Performance Analysis of PLNC Based Bidirectional Relay Network with Space Shift Keying in mmwave Communications

Transcription

1 rformanc Analysis of LNC Basd Bidirctional lay Ntwork with ac hift Kying in mmwav Communications E.MUUGAVALLI,.J.THIUVENGADAM TIAC COE in Wirlss Tchnologis Dartmnt of Elctronics and Communication Enginring Thiagarajar Collg of Enginring, Madurai 65015, Tamil Nadu, India Millimtr-wav (mmwav) communication is on of th mrging ky comonnts for nxt gnration wirlss ntworks. It xloits unlicnsd band at 60 GHz in an indoor nvironmnt. inc th wav roagation at mmwav frquncis xhibits a quasi-otical bhaviour, th inhrnt lin of sight (Lo) channl modls rovid nw rsarch dirctions. Th major challngs in mmwav communication ar highr fr sac ath loss (L) du to its smallr wavlngth, quasi-otical bhaviour of wav roagation and blockag and ntration losss in indoor scnario. Th losss can b comnsatd using multil antnna (MA) systms and th sars channl bhaviour of mmwav roagation is comnsatd by otimal and alignd antnna gomtry. Howvr, MA systm incrass hardwar constraints as th numbr of radio frquncy () chains incrass. In th rcnt yars, sac shift kying (K) modulation schm has bn idntifid as a romising MA tchniqu with singl hardwar rquirmnt. In K, only on antnna is activatd for transmission at any tim instant and th indx of this activ antnna is usd to convy information. liabl communication btwn th nods in a ntwork can b stablishd with th aid of rlay nod in mmwav communication. In this ar, a bidirctional rlay ntwork modl using mmwav communication in indoor-lo nvironmnt is considrd. Th conct of hysical layr ntwork coding (LNC) is alid at th dcod-and-forward (D) rlay nod to nabl th ntwork orats in bidirctional half dulx mod. cifically, th transcivr at th nods snds th information symbol by mloying K modulation and dtcts th symbol basd on th maximum liklihood (ML) dtction critrion. By considring otimal antnna gomtry orating conditions in Lo nvironmnt, th nd-to-nd bit rror rat (BE) robability of th roosd LNC basd bidirctional rlay ntwork using K in mmwav communication is drivd in closd form. Analytical framworks and findings ar also substantiatd via Mont Carlo simulations. Kywords: Bidirctional rlay ntwork, hysical Layr Ntwork Coding, Bit Error robability, Indoor Lin-of- ight, ac hift Kying and mmwav communications. 1. Introduction Communication at mmwav band is on of th mrging aras for nxt gnration wirlss communication systms whrin th inhrnt Lo channl modl rovids nw rsarch dirctions. It rovids multi gigabit-r-scond data rat and is usd to mt th high xctations of futur wirlss srvics such as high lvl of rliability, low lvl of latncy and constant connctivity. It has wid alications in fifth gnration (5G) broadband cllular communication, wirlss backhaul connctions, wirlss rsonal ara ntworks, vhicular ara ntworks, and mobil ad hoc ntworks [1]. Howvr, 1

2 th communication at mmwav frquncis suffrs from th challngs such as highr L, quasiotical bhaviour of wav roagation, high rflction loss and blockag and ntration losss []. Th small carrir wavlngth at mmwav frquncis nabls faturing a larg numbr of colocatd antnnas. Howvr, with hundrds of antnnas mloyd at mmwav frquncis, th numbr of chains rquird by mmwav MIMO is also hug. This rsults in unaffordabl hardwar cost and nrgy consumtion in mmwav MIMO systms. Antnna slction and analog bamforming mthods [3-6] hav bn usd as low comlxity tchniqus. Antnna subst modulation [3] is an antnnalvl modulation tchniqu that liminats convntional basband circuitry and taks advantag of th full antnna array with a limitd numbr of chains. This tchniqu is motivatd by th larg numbr of antnnas availabl in mmwav communication and th rquirmnts for lowr comlxity mixdsignal hardwar. It uss multil antnnas for dirctional bamforming at mmwav frquncis to ovrcom th hug ath loss, th atmoshric absortion and th high nois lvls. In mmwav communications, th rank of th MIMO channl matrix tnds to b low, du to th rsnc of strong Lo comonnts. In [6], antnna array architctur of multil bamformrs is mloyd, whr ach bamfomr is sacd sufficintly aart from ach othr to xrinc indndnt fading. Th advantag of analog bamforming is that it only rquirs on chain, lading to quit low hardwar cost and nrgy consumtion. Howvr, sinc only th hass of signals can b controlld, th rformanc loss of analog bamforming is obvious. Also, it rquirs known channl stat information at th transmittr. Th low comlxity dirctional modulation tchniqus of [7] [9] ar dsignd ntirly around th suort of dirctional transmission and rction including faturs such as dirctional dvic discovry, hirarchical bam slction and bam tracking. A Gnralizd atial Modulation (GM)-basd mmwav communications systm is roosd in [10] which has lowr numbr of chains than th numbr of transmit antnnas. But, it rquirs minimum of two chains in th transmittr. atial multilxing at mmwav carrir frquncis is invstigatd for short-rang indoor alications by quantifying fundamntal limits in Lo nvironmnts and thn rformanc in th rsnc of multiath and Lo blockag [11]. vral tchnical aroachs to th nxt gnration wirlss local ara ntwork (WLAN) ar bing considrd with th ossibility of using th 60 GHz mmwav frquncy rang. In this ar, th antnna alignmnt schm [17] is alid to singl chain K basd mmwav systm. Morovr, K dos not rquir CI at th transmittr. K modulation is an mrging MIMO wirlss communication tchniqu, which was first roosd in [1] as a novl sac modulation schm. It was thn xtndd as satial modulation (M) to incras th data rat. Now, M is dfind as a modulation schm in which transmittd symbols ar drawn from both th satial constllation and th signal constllation, whras K modulation uss only th satial constllation. Although th sctral fficincy is slightly rducd in K, it rovids xctional advantags ovr M in trms of low dtction comlxity and siml transcivr structur [13]-[15]. Lin-of-sight sac shift kying (Lo-K) [17] is a romising tchniqu usd in mmwav indoor-lo communications. Du to small wavlngth of oration, it uss Lo transmission and nabls acking of a larg numbr of antnnas in th nods. Th rcivr in K utilizs th distinct rcivd signals

3 from diffrnt antnnas to discriminat th transmittd mssags, which rsults in siml rcivr comlxity. Hnc, th dmodulation and dtction of th K signalling will b asir to imlmnt. K can b ffctivly usd in indoor-lo scnario by xloiting th otimal antnna array gomtry orating conditions, namly orthogonal K (OK) and biothogonal K (BiOK). In [17]-[19], th Lo orating conditions for mmwav communication to maximiz th Euclidan distanc btwn two rcivd symbols ar obtaind. Th ur Lo MIMO channl matrix could b mad high rank by mloying th shrical wav modl, by ror dsign of th antnna arrays [17]. This is usful for systms which can b subjct to strong Lo channls such as for xaml WLAN systms and othr short rang communication. At rsnt, communication using bidirctional rlay ntwork has rcivd considrabl attntion du to its high bandwidth fficincy. In bidirctional rlay ntworks, two sourc nods xchang thir information with th hl of a rlay nod. LNC rotocol is usd to xchang th mssag btwn two diffrnt sourc nods with th hl of rlay nod in bidirctional rlay ntworks. It uss two hass of communication stratgy, multil-accss has in tim slot I and broadcasting has in tim slot II. In multil-accss has, two sourc nods transmit simultanously thir signals to a rlay nod ovr a multil accss channl. In broadcasting has, th rlay nod broadcasts th XOd vrsion of th two rcivd signals to th two sourc nods ovr a broadcast channl. Th rror rformanc of th LNC rotocol is analyzd in bidirctional rlay ntworks for BK modulation ovr ayligh fading channls using ML dtction mtric at th rlay with th maxlog aroximation [0]. Th contributions of this ar ar as follows: i) A LNC basd bidirctional D rlay ntwork in half dulx mod is roosd as a ntwork modl for mmwav band in indoor-lo nvironmnt using singl chain K modulation with otimal and alignd antnna array gomtry by xloiting th orating mods, OK and BiK. ii) A closd form xrssions for th BE for th sourc nods to rlay nod, rlay nod to sourc nods and th ovrall systm ar drivd for th roosd ntwork. iii) Th rformanc of th roosd LNC basd systm is comard with non- LNC basd systm. Notations: vctors and matrics ar writtn in boldfac with matrics in caitals. or a matrix A, T A and H A indicat th transos, and conjugat transos rsctivly. In stands for th idntity matrix of siz n n. absolut valu and and 10 rrsnts robnius norm. rrsnt binary and dcimal quivalnts. dnots This ar is organizd as follows: ction II rsnts th systm modl and otimal ML dtction schm of th roosd LNC basd bidirctional rlay ntwork using K modulation in mmwav-indoor-lo scnario. ction III analyzs th nd to nd air-wis rror (E) robability and BE robability for th roosd modl. imulation rsults ar discussd in ction IV and ction V concluds th ar. 3

4 . ystm Modl Considr a bidirctional rlay ntwork shown in igur.1. In this ntwork, rlay nod btwn two sourc nods 1 and, assists in xchang of data btwn th sourc nods using th conct of LNC. ourc nods 1 & and rlay nod ar quid with array of N and N antnnas rsctivly. or th analytical tractability, N max N, N orats at half dulx mod. Lt H 1 b th N N 1 matrix and 1 G b N 1. Th rlay nod N N matrix, rrsnting th channl rsons btwn th sourc nod 1 & rlay nod, and sourc nod & rlay nod rsctivly. In mmwav indoor-lo nvironmnt, th fading comonnt of Lo can b nglctd comard to ath loss comonnt. Hnc, th channl cofficints in channl matrics ar writtn as c c x jkd, whr k is th wav numbr, d mn is th roagation ath mn mn mn lngth btwn n th transmit antnna and m th rciv antnna of two diffrnt nods and cmn is th channl gain, calculatd from riis transmission quation. In an indoor-lo nvironmnt, th fading comonnt of Lo can b nglctd comard to ath loss comonnt. Hnc, th small chang in channl gain is ignord and channl cofficints ar writtn as c x jkd mn. mn In mmwav basd Lo nvironmnt, ig. 1. ystm Modl of Bidirctional lay Ntwork H 1 and G ar constraind by th distanc btwn, 1, and, thir antnna saration and array structur. In K modulation, only on antnna is activatd at a tim and th othr antnnas ar kt silnt in ordr to xloit th multiath charactristics, but with singl chain. In th roosd systm, th conct of LNC is alid at th rlay nod to xchang th data btwn sourc nods 1 and with th aid of rlay nod, locatd in indoor-lo nvironmnt. Th K maing rul adotd by 1, and of th roosd systm is givn in Tabl. 1. 4

5 .1 Multil-accss has from sourc nods to rlay nod in Tim lot I: In tim slot I, both sourc nods 1 and transmit M M N N data symbols to 1 rlay nod using K modulation. In this modulation, grous of log M bits ar mad to a satial symbol x to activat a articular antnna indx to transmit data, whil all othr antnnas rmain idl. Lt x b N 1 satial symbol mad at th sourc nod, 1,. Th N 1 rciv signal vctor at rlay nod is givn by, y = H x + G x + n, (1) 1 1 T whr x E , 1, and n is N 1 nois vctor and its lmnts antnna osition ar circularly symmtric indndnt and idntically distributd whit Gaussian random variabls with man zro. Its covarianc matrix is N0I N. inc th data vctors x 1 and x1 hav only on non-zro lmnt as r th signal and nrgy mar of K in th roosd systm, (1) can b simlifid as, whr h i and j y E h E g n, i 1,,, N, j 1,,, N, () 1 i j 1 g rrsnt i th column of channl matrix H 1 and j th column of channl matrix G rsctivly. inc both th channl matrics ar known at th rlay nod, th robability dnsity function or th liklihood function of th Nr 1 rciv signal vctor 1 N N N N s 0 1 i s j 0 y is givn by, 1 1 f y H,G x y E h E g. (3) inc th data transmittd by th sourc nods ar rrsntd by antnna indics i and j, thy ar stimatd using ML critrion as follows, arg min ˆ ˆ i, j E i E j. i N j N y h g 1 1,,,, 1,,, 1 In K maing, k log N bits ar groud and mad into th antnna indx. Lt i ˆ 1 b 1 b 1 and ˆ j b b b 10 k b th K mar at sourc nods 1 & b 10 k rsctivly to slct th antnna indx. In th D stratgy of rlay nod, th joint dtction iˆ ˆj, is don using ML critrion. Th numbr of lmnts of th st of all ossibl airs of iˆ, ˆj (4) is N. With LNC rotocol, th D rlay r-mas it into a nw st with th numbr of lmnts N, using many-to-on maing. Lt b b1 b, n 0,1, k 1 b th XOd vrsion of th surimosd n n n signal of 1& at th rlay nod rsctivly and q b th antnna indx to b slctd to broadcast th LNC ncodd data symbols using th K mar at th rlay nod and it is dfind by q b b. or xaml, basd on th stimats of î and ĵ in 4 4 systm b 10 k

6 (i. N N N 4 ), th data to b transmittd by rlay nod using th conct of LNC in 1 tim slot II is dcidd as follows using th K mar rul givn in Tabl. 1. Binary data to b transmittd at sourc nods Data symbol and Antnna Indx at sourc nods b1, b M, M, 1 Tabl 1. K Mar ul of th 4 4 i j 1 atial symbol at sourc nods x x E T 1 E T 1 ystm Binary data to b broadcastd at rlay nod and its corrsonding antnna Indx b q (LNC) atial symbol at lay nod x E T E 0 0 T 0 E 0 0 T E 0 T 0 E 0 0 T E T E T E E 1 T T E T. Data broadcasting has from rlay nod to sourc nods in Tim lot II: In tim slot II, rlay nod broadcasts th LNC ncodd symbol to th sourc nods using K modulation. Lt x b th mad nrgy vctor to b broadcastd from rlay nod to sourc nods 1and as shown in Tabl 1. Undr th assumtion that th channls from rlay nod to 1 and to is symmtric H H & G G, th N 1 rciv signal vctors at sourc nods, 1, ar givn by, whr 1 1 y H x n (5) 1 1 1, y G x n (6), T x E and n is th N 1 antnna osition nois vctor at sourc nod, 1, and its lmnts ar circularly symmtric indndnt and idntically distributd whit Gaussian random variabls with man zro. Its covarianc matrix is N0 I N. whr hq and g q dnot th y h n (7) E 1 q 1, y g n (8) E q, th q row of H 1 and of th rlay nod is dtctd using ML critrion in sourc nods as givn by, G rsctivly and Th transmit antnna indx 6

7 arg min ˆ q y E h, 1 1,,, 1 q q N 1 1,,, q q N arg min ˆ q y E g. Th transcivr structur of nods imlmnting K has K-mar (constllation maing) at transmittr and K-dmar (antnna indx to bit stram maing) at rcivr. Thus th sourc nods xchang thir information by stimating th data symbols at 1 and ar givn by, b b1 b (9) (10) ˆ ˆ, (11) ˆ ˆ. (1) b1 b b 3. Error rformanc analysis in th roosd systm Lt Th transmittd data from sourc nods undrgos two dtctions in cascad at th rlay nod., 1 1, and ar th E at rlay nod, sourc nod 1 and sourc nod rsctivly. Th nd to nd instantanous rror robability at th sourc nod is givn by, 3.1 Error robability at rlay nod EtoE, 1 1. (13) Without loss of gnrality, assuming 1 and transmit through th i and th j antnnas rsctivly, an rror vnt is said to b occurrd whn iˆ i or ˆ j j. Hnc, E at rlay nod can b xrssd as, 1 Lt i, j i ˆ, j i, j ˆ ˆ i, j i, j i, j i, j i, j i, j. (14) b th E btwn 1 i ˆ, j whn i, j was snt. rom (), it can b writtn as, 1 ˆ whr y i E h E g. It is known that,, 1 i j link of th ntwork in dciding y y, i y y, i y, i, (15) a b a b a,b, (16) whr, dnots th innr roduct. ubstituting () and (16) in (15) and simlifying furthr, H 1 ˆ E h i h i 1 E h 1 i hˆ n, (17) i 7

8 whr H dnots th Hrmitian oration. Lt Z E i 1 ˆi H h h n is a Gaussian random variabl with zro man and varianc, Z givn by, N0E 1 h ˆ, Z i h (18) i whr h h is th squard Euclidan distanc (ED) btwn two diffrnt K symbols. Th ML i ˆi dtction rformanc dnds on maximizing th ED btwn th rcivd symbols. ubstituting (15) for ED in (17), whr ˆi i ˆ ˆ i ˆ i i i i h h h h h, h, (19) h, h is th innr roduct btwn th sub channls of channl matrix i mathmatically xrssd by, jiˆ 1 N i ˆ i ˆ jk d i i ji d i N j1 h, h x, 1,,,. (0) H 1. It is It is dtrmind by alignd antnna gomtry ULA at th transmittr and rcivr in trms of intrantnna sacing and th distanc btwn transmit and rciv array. In mmwav indoor-lo nvironmnt, th high rank MIMO channl is constructd using two orating mods for orthogonal channl construction [17], namly OK and BiK. In OK schm, on transmit array and on rciv array with qual numbr of antnna lmnts ar usd with qual owr allocation and ED is maximizd whn th otimal sub channl condition, conditions in (18), h, h 0 is achivd. Alying this otimal i ˆi N N 1 E N 1 0,. Z OK (1) In BiK mod, on rciv array and two aralll transmit arrays, sacd by distanc, ach with th half of th antnna lmnts in th rciv array ar usd with qual owr allocation and maximum ED condition is achivd whn h h. Alying this otimal conditions in (18), i, ˆ N i N N 1 E N 1 0,. Z BiK () Now, (17) can b writtn as, E 1 1 Z i ˆ. i () It can b xrssd in trms of Q function as, y 1 t whr Qy dt. E Q 1 1 i ˆ, i Z h h (3) ubstituting (18), (1) and () in (3) for th two orating mods, 1, OK N N 1 E 1 Q. N0 (4) 8

9 1, BiK Lt i, j i, ˆj i, j N E. 1 Q N 1 N0 b th E btwn ˆ link of th ntwork. rom (), (5) y y, j y y, j y, j, (6) whr y, j E h E g. ubstituting () in (4), 1 i j E H j ˆj j ˆ, j E g g g g n (7) imilar to th analysis from (18) to (3), in th two orating mods can b rsctivly xrssd as,, OK N N E Q, N0 (8) 1 inc, BiK N E. Q N N0, assuming th sam numbr of data symbols M closd form xrssions for E at th rlay nod is givn by, N N E,, OK Q N0 N E., BiK Q N N0 3. Error robability at th sourc nods and 1, (9) E E E th (30) (31) Th rror rformanc at th sourc nod, 1, is masurd in trms of E,. rom Tabl 1, th rlay nod broadcasts to sourc nods 1 and through th q antnna indx. An rror vnt is said to b occurrd in 1 and whn ˆq q. Hnc, E at sourc nod, 1, can b xrssd as, q qˆ q (3) rom (7)-(9), E at 1 and is writtn rsctivly as, E H q qˆ 1 q qˆ, E h h h h n (33) 9

10 E H q qˆ q qˆ, E g g g g n (34) Considring th sam alignd antnna array st u in two orating mods for, 1, link,, OK N N E Q, N0 (35), BiK 3.3 End to End Error robability in (13), N E Q N. N0 Th End to End rror robability, EtoE of th systm is givn by, substituting (8) and (3) (36) N N N N Nt Nr N N EtoE, OK Q Q 4 Q Q, (37) N N N N N N N N EtoE, BK Q N Q N 4 Q N Q N. (38) whr E N0 and E N0 dnot th N btwn link in th multil accss has (tim slot I) and th N btwn link in th broadcasting has (tim slot II). 3.3 End to End Bit Error robability Assuming quirobabl transmit symbols, th BE for OK mod is givn by th symbolto-constllation maing as follows, whr M k 1 b, OK Q Nr Nb 0 Nb M 1 N b Nb k k M 1 1 1, N is th numbr of data symbols alid at K mar, Nb log N (39) is th grou of bits mad to th symbol, 0 Em N0 Nb and Em is th avrag transmission nrgy. It is also assumd that all ossibl dtction rrors ar qually likly and N & N ar owr of two. inc two aralll transmit antnna arrays ar usd in BiK mod, N 4. Hnc th bit rror robability is givn by, N b 1 k 1 b. BiK Q Nr Nb 0 N b M Nb k k M 1 1. (40) 10

11 4. EULT AND DICUION In this sction, BE rformanc of th roosd LNC basd bidirctional rlay ntwork using K modulation in Lo nvironmnt with mmwav carrir frquncis is analyzd using analytical and Mont Carlo simulations. Th array stu is scifid by OK and BiK mods for constructing th high rank mmwav-mimo Lo channl modl. Th following assumtions ar usd for th numrical rsults: sinc K orats ffctivly at multil antnna systm, th rformanc analysis is carrid out for N N MIMO-Lo systm. In OK orating mod, N N, but in BiK mod, N N, sinc thr ar two aralll arrays at th transmittr, ach with N antnna lmnts. It is assumd that th numbr of antnnas at ach nod is a owr of two. Th transmit owr of all thr nods ar st to b qual. Th simulation aramtrs ar as givn in Tabl. igur shows th BE rformanc of N N LNC basd bidirctional rlay ntwork in Lo orating conditions using K modulation at sourc nods and rlay nod. It is assumd that th 1 and links ar symmtric to ach othr. Tabl imulation aramtrs for BE analysis.no aramtrs Valus 1. Numbr of antnnas at 1, & -3 link. Distanc btwn antnna arrays at sourc nods and antnna array at rlay nod 3m. 3. Carrir frquncy 60GHz 4. Channl Ty Lo Dtrministic Channl 5. Otimal Array tu orating mods OK and BiK Th analytical and simulations rsults ar comard for th OK mod. It is obsrvd that rror robability for sourc nods to rlay and rlay to sourc nods dcras substantially whn N is incrasd. Th thortical BE rformanc of th roosd systm agrs wll with th simulation rsults at an N gratr than 6dB. Howvr thr xists a mismatch at an N lss than 6dB.This mismatch is du to th fact that, th robust modulation and th coding schms ar orational at an N 6 db and abov du to th inhrnt roagation charactristics of millimtr wav lin of sight indoor nvironmnt [16]. At a BE of 10-4 th N rquird for sourc to rlay systm is 8.8dB, rlay to sourc is 8.47dB and th nd to nd systm is 9 db. Hnc BE of th nd to nd systm is dominatd by th sourc to rlay BE. It is also obsrvd that th imrovd rror rformanc is achivd as that of MIMO links, but with singl chain at th transcivr structur by xloiting OK orating conditions. Thus, th transcivr systm comlxity is considrably rducd. 11

12 End-End-im. End-End-Thory to-im. to-thory to-im. to-thory BE N in db ig.. BE of roosd Bidirctional lay Ntwork with LNC in OK in N N N 1 systm igur 3 shows th comarison of nd to nd BE of LNC and non-lnc basd bidirctional rlay ntwork using K modulation for OK and Bik orating mods. Thr infrncs ar obtaind from figu.3. i) It is obsrvd that thr is 1 db N advantag for th BE rformanc of BiK mod whn it is comard to OK schm. This is achivd du to th additional divrsity of dual transmit array stu, offrd by BiK mod. ii) whn th scalability of th antnna array is incrasd, th BE rformanc is gradually imrovd whn N is incrasd du to th incras in antnna divrsity. iii) It is shown that thr is only th marginal rformanc ga btwn LNC and non- LNC basd systms. Howvr, th rformanc ga is vanishd at high N valus. Hnc, th bidirctional communication with rlays rquirs tow tim slots in a LNC systm whil a non LNC systm rquirs four tim slot with a marginal loss in BE LNC-OK-8X8 non-lnc-ok-8x8 LNC-BiK-16X8 non-lnc-bik-16x8 LNC-OK-16X16 non-lnc-ok-16x16 LNC-BiK-3X16 non-lnc-bik-3x16 BE N in db ig. 3. BE comarison of roosd bidirctional rlay ntwork with LNC and non-lnc basd systm 1

13 BE XOK :4dB N:4dB :5dB N:5dB :4dB N:4dB :5dB N:5dB XBiK N 1 in db ig. 4. BE comarison of a roosd ntwork with LNC and non-lnc in diffrnt array stu whn rlay to sourc nod link N is fixd. Th nd-to-nd BE analysis is carrid out both for LNC and non-lnc basd systm using two orating mods with various antnna configurations by varying N of on ho link whil king th N constant for othr ho link. ig. 4 shows th BE rformanc with constant N at lay to ourc nod whil, ig. 5 shows th BE rformanc with constant N at lay to ourc nod 1. rom th rsults, it bcoms vidnt that th nd-to nd BE rformanc is limitd by th minimum of N valus of ourc 1 to rlay link or ourc to rlay link, min,. 1 imilar infrncs can b obtaind from fig 6. and fig 7. whrin rformanc of OK and BiK ar rsctivly analysd XOK 10 - BE :4dB N:4dB :5dB N:5dB :4dB N:4dB :5dB N:5dB 4XBiK N in db ig. 5. BE comarison of a roosd ntwork with LNC and non-lnc in diffrnt array stu whn lay to ourc nod 1 link N is fixd. 13

14 XOK BE :snr =5dB N:snr =5dB :snr =6dB N:snr =6dB :snr =5dB 4X4OK N:snr =5dB :snr =6dB N:snr =6dB N 1 in db ig. 6. BE comarison of a roosd ntwork with LNC and non-lnc in OK array stu whn lay to ourc nod 1 link N is fixd XBiK 10-4 :snr =5dB BE N:snr =5dB :snr =6dB N:snr =6dB 8X4BiK :snr =5dB N:snr =5dB :snr =6dB N:snr =6dB N 1 in db ig. 7. BE comarison of a roosd ntwork with LNC and non-lnc in BiK array stu whn lay to ourc nod 1 link N is fixd. 5. CONCLUION Th roosd LNC basd bidirctional rlay ntwork uss low comlxity sac shift kying modulation tchniqu with otimal antnna array gomtry to combat th bhaviour of wav roagation and L of mmwav frquncis in indoor-lo channl nvironmnt. Th roosd systm consists of and N 1 numbr of antnnas in sourc nod 1, N numbr of antnnas in sourc nod N numbr of antnnas in rlay nod. Th closd form xrssions for th bit rror robability 14

15 for th sourc nods to rlay nod in tim slot I, rlay nod to sourc nods in tim slot II and th ovrall nd-to-nd systm ar drivd and comard with th Mont Carlo simulations with otimal antnna alignmnt gomtry. Also, th BE rformanc analysis is comard for both LNC basd and non-lnc basd systm dsign in half dulx mod. In addition to that, th ffct of N of on of th links in th nd-to-nd rror rformanc is analyzd. This is usful for systms which can b subjct to strong Lo channls such as WLAN systms, othr short rang communication and th nxt gnration wirlss ntworks using mmwav communication. EEENCE 1. obrt W. Hath, Nuria Gonzálz-rlcic, und angan, Wonil oh, and Akbar M. ayd, An Ovrviw of ignal rocssing Tchniqus for Millimtr Wav MIMO ystms, IEEE Journal of slctd toics in signal rocssing, vol. 10, 016, angan, T.. aaort, and E. Erki, Millimtr-wav cllular wirlss ntworks: otntials and challngs, roc. IEEE, vol. 10, no. 3, 014, Nachiaan Valliaan, Angl Lozano, and obrt W. Hath Jr., Antnna ubst Modulation for cur Millimtr-Wav Wirlss Communication, IEEE Trans. Commun., vol. 61, no. 4, 013, ugiura, C. Xu,. Ng, and L. Hanzo, ducd-comlxity cohrnt vrsus non-cohrnt QAM-aidd sac tim shift kying, IEEE Trans.Commun., vol. 59, no. 11, 011, C. Xu,. ugiura,. X. Ng, and L. Hanzo, atial modulation and sac tim shift kying: Otimal rformanc at a rducd dtction comlxity, IEEE Trans. Commun., vol. 61, no. 1, 013, Han, C.-L. I, Z. Xu, and C. owll, Larg-scal antnna systms with hybrid rcoding analog and digital bamforming for millimtr wav 5G, IEEE Commun. Mag., vol. 53, no. 1, 015, A. Babakhani, D. utldg, and A. Hajimiri, A nar-fild modulation tchniqu using antnna rflctor switching, in roc., IEEE Intl. olid-tat Circuits Conf. (ICC), b. 008, M. Daly and J. Brnhard, Dirctional modulation tchniqu for hasd arrays, IEEE Trans. Antnnas roag., vol. 57, no. 9, 009, M. Daly, E. Daly, and J. Brnhard, Dmonstration of dirctional modulation using a hasd array, IEEE Trans. Antnnas roag., vol. 58, no. 5, 010, Naoki Ishikawa, akshith ajashkar, hinya ugiura, Lajos Hanzo, Gnralizd-atial- Modulation-Basd ducd--chainmillimtr-wav Communications, IEEE Trans. on vhicular tch., Eric Torkildson, Uamanyu Madhow, and Mark odwll, Indoor Millimtr Wav MIMO: asibility and rformanc, IEEE Trans. Wirlss Commun., vol. 10, no. 1, 011,

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