Performance Analysis of MIMO Wavelet Packet Multicarrier Multicode CDMA System with Antenna Selection

INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER Pe o mance Analysis o MIMO Wa ele Packe Mul ica ie Mul icode CDMA Sys em wi h An enna Selec ion Ma yam Mahmoud AKHO-ZAHIEH, Nasse ABDELLATIF Depa men o Elec ical Enginee ing, Facul y o Enginee ing & Technology, Applied Science P i a e Uni e si y, Al A ab s . 21, 11931 Amman, Jo dan ma y[email p o ec ed], nasse _ab[email p o ec ed] DOI: 10.15598/aeee. 17i4.3437 Abs ac . Pe o mance o Mul ica ie Mul icode Code-Di ision Mul iple Access (MC/MCD-CDMA) sys ems can be imp o ed signi ican ly by using Wa ele Packe s (WPs) as subca ie s ins ead o a sinusoidal unc ion. This is because WPs ha e much lowe side- lobes and negligible sidelobe ene gy leakage compa ed o sinusoidal ca ie s; his p ope y signi ican ly dec eases he in e ca ie in e e ence and imp o es he sys em pe o mance. Fu he imp o emen can be achie ed by u ilizing mul iple an ennas a ansmi e and ecei e o cons uc a Mul iple-Inpu Mul iple-Ou pu (MIMO) sys em. Channel ha dening is he main d awback o MIMO sys ems. An enna selec ion can be employed o educe his p oblem. In his pape , we use he an- enna selec ion in MIMO WP-MC/MCD-CDMA sys- em. These combina ions o an enna selec ion, MIMO, and WP in MC/MCD-CDMA imp o e he sys em pe - o mance signi ican ly and educe he channel ha den- ing. The pe o mance o he sys em is es ed acco d- ing o he ou age p obabili y and bi e o a e. Two MIMO schemes on Nakagami-m ading channel a e conside ed, which a e: selec i e ansmi /selec i e e- cei e and selec i e ansmi /maximum a io combin- ing ecei e. The s udy includes he e ec s an ennas’ numbe , ading pa ame e -m, numbe o use s, and he h eshold signal o in e e ences plus noise a io. The pe o mance o he sys em is compa ed o ha o MC/MCD-CDMA based on a sinusoidal ca ie . The esul s e eal ha : by inc easing an ennas’ numbe , he sys em pe o mance is imp o ed signi ican ly, and MC/MCD-CDMA sys em based on WPs ca ie s ou - pe o ms MC/MCD-CDMA sys em based on a sinu- soidal ca ie . Keywo ds Di e si y, MIMO, Nakagami channel, wa ele packe s. 1. In oduc ion Mul ica ie /Mul icode-Code Di ision Mul iple- Access (MC/MCD-CDMA) communica ion sys- ems [1], [2] and [3], ha e many a ac i e cha ac e is- ics such as: •Using MC p o ides high immuni y agains In e - symbol In e e ence (ISI). This in e e ence esul s when he channel delay sp ead exceeds he symbol du a ion [4]. Also, MC can supp ess he e ec o he na ow-band jamme [5] and [6] by inc easing he signal bandwid h. •By MCD scheme, he numbe o ca ie s can be dec eased; as a esul , he In e ca ie In e e - ence (ICI) will be educed, and he sp eading gain will be inc eased. Also, mul i a e se ices can be achie ed by using MCD [7]. MC/MCD-CDMA sys em pe o mance can be enhanced signi ican ly by using Wa ele Packe s (WPs) as subca ie ins ead o sinusoidal ca i- e s [8], [9], [10], [11], [12], [13], and [14]. This can be ela ed o he lowe sidelobes and negligible side- lobe ene gy leakage o WPs compa ed o sinusoidal ca ie s. This p ope y can u he dec ease he ICI and mul iple-access in e e ence. Ano he ad an age o WPs is ha : he e is no need o equency/ ime gua d be ween di e en use signals because WPs a e na u ally o hogonal and well localized in ime and e- quency domain. c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 423 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER To u he educe he e ec o mul ipa h ading and imp o e sys em pe o mance, an enna di e si y ech- nique can be used. In di e si y schemes, he ecei ed signal ia se e al pa hs, ca ying he same in o ma- ion, a e combined o imp o e sys em pe o mance. In [8], [10], [11], [13], and [14] h ee schemes o di e - si y combining echniques we e conside ed, namely Se- lec ion Di e si y (SC), Equal Gain Combining (EGC) and Maximal Ra io Combining (MRC). I is obse ed ha he MRC ou pe o m he o he wo di e si y com- bining me hods. A Mul iple-Inpu Mul iple-Ou pu (MIMO) sys em, which uses mul iple an ennas o ansmi ing and ecei ing, o e s ad an ages o e Single-Inpu Single- Ou pu (SISO) sys em because di e si y can be used a bo h ansmi e and ecei e [15], [16] and [17]. The MIMO sys ems a e classi ied in o closed-loop sys ems o open-loop sys ems acco ding o he Channel S a e In o ma ion (CSI). In he closed-loop sys em, CSI is a ailable a he ansmi e while in open-loop sys ems i is no . In he closed-loop MIMO mul i use sys em, an enna Selec ion (SC) a he ansmi e can be em- ployed o educe channel ha dening and enhance he sys em pe o mance. The analysis o an enna selec ion a ansmi e wi h maximal- a io combining a he ecei e (SC- TX/MRC-RX) is discussed in [18], [19], [20], [21], [22], [23] and [24]. In [18], a e age ou age capaci y o mul- iuse MIMO-SC-TX/MRC-RX sys em is de i ed. The au ho demons a es he e ec s o MIMO con igu a- ion, numbe o use s, and mul iuse di e si y on he ou age capaci y pe o mance. The amewo k analy- sis o Mul iuse Di e si y (MUD) gain in selec ion an- enna MIMO sys em o e la - ading Ralyleigh chan- nel is de eloped in [19]. Only poin - o-poin commu- nica ion links a e conside ed in his pape . As an ex- ension o [19], he au ho s in [20] ocus on he pe o - mance analysis SC-TX/MRC-RX sys em in poin - o- mul ipoin communica ions. O e la - ading Ralyleigh channel, he au ho in [21] demons a es he analysis o a e age Bi E - o Ra e (BER) pe o mance o mul iuse MIMO-SC- TX/MRC-RX. Two scena ios we e conside ed which a e: •He e ogeneous: independen non-iden ical dis- ibu ed Signal o Noise Ra io (SNR). •Homogeneous: independen iden ical dis ibu ed SNR. The analysis o he impac o eedback delay be ween he ansmission selec ion pa ame e s and he ans- mission ime on mul i use sys em employing o hog- onal space- ime block coding wi h a e-adap i e mod- ula ion and use selec ion scheme is p esen ed in [22]. The au ho s analyze he BER, a e age spec al den- si y, and bi e o ou age p obabili y in he e ogeneous ime- a ying MIMO Ralyleigh ading channel. In [23], he au ho s de i ed he BER and he ou age P obabili y (Pou ) o bina y phase shi keying o he SC-TX/MRC-RX sys em in Rayleigh ading channels. By analysis and simula ion he au ho s p o e ha he SC-TX/MRC-RX sys em signi ican ly ou pe o ms he space- ime block coding, which has he same di e si y o de and he same numbe o ecei e an ennas. The au ho s in [24] pe o m he analysis o Symbol E o P obabili y (SEP) o se e al cons ella ions o pe ec CSI eedbacks. In hei analysis, hey showed ha he an enna di e si y imp o es he sys em pe o mance bu he eedback delay deg ades signi ican ly in he SEP o SC-TX/MRC-RX scheme. In [25], exp essions o Pou and BER on a la - ading Rayleigh channel o some MIMO sys ems wi h MUD we e p esen ed. The au ho s use he uni o m powe alloca ion p ocedu e a he ansmi e and assume ha he CSI o each use is known o he schedule a he base s a ion. The Nakagami-mdis ibu ion is known o span ia i s pa ame e ma wide ange o mul ipa h ading. This includes one-sided Gaussian model (m= 0.5), he Rayleigh model (m= 1) and Ricean model (m= 3) [26]. In [27], he au ho in es iga es he pe o - mance analysis o SC-TX/MRC-RX MIMO sys em on Nakagami-m ading channel. The exac closed o m ex- p ession o he SNR and BER a e de i ed by ob aining s a is ics as such as Cumula i e Dis ibu ion Func ion (CDF), he P obabili y Densi y Func ion (PDF) and he Momen Gene a ing Func ion (MGF). The le e in [28] ocuses on he s udy o he di e si y ad an age o using MIMO an ennas by de e mining he PDF o sin- gle and MIMO channel by which he s a is ical cha ac- e is ics o MIMO sys ems can be desc ibed. By Mon e Ca lo simula ions, he au ho inds o mulas ha de- ine he channel gain and he di e si y o de o single and mul iuse MIMO sys ems. Also, by using a Chi- squa e goodness-o - i es , he au ho p o es ha he dis ibu ion o he channel gain can be app oxima ed by a Nakagami-mdis ibu ion. Uni ied simple o mulas o BER and Pou o some mul iuse MIMO sys ems, such as SC-TX/SC-RX, SC-TX/MRC-RX, and space- ime block coding sys ems, on Nakagami-mchannels, a e p esen ed in [29]. The pe o mance limi s o mas- si e MIMO sys ems unde p ac ical an enna selec ion algo i hms a e in es iga ed in [30]. In his sys em, he ansmi e selec s a subse o he a ailable an- ennas wi h he s onges channel gains. They show ha wi h only 30 % o an ennas being ac i e, mo e han 90 % o he e godic a e ob ained by ull an- enna selec ion, can be achie ed. The analy ical ex- p ession o he numbe o selec ed an ennas ha can maximize ene gy e iciency is also de i ed. In [31], he au ho s in es iga e he MIMO echniques in a ehicle- c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 424 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER o- ehicle communica ion sys em. The pe o mance o SC-TX/MRC-RX and SC-TX/SC-RX schemes was an- alyzed o e n*Rayleigh ading channels; "n*Rayleigh can be de ined as a p oduc o nindependen Rayleigh andom a iables connec ed ia na ow pipes". The au ho s de i e a closed- o m exp ession o he ou age p obabili y and he amoun o ading. Thei nume - ical esul s show ha SC-TX/MRC-RX ou pe o ms SC-TX/SC-RX, bu i s pe o mance is limi ed as nin- c eases. Using Cumula i e Densi y Func ion (cd ) an exac closed- o m exp ession o he Symbol E o Ra e (SER) o SC-TX/MRC-RX wi h elay and use selec- ion o MIMO sys em o e non-iden ical Nakagami ading channels is de i ed in [32]. They show ha he SER is imp o ed by mul i- elay di e si y, mul i- use di e si y and he sum o non-iden ical ading pa- ame e s o di e en ansmi an ennas, elays, and des ina ions. In [33], Signal Space Di e si y (SSD) is employed in o a MIMO sys em wi h MRC and ans- mi an enna selec ion. The sys em pe o mance wi h Phase-Shi Keying (PSK) modula ion is in es iga ed unde a slow la Rayleigh ading channel wi h he co - ela ed ecei e an ennas. The exac closed- o m ex- p ession o pai wise e o p obabili y is de i ed using he ealis ic exponen ial co ela ion model. I is shown ha he e o pe o mance o he sys em can be im- p o ed wi h almos no ex a complexi y o cos . Many esea ch pape s combine bo h echnologies o MIMO and wa ele . In [34] o imp o e he qual- i y o he ansmi ed image in he MIMO sys em, adap i e comp ession echniques based on wa ele ans o m in a MIMO communica ion sys em is p o- posed. Wa ele comp ession is used in [35] o educe CSI eedback da a size in MIMO sys em. In [36], [37], [38], [39] and [40], he au ho s s udied he pe o mance o MIMO-O hogonal F equency Di- ision Mul iplexing (OFDM) based on wa ele ins ead o Fas Fou ie T ans o m (FFT) by using Space-Time Block Code (STBC) unde di e en channel condi ions. All hese s udies demons a ed ha using wa ele in MIMO-OFDM sys em ins ead o FFT will imp o e he BER pe o mance. The au ho s in [41] compa e he BER pe o mance o STBC- amele OFDM sys em us- ing M-PSK and M-QAM modula ion echniques wi h a ious numbe o cons ella ion poin s. The amele s elimina e a po ion o he cons ain s o wa ele s such as shi -sensi i i y, poo di ec ionali y, and lack o phase in o ma ion. In [42], he au ho p oposes a Dis- c e e Wa ele (DWT)-Join An enna Selec ion (JAS) sys em o mi iga e he pe o mance loss due o an- enna selec ions in MIMO sys ems. Ex ensi e simu- la ions demons a ed ha he DWT-JAS imp o es he capaci y in he p esence o co ela ion a he ansmi - e and he ecei e . In ou p e ious wo k [8], [9] and [10], we p opsed MC/MCD-CDMA sys em ha uses a WP as a sub- ca ie o educe ICI and mul iple-access in e e ence. The sys em pe o mance is es ed using he signal o in e e ence plus noise a io in [8] and [9]. To u - he imp o e he sys em pe o mance di e si y is used in [8] and [10], he sys em pe o mance is esed using BER and Pou pe o mances wi h and wi hou di e - si y. The e ec s o wa ele amily ype, wa ele il e leng h, di e si y ype, di e si y o de , mul ipa h in en- si y p o ile, and Nakagami pa ame s a e in es iga ed. The au ho s in [11], [13] and [14], use in e e ence sup- p ession il e a he ecei e o mi iga e he e ec o na ow-band jamme in e e ence and hus imp o e he sys em pe o mance. In [12] and [14] o accommoda e in o ma ion sou ces wi h di e en da a a es, we p o- pose he use o MCD scheme o mul i a e se ices. In his pape , which is an ex ension o [8], [9], [10], [11], [12], [13], and [14], we employ mul iple an ennae a he ansmi e and ecei e o he WP-MC/MCD- CDMA sys em. Ins ead o STBC which is used in [36], [37], [38], [39], [40], [41] and [42], in ou sys- em we use he selec ion di e si y a he ansmi e o educe he channel ha dening which is he main d aw- back o MIMO sys ems. The pe o mance analysis o MIMO WP-MC/MCD-CDMA sys em in slow ading Nakagami-mchannel is p esen ed. Two schemes o MIMO sys em a e in oduced, which a e: SC-TX/SC- RX and SC-TX/MRC-RX. The pe o mances o hem a e in es iga ed acco ding o bi e o a e and ou - age p obabili y. The pe o mance analysis includes he e ec s o an ennas’ numbe , numbe o use s, ading pa ame e , and he h eshold signal o in e e ences plus noise a io. The pe o mance o he MIMO-WP- MC/MCD-CDMA sys em is compa ed wi h he pe o - mance o Sinusoidal (SIN) based MIMO sys em, which is deno ed by MIMO-SIN-MC/MCD-CDMA. The o ganiza ion o he pape is as ollows. In Sec. 2. , we p opose he anscei e sys em o MIMO-WP-MC/MCD-CDMA. Signal o in e e ence plus noise a io is illus a ed in Sec. 3. In Sec. 4. and Sec. 5. , espec i ely, he BER and Pou o SC- TX/SC-RX and SC-TX/MRC-RX sys ems a e gi en. Speci ic nume ical esul s o he sys em BER and Pou pe o mances a e p esen ed in Sec. 6. A las , in Sec. 7. , he conclusions a e gi en. 2. Sys em Model and Desc ip ion In his s udy, he channel o he sys em unde consid- e a ion consis s o N ansmission an ennas and N ecep ion an ennas and cha ac e ized by a N ×N ma- c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 425 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER ix gi en by: Hk=       h11 kh12 k. . . h1N k h21 kh22 k. . . h2N k . . .. . .. . . . . . hN 1 khN 2 k. . . hN N k        = =hk 1hk 2. . . hk N . (1) The channel is assumed o be slowly ading Nak- agami channel [26], and i s elemen s a e independen and iden ically dis ibu ed (i.i.d.) complex Gaussian andom a iable wi h µ= 0 and σ2= 1 . The impulse esponses om each ξ h ansmi an enna o each χ h ecei e an enna can be w i en as: hχξ k( ) = L−1 X l=0 hχξ k(l)δ( −lTc),(2) whe e Lis he numbe o p opaga ion pa hs and hχξ k(l) is he pa ame e o he l h pa h which depends on he gain, phase and ime delay o he pa h be ween he ξ h ansmi an enna and χ h ecei e an enna. Each use can ansmi using only one an enna, he op imal an enna, and i s signal is ecei ed by N an ennas. The anscei e o he sys em unde conside a ion is shown in Fig. 1. Each o he ansmi e and ecei e consis s o wo pa s, which a e he mul icoding pa and he sp eading/WPs pa . The da a o k h use : dk( ) = dI k( )−jdQ k( ) = ∞ X i=−∞ di kΠT JV −iT JV !,(3) is a andom complex sequence, whe e Tis he bi du- a ion, Jis he o al numbe o mul icode sub-s eams, Vis he o al numbe o he WPs supe -s eams and Πx ep esen s a ec angula pulse wi h du a ion x. A he mul icode pa o he ansmi e , he k h use da a is Se ial- o-Pa allel (S/P) con e ed o gene a e he J sub-s eams, which hen coded by an o hogonal signal: aj( ) = Nc−1 X i=0 ai jΠTc( −iTc),(4) o educe he in e e ence be ween he sub-s eams hemsel es. A las , he codded sub-s eams a e added be o e being ansmi ed o he sp eading/WPs pa . A he sp eading/WPs pa o he ansmi e , he ou - pu signal o he coding pa is S/P con e ed in o V supe -s eams. These supe -s eams a e sp ead by he Pseudo-Noise (PN) sequence: ck( ) = Nn−1 X i=0 ci kΠTn( −iTn),(5) modula ed by he wa ele packe wp ( ), added, and inally modula ed by a sinusoidal ca ie , exp(jω0 ). No e ha : • he o hogonal signal, aj( ), has leng h =Ncand chip du a ion =Tc=T HNc , • he PN sequence, ck( ), has a chip du a ion =Tn and leng h =Nn=T Tn , •wp ( ) = N TnX i p N· Tn−iTn!is he h WP. The wa ele unc ion p (•)has a suppo leng h =Nand is de ined ecu si ely by a pai o quad a- u e mi o lowpass il e h0(k)and highpass il e h1(k)[8], •ai jand ci k· ∈ {±1}a e he i h bi s wi h p obabili- ies P(1) = P(−1) = 0.5. Assuming iden ical powe , P, o all use s and he ξ h an enna is he op imal an enna o k h use , he ansmi ed signal o he k h use using he ξ h an- enna is gi en by: sξ k( ) = √2P V X =1 J X j=1 Re[dξ kj ( )aj( )· ·ck( )wp ( ) exp(jω0 )], (6) whe e dξ kj ( )is he da a symbol on he ξ h ansmi ed an enna o k h use , j h sub-s eam, h supe -s eam and wi h a du a ion =T. The abo e signal, sξ k( ), is de ec ed by he ecei e a e passing h ough a noisy channel. The ecei ed signals on he χ h ecei e an- enna o he k h use is gi en by: χ k= N X ξ=1 hχξ k( )∗sξ k( ) + nχ( ),(7) whe e nχ( )is a ze o-mean Addi i e Whi e Gaussian Noise (AWGN). The o al ecei ed signal o k h use can be ep esen ed in ec o o m as ollows: k=hξ k∗sξ k+nk,(8) whe e k= [ 1 k, 2 k, . . . , N k]Tis he ecei ed signal ec- o and nk= [n1 k, n2 k, . . . , nN k]Tis he noise ec o . In his pape , wo MIMO sys em will be conside ed: •SC-TX/SC-RX Scheme In his scheme, a any bi du a ion, each use can choose he link wi h he highes Signal o In e e ence plus Noise Ra io (SINR γk) om he N N possible c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 426 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER 1 )exp( o � N � )( dk )( 1 a )()( 1 wp ck PS / J�1 PS / V�1 T ansmi e )( aJ � pa gmul icodin )()( wp c Vk pa WPssp eading/ � � )exp( o � 1 N N � � combine Di e si y )( ck )( 1 wp k b ˆ 1�V 1 x )( aJ � )()( wp c Vk �� Td 0)( �� Td 0)( V x �� Td 0)( �� Td 0)( )( 1 a k d ˆ 1�J 1 z J z Recei e pa co ela o / WPsdesp eding pa co ela o mul icode selec edisan ennaone eedbackCSI use o h k SP / SP / � Fig. 1: T anscei e o MIMO WP-MC/MCD-CDMA sys em. an enna combina ions. Thus, a any bi du a ion, he ule o signal de ec ion om he χ h op imal ans- mi an enna o he k h use is: k∗= max N |kχξ k|. Ac- co dingly, he e ec i e SINR γka he ecei e an enna combine ou pu o k h use is: γSC/SC = max        γ11 kγ12 k. . . γ1N k γ21 kγ22 k. . . γ2N k . . .. . .. . . . . . γN 1 kγN 2 k. . . γN N k        , (9) whe e γχξ k=γ|hχξ k|2and γis he a e age SINR o each use . •SC-TX/MRC-RX Scheme In his scheme, he e ec i e SINR γka he ecei e an enna combine ou pu o he k h use a any bi du a ion wi h espec o he ξ h ansmi an enna is gi en by: γSC/MRC = N X χ=1 γχξ k=γ N X χ=1 |hχξ k|2.(10) c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 427 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER The ou pu s o he combine a e demodula ed using a locally gene a ed ca ie . Then, a he disp eading WPs co ela o pa o he ecei e , each k h use ecei ed signal om he desi ed N N possible an enna combina ions, χξ, is dep essed and demodula ed by ck( ), and wp ( ), espec i ely. The signal a e being co ela ed o e a pe iod Tis Pa allel- o-Se ial (P/S) con e ed o eco e he supe - s eam. I he i s use is ou e e ence use also he i s pa h, and he i s WP is ou pa h and WP e - e ences, espec i ely, hen he ou pu o he i s co - ela o , i s P/S con e e in his pa o he ecei e , x1, is gi en by [8] as ollows: x1=ZT 0 χξ k( )c1( )wp1( )[cos(ω0 )−jsin(ω0 )]d = =x1 DS( ) + x1 MP I ( ) + x1 CDI( )+ +x1 WPI( ) + x1 MUI( ) + ˆn1( ), (11) whe e: •x1 DS is he desi ed use signal, •x1 MP I ,x1 CDI,x1 WPI, and x1 MUI a e he mul i- pa h in e e ence, he mul icode in e e ence, he wa ele packe s in e e ence and he mul iuse in- e e ence, espec i ely, due o use s o he han he desi ed use a he desi ed N N possible an- enna combina ions, •ˆnis he co ela ed AWGN. The ou pu s o he o he co ela o s in he WP pa a e gi en by: x =x MP I ( ) + x CDI( ) + x WPI( )+ +x MUI ( ) + ˆn ( ), = 2, . . . , V. (12) The ou pu signal o he i s P/S con e e in WPs pa o e e ence use is gi en by: ˆ b=x1 DS + V X =1 [x MP I +x CDI+ +x WPI +x MUI + ˆn ]. (13) A he mul icode co ela o pa , he second pa o he ecei e , he P/S con e e ou pu signals a e de- sp ead by he use code ajand co ela ed o e a pe iod T o eco e he subs eams o use ’ signal. The ou - pu signal o he e e ence use o he i s co ela o , z1, is gi en by: z1=ZT 0 ˆ b·a1( )d = =z1 DS +z1 MP I +z1 CDI +z1 WPI +z1 MUI + ˜n1. (14) The ou pu s o he co ela o s o he all Jsub- s eams a e P/S con e ed o eco e he da a signal, ˆ dk( ). 3. Signal- o-In e e ence Plus Noise Ra io Two me hods will be used o es he sys em pe o - mance: he a e age bi e o a e and he ou age p ob- abili y. The wo pe o mances depend on he ins an a- neous signal o in e e ence plus noise a io (SINR γ), which depends on he desi ed use signal powe , he a iances o he in e e ences and noise a iance. The desi ed powe signal, he in e e ences, and he noise e ms consis o wo pa s, he inphase pa and he quad a u e pa [8]. In his pape and wi hou loss o gene ali y, he inphase pa was conside ed. The desi ed inphase signal powe (S), is he powe o he signal o he i s use , o he i s wa ele packe which p opaga es ia he i s pa h o he desi ed χξ an enna combina ion. This powe is gi en by [8]: S= [z1 DS]2=P(NnT)2 2|hχξ 11 |2.(15) The in e e ence a iance consis s o ou a iances, which a e: •σ2 MP I = a [z1 MP I ]: mul ipa h in e e ence a i- ance due o pa hs o he han he desi ed pa h, •σ2 MCDI = a [z1 MCDI ]: mul icode in e e ence a iance, •σ2 WPI = a [z1 WPI]: wa ele packe s in e e ence a iance, •σ2 MUI = a [z1 MUI]: mul iuse in e e ence a i- ance. To calcula e he abo e a iances o BPSK modu- la ion, i is assumed ha all he in e e ence and he noise e ms a e Gaussian ze o-mean independen an- dom a iables. In oking he esul s in [8], he o al in e e ence a iance, σ2 T I , can be shown o be equal o: σ2 T I =σ2 MP I +σ2 MCDI +σ2 WPI +σ2 MUI = =P(NnT)2 2MI, (16) and MI is gi en by: MI =Ω 12Tn(NnV)2· ·"QK J V X =1 V X 0=1 ψ 0 −1 J2 V X 0=1 ψ 01#, (17) whe e: •ψ 0 =ZTn 0n( 0 (ρ))2+ (ˆ 0 (ρ))2odp, 0< ρ < Tn, wi h 0 (ρ) = Zρ 0 w ( )w0 ( )d c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 428 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER and 0 (ρ) = Zρ 0 w ( )w0 ( )d being he pa ial c oss-co ela ion unc ions be ween WPs [8], •Ω = a [hχξ k1]and Qis he a iance o Mul ipa h In ensi y P o ile (MIP). In his pape , he uni o m MIP will be used. In his MIP, all mul ipa h componen s ampli ude le els a e he same =hχξ k1. Thus: ΩQ= a "L X l=1 hχξ kl #= L X l=1 a hχξ kl = = a hχξ k1 L X l=1 1=ΩL. (18) The noise a iance is gi en by [8]: σ2 n=P(NnT)2 2     VΩ NnEs N0     = =P(NnT)2 2NI, (19) whe e N0 2is he double-sided powe spec al densi y o he AWGN, Es= 2PΩTis he mean ecei ed symbol ene gy. Using Eq. (15), Eq. (17), and Eq. (19), he ins an aneous SINR, γ, can be w i en as: γ=S σ2 T I +σ2 n =|hχξ 1l|2[MI +NI]−1= =|hχξ 1l|2γ. (20) 4. A e age Bi E o Ra e The BER, Pe, is ob ained by a e aging he ins an a- neous Pe(γ), o e he channel ading unc ions. Tha is: Pe=Z∞ 0 γmax (γ)Pe(γ)dγ, (21) whe e: •Pe(γ) = Q√2γ, whe e Q(•)is he Gaussian Q unc ion, • γ(γ)is he p obabili y densi y unc ion o γ. This unc ion depends on channel gain dis ibu ion, which is assumed o be Nakagami in his pape , and also on he MIMO scheme ha is used. Based on [29], he P SC−T X SC−RX eand P SC−T X MRC−RX ea e gi en by Eq. (22) and Eq. (23), espec i ely. P SC−T X SC−RX e=B1m, m γ, KN N ,(22) P SC−T X MRC−RX e=B1mN ,m γ, KN ,(23) whe e m≥1 2is he Nakagami numbe and B1(a, b, c) is gi en by [26]: B1(a, b, c) = 1 2√π· · ∞ X n=0 anbac+n L (ac +n+ 0.5) (1 + bc)ac+n+0.5; eal a≥1 2, (24) wi h a0=h1 L (a+1) ic, and: an=1 n n X j=1 L (a+ 1)[j(c+ 1) −n] L (a+1+j)an−j;n≥1. (25) No e ha L (•)deno es he gamma unc ion [43]. 5. Ou age P obabili y The Pou is he p obabili y ha he channel capaci y, C, all below speci ic h eshold capaci y, C h [18]: Pou =P(C < C h).(26) The channel capaci y is gi en by [18]: C= log2(1 + γmax)bi s ·s−1·Hz−1.(27) F om Eq. (26) and Eq. (27) we ge : Pou =P(C < C h) = P(γmax <[2C h −1] = γ h). (28) Acco ding o Eq. (26), we can de ine Pou as he p obabili y ha γmax alls below a ce ain h eshold SINR, γ h. Thus: Pou =P (γ < γ h) = Zγ h 0 γmax (γ)dγ. (29) In oke he esul in [29], he P SC−T X SC−RX ou and P SC−T X MRC−RX ou a e gi en as ollows: P SC−T X SC−RX ou ="˜ Gm, mγ h γ L (m)# KN N ,(30) P SC−T X MRC−RX ou ="˜ GmN ,mγ h γ L (mN )#KN ,(31) whe e ˜ G(•,•)is he incomple e gamma unc ion [43]. c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 429 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER 6. Resul s and Discussions Using he abo e analy ical esul s, he BER and Pou pe o mances o he sys em we e e alua ed. The e- sul s a e based on he nume ical e alua ion o Eq. (22), Eq. (23), Eq. (30), and Eq. (31) using MATLAB pack- ages. The pe o mance o he sys em is es ed o di e - en combina ions o N and N . Also, he e ec s o he numbe o use s, Nakagami pa ame e , and h esh- old alues a e es ed. The pe o mance o he sys em is compa ed o ha o MC/MCD-CDMA based on a sinu- soidal ca ie . Unless o he wise s a ed, he nume ical esul s we e p oduced using: •Daubechies wa ele packe s wi h o de 3 (db3), •Numbe o subs eams J= 4, •Numbe o supe s eam V= 3, •Ω = 10 dB, L= 3 and Nakagami-m pa ame e = 2, •P ocessing gain leng h Nn= 32 wi h chip du a ion Tn= 10−6s, •The h eshold o SINR γ h (dB), •The numbe o use s K= 2. No e: in he ollowing Figs.; SCξ/SCχand SCξ/MRCχmean ha : he numbe o an ennas a he ansmi e is ”ξ” and he numbe o an ennas a he ecei e is ”χ”. 6.1. E ec o Numbe o An ennas on BER and Ou age P obabili y Figu e 2 and Fig. 3 illus a e, espec i ely, he BER and Pou pe o mances e sus Es/N0 o SC-TX/SC- RX and SC-TX/MRC-RX using di e en numbe s o N and N combina ions. F om hose wo igu es, i is clea ha o he same numbe o an ennas, he SC- TX/MRC-RX scheme ou pe o ms he SC-TX/SC-RX scheme. These esul s a e expec ed since he MRC is he op imum combina ion di e si y. Also, o he wo schemes, he pe o mance imp o ed as he o al num- be o an enna inc eases. Fo he SC/MRC sys ems wi h a ixed o al numbe o an ennas a ansmi - e and ecei e , he di e si y gain dec eases as he numbe o ecei e an ennas inc eases. Fo example, SC2/MRC3 scheme ou pe o ms SC3/MRC2. In all di- e si y echniques, his is a ypical diminishing e ec . This con i ms he obse a ions in [18], [27] and [28]. 10 12 14 16 18 20 10−35 10−30 10−25 10−20 10−15 10−10 10−5 Es/No(dB) Bi E o Ra e SC2/SC2 SC2/SC3 SC3/SC3 SC2/MRC2 SC3/MRC2 SC2/MRC3 SC3/MRC3 Fig. 2: BER pe o mance e sus Es/N0 o SC-TX/SC-RX and SC-TX/MRC-RX wi h di e en numbe o N and N combina ions. 4 5 6 7 8 9 10 10−20 10−15 10−10 10−5 100 Es/No(dB) Ou age P obabili y SC2/SC2 SC2/SC3 SC3/SC3 SC2/MRC2 SC3/MRC2 SC2/MRC3 SC3/MRC3 Fig. 3: Pou pe o mance e sus Es/N0 o SC-TX/SC-RX and SC-TX/MRC-RX wi h di e en numbe s o N and N combina ions 6.2. E ec o Numbe o Use s on BER Fo SC-TX/MRC-RX scheme wi h Es/N0= 16 dB, m= 1 and using ou di e en N and N combina- ions, Fig. 4 illus a es he e ec o he numbe o use s (K) on BER pe o mance. I is clea om he igu e ha : he highe he numbe o use s, he be e he sys em pe o mance. This is he inhe en bene i o he mul iuse sys em, which indica es ha we can use mul iuse di e si y in a mul i-use sys em. These e- sul s a e iden ical o hose ound in [19] and [29]. Also, as in Fig. 2 and Fig. 3, as he numbe o an ennas in- c eased, he sys em pe o mance imp o ed. c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 430 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 17 |NUMBER: 4 |2019 |DECEMBER 1 2 3 4 5 6 7 8 9 10 10−45 10−40 10−35 10−30 10−25 10−20 10−15 10−10 10−5 No. o Use Bi E o Ra e SC2/MRC2 SC3/MRC2 SC2/MRC3 SC3/MRC3 Fig. 4: E ec o he numbe o use s on BER pe o mance. 6.3. E ec o Nakagami-m Pa ame e on BER Figu e 5 shows he e ec o Nakagami-mpa ame e on BER pe o mance. The SC-TX/SC-RX scheme is used wi h Es/N0= 16 dB and di e en (N N ) combina- ions. F om he igu e we can no ice ha : inc easing mpa ame e and he o al an ennas’ numbe imp o es he BER. This is expec ed since he highe alue o mmeans less ading and be e pe o mance. Fo he an ennas’ numbe , his con i ms he esul s in Fig. 2, Fig. 3, and Fig. 4. 1 1.5 2 2.5 3 3.5 4 4.5 5 10−20 10−18 10−16 10−14 10−12 10−10 10−8 m Bi E o Ra e SC2/SC2 SC2/SC3 SC3/SC3 Fig. 5: E ec o Nakagami-mpa ame e on he BER pe o - mance. 6.4. E ec o he Th eshold Value on Pou Figu e 6 illus a es Pou e sus γ h o he SC/SC and SC/MRC schemes using Es/N0= 6 dB. As ex- pec ed, SC/MRC scheme has be e pe o mance han he SC/SC scheme. Also, as he o al numbe o an- ennas inc eases, he pe o mance ge s be e . F om he igu e we can no ice ha : inc easing γ h deg aded he sys em pe o mance which is expec ed since by in- c easing γ h he e is a chance ha he channel capaci y may go below he equi ed h eshold le el. 2 4 6 8 10 12 10−20 10−15 10−10 10−5 100 Th eshold γ(dB) Ou age P obabili y SC2/SC3 SC3/SC3 SC2/MRC3 SC3/MRC3 Fig. 6: Pou e sus γ h o SC-TX/SC-RX and SC-TX/MRC- RX schemes. 6.5. Pe o mance Compa ison Figu e 7 and Fig. 8 show BER and Pou pe o mances, espec i ely, o wo MIMO sys ems, which a e MIMO- WP-MC/MCD-CDMA, ou sys em, and MIMO-SIN- MC/MCD CDMA sys em. F om hese wo igu es, i can be no ed ha o Es/N0= 8 dB he MC/MCD CDMA sys em ou pe o ms ou sys em sligh ly. Bu as Es/N0inc eases, ou sys em ou pe o ms he o he sys em and he di e ence be ween he wo sys ems pe - o mance inc eases as Es/N0inc eases. 6 8 10 12 14 16 10−20 10−15 10−10 10−5 100 Es/No(dB) Bi E o Ra e SC2/MRC2 MIMO−SIN−MC/MCD−CDMA SC2/MRC3 MIMO−SIN−MC/MCD−CDMA SC2/MRC2 MIMO−WP−MC/MCD−CDMA SC2/MRC3 MIMO−WP−MC/MCD−CDMA Fig. 7: BER pe o mance o wo MIMO sys ems. c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 431