research article minimum variance distortionless...

Research ArticleMinimum Variance Distortionless ResponseBeamformer with Enhanced Nulling Level Control viaDynamic Mutated Artificial Immune System

Tiong Sieh Kiong1 S Balasem Salem2 Johnny Koh Siaw Paw2

K Prajindra Sankar2 and Soodabeh Darzi3

1 Power Engineering Center College of Engineering Universiti Tenaga Nasional Kajang Selangor Malaysia2 Center of System and Machine Intelligence College of Engineering Universiti Tenaga Nasional Kajang Selangor Malaysia3 Department of Electrical Electronic amp Systems Engineering Universiti Kebangsaan Malaysia Bangi Selangor Malaysia

Correspondence should be addressed to Soodabeh Darzi sdtutnyahoocom

Received 18 February 2014 Accepted 23 March 2014 Published 5 June 2014

Academic Editors V Bhatnagar and Y Zhang

Copyright copy 2014 Tiong Sieh Kiong et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In smart antenna applications the adaptive beamforming technique is used to cancel interfering signals (placing nulls) and produceor steer a strong beam toward the target signal according to the calculatedweight vectorsMinimumvariance distortionless response(MVDR) beamforming is capable of determining the weight vectors for beam steering however its nulling level on the interferencesources remains unsatisfactory Beamforming can be considered as an optimization problem such that optimalweight vector shouldbe obtained through computation Hence in this paper a new dynamic mutated artificial immune system (DM-AIS) is proposedto enhance MVDR beamforming for controlling the null steering of interference and increase the signal to interference noise ratio(SINR) for wanted signals

1 Introduction

The evolution of adaptive beamforming was initiated inmilitary and aerospace applications through the employ-ment of electronically steered antennas based on phased-array technology Typical applications include long-rangesurveillance radar active jammer rejection and multibeamantennas for space communications [1] The same antennaarray techniques were then assumed suitable for mobileradio communication to solve multipath fading and thecochannel interference problem A partially adaptive antennaarray technology known as the intermediate frequency sidelobe canceller (SLC) was invented by Howells in the late1950s [2] This technology incorporates the capability ofautomatic interference nulling However SLC was not fullyadaptive because the main beam has a fixed pattern and theauxiliary array contains only a few controlled elements Thissimple adaptive antenna facilitated the development of fullyadaptive array by Howellsrsquo coworker Applebaum in 1965

The algorithm commonly known as the Howells-Applebaumalgorithm was developed to maximize the signal-to-noiseratio (SNR) at the output of the beamformer At the sametime in 1960 another independent research group led byWindrow invented another adaptive array approach basedon linear covariance minimum variance (LCMV) [3] Thisalgorithm later known as theWindrow-Hoff LMS algorithmwas developed based on the minimum mean square error(MMSE) criterion for the automatic adjustment of arrayweights This algorithm is well known for its simplicitybut only achieves satisfactory performance under specificoperational conditionsThemajor drawback of this algorithmis its low convergence rate which refers to the speed by whichthe mean of the estimated weights approaches the optimalvalue thereby making it unsuitable for certain applications

In 1969 Capon introduced another adaptive beam-former known as minimum variance distortionless response(MVDR) which is a technique capable of resolving signals

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 164053 9 pageshttpdxdoiorg1011552014164053

2 The Scientific World Journal

separated by a fraction of antenna beam width This opti-mum beamformer also known as the LCMV beamformerrequires only the knowledge of the desired signal directionof arrival (DOA) to maximize the SNR Another importantcontribution was by Reed Mallett and Brennen in 1974They introduced a fast convergence algorithm known as thesample matrix inversion (SMI) technique which overcamethe problemof slow convergence faced by the LMS algorithmOne of themost important factors in smart antenna processesis beamforming which refers to the allocation of signals inparticular positions and phase angles for each antenna for thecorresponding angle of the system [4]

Beamforming technology is a key technique in nullingantenna By performing some processes with the receivedarray signals such as weighting and summation beamform-ing can help the antenna realize many advanced functionssuch as beam shaping beam scanning and beam nulling [5]Reception beamforming is independently achieved at eachreceiver however the transmitter in transmit beamforminghas to consider all receivers to optimize the beamformeroutput [6 7]

One of the beamforming algorithmused in smart antennais MVDR beamforming which can calculate the weightvector to determine the desired signal from the interferenceMoreover MDVR maximizes the sensitivity in one directiononly [8] The MVDR beamformer also known as Caponbeamformer minimizes the output power of the beamformerunder a single linear constraint on the response of the arraytoward the desired signal The idea of combining multipleinputs in a statistically optimummanner under the constraintof no signal distortion can be attributed to Darlington Sev-eral researchers developed beamformers in which additionallinear constraints are imposed (eg Er and Cantoni) [9 10]

Many approaches proposed the use of a mathematicalmodel to improve the robustness of the MVDR beamformeras presented in [11 12] Research on the artificial immunesystem (AIS) and its application has become increasinglyimportant in the field of intelligent information systems [13ndash15] A new optimization technique was presented for thedesign of linear antenna arrays The proposed technique wasbased on a novel variant of particle swarm optimization(PSO) called Boolean PSO with adaptive velocity mutationThe antenna arrays were optimized based on the require-ments for maximizing the power gain at a desired direc-tion and minimizing the side lobe level of the radiationpattern [16] A complex-valued genetic algorithm for theoptimization of beamforming in linear array antennas wasproposed The algorithm was proven to enhance searchingefficiency significantly while effectively avoiding prematureconvergence Numerical results were presented to illustratethe advantages of the proposed technique over conventionalpattern synthesis methods [17]

In this paper the main goal is to design a beamformingmethod based on MVDR in corporation with new dynamicmutated artificial immune system (DM-AIS) algorithm inorder to enhance the null level at interference sourcesBy using this method finding a new mathematical modelchanging the filter hardware for signal processing or chang-ing the design of antenna based on the increased number

of elements is no longer necessary Another reason forproposing the new method is the difficulty in obtainingthe optimum value using any normal algorithm withoutintensification In this investigation DM-AIS have beenapplied in beamforming with uniform linear antenna arraysof 05 120582 spacing between adjacent elements and radiating ata frequency of 23 GHz The rest of this paper is organizedas follows Section 2 introduces the basics of adaptive beam-forming Sections 3 and 4 summarized a basis to describethe conventional MVDR beamforming and AIS respectivelySection 5 shows the incorporation of MVDR with DM-AISSimulation results of one user with two interferences andcomparison of conventional MVDR with mp-QP MVDRand DM-AIS are reported in Section 6 And finally Section 7concludes this investigation

2 Background of Adaptive Beamforming

Adaptive beamforming is a technique for receiving a signalof interest (SOI) from specific directions while suppressingthe interfering signals adaptively in other directions using anarray of sensors This technique can automatically optimizethe array pattern by adjusting the elemental control weightsuntil a prescribed objective function is satisfied This tech-nique provides a means for separating a desired signal frominterfering signals

Beamforming has numerous applications in radar sonarseismology microphone array speech processing and morerecently wireless communications In particular the use ofantenna arrays in combination with signal processing algo-rithms at the base station offers the possibility of exploitingthe spatial dimension to separate multiple cochannel usersThis approach provided increased channel capacity andwiderarea coverage Array beamforming methods in such systemsuse the spatial dimension to combat interference noise andmultipath fading of the desired signal [11] The outputs of theindividual sensors were linearly combined after being scaledwith the corresponding weights This process optimizes theantenna array to achieve maximum gain in the direction ofthe desired signal and nulls in the direction of interferers Fora beamformer the output at any time 119899 119910(119899) is given by alinear combination of the data at119872 antennas with 119909(119899) beingthe input vector and 119908(119899) being the weight vector as shownin Figure 1

119910 (119899) = 119908119867(119899)lowast(119899) (1)

Weight vector119882(119899) can be defined as follows

119908 (119899) =

119872minus1

sum

119873=0

119908119899

119909 (119899) =

119872minus1

sum

119899=0

119883119899

(2)

For any algorithm that evades the matrix inverse operationand uses the immediate gradient vector nabla119869(119899) for weight

The Scientific World Journal 3

z

x

y

33 22 11

d d

120579

r

120601

middot middot middotmiddot middot middotM2 M2

Figure 1 Linear array with elements along the 119910-axis

vector upgrading the weight vector at time 119899 + 1 can bewritten as follows

119882(119899 + 1) = 119882 (119899) +1

2120583 [nabla119869 (119899)] (3)

where 120583 is the step size parameter which controls the speedof convergence and lies between 0 and 1 The minimumvalues of 120583 facilitate the sluggish concurrence and high-quality estimation of the cost function Comparatively thehuge values of 120583 may direct to a rapid union However theconstancy over the least value may disappear

0 lt 120583 lt1

120582 (4)

An exact calculation of instantaneous gradient vector nabla119869(119899)is not possible because prior information on covariancematrix 119877 and cross-correlation vector 119901 is needed Thus aninstantaneous estimate of gradient vector is given by

nabla119869 (119899) = minus 2119901 (119899) + 2119877 (119899)119882 (119899)

119877 (119899) = 119883 (119899)119883119867(119899)

119875 (119899) = 119889(119899)lowast119883 (119899)

(5)

By substituting values from (5) into (3) the weight vectoris derived as follows

119882(119899 + 1) = 119882 (119899) + 120583 [119901 (119899) minus 119877 (119899)119882 (119899)]

= 119882 (119899) + 120583119883 (119899) lfloor119889lowast(119899) minus 119883 (119899)119882 (119899)rfloor

= 119882 (119899) + 120583119883119890lowast(119899)

(6)

The desired signal can be defined by the following threeequations

119910 (119899) = 119908119867(119899) 119909 (119899)

119890 (119899) = 119889 (119899) sdot 119910 (119899)119882 (119899 + 1)

= 119882 (119899) + 120583119883 (119899) 119890lowast(119899)

(7)

Numerous algorithms were introduced for the design ofan adaptive beamformer [8] One of the most popular

approaches for adaptive beamforming was proposed byCapon [4] His algorithm leads to an adaptive beamformerwith an MVDR Some constraints such as the antennagain being constant in the desired direction are used toensure that the desired signals are not filtered out alongwith the unwanted signals The MVDR beamformer notonly minimizes the array output power but also maintains adistortionless main lobe response toward the desired signalHowever the MVDR beamformer may have an unacceptablylow nulling level whichmay significantly degrade the perfor-mance in the case of unexpected interfering signals In partic-ular the performance of MVDR degrades in rapidly movingjammer environments This degradation occurs because ofjammer motion which may bring jammers out of the sharpnotches of the adapted pattern To achieve high interferencesuppression and SOI enhancement an adaptive array mustintroduce deep and widened nulls in the DOAs of stronginterferences while keeping the desired signal distortionlessThus the issue of nulling level control is especially importantfor both deterministic and adaptive arrays [18]

3 Conventional MVDR Beamforming

When a beamformer has a constant response in the directionof a useful signal the LCMV algorithm becomes an MVDRalgorithm [19] The MVDR algorithm is capable of suppress-ing the interference but with high value in SNR and lownoise At the same time theMVDRalgorithmdepends on thesteering vectors which in turn depend on the incident angleof the received signal from the element of the array antennaThe direction of useful signal must be known and the outputpower subject to a unity gain constraint in the direction ofdesired signal must be minimized The array output is givenby

119910 = 119908119867119909 (8)

The output power is as follows

119901 = 119864100381610038161003816100381611991010038161003816100381610038162 = 119864 119908

119867119909119909119867119908 = 119908

119867119864 119909119909

119867119908 = 119908

119867119877 (9)

where the 119877 covariance matrix should be (119872 1) for thereceived signal 119909 and119867 is the hermitian transpose

The optimum weights are selected to minimize the arrayoutput power119875MVDR whilemaintaining unity gain in the lookdirection 119886(120579) which is the steering vector of the desiredsignal The MVDR adaptive algorithm can be written asfollows

min119908119908119867119877119908 subject to 119908119867119886 (120579) = 1 (10)

The steering vector 119886(120579) is given by

119886 (120579) =

[[[[[[

[

1

exp 1198952120587120582(sin 120579119894) 119889

exp 1198952120587120582(sin 120579119894) (119898 minus 1) 119889

]]]]]]

]

(11)


d

Y

XZ

(a) CST program (b) Fabricated

Figure 2 (a b) Four elements of the linear array

where 119889 is the space between the elements of the antenna 120579119894is

the desired angle and119898 is the number of elements as shownin Figure 2

The optimization weight vectors can then be acquiredusing the following formula [20]

119882MVDR =119877minus1119886 (120579)

119886119867 (120579) 119877minus1119886 (120579) (12)

These weights are the solution of the optimization problemmentioned at (10) and with the use of four elements of arrayantenna four weights as below will be obtained

119908MVDR =[[[

[

1199081

1199082

1199083

1199084

]]]

]

(13)

Subsequently the beamformer weights are selected basedon minimum mean value of output power according to thenumber of users inside the coverage area while maintain-ing unity response in the desired direction Neverthelessthe restraint ensures that the signal passes through thebeamformer undistorted Consequently the output signalpower is similar to the look direction source power Thetotal noise including interferences and uncorrelated noiseis then reduced by the minimization process Notably theminimization of the total output noise while constantlymaintaining the output signal is the same as maximizingthe output SINR However for the optimal beamformer toperform as described above and to maximize the SINR bycancelling interferences the number of interferences mustbe less than or equal to 119872 minus 2 because an array with 119872elements has119872minus1 degrees of freedom and has been utilizedby the constraint in the look direction Given that theMVDRbeamformer maximizes sensitivity in one direction only thisbeamformer is unsuitable formultipath environments wherethe desired signal spreads in all directions [21]Themultipathoccurs in non-line-of-sight environments such as populatedurban areas where numeorus scatterers are close to the usersand the base stationThus theMVDR beamformer may havean unacceptably low nulling level which may significantlydegrade performance in the case of unexpected interferingsignals As a result the beamforming optimization problemis formulated as a multiparametric quadratic programming(mp-QP) [18]

4 Artificial Immune System

The proposed usage of artificial intelligent system as theenhancement method for the adaptive beamforming tech-nique is based on a framework that is built around theconcept of reactive artificial immune system (AIS) AISwhich is inspired by theoretical immunology and observedimmune functions is a branch of the metaheuristic algo-rithm with promising results in the field of optimizationWhile AIS resembles some other metaheuristics algorithmssuch as genetic algorithm (GA) except the recombinationoperator the former has code simplicity and is low incomputational costThis AIS system is indeed based upon thenormal human immune system in the way that it is reactivetowards foreign elements The immune system is highlyrobust adaptive inherently parallel and self-organized It haspowerful learning and memory capabilities and presents anevolutionary type of response to infectious foreign elements[22 23]

The main agents of the adaptive immune system arelymphocytes that are are called the B cells which produceantibodies to attack the enemy Some B cells become ldquomem-ory cellsrdquo which keep molecular records of past invaderand minimize the bodyrsquos response time to an infection Theclonal selection principle is the whole process of antigenrecognition cell proliferation and differentiation into amemory cell

The clonal-selection theory proposes that as an antigenenters the immune system certain B cells are selected basedon their reaction to this antigen to undergo rapid cloningand expansion This reaction is often termed the affinityof that B cell (or antibody) for the given antigen ThoseB cells are selected based on their affinity to an antigento produce a number of clones to attack or neutralize theinvading antigen Cells that have a higher degree of affinityare allowed to produce more clones The clonal productiondevelops immune cells that aremore adept at recognizing andreacting to the antigen through mutation B cell offspringsundergo mutation based on an inverse proportionality totheir affinity values Through this process the affinity ofsubsequent generations of B cells will have greater reactionto the antigen and more diversity will also have been addedto the system through the wider exploration afforded bythe high mutation rates of the cells with lower affinitymeasures


The process of a standard clonal selection algorithm canbe summarized as follows [24 25]

(1) Generate a random initial population of antibody119860119887given by

119875 (0) = 1198601198871 (0) 119860119887119899 (0) (14)

(2) Compute the fitness of each 119860119887

119875 (0) 119891 (1199091 (0) 119909119899 (0)) (15)

(3) Generate clones by cloning all cells in the 119860119887 popula-tion The amount of clone is given by

119873119862=

119899

sum

119894=1

round(120573 ∙ 119873

119894) (16)

where119873119862is the total clones generated for each 119860119887 120573

is the multiplying factor and119873 is the number of 119860119887(4) Mutate the clone population to produce a mature

clone population with 120575 number of childrenThe new119860119887 is composed of

1198751015840= 119860119887

1015840

1 119860119887

1015840

120575 (17)

(5) Evaluating affinity values of the clonesrsquo population is

1198751015840 119891 (119909

1015840

1 119909

1015840

120575) (18)

The next generation of119860119887 is obtained using119866 = 120576+ 120575selection by choosing the best 120576 individuals out of the119866 population

(6) Select the best119860119887 to compose the new119860119887 populationby

119875new = 1199041198661198751015840 (19)

(7) Steps 3 to 6 are repeated until a predefined stoppingcondition is reached

5 MVDR Beamforming Incorporationwith New Dynamic Mutated ArtificialImmune System

In this paper AIS with dynamic mutation (DM) was uti-lized to enhance the null level of the MVDR beamformingtechnique In analogy the adaptive antenna represents thebody of an organism whereas the interference and noisesignal sources represent external harmful attacks toward theorganism Hence the adaptive antenna system will organizeits antibody to protect the body of organism from externalantigen attacks The adaptive antenna system will try tooptimize through its AIS iteration process to develop deepnull at the DOA of the interference sources to achieve themaximum SINR

In this AIS algorithm the weight vector 119908 will be gen-erated as the system antibody The algorithm will initiate by

generating a population of119873 antibodies which is representedby weight vectors 119882

119873 The number of generated weight

vectors depends on the population size 119875size For the firstiteration the first set of weight vectors119882

1is obtained from

the computation of the conventional MVDR weight vectorThe weight vectors in every antibody contain an119872 numberof weight vectors depending on the number of sensors orantenna elements used and can be expressed as follows

1199081119872= Real119908mvdr119872 + Imag119908mvdr119872

1199082119872= Real 119908

1119872

lowastrand (119872 119875Size minus 1)

+ Imag 1199081119872


119908119873119872

= Real 119908(119873minus1)119872


+ Imag 119908(119873minus1)119872

lowast rand (119872 119875Size minus 1)

(20)

In matrix format the weight vectors in the population ofany iteration can be represented by

119882119873119872

=

[[[[[[[

[

119908mvdr1 119908mvdr2 119908mvdr3 119908mvdr411990811

11990812

11990813

11990814

11990821

11990822

11990823

11990824

1199081198991

1199081198992

1199081198993

1199081198994

]]]]]]]

]

(21)

where

119882119873119872

is weight vectors of total population119873 with119872sensors in each antenna119908mvdr is weight vectors fromMVDR beamformer119872 is number of sensor In this study antenna sensorof (4 1) is used119875size is population size119872 is number of sensor

Each set of antibodies 119882 has amplitude and phase (119860forall120579)to steer the radiation beam toward its target user and placethe deep null toward the interference sources to achievethe optimum SINR The best weight vector is determinedaccording to the fitness value obtained from fitness functionas shown below

Fitness Function (FF) =119875User

sum119873

119899=1119875Inter 119899 +Noise

(22)

where 119875User = power of target user 119875Inter = power ofinterference and119873 = number of interference sources

The new candidate population of antibodies (weightvectors) based on the mutation rate depends on the fitnessvalue of 119908 in (22) which is given by

119872rate = 119890minus(5radic(119865119908best)

2) (23)

where 119872rate = mutation rate and 119865119908best = fitness of bestpopulation weight


The mutation rate of clones is inversely proportional totheir antigenic affinity [24 26] A higher affinity denotes asmaller mutation rate

Themutations and clones needed to create the newweightare given by

119882 = 119908best +119872ratelowast(Real rand (119872 119875Size minus 1)

minusImag rand (119872 119875Size minus 1)) (24)

The 119899 antibodies generate 119873119888 clones proportional to theiraffinities The number of cloned antibodies 119873119888 can becomputed by

119873119862=

119899

sum

119894=1

round119861 sdot 119908119894 (25)

where 119861 is a multiplying factor with a value of 1 and 119908 is theweight vector

Each term of this sum corresponds to the clone size ofeach selected antibodyThe clones are then subjected to hypermutation and receptor editing To enable the algorithm tofind the best solution a deep null must be achieved to obtainthe maximum SINR Therefore the DM was introducedto identify the best solution The selection of the 10 bestsolutions depends on the maximum SINR value Thus fromthese 10 best solutions DM-AIS can select three randomvalues from the 10 best weights to achieve the SINR sizeWhen the scaling factor is (0 1 2) the best value of the deepnull is derived

119908119863119872

= 1199081119872+ sflowast (119908

2119872minus 1199083119872) (26)

where119882111988221198823= randomweight select from the best three

solutions and sf = scaling factor from (0 1 2)The next step is the clonal operation to obtain the best

solutionAffinity is applied to achieve the maximum power for

target and deep null for interference If this value is thebest it will store and yield the final weight value to stop thecalculation The DM-AIS steps in an adaptive antenna are asfollows

(1) A random initial population of119882 is generated whichis given by

119882119873 (119894) = 1198821 (119894) 119882119899 (119894) (27)

(2) The fitness of each119882 is computed

119875 (119894) 119891 (1199081 (119894) 119908119899 (119894)) (28)

(3) Clones are generated by cloning all the cells in the119882 populationThe amount of clone is obtained using(23)

(4) The clone population is mutated to produce a matureclone population with 119894 number of weightThe rate ofmutation is given by


2) (29)

Thus the new 119882 is composed of 1198821015840

119873(119894) =

1198821015840

1 119882

1015840

119894

(5) The affinity values of the clone population areexpressed as follows

1198821015840

119873(119894) 119891 (119882

1015840

1 119882

1015840

119894) (30)

The next generation of 119882 is obtained using (20)The best 119882best is selected to compose the new 119882newpopulation as follows

119882new = 119882best 1198821015840

119873(119894) (31)

(6) The 10 best weight vectors are selected depending onthe selection assumption (119875size) to identify the bestnumber of the weight

(7) The vectors are mutated by selecting three randomweights from the 10 best weights using (26)


Remarks Similar to weight vector optimization techniquesbased on the support vector regression (SVR-AS) [27] andmp-QPMVDR [18] the proposedDM-AISMVDR techniqueis also effective in finding the optimal weight vector foran antenna array under specific conditions The differencesamong the methodologies are as follows

(1) The proposed DM-AIS MVDR determines the opti-mal weight vector of an antenna array through itscloning and mutation process to fine-tune the weightvector toward a radiation pattern that can generatedeep null toward the interference source while main-taining high gain at the target usersrsquo directions for aninstantaneous scenario

(2) The mp-AP MVDR produces the optimal weightvector of an antenna array for the optimal problemof the receiving beam based on a multiparametricapproach [18]

(3) The SVR-AS requires the radiation pattern as the traindata to find the optimal weight vector of an antennaarray [27]

The benefits of the proposed approach are as follows

(1) The nulling extent can be deepened(2) This approach can guarantee that the nulling levels

in the specified areas are better than conventionalMVDR

(3) This approach does not require pretrain data and doesnot require complex mathematical computation toidentify the optimal weight vector Insteadmerely theDOAs of the target user and interference sources arerequired for DM-AISMVDR to determine its optimalweight vector for best radiation beamforming

6 Simulation and Results

61 One User with Two Interferences In this section simu-lations were conducted to validate the proposed approach


Table 1 Parameters of DM-AIS

Dynamic mutated parameters ValueNumber of population 20Allocated number of best population 10Clone size 4Number of max iteration 20Scaling factor (0 1 2)

Table 2 Weight vector after 10 and 20 iterations for one user at 40∘and interference at 50∘ and 30∘

Sensor number Weight 10 iterations 20 iterations1 119882

1minus45333 minus 06902119895 minus46171 minus 07212119895

2 1198822

minus24985 + 38447119895 minus25978 + 39071119895

3 1198823

minus13543 minus 19258119895 minus13966 minus 19127119895

4 1198824

minus37544 + 06641119895 minus37899 + 06865119895

The uniform linear array (ULA) consists of four elements(119872 = 4) equispaced by half-wavelength The desired signaland two interference signals are plane waves impinging onthe ULA from the directions 50∘ 30∘ and 40∘ respectivelyIn this simulation the SNR from 5 dB to 30 dB was usedfor the desired signal and the two interference signals Thebeam pattern nulling level should be below minus70 dB Thecomplex vector of beamformer weights calculated by theaforementioned (27)ndash(31) is presented in Table 2 whereas thebeam patterns generated are plotted in Figure 3 All the beampatterns have nulls at the DOAs of the interference signalsand maintain a distortionless response for the SOI HoweverDM-AIS place deep nulls (with nulling level equal to minus80 dB)at the DOAs of two interference signal sources The MVDRafter 10 iterations reduces nulling levels compared with theMVDR after 20 iterations (Table 1)

Figure 3 gives the ratio of SINR 679479 dB in 20 iterationswhile at 10 iterations the SINR is 405387 dB of the aforemen-tioned beamformer for the previous scenario It can be seenthat the DM-AIS at 20 iterations shows better ratio which is12249 of improvement If we compare the improvement inSINR between normal AIs andDM-AIS for the same scenarioin 10 iterations we obtain the percentage 13148

But an insignificant increase in the SINRof 02 is obtainedfor an increase in the number of iterations The iterationswere taken from 30 till 50 as shown in Figure 4 This impliesthat there is no need to increase the time required forsimulations The 20 iterations will give the best results bythe short time These results should be saved The simulatedresults demonstrate that the DM-AIS with dynamic mutationrate give a good result effectively at a faster speed Thesimulated results are dynamically adapting its value when theSINR changes In comparison the dynamicmutation rate hasshown better results with finer resolutions

We can then discriminate the difference in results afterusing the new method with DM-AIS To justify the resultsthe new method must be proven to be more effective thanany previously suggested method The new method should

0 20 40 60 80

0

10

20

30

DOA (deg)

20 iterations10 iterations

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus20

minus30

minus40

minus40

minus50

minus60

minus60

minus70

minus80minus80

Figure 3 Power response DM-AIS with 10 and 20 iterations for userat 40∘ with interference at 30∘ and 50∘

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70

Number of iterations

SIN

R (d

B)

DM-AIS

Figure 4 Number of iterations with SINR of DM-AIS for one userat 40∘ and interference at 50∘ and 30∘ by using 4 elements

Table 3 Weight vector for two users with four interferences usingDM-AIS


103330 minus 02789119895 03652 minus 02806119895

2 1198822

04506 minus 00414119895 04622 minus 00401119895

3 1198823

04590 + 00487119895 05500 + 00474119895

4 1198824

03348 + 02723119895 03292 + 02748119895

have more applications by increasing the number of usersand reducing interference The results shown in Table 3 andFigure 5 provide details for two users at angles 0∘ and 10∘ withinterference at angles 50∘ minus50∘ 30∘ and minus30∘


Table 4 Weight vector values of conventional MVDR mp-QPMVDR and DM-AIS

Sensor number ConventionalMVDR mp-QP MVDR DM-AIS MVDR

1 01626 minus 00118119895 01077 + 00469119895 01594 minus 00123119895

2 01249 + 00093119895 01269 + 00072119895 01224 + 00123119895

3 00630 minus 00026119895 00808 + 00264119895 00626 minus 00020119895

4 00143 + 00059119895 00441 minus 00007119895 00185 + 00055119895

5 01264 + 00058119895 01106 minus 00188119895 01196 + 00110119895

6 01107 minus 00291119895 01043 minus 00196119895 01232 minus 00308119895



9 01337 + 00280119895 01293 + 00069119895 01274 + 00230119895

10 01639 + 00306119895 01102 minus 00204119895 01743 + 00223119895


0

10

20

30

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

0 20 40 60 80DOA (deg)

minus20minus40minus60minus80

Figure 5 Power response for two users at 0 and 10 interferencesources at 50∘ minus50∘ 30∘ and minus30∘ with DM-AIS after 10 and 20iterations

62 Comparison of Conventional MVDR with MP-QPMVDRand DM-AIS To prove the importance of this project theresults of this work were those of previous work to enhancetheMVDR in smart antennas From the studied literature noresearcher has discussed or addressed beamforming by usingfour elements in the smart antenna or by applying DM-AISin the smart antennaTherefore the results of this project arecompared with robust MVDR beamforming for nulling levelcontrol via multiparametric quadratic programming resultsusing 10 elements and with the direction of user at 0∘ withinterference at 40∘ and minus40∘ [8] Figure 6 and Table 4 showthe results

Figure 6 shows that all beam patterns have nulls in theinterference signals and maintain a distortionless responsefor the SOIHoweverDM-AISMVDRplaces deepnulls (withnulling level equal to minus90 dB) at the two interference signalsources whereas mp-QP MVDR obtained a null level equal

mp-QP MVDRConventional MVDRDM-AIS MVDR

0 20 40 60 80DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

20

0

minus20

minus40

minus60

minus80

minus100

Figure 6 Comparison among DM-IS mp-QPMVDR and MVDRof one user at 0∘ and interference 40∘ and minus40∘

Table 5 Illustration of the SINR for DM-AIS mp-QP MVDR andMVDR

MVDR SINR(dB)

mp-QP MVDRSINR (dB)

DM-AIS MVDRSINR (dB)

25 769897 869897

to minus80 dB Therefore the DM-AIS with MVDR responsepresents lower nulling levels compared with the new mp-QPMVDRThemaximum SINRs calculation for each techniqueis compared with one another The maximum value obtainedfrom DM-AIS is shown in Table 5

This result shows that the new beamforming usingartificial intelligence to determine the desired signal ofuser is effective and that mathematical equations or filterhardware signal processing are unnecessary For the proposedapproach the weights value vectors make it difficult to obtainthe optimum value by using any other algorithm withoutintensification

7 Conclusion

A new DM-AIS was presented and applied in adaptivebeamforming with four elements of linear antenna arraysThe proposed DM-AIS was able to enhance the MVDRtechnique through further optimization of weight vectorwhich aimed to control the nulling level of interferenceand the directionality of the desired signal Very low levelsof interference with good accuracy were achieved even inthe case of multiple users or multiple interferences Theresults of the proposed approach were compared with thoseof the mp-QP MVDR and conventional MVDR and theeffectiveness of the proposed approach in minimizing thepower of interference and increasing SINR was observedFinally the DM-AIS can be useful to antenna engineers


for the pattern synthesis of antenna arrays because of itsgood accuracy and the lack of a requirement for complicatedmathematical functions

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported in part by MOSTI (Ministry ofScience Technology and Innovation Malaysia) with Projectno 01-02-03-SF0202

References

[1] M Barrett and R Arnott ldquoAdaptive antennas for mobilecommunicationsrdquo Electronics and Communication EngineeringJournal vol 6 no 4 pp 203ndash214 1994

[2] J Litva and T K Lo Digital Beamforming in Wireless Commu-nications A Tech House 1996

[3] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[4] T S Ghouse Basha P V Sridevi and M N Giri PrasadldquoEnhancement in gain and interference of smart antennasusing two stage genetic algorithm by implementing it on beamformingrdquo International Journal of Electronics Engineering vol 3no 2 pp 265ndash269 2011

[5] Z Xing-Wei L Yuan L Hui-jie and L Xu-wen ldquoThe differenceof nulling antenna technology between geo and leo satellitesrdquoEnergy Procedia vol 13 pp 559ndash567 2011

[6] C A Balanisand and P I Ioannides Introduction of SmartAntennas Morgan and Claypool Publication San Rafael CalifUSA 2007

[7] H Dahrouj and W Yu ldquoCoordinated beamforming for themulticell multi-antenna wireless systemrdquo IEEE Transactions onWireless Communications vol 9 no 5 pp 1748ndash1759 2010

[8] B Salem S K Tiong and S P Koh ldquoBeamforming algorithmstechnique by using MVDR and LCMVrdquo World Applied Pro-gramming vol 2 no 5 pp 315ndash324 2012

[9] E A P Habets J Benesty I Cohen S Gannot and J Dmo-chowski ldquoNew insights into the MVDR beamformer in roomacousticsrdquo IEEE Transactions on Audio Speech and LanguageProcessing vol 18 no 1 pp 158ndash170 2010

[10] T S Kiong M Ismail and A Hassan ldquoWCDMA forward linkcapacity improvement by using adaptive antenna with geneticalgorithm assisted MDPC beamforming techniquerdquo Journal ofApplied Sciences vol 6 no 8 pp 1766ndash1773 2006

[11] D Li Q Yin P Mu andW Guo ldquoRobust MVDR beamformingusing the DOAmatrix decompositionrdquo in Proceedings of the 1stInternational SymposiumonAccess Spaces (ISAS rsquo11) pp 105ndash110June 2011

[12] R Michael and I Psaromiligkos ldquoRobust minimum variancebeamformingwith dual response constraintsrdquo IEEETransactionon Signal Processing vol 60 2010

[13] J Ye W Pang Y Wang D Lv and Y Chen ldquoSide lobereduction in thinned array synthesis using immune algorithmrdquoin Proceedings of the International Conference onMicrowave and

Millimeter Wave Technology (ICMMT rsquo08) pp 1131ndash1133 April2008

[14] L N de Castro Fundamentals of Natural Computing Chapmanamp HallCRC 2006

[15] F M BurnetTheClonal SelectionTheory of Acquired ImmunityUniversity Press Cambridge 1959

[16] ZD Zaharis andTV Yioultsis ldquoAnovel adaptive beamformingtechnique applied on linear antenna arrays using adaptivemutated Boolean PSOrdquo Progress in Electromagnetics Researchvol 117 pp 165ndash179 2011

[17] YWang S Gao H Yu and Z Tang ldquoSynthesis of antenna arrayby complex-valued genetic algorithmrdquo International Journal ofComputer Science and Network Security vol 11 no 1 pp 91ndash962011

[18] F L Liu J K Wang C Y Sun and R Y Du ldquoRobust MVDRbeamformer for nulling level control via multi-parametricquadratic programmingrdquo Progress In Electromagnetics ResearchC vol 20 pp 239ndash254 2011

[19] J R Al-Enezi M F Abbod and S Alsharhan ldquoArtificialimmune system models algorithm and applicationsrdquo Interna-tional Journal of Research and Reviews in Applied Sciences vol3 no 2 pp 118ndash131 2010

[20] G Renzhou ldquoSuppressing radio frequency interferences withadaptive beamformer based on weight iterative algorithmrdquo inProceedings of the IET Conference Wireless Mobile and SensorNetworks (CCWMSN rsquo07) pp 648ndash651 2007

[21] A Ali Anum R L Ali and A ur-Rehman ldquoAn improved gainvector to enhance convergence characteristics of recursive leastsquares algorithmrdquo International Journal of Hybrid InformationTechnology vol 4 pp 99ndash107 2011

[22] H Bersini and F Varela ldquoHints for adaptive problem solvinggleaned from immune networksrdquo in Parallel Problem Solvingfrom Nature vol 496 of Lecture Notes in Computer Science pp343ndash354 Springer Berlin Germany 1991

[23] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986

[24] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002

[25] L Lin X Guanghua L Dan and Z Shuanfeng ldquoImmuneclonal selection optimization method with mixed mutationstrategiesrdquo in Proceedings of the 2nd International Conference onBio-Inspired ComputingTheories and Applications (BICTA rsquo07)pp 37ndash41 September 2007

[26] L N de Castro and F J von Zuben ldquoThe clonal selectionalgorithm with engineering applicationsrdquo in Proceedings ofGECCO pp 36ndash39 2000

[27] R Gonzalez Ayestaran M F Campillo and F Las-HerasldquoMultiple support vector regression for antenna array charac-terization and synthesisrdquo IEEE Transactions on Antennas andPropagation vol 55 no 9 pp 2495ndash2501 2007

Submit your manuscripts athttpwwwhindawicom

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Distributed Sensor Networks


Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


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Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



separated by a fraction of antenna beam width This opti-mum beamformer also known as the LCMV beamformerrequires only the knowledge of the desired signal directionof arrival (DOA) to maximize the SNR Another importantcontribution was by Reed Mallett and Brennen in 1974They introduced a fast convergence algorithm known as thesample matrix inversion (SMI) technique which overcamethe problemof slow convergence faced by the LMS algorithmOne of themost important factors in smart antenna processesis beamforming which refers to the allocation of signals inparticular positions and phase angles for each antenna for thecorresponding angle of the system [4]

Beamforming technology is a key technique in nullingantenna By performing some processes with the receivedarray signals such as weighting and summation beamform-ing can help the antenna realize many advanced functionssuch as beam shaping beam scanning and beam nulling [5]Reception beamforming is independently achieved at eachreceiver however the transmitter in transmit beamforminghas to consider all receivers to optimize the beamformeroutput [6 7]

One of the beamforming algorithmused in smart antennais MVDR beamforming which can calculate the weightvector to determine the desired signal from the interferenceMoreover MDVR maximizes the sensitivity in one directiononly [8] The MVDR beamformer also known as Caponbeamformer minimizes the output power of the beamformerunder a single linear constraint on the response of the arraytoward the desired signal The idea of combining multipleinputs in a statistically optimummanner under the constraintof no signal distortion can be attributed to Darlington Sev-eral researchers developed beamformers in which additionallinear constraints are imposed (eg Er and Cantoni) [9 10]

Many approaches proposed the use of a mathematicalmodel to improve the robustness of the MVDR beamformeras presented in [11 12] Research on the artificial immunesystem (AIS) and its application has become increasinglyimportant in the field of intelligent information systems [13ndash15] A new optimization technique was presented for thedesign of linear antenna arrays The proposed technique wasbased on a novel variant of particle swarm optimization(PSO) called Boolean PSO with adaptive velocity mutationThe antenna arrays were optimized based on the require-ments for maximizing the power gain at a desired direc-tion and minimizing the side lobe level of the radiationpattern [16] A complex-valued genetic algorithm for theoptimization of beamforming in linear array antennas wasproposed The algorithm was proven to enhance searchingefficiency significantly while effectively avoiding prematureconvergence Numerical results were presented to illustratethe advantages of the proposed technique over conventionalpattern synthesis methods [17]

In this paper the main goal is to design a beamformingmethod based on MVDR in corporation with new dynamicmutated artificial immune system (DM-AIS) algorithm inorder to enhance the null level at interference sourcesBy using this method finding a new mathematical modelchanging the filter hardware for signal processing or chang-ing the design of antenna based on the increased number

of elements is no longer necessary Another reason forproposing the new method is the difficulty in obtainingthe optimum value using any normal algorithm withoutintensification In this investigation DM-AIS have beenapplied in beamforming with uniform linear antenna arraysof 05 120582 spacing between adjacent elements and radiating ata frequency of 23 GHz The rest of this paper is organizedas follows Section 2 introduces the basics of adaptive beam-forming Sections 3 and 4 summarized a basis to describethe conventional MVDR beamforming and AIS respectivelySection 5 shows the incorporation of MVDR with DM-AISSimulation results of one user with two interferences andcomparison of conventional MVDR with mp-QP MVDRand DM-AIS are reported in Section 6 And finally Section 7concludes this investigation

2 Background of Adaptive Beamforming

Adaptive beamforming is a technique for receiving a signalof interest (SOI) from specific directions while suppressingthe interfering signals adaptively in other directions using anarray of sensors This technique can automatically optimizethe array pattern by adjusting the elemental control weightsuntil a prescribed objective function is satisfied This tech-nique provides a means for separating a desired signal frominterfering signals

Beamforming has numerous applications in radar sonarseismology microphone array speech processing and morerecently wireless communications In particular the use ofantenna arrays in combination with signal processing algo-rithms at the base station offers the possibility of exploitingthe spatial dimension to separate multiple cochannel usersThis approach provided increased channel capacity andwiderarea coverage Array beamforming methods in such systemsuse the spatial dimension to combat interference noise andmultipath fading of the desired signal [11] The outputs of theindividual sensors were linearly combined after being scaledwith the corresponding weights This process optimizes theantenna array to achieve maximum gain in the direction ofthe desired signal and nulls in the direction of interferers Fora beamformer the output at any time 119899 119910(119899) is given by alinear combination of the data at119872 antennas with 119909(119899) beingthe input vector and 119908(119899) being the weight vector as shownin Figure 1

119910 (119899) = 119908119867(119899)lowast(119899) (1)

Weight vector119882(119899) can be defined as follows

119908 (119899) =

119872minus1

sum

119873=0

119908119899

119909 (119899) =

119872minus1

sum

119899=0

119883119899

(2)

For any algorithm that evades the matrix inverse operationand uses the immediate gradient vector nabla119869(119899) for weight


z

x

y

33 22 11

d d

120579

r

120601




119882(119899 + 1) = 119882 (119899) +1

2120583 [nabla119869 (119899)] (3)


0 lt 120583 lt1

120582 (4)


nabla119869 (119899) = minus 2119901 (119899) + 2119877 (119899)119882 (119899)

119877 (119899) = 119883 (119899)119883119867(119899)

119875 (119899) = 119889(119899)lowast119883 (119899)

(5)


119882(119899 + 1) = 119882 (119899) + 120583 [119901 (119899) minus 119877 (119899)119882 (119899)]


= 119882 (119899) + 120583119883119890lowast(119899)

(6)


119910 (119899) = 119908119867(119899) 119909 (119899)

119890 (119899) = 119889 (119899) sdot 119910 (119899)119882 (119899 + 1)

= 119882 (119899) + 120583119883 (119899) 119890lowast(119899)

(7)





119910 = 119908119867119909 (8)


119901 = 119864100381610038161003816100381611991010038161003816100381610038162 = 119864 119908

119867119909119909119867119908 = 119908

119867119864 119909119909

119867119908 = 119908

119867119877 (9)



min119908119908119867119877119908 subject to 119908119867119886 (120579) = 1 (10)


119886 (120579) =

[[[[[[

[

1

exp 1198952120587120582(sin 120579119894) 119889

exp 1198952120587120582(sin 120579119894) (119898 minus 1) 119889

]]]]]]

]

(11)


d

Y

XZ






119882MVDR =119877minus1119886 (120579)

119886119867 (120579) 119877minus1119886 (120579) (12)


119908MVDR =[[[

[

1199081

1199082

1199083

1199084

]]]

]

(13)









119875 (0) = 1198601198871 (0) 119860119887119899 (0) (14)


119875 (0) 119891 (1199091 (0) 119909119899 (0)) (15)


119873119862=

119899

sum

119894=1

round(120573 ∙ 119873

119894) (16)




1198751015840= 119860119887

1015840

1 119860119887

1015840

120575 (17)


1198751015840 119891 (119909

1015840

1 119909

1015840

120575) (18)



119875new = 1199041198661198751015840 (19)








1is obtained from



1199082119872= Real 119908

1119872


+ Imag 1199081119872


119908119873119872

= Real 119908(119873minus1)119872


+ Imag 119908(119873minus1)119872


(20)


119882119873119872

=

[[[[[[[

[


11990812

11990813

11990814

11990821

11990822

11990823

11990824

1199081198991

1199081198992

1199081198993

1199081198994

]]]]]]]

]

(21)

where

119882119873119872




sum119873

119899=1119875Inter 119899 +Noise

(22)




2) (23)








119873119862=

119899

sum

119894=1

round119861 sdot 119908119894 (25)



119908119863119872

= 1199081119872+ sflowast (119908

2119872minus 1199083119872) (26)






119882119873 (119894) = 1198821 (119894) 119882119899 (119894) (27)


119875 (119894) 119891 (1199081 (119894) 119908119899 (119894)) (28)




2) (29)


119873(119894) =

1198821015840

1 119882

1015840

119894


1198821015840

119873(119894) 119891 (119882

1015840

1 119882

1015840

119894) (30)


119882new = 119882best 1198821015840

119873(119894) (31)




















2 1198822

minus24985 + 38447119895 minus25978 + 39071119895

3 1198823


4 1198824

minus37544 + 06641119895 minus37899 + 06865119895





0 20 40 60 80

0

10

20

30

DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus20

minus30

minus40

minus40

minus50

minus60

minus60

minus70

minus80minus80


0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70


SIN

R (d

B)

DM-AIS




103330 minus 02789119895 03652 minus 02806119895

2 1198822

04506 minus 00414119895 04622 minus 00401119895

3 1198823

04590 + 00487119895 05500 + 00474119895

4 1198824

03348 + 02723119895 03292 + 02748119895





1 01626 minus 00118119895 01077 + 00469119895 01594 minus 00123119895

2 01249 + 00093119895 01269 + 00072119895 01224 + 00123119895

3 00630 minus 00026119895 00808 + 00264119895 00626 minus 00020119895

4 00143 + 00059119895 00441 minus 00007119895 00185 + 00055119895

5 01264 + 00058119895 01106 minus 00188119895 01196 + 00110119895




9 01337 + 00280119895 01293 + 00069119895 01274 + 00230119895

10 01639 + 00306119895 01102 minus 00204119895 01743 + 00223119895


0

10

20

30

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

0 20 40 60 80DOA (deg)






0 20 40 60 80DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

20

0

minus20

minus40

minus60

minus80

minus100



MVDR SINR(dB)

mp-QP MVDRSINR (dB)


25 769897 869897



7 Conclusion






Acknowledgment


References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




z

x

y

33 22 11

d d

120579

r

120601




119882(119899 + 1) = 119882 (119899) +1

2120583 [nabla119869 (119899)] (3)


0 lt 120583 lt1

120582 (4)


nabla119869 (119899) = minus 2119901 (119899) + 2119877 (119899)119882 (119899)

119877 (119899) = 119883 (119899)119883119867(119899)

119875 (119899) = 119889(119899)lowast119883 (119899)

(5)


119882(119899 + 1) = 119882 (119899) + 120583 [119901 (119899) minus 119877 (119899)119882 (119899)]


= 119882 (119899) + 120583119883119890lowast(119899)

(6)


119910 (119899) = 119908119867(119899) 119909 (119899)

119890 (119899) = 119889 (119899) sdot 119910 (119899)119882 (119899 + 1)

= 119882 (119899) + 120583119883 (119899) 119890lowast(119899)

(7)





119910 = 119908119867119909 (8)


119901 = 119864100381610038161003816100381611991010038161003816100381610038162 = 119864 119908

119867119909119909119867119908 = 119908

119867119864 119909119909

119867119908 = 119908

119867119877 (9)



min119908119908119867119877119908 subject to 119908119867119886 (120579) = 1 (10)


119886 (120579) =

[[[[[[

[

1

exp 1198952120587120582(sin 120579119894) 119889

exp 1198952120587120582(sin 120579119894) (119898 minus 1) 119889

]]]]]]

]

(11)


d

Y

XZ






119882MVDR =119877minus1119886 (120579)

119886119867 (120579) 119877minus1119886 (120579) (12)


119908MVDR =[[[

[

1199081

1199082

1199083

1199084

]]]

]

(13)









119875 (0) = 1198601198871 (0) 119860119887119899 (0) (14)


119875 (0) 119891 (1199091 (0) 119909119899 (0)) (15)


119873119862=

119899

sum

119894=1

round(120573 ∙ 119873

119894) (16)




1198751015840= 119860119887

1015840

1 119860119887

1015840

120575 (17)


1198751015840 119891 (119909

1015840

1 119909

1015840

120575) (18)



119875new = 1199041198661198751015840 (19)








1is obtained from



1199082119872= Real 119908

1119872


+ Imag 1199081119872


119908119873119872

= Real 119908(119873minus1)119872


+ Imag 119908(119873minus1)119872


(20)


119882119873119872

=

[[[[[[[

[


11990812

11990813

11990814

11990821

11990822

11990823

11990824

1199081198991

1199081198992

1199081198993

1199081198994

]]]]]]]

]

(21)

where

119882119873119872




sum119873

119899=1119875Inter 119899 +Noise

(22)




2) (23)








119873119862=

119899

sum

119894=1

round119861 sdot 119908119894 (25)



119908119863119872

= 1199081119872+ sflowast (119908

2119872minus 1199083119872) (26)






119882119873 (119894) = 1198821 (119894) 119882119899 (119894) (27)


119875 (119894) 119891 (1199081 (119894) 119908119899 (119894)) (28)




2) (29)


119873(119894) =

1198821015840

1 119882

1015840

119894


1198821015840

119873(119894) 119891 (119882

1015840

1 119882

1015840

119894) (30)


119882new = 119882best 1198821015840

119873(119894) (31)




















2 1198822

minus24985 + 38447119895 minus25978 + 39071119895

3 1198823


4 1198824

minus37544 + 06641119895 minus37899 + 06865119895





0 20 40 60 80

0

10

20

30

DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus20

minus30

minus40

minus40

minus50

minus60

minus60

minus70

minus80minus80


0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70


SIN

R (d

B)

DM-AIS




103330 minus 02789119895 03652 minus 02806119895

2 1198822

04506 minus 00414119895 04622 minus 00401119895

3 1198823

04590 + 00487119895 05500 + 00474119895

4 1198824

03348 + 02723119895 03292 + 02748119895





1 01626 minus 00118119895 01077 + 00469119895 01594 minus 00123119895

2 01249 + 00093119895 01269 + 00072119895 01224 + 00123119895

3 00630 minus 00026119895 00808 + 00264119895 00626 minus 00020119895

4 00143 + 00059119895 00441 minus 00007119895 00185 + 00055119895

5 01264 + 00058119895 01106 minus 00188119895 01196 + 00110119895




9 01337 + 00280119895 01293 + 00069119895 01274 + 00230119895

10 01639 + 00306119895 01102 minus 00204119895 01743 + 00223119895


0

10

20

30

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

0 20 40 60 80DOA (deg)






0 20 40 60 80DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

20

0

minus20

minus40

minus60

minus80

minus100



MVDR SINR(dB)

mp-QP MVDRSINR (dB)


25 769897 869897



7 Conclusion






Acknowledgment


References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




d

Y

XZ






119882MVDR =119877minus1119886 (120579)

119886119867 (120579) 119877minus1119886 (120579) (12)


119908MVDR =[[[

[

1199081

1199082

1199083

1199084

]]]

]

(13)









119875 (0) = 1198601198871 (0) 119860119887119899 (0) (14)


119875 (0) 119891 (1199091 (0) 119909119899 (0)) (15)


119873119862=

119899

sum

119894=1

round(120573 ∙ 119873

119894) (16)




1198751015840= 119860119887

1015840

1 119860119887

1015840

120575 (17)


1198751015840 119891 (119909

1015840

1 119909

1015840

120575) (18)



119875new = 1199041198661198751015840 (19)








1is obtained from



1199082119872= Real 119908

1119872


+ Imag 1199081119872


119908119873119872

= Real 119908(119873minus1)119872


+ Imag 119908(119873minus1)119872


(20)


119882119873119872

=

[[[[[[[

[


11990812

11990813

11990814

11990821

11990822

11990823

11990824

1199081198991

1199081198992

1199081198993

1199081198994

]]]]]]]

]

(21)

where

119882119873119872




sum119873

119899=1119875Inter 119899 +Noise

(22)




2) (23)








119873119862=

119899

sum

119894=1

round119861 sdot 119908119894 (25)



119908119863119872

= 1199081119872+ sflowast (119908

2119872minus 1199083119872) (26)






119882119873 (119894) = 1198821 (119894) 119882119899 (119894) (27)


119875 (119894) 119891 (1199081 (119894) 119908119899 (119894)) (28)




2) (29)


119873(119894) =

1198821015840

1 119882

1015840

119894


1198821015840

119873(119894) 119891 (119882

1015840

1 119882

1015840

119894) (30)


119882new = 119882best 1198821015840

119873(119894) (31)




















2 1198822

minus24985 + 38447119895 minus25978 + 39071119895

3 1198823


4 1198824

minus37544 + 06641119895 minus37899 + 06865119895





0 20 40 60 80

0

10

20

30

DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus20

minus30

minus40

minus40

minus50

minus60

minus60

minus70

minus80minus80


0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70


SIN

R (d

B)

DM-AIS




103330 minus 02789119895 03652 minus 02806119895

2 1198822

04506 minus 00414119895 04622 minus 00401119895

3 1198823

04590 + 00487119895 05500 + 00474119895

4 1198824

03348 + 02723119895 03292 + 02748119895





1 01626 minus 00118119895 01077 + 00469119895 01594 minus 00123119895

2 01249 + 00093119895 01269 + 00072119895 01224 + 00123119895

3 00630 minus 00026119895 00808 + 00264119895 00626 minus 00020119895

4 00143 + 00059119895 00441 minus 00007119895 00185 + 00055119895

5 01264 + 00058119895 01106 minus 00188119895 01196 + 00110119895




9 01337 + 00280119895 01293 + 00069119895 01274 + 00230119895

10 01639 + 00306119895 01102 minus 00204119895 01743 + 00223119895


0

10

20

30

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

0 20 40 60 80DOA (deg)






0 20 40 60 80DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

20

0

minus20

minus40

minus60

minus80

minus100



MVDR SINR(dB)

mp-QP MVDRSINR (dB)


25 769897 869897



7 Conclusion






Acknowledgment


References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119875 (0) = 1198601198871 (0) 119860119887119899 (0) (14)


119875 (0) 119891 (1199091 (0) 119909119899 (0)) (15)


119873119862=

119899

sum

119894=1

round(120573 ∙ 119873

119894) (16)




1198751015840= 119860119887

1015840

1 119860119887

1015840

120575 (17)


1198751015840 119891 (119909

1015840

1 119909

1015840

120575) (18)



119875new = 1199041198661198751015840 (19)








1is obtained from



1199082119872= Real 119908

1119872


+ Imag 1199081119872


119908119873119872

= Real 119908(119873minus1)119872


+ Imag 119908(119873minus1)119872


(20)


119882119873119872

=

[[[[[[[

[


11990812

11990813

11990814

11990821

11990822

11990823

11990824

1199081198991

1199081198992

1199081198993

1199081198994

]]]]]]]

]

(21)

where

119882119873119872




sum119873

119899=1119875Inter 119899 +Noise

(22)




2) (23)








119873119862=

119899

sum

119894=1

round119861 sdot 119908119894 (25)



119908119863119872

= 1199081119872+ sflowast (119908

2119872minus 1199083119872) (26)






119882119873 (119894) = 1198821 (119894) 119882119899 (119894) (27)


119875 (119894) 119891 (1199081 (119894) 119908119899 (119894)) (28)




2) (29)


119873(119894) =

1198821015840

1 119882

1015840

119894


1198821015840

119873(119894) 119891 (119882

1015840

1 119882

1015840

119894) (30)


119882new = 119882best 1198821015840

119873(119894) (31)




















2 1198822

minus24985 + 38447119895 minus25978 + 39071119895

3 1198823


4 1198824

minus37544 + 06641119895 minus37899 + 06865119895





0 20 40 60 80

0

10

20

30

DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus20

minus30

minus40

minus40

minus50

minus60

minus60

minus70

minus80minus80


0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70


SIN

R (d

B)

DM-AIS




103330 minus 02789119895 03652 minus 02806119895

2 1198822

04506 minus 00414119895 04622 minus 00401119895

3 1198823

04590 + 00487119895 05500 + 00474119895

4 1198824

03348 + 02723119895 03292 + 02748119895





1 01626 minus 00118119895 01077 + 00469119895 01594 minus 00123119895

2 01249 + 00093119895 01269 + 00072119895 01224 + 00123119895

3 00630 minus 00026119895 00808 + 00264119895 00626 minus 00020119895

4 00143 + 00059119895 00441 minus 00007119895 00185 + 00055119895

5 01264 + 00058119895 01106 minus 00188119895 01196 + 00110119895




9 01337 + 00280119895 01293 + 00069119895 01274 + 00230119895

10 01639 + 00306119895 01102 minus 00204119895 01743 + 00223119895


0

10

20

30

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

0 20 40 60 80DOA (deg)






0 20 40 60 80DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

20

0

minus20

minus40

minus60

minus80

minus100



MVDR SINR(dB)

mp-QP MVDRSINR (dB)


25 769897 869897



7 Conclusion






Acknowledgment


References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









119873119862=

119899

sum

119894=1

round119861 sdot 119908119894 (25)



119908119863119872

= 1199081119872+ sflowast (119908

2119872minus 1199083119872) (26)






119882119873 (119894) = 1198821 (119894) 119882119899 (119894) (27)


119875 (119894) 119891 (1199081 (119894) 119908119899 (119894)) (28)




2) (29)


119873(119894) =

1198821015840

1 119882

1015840

119894


1198821015840

119873(119894) 119891 (119882

1015840

1 119882

1015840

119894) (30)


119882new = 119882best 1198821015840

119873(119894) (31)




















2 1198822

minus24985 + 38447119895 minus25978 + 39071119895

3 1198823


4 1198824

minus37544 + 06641119895 minus37899 + 06865119895





0 20 40 60 80

0

10

20

30

DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus20

minus30

minus40

minus40

minus50

minus60

minus60

minus70

minus80minus80


0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70


SIN

R (d

B)

DM-AIS




103330 minus 02789119895 03652 minus 02806119895

2 1198822

04506 minus 00414119895 04622 minus 00401119895

3 1198823

04590 + 00487119895 05500 + 00474119895

4 1198824

03348 + 02723119895 03292 + 02748119895





1 01626 minus 00118119895 01077 + 00469119895 01594 minus 00123119895

2 01249 + 00093119895 01269 + 00072119895 01224 + 00123119895

3 00630 minus 00026119895 00808 + 00264119895 00626 minus 00020119895

4 00143 + 00059119895 00441 minus 00007119895 00185 + 00055119895

5 01264 + 00058119895 01106 minus 00188119895 01196 + 00110119895




9 01337 + 00280119895 01293 + 00069119895 01274 + 00230119895

10 01639 + 00306119895 01102 minus 00204119895 01743 + 00223119895


0

10

20

30

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

0 20 40 60 80DOA (deg)






0 20 40 60 80DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

20

0

minus20

minus40

minus60

minus80

minus100



MVDR SINR(dB)

mp-QP MVDRSINR (dB)


25 769897 869897



7 Conclusion






Acknowledgment


References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









2 1198822

minus24985 + 38447119895 minus25978 + 39071119895

3 1198823


4 1198824

minus37544 + 06641119895 minus37899 + 06865119895





0 20 40 60 80

0

10

20

30

DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus20

minus30

minus40

minus40

minus50

minus60

minus60

minus70

minus80minus80


0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70


SIN

R (d

B)

DM-AIS




103330 minus 02789119895 03652 minus 02806119895

2 1198822

04506 minus 00414119895 04622 minus 00401119895

3 1198823

04590 + 00487119895 05500 + 00474119895

4 1198824

03348 + 02723119895 03292 + 02748119895





1 01626 minus 00118119895 01077 + 00469119895 01594 minus 00123119895

2 01249 + 00093119895 01269 + 00072119895 01224 + 00123119895

3 00630 minus 00026119895 00808 + 00264119895 00626 minus 00020119895

4 00143 + 00059119895 00441 minus 00007119895 00185 + 00055119895

5 01264 + 00058119895 01106 minus 00188119895 01196 + 00110119895




9 01337 + 00280119895 01293 + 00069119895 01274 + 00230119895

10 01639 + 00306119895 01102 minus 00204119895 01743 + 00223119895


0

10

20

30

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

0 20 40 60 80DOA (deg)






0 20 40 60 80DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

20

0

minus20

minus40

minus60

minus80

minus100



MVDR SINR(dB)

mp-QP MVDRSINR (dB)


25 769897 869897



7 Conclusion






Acknowledgment


References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






1 01626 minus 00118119895 01077 + 00469119895 01594 minus 00123119895

2 01249 + 00093119895 01269 + 00072119895 01224 + 00123119895

3 00630 minus 00026119895 00808 + 00264119895 00626 minus 00020119895

4 00143 + 00059119895 00441 minus 00007119895 00185 + 00055119895

5 01264 + 00058119895 01106 minus 00188119895 01196 + 00110119895




9 01337 + 00280119895 01293 + 00069119895 01274 + 00230119895

10 01639 + 00306119895 01102 minus 00204119895 01743 + 00223119895


0

10

20

30

Dire

ctio

nal p

atte

rn (d

B)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

0 20 40 60 80DOA (deg)






0 20 40 60 80DOA (deg)


Dire

ctio

nal p

atte

rn (d

B)

20

0

minus20

minus40

minus60

minus80

minus100



MVDR SINR(dB)

mp-QP MVDRSINR (dB)


25 769897 869897



7 Conclusion






Acknowledgment


References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







Acknowledgment


References




































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



research article minimum variance distortionless...

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