electromagnetism-like method tuned ... -...

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMSInt. J. Commun. Syst. 2014; 27:233–247Published online 24 May 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/dac.2351

Electromagnetism-like method tuned constant modulus algorithmfor blind detector in multicarrier CDMA system

Ho-Lung Hung*,†

Department of Electrical Engineering, Chien-Kuo Technology University No. 1, Chieh Shou N.Rd, Changhua City, 500,Taiwan, R.O.C.

SUMMARY

This paper presents an efficient meta-heuristic algorithm based on electromagnetism-like method, whichhas been successfully implemented in multiuser detection problems. The contribution revisits blindmultiuser detection for multicarrier code division multiple access systems using a novel combined adaptivestep-size constant modulus algorithm (CMA) and electromagnetism-like method scheme. To work aroundpotentially computational intractability and improved the capability of suppressing multiple access inter-ference (MAI) for Multicarrier CDMA System, the proposed scheme exploits heuristics in considerationof both global and local exploration of the step size of the CMA. Simulation results obtained confirm thatfaster convergence and desirable BER performance with low computational complexity can be achieved withelectromagnetism-like method based CMA scheme, compared with the previous step-size CMA scheme,genetic algorithm, and particle swarm optimization with CMA scheme. Copyright © 2012 John Wiley &Sons, Ltd.

Received 25 October 2010; Revised 25 January 2012; Accepted 26 February 2012

KEY WORDS: constant modulus algorithm; blind multiuser detection; electromagnetism-like method;artificial intelligence scheme; multi-carrier code division multiple access

1. INTRODUCTION

The multicarrier code division multiple access (MC-CDMA) system has been widely studied forfuture high-speed wireless communication, in that it provides spectral efficiency and interferencessuppression capability [1, 2]. In wireless communication systems because of their operation asmultiple access systems, the significant structure interference is inherent in wireless channels, andis referred to as the multiple-access interference (MAI). The multiuser detector (MUD), which isthe focus of research on MC-CDMA receivers, attempts to simultaneously eliminate MAIs andthe near–far problem. It has been accepted as a technique that improves system capacity and isnear–far resistant [3, 4]. However, the large complexity involved in optimal multiuser detection [3]is exponential in the number of active users and the length of the bit sequence. Therefore, it isunsuitable for implementation. A large amount of MUD research has focused on the complexityproblem [4–7].

Consequently, the blind algorithms for the adaptive MUD have attracted much attention toimprove the system capacity. Many adaptive algorithms using the constant modulus algorithm(CMA) criterion have been reported for implementation of MUD problems [4–12]. The mainmotivation for employing a blind detector is to avoid the training sequence commonly requiredby most adaptive multiuser detectors proposed previously. The key advantage of CMA is that it isa blind adaptive algorithm, that is, requires no training signal. It is widely applied to multiuser

*Correspondence to: Ho-Lung Hung, Department of Electrical Engineering, Chien-Kuo Technology University No. 1,Chieh Shou N.Rd, Changhua City, 500, Taiwan, R.O.C.

†E-mail: [email protected]

Copyright © 2012 John Wiley & Sons, Ltd.

234 H.-L. HUNG

detection, array processing, adaptive beamforming, and blind equalisation. A serious problemassociated with CMA is that its steady-state mean square error (MSE) many not be sufficientlylow for the system to achieve an adequate symbol error rate performance and its slow convergence.To improve tracking capability, use of linearly constrained constant modulus algorithm (LCCMA)based on the stochastic gradient algorithm to capture desired user instead of an interfering onewas reported in [6, 7], yet their convergence is more readily influenced by step size. Another well-known algorithm is the signed-error CMA, which is proposed to simplify the CMA technique bytransforming multiplications into sign operations. However, it does not inherit the desirable robust-ness of CMA. The recursive least squares [8,9] updates the weight vector with fast convergence rateand superior performance. This improvement in performance, however, is achieved at the expense ofa large increase in computation complexity. In time-varying channel, randomly rotating phase distor-tion may seriously degrade performance of algorithms. In [1–12], it is suggested that subspace-basedlinear minimum mean-squared error (MMSE) detection be used in Multicarrier direct sequencecode division multiple (MC DS-CDMA) systems. The subspace-based method has much matrixcomputation which makes complexity increase.

For a stochastic gradient [13–15] adaptive algorithm, such as training-based least mean square(LMS), step size must be sufficiently small to avoid divergence. Within the range of step sizevalues that ensures convergence, a smaller step size achieves better steady-state performance withslower convergence speed, while larger step size boosts convergence speed with poorer steady-state performance. Hence, performance and stability of stochastic gradient algorithm used within anMC-CDMA receiver designed to mitigate MAI depending upon the choice of an appropriatestep size. Constant step size LMS algorithm thus represents trade-off between steady-stateperformance and convergence speed when choosing step size value. In attempts to optimize boththe steady-state performance and convergence speed, techniques based on fuzzy logic tuning ofLMS’s step size have been developed [14–18]. The CMA is a stochastic gradient blind adaptivealgorithm; step size must be chosen with extreme care, much more than the training-basedLMS algorithm.

In recent years, much attention has been devoted to meta-heuristics, new techniques emergingfrom the field of artificial intelligence: fuzzy inference system [19], genetic algorithm (GA) [20,21],particle swarm optimization (PSO) [22–24], simulated annealing [24], ant colony optimization[25], artificial neural network [26], electromagnetism-like method (EM) [27–30], and so on. Thesemeta-heuristics can be regarded as problem-independent approaches well suited to solve complexproblems difficult to solve by traditional techniques. Likewise, they can produce high-qualitysolutions with reasonable computational effort. Heuristic optimization techniques are fast-growingtools for overcoming most limitations arising from derivative-based techniques. This paper will putforward a novel receiver that combines the CMA blind adaptive multiuser detection with artificialintelligence, and then compare the performance of the system with that of different CM algorithmsin Rayleigh fading channel.

Electromagnetism-like mechanism is a population based meta-heuristic that has been proposedto solve continuous problems effectively On the basis of the points above, we state our interestin a novel CMA technique based on electromagnetism-like method to suppress MAI in theMC-CDMA signal. Performance and capacity improvement allowed by this approach has motivatedthe search for suboptimal schemes, which reach a good compromise between complexity andperformance. The proposed receiver has a two-stage parallel structure. In the first stage, anindividual CMA receiver processes every received signal. The decision variable at each CMAreceiver output is compared with a suitable weight factor value. If the decision variable overcomessuch a weight, the received signal is considered reliable; otherwise, it is assumed unreliable.Multiple-access interference effects of reliable signals on other signals are canceled in the secondstage of the proposed receiver. Specifically, this paper proposes an improved CMA algorithm byutilizing error function, which is deduced from CMA philosophy, in the sign operation of theEM-based CMA to speed convergence process and reduce computational complexity. Againstthis background, the main contribution of the proposed algorithm is to minimize computationalcomplexity with optimum weight factor and suppress MAI. Simulation results confirm theseimprovements achieved by the proposed algorithm.

Copyright © 2012 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2014; 27:233–247DOI: 10.1002/dac

EM ALGORITHM 235

The rest of this paper is organized as follows. In Section 2, we summarize the system model.The EM-assisted CMA blind detection in multipath fading domain is demonstrated in Section 3.Simulation results are provided in Section 4 and Section 5 contains the conclusions.

2. SYSTEM MODEL

Let us consider a synchronous MC-CDMA system with Ksimultaneous users and N subcarriers ina frequency selective Rayleigh fading channel. After the data and pilot symbols are multiplexedand modulated by binary phase-shift keying (BPSK), these symbols are copied and multipliedby each chip of the spreading code. These chips are modulated by the inverse discrete Fouriertransform and converted to serial samples of the OFDM symbols. The BPSK-modulated symbolsbk 2 .�1,C1/ are spread using a spreading sequence ak D

�a1k

, a2k

, � � � aNk

�of length N . Then N

consecutive chips of the spreading sequences were mapped N different subcarriers by the inverseFast Fourier Transform Several multipath models have been used in the literature, varying from thevery comprehensive one to the simple tapped delay line model. In this paper, the multipath fad-ing channel is modeled as consisting of a fixed number of resolvable Rayleigh fading paths. Thelow-pass impulse response of the channel for user k is given by

sk.t/D

LXlD1

alkpc.t � .n� 1/Tc/, t 2 Œ0,Ts�, (1)

where Tc is the chip interval. Ts is the symbol interval.�a1k

, a2k

, � � � aNk

�is the spreading code of the

k-th user, taking the value +1 or –1. N D Ts=Tc is the spreading gain. pc.t/ is the chip waveform.The energy of sk.t/ is normalized, that is,

R Ts0 s2

k.t/dt D 1. The k-th user, for 16 k 6K, generates

a stream of mapped data symbols bk D�� , bk0 , bk1 , bk2 , � � �

�. The baseband model of transmitted

signal of the kth user is expressed as

Zk.t/D

MXmD1

Ak

´1XiD1

bki sk.t � iTs/

μexp

�j 2�

m� 1

Mt

�, (2)

whereAk and bki respectively denote the amplitude and the complex symbol of the k-th user signal.M denotes the number of parallel branches, and it is also the number of subcarriers. Each subcarrieris assumed to experience slowly varying flat fading and adjacent subcarriers are assumed not tointerfere with each other. The received signal can be expressed as

r.t/D

KXkD1

MXmD1

Ak˛k,m

´1X

iD�1

bki sk.t � iTs/

μexp

�j 2�

m� 1

Mt

�C n.t/, (3)

where ˛k,m accounts for the overall effects of phase shifts and fading for the m-th carrier ofthe k-th user, and n.t/ is the zero-mean complex Gaussian noise. The received signal r.t/ is firstdemodulated and then passed through a chip-matched filter, where !1,!2, � � �!M denote differentcarrier frequencies. Figure 1 shows the block diagram of the EM algorithm-based MRC Rakereceiver. The output of the chip matched filter on each branch is sampled at chip rate. Hence, thereceived signal can be expressed in vectorial form as

rDKXkD1

AkbkDk�k C n, (4)

where

Dk D diag

8<:˛k,1, � � �˛k,1,„ ƒ‚ …

N

� � � ,˛k,M , � � �˛k,M„ ƒ‚ …N

9>=>; (5)


236 H.-L. HUNG

Figure 1. Block diagram of EM algorithm-based MRC Rake receiver.

�k D

264sTk � � � sTk„ ƒ‚ …

M

375

T

(6)

sk D1pN

�a1ka

2k � � � a

Nk

T, (7)

where Ak and bk denote the received amplitude and the transmitted symbols of the k-th user,respectively. T denotes transposition; n denotes a white Gaussian noise vector with zero meanand covariance matrix. Equation (4) denotes signals of all subcarriers after demodulation at thereceiver, which can be viewed as signal in frequency domain. To implement blind detection of MCDS-CDMA systems, Equation (4) is slightly changed to

rDKXkD1

Akbk“k’k C n , (8)

where “k is the diagonal matrix with the spreading code of thek-th user as the diagonal elements,

“k D

2666666664

sksk

. . .sk„ ƒ‚ …

M

3777777775

(9)

parameter ˛k denotes a vector consisting ofM elements of complex fading onM subcarriers of thek-th user,

˛k D�˛k,1˛k,2 � � �˛k,M

T. (10)

To recover original signals, Equation (8) is first despread to partly eliminate MAI, followed by CMAblind detection. In the conventional CMA, a linear receiver is chosen comprising a weight vectorw that operates on the vector r to yield the output y. The weight vector w is chosen to minimizethe deviation of the receiver’s output from a constant modulus. Figure 2 shows the block diagramof a blind multiuser detector based on EM-CMA in multipath channels. Assuming the user 1 is thedesired user, according to the above idea the cost function can be defined by

J.w/DE�jwHˇH

1 r j � 12

, (11)


EM ALGORITHM 237

Figure 2. The block diagram of a blind multiuser detector based on EM-CMA in multipath channels.

where ˇH1 r is the despread signal for the user 1. w D Œw1 w2 � � �wM �

T is the weigh vector. Hdenotes the conjugate transposition. The optimum weight vector Ow of CMA blind detection is

Ow D arg minwJ.w/ . (12)

The disadvantage of the CMA is that it may capture a constant modulus signal other than the desiredone. The problem stems from the fact that the CMA cost function does not have a unique minimum,and that it will be minimized for any constant modulus filter output. The other disadvantage is thatthe CMA may be too slow for a practical wireless application. To find a good tradeoff between theCMA performance on BER reduction and the complexity in the process of weight factor selection,we propose a novel EM algorithm-based CMA that is useful in solving combinatorial optimizationproblems. The objective of the technique is to find the weight factors that achieve blind detectionstatistic close to that of the CMA technique with reduced search complexity and little performancedegradation. Basically, the EM-based CMA technique described below can be implemented byappropriately changing the optimization weight factor (OWF) for w block in Figure 2.

Let us first consider the Steepest-Descent CMA (SDCMA), which is deducted from least meansquare. The restrictive function of mean square error is as follows:

J.w/DE®jb.i/�wTr.i/j2

¯, (13)

where b.i/ is the transmit signals of the expected user, r.t/is the receive signal, wTr.i/ is theestimation of the transmit signal. The self-adoption expression of w

w.i/D w.i C 1/C�.i/v.i � 1/, (14)


238 H.-L. HUNG

where w.i/ is the weight vector of the i-th refresh; �.i/ is the step of the i-th compute; v.i � 1/ isthe refresh direction vector and equal to the negative gradient of J Œw.i � 1/�. SDCMA has advan-tages, such as better stability and BER performance, but its convergence is slower. The optimumweight vector of SDCMA blind detection is

Ow D arg minwJ.w/. (15)

There, the specific algorithm of SDCMA detection is as follows. The output y.i/ of the detector isgiven by

y.i/D wH.i/V H1 r.i/. (16)

End

Find the xbest

Movement

Total ForceCalculation

Best ParticleDefined as xbest

Fitness Ranking

New ParticlesFitness Function

Evaluation

Initial Particles

Coding

Start

TerminationSatisfies ?

Yes

No

OperationPhase

EvaluationPhase

InitializationPhase

Figure 3. Flow chart of EM algorithm.


EM ALGORITHM 239

The error information e.i/is denoted as e.i/ D y.i/ � y.i/= jy.i/j. The renewing formula of theweight vector wwith the stochastic gradient descent approach is expressed by

w.i C 1/D w.i/��V H1 r.i/e

�.i/ , (17)

where w is initialized, and the initial value of w is w D Œ111 � � � 111�T. Then Equations (16) to (17)are repeated until wconverges. The method is simply implemented and needs no complex matrixcomputation. SDCMA has advantages, such as better stability and BER performance, but its conver-gence is slower. Some new methods have been put forward to overcome the disadvantage. LSCMA[10] is one of these.

The LSCMA is a technique for minimizing the J.1, 2/cost function given by

J.w/D J.1, 2/DEŒ.jyj � 1/2� . (18)

The least squares CMA (LSCMA) is shown to be globally stable and convergent for any linearlyindependent set of input data and converge faster than some conventional CMA. The restrictivefunction of LSCMA is the same as SDCMA. The LSCMA is a technique for minimizing and theF (1,2) cost function is given by:

J.w/D J.1, 2/DEŒ.jyj � 1/2� subject to wTs1 D 1 . (19)

The LCCMA [13] cost function is given by

minwJ.w/DE

�.jyj2 � 1/2

, (20)

subject to the linear constraint wTs1 D 1, where s1 is the received desired user. The tap-weightupdate equation will be

w.i C 1/D w.i/��jy.i/jp�2.jy.i/jp � 1/y�.i/x.i/. (21)

3. ELECTROMAGNETISM-LIKE METHOD-BASED BLIND MUD

3.1. Electromagnetism-like optimization algorithm

The electromagnetism-like method developed by Birbil et al. [28,29] is a population-based stochas-tic global optimization method inspired by Coulomb’s Law of electromagnetism theory. Thismethod starts with an initial solution set (particles), and then attraction–repulsion mechanism is usediteratively to move those particles towards optimality. The general school for EM method is shownin Figure 3, consisting of four main steps: initialization, local search, calculation of total force, andmovement of particles. These procedures are interpreted as follows. Initialization is used to sampleM points (particles)randomly from the feasible region. Local search is a neighborhood search pro-cedure that can be applied to one or many points for local refinement to get better solutions at eachiteration. Total force exerted on each point by all other points is calculated in total force procedure.Movement of particles is used for moving sample points along the direction of total force. For anin-depth discussion of the EM method, the reader is referred to Refs. [29, 30]. Algorithm 1 showsthe general scheme of EM. We also provide the description of each step following the algorithm.

3.2. Electromagnetism-like algorithm-based constant modulus algorithm technique

Figure 3 depicts the EM algorithm flow chart. In principle, EM algorithm is a population-basedsearch method in which a set of potential solutions (points) to a problem evolve. At iteration, apopulation withM points is generated. Each solution is considered as a point in a multidimensionalsolution space with a certain charge, which relates to the objective function values associated withall solution points. Population is derived by utilizing an attraction–repulsion mechanism to movesample points towards optimality. Multiuser detection can be regarded as an optimization prob-lem that finds the most likely combination of weigh vector OwOMP,p . Configuration of trial solution


240 H.-L. HUNG

Algorithm 1.

Initialize; While termination criteria are not satisfied do;

Local search;

Calculation of charge and total force vector;

Movement according to the total force;

End while

Œ Ow1,p , Ow2,p , � � � , OwK,p� is already an antipodal binary string of length K, making the encoding pro-cess unnecessary. Procedures of EM-based CMA detector for aK-user synchronous MC-CDMAsystem are outlined below:

Step (1) Initialize particle population at � D 0. The input of the first stage w.k/ is a CMA of theoutput vector. Like most stochastic algorithms, this EM method starts with generating M

random sample points (or particles, a.k.a. weight vector w)°®wkm,�

¯V�D1

±MmD1

from a fea-

sible region, where V is the dimension of the problem andwKm,� denotes �-th coordinate ofthe particle mof the population at iterationk. Analogous to electromagnetism, each point

�km D®wkm,�

¯V�D1

is regarded as a virtually charged particle released in the space. Notethat in multidimensional solution space where each point represents a solution, a chargeis associated with each point. As such, each coordinate of a point, denoted as wkm,� , iscomputed by

wkm,� D l� C �.u� � l�/, (22)

where u� is the upper and l� the lower bound of �-th dimension, � a uniform randomnumber generator within [0, 1]. After a point is sampled from the space, objective func-tion value for the point is calculated. Given point ‰km , objective function [11–13] isexpressed as

J.w/DE�jwHˇH

1 r j � 12

. (23)

When M points are all identified, the point with the best objective function value is storedinto ‰kbest D ¹wbest,�º

V�D1. The system aims to find the Ow at minimum cost.

Step (2) Local search is used to gather the neighborhood information for a sampled point, whichcan be applied to one or to all points in the population for local refinement at each iteration.Theoretically, local search is expected to find a better solution, especially when applied toall particles. However, local search is usually time-consuming. Therefore, in this study, EMalgorithm is implemented with local search on the current better particle. The procedure ofthe local search is as follows:

– Step (2.1) Calculate maximum feasible step length smax based on the parameterı 2 [0,1], where the maximum feasible step length can be computed using thefollowing equation:

smax D ı. max16v6V

.uv � lv//. (24)

– Step (2.2) Generate a candidate of point M‰ D ¹ Mw�ºV�D1: A new particle M‰ is generated

from the current best point M‰›best. Because M‰ is a small random change coming from


EM ALGORITHM 241

M‰›best here, we randomly change two coordinates to generate M‰, where the modifiedcoordinate of the current best point, denoted as M‰� , is computed using the followingequation:

Mw� D wkbest,v C � � smax. (25)

– Step (2.3) Decide whether to update the current best point M‰kbest: If the new point M‰observes a better point, the sample point M‰kbest is replaced by this new point M‰.

– Step (2.4) Repeat Step 2.1 to Step 2.3 until maximum number of local search iterationis met.

Step (3) Calculation of total force: In this procedure, artificial electromagnetism field is built topropel particles to new positions via Coulomb’s law of electromagnetism theory. Artifi-cial charge qkm at point ‰km is determined by fitness function value, calculated using thefollowing equation:

qkm D exp

´�V

f .‰km/� f�‰kbest

�PMmD1

�f�‰km

�� f

�‰kbest

�μ

. (26)

By observing (26), we find (1) large f .‰km/ results in small qkm, and vice versa; and (2)artificial charges are all positive. Now the problem is to determine the force of attractionor repulsion between each pair of particles ‰km and ‰kr . Suppose that f .‰km/ < f

�‰kr�,

which implies that qkm > qkr ; in this case better fitness function value is preferred: that is,

‰km the preferred point and particle ‰kr ‘attracted’ to particle ‰km. That means a particleattracts other particles with better fitness function values and repels other particles withfitness cost function values. After determining the charge of each point on ¹‰kmº

MmD1 and

defining the rule of attraction–repulsion mechanism of artificial charge force vector, F km,r ,between two points ‰km and ‰kr , is computed as

F km,r D

8<:�qkr � q

km

� qkr �qkm

jjqkr �qkmjj

2, iff

�‰kr�< f

�‰km

�.attraction/�

qkm � qkr

� qkr �qkm

jjqkr �qkmjj

2, iff

�‰kr�> f

�‰km

�.repulsion/

. (27)

Total force }km exerted on each point ‰km by other (M–1) points is then calculated by

}km D

MXr � 1r ¤m

F km,r , mD 1, 2, � � ��,M . (28)

Step (4) Particle movement: After calculating total force }km, point m is updated in v-th coordinateof the force by a random step length given as

wkC1m,v D

8<ˆ:#km,v C �

}km,v

jj}km,v jj

�uv �w

km,v

�, if }km,v > 0

#km,v C �}km,v

jj}km,v jj

�wkm,v � lv

�, if }km,v 6 0

mD 1, 2, � � ��,M I m¤ best.

(29)Step (5) Repeat step 2 to step 4 for k D kC 1 until the maximum number of iteration is met.

This procedure enables the state trajectory to climb out of local minima thereby to con-verge toward the optimal or near-optimal solution. This algorithm, justified by simulation exper-iments, is extremely effective because of its global convergence capability together with squarecomputation complexity.


242 H.-L. HUNG

4. COMPUTATION COMPLEXITY

The computational complexity of EM-based detection scheme compared with that of ML detectionis discussed here. Computational complexity is taken in terms of the number of transmit bit persymbol . As we know, computational complexity of full complexity OMD is O.K2K/ per bit periteration. Receivers based on EM-based, GA-based, and PSO-based CMA number of operationsgrows followingO.KPpST/. Complexity of SDCMA method isO.KNST/. Number of operationsfor computational complexity of EM-CMA MUD can be significantly reduced by employing a can-didate list. In this way complexity turns proportional with the cardinality of candidate list Pd. Weassume total steps ST and number of particles in generations Pp. Thus, computational complexityper bit iteration of EM-based CMA MUD is then .O.KSTPp/. It is worth noting that K is fixed incertain systems, which depends on the number of active users, modulation schemes, and transmitantennas. Therefore, the complexity of the EM-based CMA MUD is directly decided by Pp and ST.

5. NUMERICAL RESULTS

This section carries out computer simulation to validate the capacity of the proposed algorithm forMAI suppression in an MC-CDMA system with combining process under Rayleigh fading chan-nel. We compare the proposed EM-based CMA scheme with other existing stochastic optimizationbased CMA approaches for the same number of samples, SamD3000. Signal-to-noise ratio (SNR)is 20 dB. In the simulations, quadrature phase-shift keying (QPSK) is adopted as the modulationscheme. Considering one synchronous MC-DS-CDMA communication system, we adopt differen-tial encoding and QPSK mapping. Spreading code is Gold 31, spreading gain G D 31, number ofsubcarriers S D 64, number of active users K D 10, and user 1 the desired user. The amplitude offading of every subcarrier has Rayleigh distribution, and the phase has uniform distribution. Fadingof different subcarriers of different users is assumed independent of each other and invariable indetection process. Figure 3 plots average BER against input SNR for different algorithms. The MAIare defined as MAI.k/ D 10 log.A2

k=A21/ D 10 dB, and k D 2 � 10. The performance measure is

signal-to-interference plus noise ratio (SIR):

SIRDE2¹wTrº

var ¹wTrºD A21

�wTs1

�2=

KXkD2

Ak.wTsk/

2C &2wTw

!. (30)

Figure 4 shows average SIRs achieved by six algorithms against the number of symbols in themultipath channel. Fixed-step length � D 0.001. It is observed that, with slow convergence, CMAreaches the steady state after about 210 symbols are received with low values of SIR, and SDCMA

Symbol index

0 200 400 600 800 1000

SIR

-2

0

2

4

6

8

10

12

EMCMAGACMAPSOCMALCCMACMASDCMA

Figure 4. Comparison of CMA, SDCMA, GS-CMA, PSO-CMA, and EM-CMA in MAI D 20 dBsuppression and SNRD 10 dB.


EM ALGORITHM 243

achieves better SIR with a slower convergence. The SIR achieved by the LCCMA is higher thanthat of SDCMA and lower than that of artificial intelligence-based CMA. It can also be observedthat SIRs achieved by LCCMA and SDCMA have a similar tendency when the number of processedsymbols is large. In addition, we can see that both GA-CMA and PSO-CMA algorithms can adaptrapidly to the changing environment, when the convergence speed and performance in terms of SIRof GA-CMA is slightly slower than PSO-CMA algorithm. GA-based CMA has convergence similarto that of PSO-based CMA, with slightly worse SIR performance. Similar observations emerge fromSIRs of PSO-based CMA and EM-based CMA: (1) EM-CMA presents excellent SIR performance,especially in low SNR; (2) EM-CMA presents better and faster convergent performance than otherstochastic optimization-based CMA approaches; (3). EM-CMA has better robustness, because itquickly attains stable state. It also decreases computational complexity and is more suited for adap-tive environment. In Figure 4, during transmitting 1000 bits, the stable SIR of EM-CDMA detectoris 10 dB, while the CMA, SDCMA, LCCMA, and GACMA detector is only about 6 dB, 6.9 dB,7 dB and 8 dB, respectively. Especially when there are some changes in the system, the SIR ofEMC-MA is always higher than that of the other CMA detectors.

Figures 5 and 6 depict BER performance versus different SNR, where MAI D 15 dB, K D 10and K D 5. It is clear that BER values of all methods decline following a rise of SNR. Resultsshow LCCMA as globally stable, converging for any linearly independent set of input data andfaster than the conventional SDCMA and CMA. The BER performance is good, but its complexity

SNR (dB)0 2 4 6 8 10 12 14 16

BE

R

10-5

10-4

10-3

10-2

10-1

PSOCMAGACMALCCMA MMSESDCMACMAEMCMA

100

Figure 5. BER performance curves of various detectors considered: CMA, LCCMA, GA-CMA, PSO-CMA,and EM-CMA blind detection methods and K D 5 users.

SNR (dB)0 2 4 6 8 10 12 14 16

BE

R

10-5

10-4

10-3

10-2

10-1

PSOCMAGACMALCCMA MMSESDCMACMAEMCMA

100

Figure 6. BER performance curves of various detectors considered: CMA, SDCMA, and EM-CMA blinddetection methods and K D 10 users with SNRD 8 dB.


244 H.-L. HUNG

is relatively high. From Figures 5 and 6, we learn that the robust stochastic optimization-basedCMA algorithm outperformed other conventional CMA methods, with BER very close to optimal.In this case with robust GA-CMA and PSO-CMA algorithms, both were derived based on con-strained CMA criterion. Performance might improve dramatically when the discrepancy of channelestimation occur especially when SNR is greater than 12 dB, because the desired signal cancellationand noise enhancement may easily occur in higher SNR environment. Yet with the approach basedon CM criterion, robust GA-CMA and PSO-CMA algorithms, performance is more stable and theimpact because of channel mismatch is less significant compared with methods using other criteria.

In fact, optimal weight vector was solved by updating the weight vector with LMS-type blindadaptation algorithm. From Figures 5 and 6 we learned that the proposed EM-CMA algorithm hasfaster convergence rate approaching optimal weight solution than other techniques. Also, EM algo-rithm with CMA converges much faster than GA and PSO with CMA. That is, with more iteration(more recirculation) in each symbol period, the weight vector could converge much closer to theoptimal weight vector. In practice, it should be selected properly; tradeoff between performanceand convergence rate must be considered. Moreover, as evident from these figures performance ofLMS-type blind adaptation algorithm with differential detector did improve BER compared withthe same algorithm without using differential detector, but with the paid of requiring extra encoderand decoder, they perform differentially coherent detection. Also, with the stochastic optimization-based CMA approaches-type blind adaptation algorithm, BER performance improves as shown inFigures 5 and 6, where estimated projection and tuning of optimization weight factor are requiredThese attain greater overall computational complexity than LMS-type algorithm. Performancedegradation of BER with stochastic optimization-based CMA approaches-type blind adaptationalgorithm is 1–2 dB compared with the optimal solution. Yet BER performance with the proposedalgorithm achieved optimal solution and outperformed others. This new algorithm EM-CMA bringsabout much better BER performance than PSOCMA and GACMA; it converges to the desired userand suppresses MAI effectively.

Figure 7 shows bigger step length � giving faster and smaller step length � slower convergence(� D 0.001 and � D 0.006) In all simulations, the simulations parameters are: K D 10, QPSKmodulation, perfect power control is assumed. In all the simulations, the maximum iterations isI D 200. Complexity of LCCMA is higher than SDCMA; both CMAs need to select an appropriatestep length� to gain perfect performance. It is observed that LCCMA has a faster convergence speedand higher stable SIR than SDCMA, while SDCMA and CMA yield similar performance. LCCMAhas faster convergence with reduced computational complexity. Finally, Figure 7 shows MSE per-formance of EM-CMA and PSO-CMA better than GA-CMA and other CMA; their convergencetime is almost the same. From the simulations, we know: (1) convergent rate of EM-CMA is fasterthan the others, its stable performance best. (2) When we increase step length, convergent rate ofSDCMA and LCCMA increase, like LMS algorithm, that is, step udetermines the convergent rateand stable performance of the filter, so attention should be paid to convergent rate, track performanceand stable square error of u value. (3) Figure 7 shows MSE performance of LSCMA and LCCMAbetter than CMA; their convergence time is almost the same. When we increase step u, MSE per-formance of LCCMA improves, too. (4) Deducing complexity of three algorithms using MATLAB(Cleve Moler, New Mexico, USA), it is shown that LSCMA has fastest convergence and highestcomplexity. Results suggest robustness of the algorithm to initialization of step sizes. Bigger u cangive faster convergence but worse BER performance; smaller u can give slower convergence butbetter BER performance.

In the last case, the performance of BER versus number of user for different CMA basedalgorithms is investigated. More specifically, we assume that each user has power 20 dB strongerthan the desired user. From Figure 8 we learn that in all cases with different SNR value the proposedrobust EM-CMA algorithm has superior performance compared with GA-CMA or PSOCMA algo-rithm. On the basis of the above discussion, we may conclude that the proposed robust EM-CMAalgorithm could be used to suppress MAI effectively and achieve desired performance in terms ofoutput SNR, output power and BER in an MC-CDMA system with stronger interferers. Likewise,compared with other existing methods, EM-CMA performed more robustly against near/far effectand the problem of channel mismatch, because of imperfect channel estimation.


EM ALGORITHM 245

(a) MSE versus number of iterations when u = 0. 001

(b) MSE versus number of iterations when u = 0. 006

Figure 7. (a) MSE versus number of iterations when uD 0.001. (b) MSE versus number of iterations whenuD 0.006.

Numbers of User

5 10 15 20 25

BE

R

CMAGACMAMMSEPSOCMAEMCMA

10-5

10-4

10-3

10-2

10-1

100

Figure 8. BER performance versus the number of active user with SNRD 8 dB.

6. CONCLUSIONS

This paper proposed a novel blind multiuser detector to suppress multiuser interference in MC-CDMA system over a Rayleigh-fading channel, which utilizes an electromagnetism-like method


246 H.-L. HUNG

based CMA algorithm to decide on the transmitted bits. The main advantage of the proposed detec-tor is its simplicity and suitability for MC-CDMA systems. An electromagnetism-like method isdesigned to adjust step size to minimize the constant modulus criterion; potential benefits of usingthis adaptive size approach are investigated. The complexity of the proposed detector is approxi-mately O.KSTPp/; its performance is significantly better and more robust compared with existingsuboptimum schemes. Compared with various CMA schemes developed previously, simulationsshow that good performance of the proposed electromagnetism-like method can not only achievesignificant BER performance but also enjoy complexity advantages.

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AUTHOR’S BIOGRAPHY

Ho-Lung Hung received the M.S. degree in Electrical Engineering from the University ofDetroit Mercy, Michigan, USA, in 1994 and the Ph.D. degree in Electrical Engineering fromNational Chung Cheng University, Chia-Yi, Taiwan, in 2007. From1995 to 2006, he wasa lecturer with the Department of Electrical Engineering, Chienkuo Technology Univer-sity, Taiwan. Since 2007, he was an associate professor with the Department of ElectricalEngineering, Chienkuo Technology University, Taiwan. His current research interests arein wireless communications, detection of spread-spectrum signal, wireless sensor networks,evolutionary computation, and intelligent systems. Dr. Hung serves as an associate editor forthe Telecommunication Systems.


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