [p1p2]. We analyzed four different approaches for parent variety: eugenic selection,
alpha-male selection, preferred selection, and random selection. In the eugenic selection, the two best parents
are: p1=w1and p2∈ {wk,2< k ≤K. In the preferred selection, p1is selected from p1∈ {wj,1< j < k}
excluding the finest ones, and p2is selected randomly from the outstanding population p2∈ {wk,2< k ≤K
superior to p1. In the last strategy of random selection, p1and p2are selected randomly at each cycle. We
find that the preferred selection gives the best result in our analysis. The two selected parents produce two
children c1and c2. The c1and c2have the same genes as the parents altogether. Any of the children, c1or
c2, have the same number of genes from parent p1and outstanding genes from p2.
We observed two crossover ratios: 1/2, 1/2 and 3/4, 1/4. The crossover of parents with ratios of 3/4
and 1/4 gave good results in our case. We chose Nindividuals that gave us the minimized cost function. We
further chose one random index from both columns and rows. We changed the sign of the bit placed in those
locations. This new generation was replaced by the following:
min
x∈χw1= arg CN1(x) (16)
min
x∈χw2= arg CN2(x)
This new generation replaced the old generation ofW. The population was rearranged in a mounting order of
cost after the population had been reorganized. The algorithm moves on to the next generation or ends if the
stopping condition is achieved or the number of cycles is completed.
6. Results
The uplink MC-CDMA system is implemented with M= 32 subcarriers. The subcarriers are equal to the
dimension of the spreading code. The real and imaginary parts of the spreading code are independently chosen
from 1/√2 and −1/√2 at random. The Rayleigh flat fading channel is implemented using three paths. The
fading gains are generated by using complex Gaussian distributions that are normalized such that the average
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KHAN et al./Turk J Elec Eng & Comp Sci
energy of the channel is unity. In all cycles, the channel coefficients as well as the spreading code sequence are
constant. Figures 3 and 4 represent the simulations of the conventional cost function without a relationship with
the GA, while Figures 5 and 6 represent the comparison study of the improved cost function with a relationship
with the GA and the conventional cost function without a relationship with the GA, respectively.
0 5 10 15 20 25
10–3
10–2
10–1
100Signal to Noise Ratio vs Bit Error Rate
Signal to Noise Ratio (SNR)
Bit Error Rate (BER)
Proposed(Accelerated-GA Gn=75 Ch=60)
Proposed(Accelerated-GA Gn=75 Ch=40)
Proposed(Accelerated-GA Gn=75 Ch=20)
Conventional, µ(c)=0.01
Conventional, µ(c)=0.02
Figure 3. Signal to noise ratio (SNR) vs. bit error rate (BER) with number of genes =75 and a varying number of
chromosomes.
5 10 15 20 25 30
10–4
10–3
10–2
10–1
100
Signal to Noise Ratio (SNR)
Bit Error Rate (BER)
Signal to Noise Ratio vs Bit Error Rate for K=16
Proposed(Accelerated-GA Gn=100 Ch=50)
Proposed(Accelerated-GA Gn=150 Ch=25)
Proposed(Accelerated-GA Gn= 50 Ch=50)
Proposed(Accelerated-GA Gn= 25 Ch=100)
Conventional, µ(c)=0.01
Conventional, µ(c)=0.02
Figure 4. Signal to noise ratio (SNR) vs. bit error rate (BER) with varying numbers of genes and chromosomes.
Figure 3 shows the SNR vs. BER for different variations of the proposed scheme with respect to a fixed
number of genes and a varying number of chromosomes. The topmost two curves are for the conventional LMS
schemes. It can be easily seen that at SNR = 0 dB, these schemes give a BER of almost 0.9. The BER comes
down by increasing the SNR. At SNR = 25 dB, the BER falls nearest to 0.1. The 3rd curve is one of our GA
based proposed schemes with 75 genes and 20 chromosome. This scheme gives a BER of 0.4 at SNR = 0 dB.
The BER also falls down by increasing the SNR. This scheme gives a BER of 0.1 at a medium SNR. The BER
decreases to 0.02 at SNR = 25 dB. The 4th most curve from top to bottom is also proposed, with 75 genes and
40 chromosomes. This scheme also gives a BER of 0.4 at SNR = 0 dB. It gives a BER of 0.06 at a medium
SNR. Its BER lowers to 0.01 at SNR = 25 dB. The 5th most curve from top to bottom is also proposed, with
75 genes and 60 chromosomes. This GA based scheme gives the best result. This scheme gives a BER of 0.4 at
SNR = 0 dB. It gives BER of almost 0.02 at a medium SNR. The BER falls almost to zero at SNR = 25 dB.
Therefore, it can be said that if we fix the number of genes and increase the number of chromosomes of GA,
the BER can be minimized.
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KHAN et al./Turk J Elec Eng & Comp Sci
Figure 4 shows the SNR vs. BER of our proposed scheme with varying number of genes and chromosomes.
The top two curves are for the conventional schemes. It can be easily seen that these conventional schemes give
a BER of almost 0.9 at SNR = 0 dB. These schemes give a BER of 0.375 at an approximately medium SNR.
However, both give a BER of 0.02 at SNR = 30 dB. The third curve of our proposed scheme is with 25 genes
and 100 chromosomes. It can be seen that this scheme gives a BER of 0.8 at SNR= 0 dB. Further at a medium
SNR, this scheme gives a BER of approximately 0.18. However, this scheme gives a BER of 0.01 at SNR = 30
dB. The fourth curve is also for the proposed scheme with 50 genes and 50 chromosomes. This scheme gives a
BER of 0.64 at SNR = 0 dB, and a BER of 0.16 at a medium SNR. However, it gives the same BER of 0.01 at
SNR = 30 dB. The fifth curve from the top is from our proposed scheme with 150 genes and 25 chromosomes.
This scheme gives a BER of 0.4 at SNR = 0 dB, and a BER of approximately 0.1 at a medium SNR. However,
it gives a BER of 0 at SNR = 30 dB. The last curve from the top is for 100 genes and 50 chromosomes. This
scheme gives a BER of 0.57 at SNR = 0 dB, and a BER of 0.02 at a medium SNR. This scheme gives a BER of
0 at SNR = 30 dB. Therefore, it can be said that if we fix one of the two, the number of genes or the number
of chromosomes, and vary the other one, the same result will be achieved. However, better results can only be
achieved by increasing both.
Figure 5 shows the number of users vs. factor of complexity for a fixed number of genes and a varying
number of chromosomes. The complexity factor of the GA is calculated by the following:
2k
genes ×choromosomes
and a conventional scheme is calculated by k(N−1) (N+ 1). We fixed the BER to 0.001 and SNR to 25 dB. It
can be seen from the topmost curve that the conventional scheme needs 980 iterations to achieve a 0.001 BER.
It can be further seen from the 2nd topmost curve that if we fix the number of genes to 75 and the number of
chromosomes to 20, 700 iterations are needed to converge to a 0.001 BER. But if we increase the number of
chromosomes from 20 to 40, 350 iterations will be sufficient to achieve the same BER. However, if we increase
the number of chromosomes to 60, 235 iterations will achieve the same BER. Therefore, it can be said that if
we increase the number of chromosomes with a fixed number of genes, then the convergence rate will be high.
Further, it is established that the proposed scheme is much better than the conventional one.
12 13 14 15 16 17 18 19 20
100
101
102
103
Numbers of users (K)
Factor of Complexity (FC)
Numbers of users (K) vs Factor of Complexity (FC)
Conventional
Proposed (Accelerated- GA Gn=75 Ch=20)
Proposed (Accelerated- GA Gn=75 Ch=40)
Proposed (Accelerated- GA Gn=75 Ch=60)
Figure 5. Number of users vs. factor of complexity for a fixed number of genes and a varying number of chromosomes.
Figure 6 shows the number of users vs. factor of complexity for achieving different BERs. It can be seen
from the topmost curve that the conventional scheme needs 980 iterations to achieve an approximately 0.001
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KHAN et al./Turk J Elec Eng & Comp Sci
BER. For the GA based scheme, we have fixed the number of genes to 100 and the number of chromosomes to
50. It can be seen that 420 iterations are needed to achieve a BER of 0.0001 for the topmost curve. Further,
the second curve shows that 280 iterations are needed to achieve a BER of 0.001. The third curve shows that
it takes 210 iterations to achieve a BER of 0.01. Therefore, it can be said that it takes a higher number of
iterations to achieve a low BER.
12 13 14 15 16 17 18 19 20
100
101
102
103
Number of users (K)
Factor of Complexity (FC)
Number of users (K) vs Factor of Complexity (FC)
Conventional Bounded at a BER of = 10-
1.8
Proposed Bounded at a BER of =10 -
3
Proposed Bounded at a BER of =10 -
2
Proposed Bounded at a BER of = 10 -
1
Figure 6. Number of users vs. factor of complexity for achieving different BERs.
Figure 7 shows the number of cycles vs. the mean square error with a fixed number of chromosomes.
The SNR is also fixed to 25 dB. The topmost curve shows that the conventional scheme without a relationship
converges at the 350th iteration to achieve a BER of 0.03.The second topmost curve shows that the conventional
scheme with a relationship converges at the 250th iteration to achieve a BER of 0.03. The 3rd topmost curve
represents the proposed accelerated GA without a relationship. The bottom curve represents the proposed
accelerated GA with a relationship. It can be seen that the accelerated GA receiver without a relationship
converges at the 166th cycle. The accelerated GA receiver with a relationship converges at approximately the
90th cycle. Therefore, it can be said that the accelerated GA receiver with a relationship converges faster than
the accelerated GA receiver without a relationship and the conventional schemes.
0 50 100 150 200 250 300 350 400 450 500
10–3
10–2
10–1
100
Number of Cycles
Mean-Square Error (MSE)
Number of Cycles vs Mean-Square Error (MSE)
Conventional, µ(c)=0.01 with out Relationship
Conventional, µ(c)=0.01 with Relalationship
Proposed ( Accelerated-GA with out Relationship)
Proposed ( Accelerated-GA with Relationship)
Figure 7. Number of cycles vs. the mean square error with a fixed number of chromosomes.
Figure 8 shows the number of users vs. factor of complexity with varying number of chromosomes and
BER. The curve representations from top to bottom are as follows:
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KHAN et al./Turk J Elec Eng & Comp Sci
10 11 12 13 14 15 16 17 18 19 20
100
101
102
103Number of users (K) vs Factor of complexity (FC) Bounded at dierent BER
Number of users (K)
Factor of complexity (FC)
Conventional Bounded at a BER of =10-
1.8
Proposed(Accelerated-GA without Relationship Bounded at a BER of =10-
3, Ch=60)
Proposed(Accelerated-GA without Relationship Bounded at a BER of =10-
2, Ch=40)
Proposed(Accelerated-GA without Relationship Bounded at a BER of =10-
1, Ch=20)
Proposed(Accelerated-GA with Relationship Bounded at a BER of =10-
3, Ch=60)
Proposed(Accelerated-GA with Relationship Bounded at a BER of =10-
2, Ch=40)
Proposed(Accelerated-GA with Relationship Bounded at a BER of =10-
1, Ch=20)
Figure 8. Number of users vs. factor of complexity bounded at different BERs.
•It can be seen from the topmost curve that the conventional scheme needs 980 iterations to achieve an
approximate BER of 0.001.
•The 2nd curve is for the accelerated GA without a relationship bounded at BER = 10−1and the number
of chromosomes = 20. It is noted that it needs 700 iterations for K = 20 in order to achieve a BER =
10−1.
•The 3rd curve is overlapped by another curve as well. This other curve is for the accelerated GA with
a relationship bounded at the same BER and number of chromosomes, and the 3rd curve is for the
accelerated GA without a relationship bounded at BER = 10−2. It is noted that both schemes need 350
iterations for K = 20 in order to achieve the mentioned BER.
•The 4th curve is for the accelerated GA without a relationship bounded at BER = 10−3and the number
of chromosomes = 60. It is noted that it takes 235 iterations for K = 20 in order to achieve a BER =
10−3.
•The 5th curve is for the accelerated GA with a relationship bounded at BER = 10−2and the number
of chromosomes = 40. It is noted that it takes 175 iterations for K = 20 in order to achieve the BER =
10−2.
•The 6th curve is for the accelerated GA with a relationship bounded at BER = 10−3and the number of
chromosomes = 60. It is noted that it takes 117 iterations for K = 20 in order to achieve a BER = 10−3.
Therefore, it can be said that the accelerated GA receiver with a relationship requires a smaller number
of iterations to achieve any BER for a number of users K as compared with the accelerated GA receiver without
a relationship.
7. Conclusion
Multicarrier systems like MC-CDMA systems are designed for maximum usability of on-hand bandwidth. We
used MC-CDMA with Alamouti’s space time coding in this paper. We proposed a GA with two variations
for the MC-CDMA system in order to calculate MMSE weights in this paper. The variations on the receiver
were either without a relationship or with a relationship. We found that this scheme gives a better BER and
convergence rate than the conventional LMS based MC-CDMA receiver. It can be seen that if we increase the
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KHAN et al./Turk J Elec Eng & Comp Sci
number of genes and chromosomes with the same effect, these receivers have a better convergence rate and a
better BER. Further, it is observed that the accelerated GA calculation scheme with a relationship converge
faster than the accelerated GA scheme without a relationship. However, the BER remains steady.
References
[1] Hara S, Prasad R. Overview of multicarrier CDMA. IEEE Commun Mag 1997; 35: 126–133.
[2] Alamouti S. A simple transmit diversity technique for wireless communications. IEEE J Sel Areas Comm 1998; 16:
1451–1458.
[3] Verdu S. Multiuser Detection. Cambridge, UK: Cambridge University Press, 1998.
[4] Li H, Lu X, Giannakis GB. Capon multiuser receiver for CDMA systems with space-time coding. IEEE T Signal
Proces 2002; 50: 1193–1204.
[5] Shafi M, Da-shan S, Smith PJ, Naguib A. An overview of MIMO space-time coded wireless systems. IEEE J Sel
Areas Comm 2003; 21: 281–302.
[6] Li Z, Latva-aho M. Nonblind and semibind space-time frequency multiuser detection for space-time block coded
MC-COMA. IEEE T Wirel Commun 2005; 4: 1311–1318.
[7] Yu JL, Lee IT. MIMO Capon receiver and channel estimation for space-time coded CDMA systems. IEEE T Wirel
Commun 2006; 5: 3023–3028.
[8] Dejong KA. Evolutionary Computation: A Unified Approach. Cambridge, MA, USA: MIT Press, 2006.
[9] 3GPP Technical Specification 36.211 V8.6.0. Evolved universal terrestrial radio access: Physical channels and
modulation. March 2009.
[10] Seo B, Ahn JY. LMS adaptive receiver for uplink space-time coded MC-CDMA system. In: The 12th International
Conference on Advanced Communication Technology; 7–10 February 2010; Phoenix Park, Korea: ICACT. pp.
839–843.
[11] Seo B, Ahn WG, Jeong C, Kim HM. Fast convergent LMS adaptive receiver for MC-CDMA system with space-time
block coding. IEEE Commun Lett 2010; 14: 8–11.
[12] Navid D, Babak E. Evaluation of channel estimation algorithms in MIMO-OFDM systems with considering the
carrier frequency offset. International Journal of Computer Sciences and Telecommunications 2012; 3: 5–7.
[13] Muhammad AK, Muhammad U, Muhammad ASC. Accelerated assistant to sub-optimum receiver for multi carrier
code division multiple acess system. In: FTCOM; 26–29 December, 2012; Malacca, Malaysia: FTCOM. pp 26–29.
[14] Muhammad U, Muhammad AK, Muhammad ASC. GA backing to STBC based MC-CDMA systems. In: IEEE 4th
International conference on Intelligent Systems, Modeling and Simulation; 29–31 January 2013; Bangkok, Thailand:
IEEE. pp. 503–506.
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