Zero-Forcing based Multiuser Two-Way AF Relay Network under Relay Power Constraint

Transcription

1 KAGEE LEE et al: ZERO-ORCIG BASED ULIUSER WO-WAY A RELAY EWORK UDER... Zeo-ocing based ultiuse wo-way A Relay etwo unde Relay Powe Constaint Kanghee Lee, Inha yun, 3 eonjoong Kim, 4 Sun Jo Infomation & Communications Squadon, th ighte Wing, ROKA, Seosan-si 304, Koea xlee@wichita.edu Diectoate of Comm & Communications, Logistics Comm, ROKA, Daegu-si 405, Koea inhahyun@nave.com 3 Diectoate of oce Develoment, Joint Chiefs of Staff, Seoul 04383, Koea hjic093@gmail.com 4 7 th Aeosace Communications Sevice Gou, ROKA, Pyeongtae-si 798, Koea soleil5@hanmail.net Abstact - A two-way amlify--fowad (A) wieless elay netwo consisting of souces with only a single antenna e souce one elay with multile antennas is studied with a self-intefeence cancelation ocess at the destinations in this ae. All souces act as both souces destinations. he closed fom of the elay amlifying matix is otimized unde the elay tansmit owe constaint based on the zeo-focing (Z) citeion. Additionally, the no-owe constaint case of the Z elaying scheme is investigated, as well. uthemoe, the tansmit owe consumtion at the elay is studied duing data tansmission. he oosed system efomance is evaluated in elation to the aveage bit eo ate (BER) by comute simulation. inally, numeical esults show that the system efomance imoves as eithe o inut SR inceases. Keywods - Amlify--fowad (A), wo-way elaying, elay amlifying matix, owe constaint, zeo-focing (Z). I. IRODUCIO Consideable wos on the elay amlifying matix design in the amlify--fowad (A) wieless elay netwos have been studied ove the ast decades. o educe the sectal efficiency loss, the two-way elaying scheme is alied in half-dulex wieless elay netwos. As a esult, the authos in [] have studied the imact of channel estimation eo on the efomance of a multile-inut-multile-outut (IO) two-way elaying netwo based on the zeo-focing (Z) citeion. In addition, the authos in [] have investigated the sum ate of IO A two-way wieless elay netwos with Z tansmission. In [3], the outage efomance of Z based IO two-way elaying netwo with channel estimation eo was studied. he authos in [4], [5] have studied two-way A wieless elay netwos consisting of one elay with multile antennas between two souces with multile antennas e souce. hey designed the elay amlifying matices fo two-way A wieless elay netwos unde the tansmit owe constaint based on the minimum mean squae eo Z citeions [4], [5]. In addition, the elay amlifying matix was designed by maximizing the weighted sum of the obenius noms of the effective channels based on the algebaic nommaximizing tansmit stategy [6]. In [7], the authos have his wo was suoted by the Reublic of Koea Ai oce unde Gant ROKAA6-03. studied the otimal elay beamfoming in two-way elay channels emloyed by the weighted sum ate. In [6], [7], a self-intefeence cancelation ocess was not fulfilled at the destinations duing data tansmission. oweve, in [8], the authos develoed a two-way A wieless elay stategy with a self-intefeence cancelation ocess duing data tansmission. uthemoe, u to now, a two-way A wieless elay netwo consisting of souces with only a single antenna e souce one elay with multile antennas was not much studied in the liteatue. ence, in this ae, we foce on a two-way A wieless elay netwo consisting of souces with only a single antenna e souce one elay (o base station) with multile antennas. Duing data tansmission, a self-intefeence cancelation ocess at the destinations is alied. In addition, all souces act as both souces destinations. he closed fom of the otimal elay amlifying matix is detemined with the elay tansmit owe constaint based on the Z citeion. he no-owe constaint case of the Z elaying scheme is also investigated. Additionally, the system efomance is evaluated in elation to the aveage bit eo ate (BER) by comute simulation. uthemoe, it is shown that the BER efomance imoves as eithe o inut SR inceases. inally, the tansmit owe consumtion at the elay is studied duing data tansmission. he emainde of this ae is oganized into fou sections. Section II descibes the oosed system model data tansmission stategies. Section III ovides the DOI 0.503/IJSSS.a ISS: x online, int

2 KAGEE LEE et al: ZERO-ORCIG BASED ULIUSER WO-WAY A RELAY EWORK UDER... Z elay scheme fo the distibuted multiuse two-way A wieless elay netwo unde the tansmit owe constaint at the elay. In addition, the no-owe constaint case of the Z elaying scheme is also esented. Section IV shows the aveage BER elay owe consumtion esults. inally, Section V concludes the ae. II. SYSE ODEL AD DAA RASISSIO division dulex is emloyed fo data tansmission. In othe wods, thee ae two time slots fo one exchange of infomation between the left souces (gou ) the ight souces (gou ) though the elay. In the fist time slot, all souces boadcast thei signal vectos s C = s,,, s, s C = s,,, s, multilied by diagonal tansmit ecode matices A C A C, i.e., d = A s d = A s, to the elay, simultaneously, with E s = E s =, whee a E[ ] ae denoted by the -nom of a vecto a the exectation oeato, esectively. he eceived signal vecto C at the elay inut can be witten as d d v s (5) ig.. Distibuted multiuse two-way A IO wieless elaying netwo unde elay owe constaint. igue shows the distibuted multiuse two-way A wieless elay system consisting of souces with only a single antenna e souce, exchanging thei infomation with each othe, a elay (o base station) with multile antennas to hel thei eliable communications, whee ae geate than o equal to fo beamfoming uoses with. ee, all souces act as both souces destinations, as shown in ig.. he comlex channel matices between the souces (gou ) located in the left side of the elay the elay, the souces (gou ) located in the ight side of the elay the elay, the elay the souces located in the left side of the elay, the elay the souces located in the ight side of the elay ae eesented as =,,,,,, C = h,, h,,, h, () () G =,,,,,, (3) G =,,,,,, (4) with, m = h, m,, h, m,,, h, m, h, h, m = h, h,, m,, m,, h, m,, g, m = g, m,, g, m,,, g, m,, g =, m g, m,, g, m,,, g, m,, esectively. ee, atices, vectos, scalas ae denoted, esectively, by uecase boldface, lowecase boldface, italic chaactes (e.g., A, a, a). Additionally, the tansose emitian of A ae denoted, esectively, by A A. he enties of all bacwad fowad channels ae indeendent identically distibuted (i.i.d.) zeo-mean unit-vaiance cicula comlex Gaussian. he time whee v s C is an additive white Gaussian noise (AW- G) vecto with zeo-mean covaiance matix v I. ee, s I is an identity matix. In the second time slot, the elay etansmits its eceived signals to the left ight souces (o called left ight destinations) multilied by an elay amlifying matix fo the linea ocessing oeation. ence, the x tansmitted signal vecto x C at the elay outut is eesented as x = (6) with the aveage total tansmitted owe given by E x =. he eceived signal vectos y C y C at the left ight destinations ae witten, esectively, as y Gx v whee = v,,, v, y G x v (7) v v = v,, v,, ae AWG vectos with zeo-mean covaiance matices I I, esectively. Substituting (5) v v (6) into (7), esectively, the eceived signal vectos y y afte efect cancelation of self-intefeence at the two gous of the destinations can be ewitten, esectively, as y G d G v v (8) s y G d G v v (9) s Accodingly, the detected signal vectos ŷ ŷ DOI 0.503/IJSSS.a ISS: x online, int

3 KAGEE LEE et al: ZERO-ORCIG BASED ULIUSER WO-WAY A RELAY EWORK UDER... alying diagonal eceive decode matices B C B C can be exessed, esectively, as yˆ By BG As BGv s Bv (0) yˆ B y B G A s B G v B v () s he channel state infomation of,, G, G at the elay the destinations can be obtained though stad taining methods fed bac to the souces [9]. In addition, evey channel coefficient is assumed to be invaiant duing data tansmission. uthemoe, the eigen beamfoming can be alied if two souces (o destinations) have efect nowledge of bacwad fowad channel coefficients [0]. ence, using the eigen beamfome, the diagonal enties of the diagonal A A at two souces can be obtained as the ight singula vectos coesonding to the lagest singula value of, while those of the diagonal B B at two destinations can be obtained as the left singula vectos coesonding to the lagest singula value of G G. In the next section, the otimal elay amlifying matix will be detemined by using the Z citeion with the elay tansmit owe constaint, whee the suescit means the otimum. III. Distibuted Z Relay Stategy In this section, we conside the Z citeion to effectively eliminate channel intefeences with ignoing noise. he numbe of elay antennas should be equal o geate than the numbe of souces, i.e.,, since the an of the elay amlifying matix should be the same as the numbe of souces to effectively mitigate channel intefeences. Let b C c C denote A A BG BG, i.e., G G b 4 3 c 3 4 with 3 A, 4 A, G3 BG, G4 BG, esectively. Additionally, using the singula value decomosition oeation [], the b c can be witten, esectively, as Σ U U V U Σ V () b Γ V (i.e., c U Σ Γ U Σ V V (3) whee UU I UU U U I ) VV I VV (i.e., VV I ) such that UU VV ae unitay matices. ee, the dimensions of V, U, Σ, Σ ae,,,, esectively. Additionally, Γ Γ ae matices consisting of all zeo enties, esectively. In aticula, Σ Σ ae, in fact, diagonal matices, whee all enties ae the squae oot of the ositive eigenvalues of , esectively. In addition, V V V U U U ae unitay matices with V i V i UiU i I, i =,. Using () (3), G, = 3, 4, can be witten, esectively, as UΣV i i i G U Σ V,,. (4) ence, using (4), the otimal elay amlifying matix can be witten, using the singula value decomosition oeation, as V V Ω Ω U Ω Ω U (5) whee the dimensions of Ω, Ω, Ω, Ω ae,,,, esectively. Afte substituting (4) (5) / into AA AA v I, it s can be easily obseved that the aveage total owe consumtion at the elay deends only on the Ω, i.e., vs / Ω Σ I. amely, only the Ω in (5) needs to minimize on elay owe consumtion, i.e. Ω, Ω, Ω consist of all zeo enties with the aoiate dimensions, esectively. hus, the can be witten as VΩU. (6) In (6), Ω is a nondiagonal matix with an. o cancel channel intefeences, the effective channel matix should be educed to a diagonal matix. Accodingly, using the Z citeion with, Ω can be obtained as Ω Σ U VΣ (7) with the aveage total elay owe nomalizing coefficient DOI 0.503/IJSSS.a ISS: x online, int

4 KAGEE LEE et al: ZERO-ORCIG BASED ULIUSER WO-WAY A RELAY EWORK UDER... given by Σ U VΣ Γ / (8) the elay is set to with = = ~ 4. It is assumed that all nodes have the same themal noise owe, i.e.,. vs v v whee ΓΣΣ v I. s ee, is an effective channel gain facto the invese of a squae matix A is denoted by A. ence, using (7) (8), the otimal fo the distibuted multiuse two-way Z elaying scheme unde the elay tansmit owe constaint can be witten as ΛΛ Σ U VΣ Γ / (9) whee ΛC VΣ U Λ C V Σ U. he otimal has a lowe comutational comlexity at the elay as well as the destinations. oweve, it equies that, as stated ealie, i.e., an( ) =. ote that the otimal fo the distibuted multiuse two-way Z elaying scheme unde the no-owe constaint can be witten as ΛΛ. (0) In addition, when the two-way Z elaying scheme with the no-owe constaint is emloyed duing data tansmission, the total elay tansmit owe consumtion can be witten ig.. Aveage BER efomance fo = inut SR = 5, 0 db vesus numbe of elay antennas ( = ~ ) in distibuted multiuse two-way A wieless elay netwo unde elay tansmit owe constaint using deived elay amlifying matix in (9). igue esents the aveage BER efomance fo = inut SR = 5, 0 db vesus the numbe of elay antennas ( = ~ ) in the distibuted multiuse twoway A wieless elay netwos unde the elay tansmit owe constaint using the deived elay amlifying matix in (9). he BER efomance imoves as eithe o inut SR inceases. / ΛΛ VΣV VΣV. () It can be seen that the total tansmit owe usage in () deceases as inceases fo a given due to the invese tems Σ Σ inside Λ Λ, esectively. his analytical esult will be veified in Section IV. IV. SIULAIO RESULS he BER efomance is ovided unde the total elay tansmit owe constaint by alying the deived otimal elay amlifying matix. he BER is defined as the BER aveaged ove souces. he comlex channel matices,, G, G ae geneated fom zeo mean unit vaiance i.i.d. Gaussian om vaiables. It is assumed that the oiginally tansmitted signals fom souces ae modulated by quadatue hase shift eying with unity owe. he total tansmit owe constaint at ig. 3. BER comaison elay owe consumtion fo = inut SR = 0 db vesus numbe of elay antennas ( = 6 ~ 4) in distibuted multiuse two-way A wieless elay netwo without owe constaint using (0). igue 3 ovides the BER comaison the elay owe consumtion fo = inut SR = 0 db vesus numbe of elay antennas ( = 6 ~ 4) in the DOI 0.503/IJSSS.a ISS: x online, int

5 KAGEE LEE et al: ZERO-ORCIG BASED ULIUSER WO-WAY A RELAY EWORK UDER... distibuted multiuse two-way A wieless elay netwo without owe constaint using (9) duing data tansmission. he total elay owe consumtion deceases conveges as inceases fo given inut SR. As a esult, the BER efomance conveges as inceases fo given inut SR. In addition, fom this esult, it can be seen that owe is constained duing data tansmission even though the otimal elay amlifying matices deived with the no-owe constaint ae alied. 5, , ay 006. [] J. R. Schott, atix Analysis fo Statistics. nd ed., oboen, J: V. COCLUSIO his ae investigated the distibuted multiuse twoway A wieless elaying stategy unde the elay tansmit owe constaint. he closed fom of the otimal elay amlifying matix was detemined by the Z citeion. Additionally, duing data tansmission, a selfintefeence cancelation ocess was caied out at the two gous of the destinations. It was seen that the gain of divesity ode can haen as eithe o SR inceases fo a given. uthemoe, the no-owe constaint case of the Z elaying scheme was also investigated. inally, the tansmit owe consumtion at the elay is studied duing data tansmission. REERECES [] D. S. Guja P. K. Uadhyay, Imact of channel estimation eo on zeo-focing-based multile-inut-multile-outut two-way elaying, IE Signal Pocessing, vol. 0, no. 3,. 0-7, ay 06. [] A. Abdel-Samad,.. Davidson, A. B. Geshman, Sum ate analysis of two-way IO A elay netwos with zeo-focing, IEEE ansactions on Wieless Communications, vol., no. 9, , Aug. 03. [3] D. S. Guja P. K. Uadhyay, Outage efomance of zeo focing based IO two-way elaying with channel estimation eo, Poceedings of IEEE GLOBECO, umbai, India, eb. 04. [4]. Unge A. Klein, On the efomance of two-way elaying with multile antenna elay stations, Poceedings of IEEE IS 007, Budaest, ungay, July 007. [5]. Unge A. Klein, Linea tansceive filtes fo elay stations with multile antennas in the two-way elay channel, Poceedings of IEEE IS 007, Budaest, ungay, July 007. [6]. Roeme. aadt, Algebaic nom-maximizing (AOAX) tansmit stategy fo two-way elaying with IO amlify fowad elays, IEEE Signal Pocessing Lettes, vol. 6, no. 0, , Oct [7] X. Wang X-D. Zhang, Otimal beamfoming in IO twoway elay channels, Poceedings of IEEE GLOBECO 00, iami, L, Dec. 00. [8]. Lee,. Pa, J. Chun, Linea ecode decode design fo two-way A IO elay system, Poceedings of IEEE VC Sing 008, aina Bay, Singaoe, ay 008. [9].. Gao, R. Zhang, Y. C. Liang, On channel estimation fo amlify--fowad two-way elay netwos, Poceedings of IEEE GLOBECO, ew Oleans, Louisiana, Dec [0] A. Abdel-Samad,.. Davidson, A. B. Geshman, Robust tansmit eigen beamfoming based on imefect channel state infomation, IEEE ansactions on Signal Pocessings, vol. 54, no. DOI 0.503/IJSSS.a ISS: x online, int