Transceiver Design for Cognitive Full-Duplex Two-Way MIMO Relaying System

Transcription

1 Transcever Desgn for Cogntve Full-Duplex Two-Way MIMO Relayng System by Nachket Ayr, Ubadulla P n 07 IEEE 85th Vehcular Technology Conference: VTC07-Sprng Report No: IIIT/TR/07/- Centre for Communcatons Internatonal Insttute of Informaton Technology Hyderabad , INDIA June 07

2 Transcever Desgn for Cogntve Full-Duplex Two-Way MIMO Relayng System Nachket Ayr and P. Ubadulla Sgnal Processng and Communcaton Research Center (SPCRC), Internatonal Insttute of Informaton Technology (IIIT), Hyderabad, Inda. Abstract In ths paper, we present the desgn of optmal precoders and receve flters for a full-duplex (FD) two-way amplfyand-forward (AF) multple-nput multple-output (MIMO) relayng system n a cogntve rado network. The secondary user (SU) or cogntve nodes share the spectrum wth the lcensed prmary user (PU) nodes whle keepng the nterference to PU nodes below a threshold. The cogntve transcevers communcate wth each other wth the assstance of a cogntve AF relay. The precoders for the cogntve transcevers are desgned so as to maxmze the sgnal to nose rato (SNR) at the relay whle lmtng the nterference to the PU node below a specfed threshold. Due to FD mode of operaton, all the nodes suffer from self-nterference (SI). We assume the avalable channel state nformaton (CSI) of loopback self-nterference channels at relay and transcevers to be mperfect. We desgn the optmal relay precoder and transcever receve flter, for suppressng the resdual SI, by mnmzng the sum of mean square error (SMSE) at the cogntve transcevers wth constrant on transmt power at relay. The precoders and receve flters are updated at each tme slot, takng nto account the cumulatve nterference effect from all prevous tme slots, whch enhances the performance of the system over tme. The smulaton results llustrate the effectveness of the proposed desgn n terms of the achevable sum-rate. I. INTRODUCTION In-band full-duplex wreless communcaton has the potental to double spectral effcency by smultaneous transmsson and recepton on the same frequency and tme resource. Recent mprovements n self-nterference cancellaton (SIC) technques [],[] have made MIMO FD systems vable. Hence, FD s regarded as one of the promsng technologes for the next generaton wreless networks. Relayng technques have been nvestgated as a means to facltate better qualty of servce, mproved lnk capacty, and enhanced network coverage. Cooperatve relayng, where one or more relay nodes are used for communcaton between end users, s envsoned to be a key enablng technology for 5G. Two-way n-band full-duplex relayng [] ncorporates the merts of both these technologes. In a two-hop two-way FD AF relayng system, two transcevers transmt and receve smultaneously on the same frequency n each tme slot, wth the ad of a FD relay. The two-way FD AF MIMO relayng system consstng of a MIMO relay, but sngle antenna transcevers s studed n [4]. A smlar system n [5] comprses of two MIMO Ths work was supported n part by the Vsvesvaraya Young Faculty Research Fellowshp, Department of Electroncs and Informaton Technology (DetY), Government of Inda. transcevers and a MIMO relay, wheren the beamformers at relay and transcevers were jontly desgned for mnmzng the SMSE at the two transcevers. The effect of path loss on the system desgn s neglected n these and most of such prevous work on two-way FD AF MIMO relayng. Cogntve rado technology enhances the spectrum utlzaton n wreless communcatons. The secondary users n a cogntve rado network operate under a severe power constrant n order to lmt the nterference to the prmary user. In such a scenaro, FD two-way relayng, whch has better effcency than one-way relayng, wll be benefcal to enhance the range as well as rate of communcaton A robust MSEbased transcever desgn problem for a one-way FD MIMO cogntve cellular system was studed n [6], where the relay base staton was FD, but the transcevers were operatng n half-duplex (HD) mode. The problem of sum-rate maxmzaton for a HD two-way relayng cogntve rado network was studed n [7] for a MIMO relay and sngle antenna secondary transcevers and prmary user. In ths paper, we present the desgn of a cogntve two-way n-band FD AF relayng MIMO system wth two secondary transcevers, one secondary relay, and a prmary user. Frst we desgn the precoders at the secondary transcevers by maxmzng the SNR at the secondary relay, whle keepng the total nterference to the prmary user node, due to the operaton of cogntve nodes, under a threshold. Then, we jontly desgn the precoder at the relay and the receve flters at the secondary transcevers by mnmzng the SMSE at the secondary transcevers. Ths problem s non-convex n nature. Fnally, we analyze the performance of the proposed desgns n a LTE cellular cogntve network scenaro, n terms of the achevable transmt power effcency and sum-rate. The man contrbutons of ths paper are twofold: () prmary user nterference constraned precoder desgn and power optmzaton at the transcevers, and () recursve computaton of relay precoder, receve flters wth mnmal memory requrements. The rest of ths paper s organzed as follows. Secton II descrbes the system model. The desgn of optmal precoders and receve flters s dscussed n Secton III. Smulaton results are presented n Secton IV and the conclusons n Secton V. Notatons : We denote a scalar, vector, and matrx by talc lowercase, boldface lowercase, and boldface uppercase, respectvely. For a matrx Y, ts transpose, conjugate, conjugate transpose, nverse, determnant, vectorza /7/$ IEEE

3 ton operaton, trace, and Frobenus norm are denoted by Y T, Y C, Y H, Y, Y, vec(y), tr(y), Y F, respectvely. X Y represents the kronecker product of matrces X and Y. E{ } s the expectaton operator, y represents -norm of y, mat( ) performs the nverse operaton of vec( ). If a varable m =, then m = and vce versa. Tme-slot dependent varables b, b, B denote a scalar, vector, matrx, respectvely, n the current tme slot t, whle b (j), b (j), B (j) denote a scalar, vector, matrx,respectvely, n any tme slot j. II. SYSTEM MODEL We consder a cogntve two-way FD relayng system as shown n Fg.. The system comprses of a prmary user P, two secondary transcevers S, S ; and a secondary AF relay R. Nodes P, S and S are each equpped wth N s antennas. Relay R has N r antennas, of whch N s antennas are used for sgnal recepton whle all N r antennas are used for sgnal transmsson, such that N r N s. All the nodes operate n FD mode, on the same frequency whch was ntended for use by P only. We assume that there s no drect communcaton lnk between the secondary nodes S and S, and so all ther communcaton happens va the relay R. All the channel lnks are modeled as ndependent and frequency-flat Raylegh fadng channels and are assumed to be statc for the duraton of each tme slot. The matrx G j represents the MIMO channel matrx between transmtter and recever j. Thus, the matrces G mr C Ns Ns, G rm C Ns Nr, G np C Ns Ns and G pn C Ns Ns, m {,, p}, n {, }, represent the MIMO channels as shown n Fg.. These channel matrces are assumed to be perfectly known. The matrces G rr C Ns Nr and G mm C Ns Ns, m {,, p}, represent the loopback self-nterference MIMO channels. We assume that the avalable CSI of the loopback channels s mperfect, such that G jj = Ĝjj + Φ j, j =,, p, r, () where Ĝjj s the avalable channel estmate and Φ j s the CSI error wth zero mean and covarance E{Φ j Φ H j } = N sσej I N s [8]. The symbol α j represents the path loss between nodes and j;, j {,, p, r}, such that α j = α j. We assume α =and t wll be not be explctly mentoned henceforth. Durng each tme slot t the followng events occur : () The prmary user P transmts sgnal x p C Ns whch acts as nterference for all the secondary nodes. () Each secondary transcever precodes data vector d m C Ns havng covarance E{d m d H m} = I Ns wth precodng matrx T m C Ns Ns to generate x m, m {, }, and transmts t to R, where the sgnal receved s gven by y r = α r G r x + α r G r x +G rr x r + α pr G pr x p +n r, () where the nose n r s a crcularly symmetrc complex Gaussan random vector wth zero mean and covarance E{n r n H r } = σnri Ns. The sgnal at the relay after SIC s gven by ỹ r = α r G r T d + α r G r T d + Φ r x r + αpr G pr x p + n r. () The thrd term n () refers to the resdual SI due to error n the avalable loopback CSI as modeled n (). Fg. : System dagram of a FD two-way cogntve rado network. () The secondary AF relay precodes the sgnal receved n the prevous tme slot, y r (t ), usng the precodng matrx F C Nr Ns and transmts the resultng sgnal x r = Fỹ r (t ), t. (4) (v) Each secondary transcever receves the relay sgnal as y m = α rm G rm x r +G mm x m + α pm G pm x p +n m,m=,, (5) where nose n m s a crcularly symmetrc complex Gaussan random vector wth zero mean and covarance E{n m n H m} = σnmi Ns. Snce, each secondary transcever has knowledge of ts own transmtted sgnals, d m (t ) and x m,aswellasofcsi αrm G rm, Ĝmm, and F, t cancels out the SI resultng n ỹ m = α rm G rm F{ α mr G mr (t ) T m (t ) d m (t ) + Φ (t ) r x (t ) r + n r (t ) } + Φ m T m d m + α pm G pm x p + n m. (6) Here agan, the resdual SI s represented by the term contanng Φ m. Each secondary transcever then apples a receve flter V m C Ns Ns to ỹ m to obtan an estmate of the data, ˆd m, transmtted by the other secondary transcever. (v) The sgnals transmtted from the secondary nodes cause nterference at the prmary transcever. The total power of nterferng sgnals at P s I p = I + I + I r, (7) where, I m = α mp tr(g mp x m x H mg H mp), m =,, r. (8) III. DESIGN OF OPTIMAL PRECODERS AND RECEIVE FILTERS In ths secton, we present the proposed desgn of the relay precoder F, the transcever precoders T and T, and the transcever receve flters V and V. A. Transcever Precoder Desgn We start wth the QR-decomposton of the hermtan of the MIMO channel matrx G mr as: G H mr = Q m R m. Then, the precoder matrces are gven by T m = β m Q m W m, m =,. (9) and the resultant transmt power s gven by P m = E{ T m d m } = β mtr(w m W H m), m =,, (0) where, the scalng factor β m wll be derved n the sequel and W m s derved from R m such that: G mr T m = β m I Ns. ()

4 We desgn T, T by maxmzng the receved SNR at R under a constrant on total nterference power, I p, at P and bounds on transmt power of S, S. The constrant on I p s I p θ, () where, θ s the maxmum permssble nterference to P from all the secondary nodes n a cogntve scenaro. From (7), (8), (9), (0) and (), () can be wrtten as θ α p G p x + α p G p x + α rp G rp x r = α p β b + α p β b + α rp p r G rp F, () where, b m = tr(g mp Q m W m WmQ H H mg H mp),m {, } and E{x r x H r } = p r I Ns, where, p r s the per-antenna power of R. As wll be seen n the next secton, R always transmts full power, such that p r = Pr max /N r = p max r. (4) As a result, () can be wrtten as α p βb + α p βb θ α rp p max r G rp F = θ. (5) Equaton (4) s also the reason for choosng SNR R as the functon to be maxmzed. Snce R s always transmttng at full power, we optmze P, P to lmt the nterference at P. From () and (), the SNR at R at tme t s gven by: SNR R = α rβn s + α r βn s σnrn. (6) s We observe that maxmzng the SNR at the relay s same as maxmzng the sgnal power n (6), for fxed nose power. So, the optmzaton problem can nstead be formulated as: α r βn s + α r βn s max β,β subject to α p β b + α p β b θ P mn m P m P max m,m=,. (7) The problem n (7) s a lnear optmzaton problem n β and β and can be easly solved by a optmzaton tool such as lnprog n MATLAB. The optmal values thus obtaned are β and β. The correspondng optmal precoder matrces and optmal transmt power are gven by (9) and (0), respectvely. B. Relay Precoder and Transcever Receve Flter Desgn We desgn F, V, V by mnmzng the SMSE of the transcevers S, S, wth a constrant on the transmt power of relay R. MatrxF s decomposed as F = γ F, where γ s a postve scalng factor and F F =. Ths decomposton smplfes the dervaton of the relay precoder n closed form. For the same reason, the term γ s ntroduced n (9). Thus, the SMSE = f(γ, F, V, V ). The optmal desgn s obtaned by solvng the followng optmzaton problem: mn f(γ, F, V, V ) γ, F,V,V (8) subject to E{ x r } Pr max. Due to space constrants, throughout ths paper we ll denote (α r β (j) + α r β (j) + σnr)i Ns + α pr p (j) p G (j) pr G (j)h pr by Ψ (j). The SMSE of the two transcevers s gven by f(γ, F, V, V ) = = E{ d (t ) γ ˆd } = = E{ d (t ) } + γ E{ V H ỹ } γ [tr(e{v H (t )H ỹd })+tr(e{d (t ) ỹ H V })]. (9) To proceed further, we express each term of SMSE equaton n terms of the relevant optmzaton varables. Thus, E{ d (t ) } = N s, E{d (t ) ỹ H V } = β (t ) αr α r tr(f H G H r V ). (0) Further, usng (6) and (), we have E{ V H ỹ } = α r tr[v H G r F(E{J 0 } + α r β (t ) I Ns + σnri Ns + α pr p p (t ) G pr (t ) G (t )H pr )F H G H r V ]+σntr(v V H ) + E{tr(V H Φ T d d H T H Φ H V )}+ α p p p tr(v H G p G H pv ), () where, t J 0 = k=0 t k l= t k Φ r (t l) F (t l) Ψ (k) l= F (k+l)h Φ (k+l)h r. () for t and 0 Ns for t =,. In ths paper, t s assumed that b =a ( ) =,fb<a. Usng Lemma from [9] and proceedng as n Theorem from [5], we obtan E{J 0 } as: t J q = E{J 0 } = (σer) k tr(f (t k) Ψ (t k ) F (t k)h )I Ns k= k tr(f (t l) F (t l)h ), () l= The term J q represents the contrbuton of all prevous F (k), t =onwards, whch s requred to suppress the SI caused by FD operaton. Snce, the frst F s computed at t =,thevalue of J q s 0 Ns for the frst two tme slots. After a few algebrac manpulatons on (), J q can be recursvely computed as J q =σer[tr(f (t ) Ψ (t ) F (t )H )I Ns + J q (t ) tr(f (t ) F (t )H )]. (4) The recursve structure of J q plays a sgnfcant role n the desgn of F, V. As a consequence, the nodes need not store all the prevous relay precoders and transcever receve flters. Ths not only greatly reduces the memory requrement at the relay but also results n reduced computaton tme for J q. Moreover, the precoder desgned usng (4) wll lead to better performance than that of the system proposed n [5] where only the n latest tme slots are used for computng J q. Usng Lemma from [9] and (0), we can rewrte the second to last term of () as E{tr(V H Φ T d d H T H Φ H V )} = σep tr(v V H ). (5) Usng (), (4), (), we express the relay transmt power as E{ x r } = tr[f(j q + Ψ (t ) )F H ]=tr(fj r F H ). (6) Havng expressed the terms of SMSE and relay transmt power n terms of the optmzaton varables, we now turn to

5 .8 α p / dstance -9dBm/700m -05dBm/500m Transmt power P (W) SMSE θ = -94dBm INR=0 INR=0. INR= INR= θ (dbm) Fg. : Varaton of transmt power versus θ, for dfferent values of path loss. the soluton of the problem n (8). The Lagrangan correspondng to ths problem s gven by L(γ, F, V, V,λ) = f(γ, F, V, V )+λ(e{ x r } Pr max + z ), (7) where λ s the lagrangan varable and z s the slack varable. On substtutng the results of (9), (0), (), (6), (),(5) n (7) and puttng F = γ F, we get L = {N s β (t ) αr α r tr(v H G r F + FH G H r V )+ = γ (σn + σep )tr(v V H )+α p p p tr(v H G p G H pv ) + α r tr(v H G r FJ FH G H r V } + λ[γ tr( FJ FH r ) Pr max + z ], (8) where J = J q +(α r β (t ) + σ nr)i Ns + α pr p (t ) p G (t ) pr G (t )H pr. The optmzaton problem n (8) can be solved usng the Karush-Kuhn-Tucker (KKT) condtons [0]. Snce the SMSE functon s not jontly convex n the optmzaton varables, we use the coordnate descent method. Thus, the optmal values of F, V, {, }, are obtaned teratvely. Frst, keepng V fxed, we apply the KKT condtons to get: γ =0 λγtr( FJ FH r )=γ (v + v ), (9) where v =(σn + σep )tr(v V H ) F = 0 c N r N s α r α r (β (t ) G H rv + β (t ) G H rv ) = λγ FJr + α r G H rv V H G r FJ + α r G H rv V H G r FJ. (0) λ =0 tr( FJ FH r )=γ (Pr max z ). () z =0 λ[γ tr( FJ FH r ) Pr max ]=0. () Now, from (9) and (), we observe that at optmal pont, λ = 0 and so the constrant n (8) becomes equalty constrant,.e., the relay R transmts at full power Pr max. So, () becomes: tr( FJ FH r )=γ (Pr max ). () Now, from (9) and (), we get: λγ = (v+v) P. Substtutng r max ths value n (0) and followng Theorem of [5], we get Number of teratons Fg. : Number of teratons requred to obtan optmal F,V, for dfferent values of INR, for θ = -94dBm and SNR = 5dB. F =mat(m α r α r vec[β (t ) G H rv +β (t ) G H rv ]), (4) where M =(J T α r G H rv V H G r )+(J T α r G H rv V H G r ) γ = +(J T r (v + v )I Nr Pr max ), P max r tr( FJ r FH ). Therefore, optmal relay precoder s gven by F = γ F. Now, usng the optmal F, we compute optmal receve flters by applyng the KKT condton: V =0 c Ns, {, }, whch gves the optmal receve flter at the transcever as: V =[(σn + σep )I Ns + α r G r F J F H G H r ] γ α r α r β (t ) G r F. (5) It must be noted that the optmal matrces F, V are obtaned by teratvely computng each other s flter untl a stable value of SMSE s reached. The ntal value of V for computng F can be any random N s N s complex matrx. IV. SIMULATION RESULTS For smulatons, we consder the followng parameters: N s =, N r =4, p max r =,Pj mn =0.6,Pj max =,j {, }. σem = INRσ nm P,m {,, r}. σnr = αrβ +αrβ SNR, σn = αrpr Gr F N s SNR, {, }. We consder the path loss as defned by the GPP LTE for outdoor macro cells [], vz., α = log 0 (d)db, where d s the dstance between nodes, n metres, at an operatng frequency of GHz. We consder α r = α r,α p = α p = α rp. We assume the MIMO channel matrces G mr, G rm,m {,, p}, G np, G pn, n {, } and channel estmaton error matrces φ j,j {,,r,p} to follow Raylegh fadng and ther elements to be ndependent and dentcally dstrbuted complex Gaussan random varables, each wth zero mean and unt varance. Unless specfed otherwse, we consder α r = -9dBm and α p = -0dBm. Around 000 Monte Carlo smulatons were averaged to arrve at each of the results. Fg. shows the varaton n transmt power of the transcever versus prmary user nterference threshold θ for

6 SMSE θ = -9dBm INR=0 INR= INR=5 INR= tme slots Fg. 4: Varaton of SMSE over tme, for dfferent values of INR, at θ = -9dBm and SNR = 0dB. SMSE INR / θ 0.5/-9dBm 5.0/-9dBm 0.5/-94dBm 5.0/-94dBm SNR (db) Fg. 5: SMSE, n the 7 th tme slot, versus SNR, for dfferent values of INR and θ. dfferent values of path loss α p. As expected, the transmt power ncreases wth ncrease n tolerance lmt of P. Fg. llustrates the number of teratons requred, n the 7 th tme slot, to obtan the optmal value of F and V m,m {, }, at SNR = 5dB, at dfferent INR values and θ = - 94dBm. We observe that begnnng wth any random complex x matrx V m, the SMSE converges after 6 teratons for all the INR values.ths makes the desgn of optmal flters vable. Fg. 4 descrbes the performance of the system over tme. It shows the varaton of SMSE, for dfferent INR values, wth θ = -9dBm. The SMSE stablzes from th tme slot due to the effect of feedback term J q, whch starts from t =. We evaluated the SMSE and sum-rate performance of the system versus SNR for dfferent values of INR and θ and the results are as shown n Fg. 5 and Fg. 6, respectvely. The equaton for sum-rate s smlar to that n [5], but wth path loss ncluded and effcent computaton. The proposed desgns exhbt good SMSE and sum-rate performance at low INR values. Ths hghlghts the need for precodng wth multple antennas to suppress the resdual SI. As seen n Fg. 6, the sum-rate tends to saturate above SNR = 5dB. Also, as expected, the system performs better at hgher values of θ. V. CONCLUSION We consdered a full-duplex two-way MIMO relayng system n a cogntve rado network, operatng under transmt power constrants. We desgned the optmal precoder matrces SUM-RATE (bts/sec/hz) INR / θ 0.5/-9dBm 5.0/-9dBm 0.5/-94dBm 5.0/-94dBm SNR (db) Fg. 6: Sum-rate, n the 7 th tme slot, versus SNR, for dfferent values of INR and θ. for the cogntve transcevers, based on SNR maxmzaton at the cogntve relay, to restrct prmary user nterference. We also proposed the optmal desgn of cogntve relay precoder and receve flters for the cogntve transcevers, based on SMSE mnmzaton, to curb resdual SI. To compensate for the contnuously varyng SI at the nodes, the relay precoder and receve flter matrces need to be updated n each tme slot wth the feedback from all the prevous tme slots. We presented an teratve technque for ths update, havng low memory requrement and hgh computatonal effcency. The performance of the proposed desgns was llustrated n the smulaton results for dfferent operatng condtons. The proposed desgns provde power effcency wth hgh sum-rate. REFERENCES [] D. Bharada and S. Katt, Full duplex MIMO rados, n th USENIX Symposum on Networked Systems Desgn and Implementaton (NSDI 4), 04, pp [] T. Rhonen, S. Werner, and R. Wchman, Mtgaton of loopback selfnterference n full-duplex MIMO relays, IEEE Transactons on Sgnal Processng, vol. 59, no., pp , 0. [] G. Lu, F. R. Yu, H. J, V. C. Leung, and X. L, In-band full-duplex relayng: A survey, research ssues and challenges, IEEE Communcatons Surveys & Tutorals, vol. 7, no., pp , 05. [4] G. Zheng, Jont beamformng optmzaton and power control for fullduplex MIMO two-way relay channel, IEEE Transactons on Sgnal Processng, vol. 6, no., pp , 05. [5] Y. Shm, W. Cho, and H. Park, Beamformng desgn for full-duplex two-way amplfy-and-forward MIMO relay, IEEE Transactons on Wreless Communcatons, vol. 5, no. 0, pp , Oct 06. [6] A. C. Crk, S. Bswas, O. Taghzadeh, A. Lu, and T. Ratnarajah, Robust transcever desgn n full-duplex MIMO cogntve rados, n Proc. IEEE Internatonal Conference on Communcatons (ICC). IEEE, 06, pp. 7. [7] D. Jang, H. Zhang, D. Yuan, and Z. Ba, Two-way relayng wth lnear processng and power control for cogntve rado systems, n Proc. IEEE Internatonal Conference on Communcaton Systems (ICCS). IEEE, 00, pp [8] P. Ubadulla and A. Chockalngam, Robust THP transcever desgns for multuser MIMO downlnk, n 009 IEEE Wreless Communcatons and Networkng Conference, Aprl 009, pp. 6. [9], Relay precoder optmzaton n MIMO-relay networks wth mperfect cs, IEEE Transactons on Sgnal Processng, vol. 59, no., pp , 0. [0] S. Boyd and L. Vandenberghe, Convex Optmzaton. Cambrdge, U.K.: Cambrdge unversty press, 004. [] European Telecommuncatons Standards Insttute (ETSI). LTE; Evolved Unversal Terrestral Rado Access (E-UTRA); Rado Frequency (RF) requrements for LTE Pco Node B (GPP TR 6.9 verson.0.0 Release ). [Onlne]. Avalable: