Relay Deployment for AF-MIMO Two-Way Relaying Networks with Antenna Selection

Journal of Counications Vol 9, o 7, July 04 elay Deployent for AF-MIMO Two-Way elaying etworks with Antenna Selection Yizhen Zhang,, Guobing Li, Guoei Zhang, Ganging Lv, and Chao Zhang, School of Electronics and Inforation Engineering, Xi'an Jiaotong University, Xi'an, 70049, China ational Mobile Counications esearch Laboratory, Southeast University, anjing, 0096, China Eail: zhangyizhen0@6co; {gbli, zhangg, glv, chaozhang}@ailxjtueducn Abstract In this paper the outage-optial relay deployent proble for aplify-and-forward (AF) ulti-input ulti-output (MIMO) two-way relaying network with antenna selection is studied By utilizing an approxiation of the outage probability, the outage-optial relay location is shown feasible On this basis a relay deployent schee is developed by providing the near-optial relay position in an approxiate closed for Theoretical analysis shows that the optial relay position is affected by the ner of antennas at sources but independent of the ner of antennas at the relay Siulations confir the theoretical analysis and show the perforance gain achieved by the developed relay deployent schee Index Ters AF-MIMO, two-way relaying, antenna selection, relay deployent I ITODUCTIO In half-duplex wireless counication networks, twoway relaying has been well recognized to achieve high spectru efficiency In a two-way relaying network (TW), the syste throughput can be twice as high as that in traditional one-way relay work []-[3] With the utilization of Multi-input Multi-output (MIMO) technique, the spectru efficiency can be further significantly iproved [4] However, the ain drawback of any MIMO syste is the increased syste coplexity due to the additional cost for enabling ultiple transit and receive radio frequency (F) chains [5] For exaple, the bea-foring or other pre-coding algoriths for MIMO TW are greatly challenged by increased coplexity on coputation, signaling overhead as well as the hardware cost on adio Frequency chains [6]-[8] To ake the perforance gain achieved by MIMO ore affordable, antenna selection schees have been proposed to reduce the coplexity of the transitter as well as hardware cost [9]-[0] In [9], a ax-in antenna selection schee is proposed and it is proved that diversi- Manuscript received March 3, 04; revised July 8, 04 This work was supported by the ational atural Science Foundation of China under Grant 60079, 60080, the Industrial esearch Project of Science and Technology of Shaanxi Province under grant 0K06-35, the open research fund of ational Mobile Counications esearch Laboratory, Southeast University under grant 0D4, the Fundaental esearch Funds for the Central Universities, and the ational 863 Progra of China under Grant 04AA0A707 Corresponding author eail: zhangyizhen0@6co doi:070/jc97556-56 ty gain is still achievable with antenna selection at the relay In [0], two antenna selection schees are studied for aplify-and-forward (AF) MIMO two-way relaying networks, both showing high perforance gain in outage probability Moreover, in []-[] MMSE precoders are designed for cooperative two-way relaying networks with ultiple single-antenna and ultiple-antenna half-duplex aplify-and-forward relays In the eantie, relay location/placeent/deployent has been recognized as a non-negligible factor in a twoway relaying network [3]-[6] In [3], the analysis and tests in practical indoor Environents show that even a s-optial relay placeent algorith can iprove the syste perforance In [4], a joint power and location optiization solution for MIMO TW is proposed and shows that optial relay location can bring ore perforance gain copared with optial power allocation In [5], relay location optiization proble is investigated to illustrate the effects on energy efficiency for two-way relaying In [6], it is suggested that the relay is best positioned in the iddle point of the two sources for energy consuption All the studies in [3]- [6] reveal the iportance of relay deployent optiization However, the conclusions in the literature are ade for specific scenarios thus not applied directly to the AF-MIMO two-way relaying network with antenna selection In this paper, utilizing an approxiation of the outage probability for AF MIMO two-way relaying networks with antenna selection, we reveal the feasibility of the outage-optial relay location and developed a nearoptial relay deployent schee by approxiately locating the stationary point of the outage probability as a function of the relay position The near-optial relay position is expressed in closed for so that an insightful discussion can be provided in this paper The reainder of the paper is organized as the following: Section II describes the syste odel In Section III, the near-optial relay deployent schee is studied by the outage approxiation Section VI reports siulation results and Section VII concludes the paper II SYSTEM MODEL We consider an AF-MIMO two-way relaying network with two source nodes and one relay, as shown in Fig, 04 Engineering and Technology Plishing 556

Journal of Counications Vol 9, o 7, July 04 YS GhS,l Y n S, S and are equipped with, and antennas, respectively During the transission, all nodes are assued working in half-duplex ode and channels are assued reciprocal, sei-static and frequency-flat ayleigh fading, ie, the channel state keeps constant within a transission slot for both uplink and downlink while independent identical distributed aong different tie slots In assuption, the channel states of the link between Si i and and the link between and Gaussian, assued between S and S due to heavy path-loss and shadowing, so that any counication between the two sources has to be ipleented by relaying In addition, we assue the additive noise at each receiver is odeled as coplex zero ean white Gaussian noise ( j,l, ) S ( P hs, j / )( PS hs,l / ) ( P / PS / ) hs, j PS hs,l / log( S(j,l, ) ) log( S( j,l, ) ) ( j,l, ) )( S( j,l, ) ) log ( S (4) (5) S Then the best ( J, L, M ) can be obtained by j,l, j,l, {J, L, M } arg ax S S j, l Fig Syste odel of MIMO two-way relaying (6) In the syste odel above, in each transission tie slot, the inforation sybols and, III ELAY DEPLOYMET { } { }, are exchanged between S and the ( j, l, ) denotes, and S, ie, ( J, L, M ), can be selected by the axiization of the syste su rate The instantaneous su-rate of S and S can be expressed as As is known in [0], when the optial relay location is deterined, the best cobination of antenna at S, loss exponent of Si channel o direct link is at we take S as exaple and express its S by ie, distance between Si and, and (,6) denotes path power Gaussian noise at Si Once the signal is received by sstituting () into () and (3) and canceling the so called self-interference before signal detection, the end-to-end signal-noise-ratio (S) at Si i can be derived Without loss of generality, and assued that i ~ (d Si ), d Si i is the S transitting aplification gain, and ni i ~ C (0, i ) is the additive hspi,l ~ C (0, i ) Here i i is the long-tie path loss the hspi,l, the ( p, l ) -th eleent of H Si, is assued coplex is G P /( PS hs, j PS hs,l ) Si i can be denoted by H Si and HTSi, respectively circularly-syetric P (3) In this section, we first derive the closed-for approxiate outage probability by the antenna selection strategy in (6), then use the closed-for outage probability approxiation to study the best position of the relay that achieves globally iniu outage probability As will be shown in this section and siulations, although our study is based on an approxiation of outage probability due to the lack of the accurate closed-for expression, the perforance can still be significantly iproved by the developed relay deployent schee The outage probability can be defined as the probability that the instantaneous su-rate falls below a target rate th which is given by S via two phases In Phase I, the j -th and l -th antenna are selected respectively by S and S to broadcast their corresponding essage and over a ultiple access channel At relay, the ixed signals in the air received by selecting the -th antenna is Y PS hs, j PS hs,l n () Si i is the transitting power at S i, and n is the additive Gaussian noise (AWG) at with zero ean and variance In Phase II, the relay aplifies its received signal with aplifying gain G via its -th antenna and then forward it to Si i In the eantie, this relayed signal is received with j -th antenna of S and l -th antenna of S The received signal can be expressed by YS GhS, jy n Pout P arg ax { j,l, } th P[W th ] (7) j, l W is given by () W and 04 Engineering and Technology Plishing 557 ax j, l S(j,l, ) S( j,l, ) S(j,l, ) S( j,l, )

Journal of Counications Vol 9, o 7, July 04 Therefore the outage probability can be derived through the CDF of W, which will be expressed below in detail When S is sufficiently large, the instantaneous su-rate of MIMO AF TWs can be approxiated as follows: ( j, l, ) log ( j, l, ) ( j, l, ) S S (8) Hence the CDF of approxiated effective S can be derived as F ( ) Pr W ax { } ( J, L, ) ( J, L, ) Pr ax { S } S z ( j, l ) ( j, l ) W S S j, l ext we define ax ( ) ( J, L, ) ( j, l ) S j, l S ( J, L, ) S ax ( ) j, l ( j, l ) S W and then expand it as follows: ( J, L, ) ( J, L, ) W S S 0 XY ( u X Y / )( X u Y / ) S S (, J ) (, j) S S j X h ax ( h ) Y h 0 / ( J, ) S l ( l, ) S ax ( h ), u ( S ) / S u ( + ) / S S In the further, the upper bound of approxiated as F 0 XY W ( u X Y )( X u Y ) (9) (0) W can be u X uy ( u X uy ) 0 uu u X uy ( u X uy ) 0 uu ux uy uu (in( u X, u Y )) W 0 So the CDF of W ( ) F ( ) W u X u Y () W in () can be derived as follows: (in( ux, uy )) Pr W 0 uu ( FX ( 0 u ))( F ( 0 ) Y u () FX ( x ) and FY ( x ) are the CDFs of X and Y x/ which are defined as F ( x) ( e ) and X x/, respectively Further, the CDF of F ( x) ( e ) Y W ax { W } can be derived as follows: F ( ) ( ( 0 )) W FX u ( F ( u) Y 0 0 u exp 0 u exp Thus the corresponding outage probability is P out F ( ) W 0 u exp 0 u exp (3) (4) As can be observed fro (4), the outage probability is clearly a function of the distance between the sources and the relay In the following, the best position of the relay to achieve globally iniu outage probability is analyzed by using the closed-for outage probability approxiation in (4) Letting : 0, we can obtain P out u ( w) exp u exp (5) It can be concluded fro (5) that the optial relay location is irrelevant to the ner of antennas at the relay Further, the iniization of (5) is equivalent to iniizing S u u gd ( ) exp exp u u exp exp (6) A nuerical ethod can be readily developed to get the iniu point and its corresponding distance by exhaust search However, this search is at the price of the 04 Engineering and Technology Plishing 558

Journal of Counications Vol 9, o 7, July 04 high coplexity, which ay not be affordable in practice To reduce the coplexity and offer a deeper insight into the relationship between outage perforance and the location of the relay, in the following the analytical expression of d is developed S Since : 0 is sufficiently sall when S is sufficiently large, the last ter on the right side of (6) can be treated as negligible thus can be reoved away Applying : 0 and considering the optial position ust fall in the line between the two sources, the new optiization proble can be forulated as u ds f ( ds) e (P): iniize u ds e ( ) sject to 0 (7) d S It can be proved that (P) is a quasi-convex proble thus has a unique globally optial solution But still, the proble (P) is not trivial since the coplexity of nuerical ethod is usually not affordable in practical two-way relaying networks with ultiple potential relays To reveal the analytical solution for (P), we first convert this optiization into solving the equation in the following by finding the stationary point of f( d ) So we can take derivation in two sides of S ake it equal to zero to find the stationary point uds uds S e e u d u ( ds) e u ( ds) ( S) e u d S f( d ), and then (8) When S is sufficiently large, we obtain 0, then it is readily known that u ( d S ) e u d S ~ ( ) u d e S ~ u d S, / ( u) For siplicity, letting t yields / ( u ) td S u d S S S d u ( d ) (9) A further approxiation can be perfored by reoving all ters related to since approaches to 0 asyptotically Utilizing the polynoial approxiation of (9), we can obtain td ( d ) (0) S S which sees quite a siple expression at first sight Unfortunately, it has been well-known that there is no atheatical general solution for (0) for arbitrary and evertheless, it is clear that definitely there exists a solution for (0) since f ( d S ) is continuous and f (0) 0, f () 0 To approxiate the solution, we rewrite (0) into an equivalent for, which is ln t ( ) ln d ( ) ln( d ) () S S and fit ln d S and ln( d ) S into polynoial fors by 3 using ln( x) ax bx O( x ) for x It is tested that for / x 0, a, b 03 is an acceptable pair of fitting factor; for x /, the fitting factors a, b can be found in a siilar way So when, the optial approxiated by S d can be S d / ln t / ( a b)( ) (a) while when, the optial d S will be less than /, which coincides with the siulation results in [0] So when, the optial d can be approxiated by d S S 4 [ln t 4 ( a b) ( a b)] (b) b( ) a ( ) b ( a b) As a result of (), the optial distance between the relay and the source S is a function of transitting power and the ner of antennas at sources, but irrelevant to the ner of antennas at the relay, which iplies that, once the source nodes are paired for twoway relaying, the optial location of the relay is predeterined On this basis, the relay can be deployed in this near-optial position to achieve perforance gain Furtherore, in the scenarios with ultiple potential relays, since a relay closer to this near-optial relay position achieves better outage perforance, the proposed near-optial relay position can also help with quick relay selection IV SIMULATIO ESULTS In this section, nuerical results and Monte-Carlo siulations are provided to reveal the perforance gain brought by the developed relay deployent schee Without loss of generality, in the siulation the path loss exponent is set to 35 ; the variances of the noise are equally allocated to the sources and the relay; the overall target rate of the syste is set to 5 bps / Hz (iplying the target rate of the each source node is 5 bps / Hz ) 04 Engineering and Technology Plishing 559

Journal of Counications Vol 9, o 7, July 04 =,=,= =,=,= =,=,= =,=,= =,=,=3 =,=3,=, but which is consistent with each other Again, the optial relay location will also be closer to the source with less power in any antenna configuration of the two sources Moreover, Fig and Fig 3 show that the approxiations of the outage probability is very close to the Monte-Carlo siulation results, which eans although our study is based on the approxiate expressions of outage probability, the derived nearoptial relay position is actually very close to the optial one 0 0 0 - Approxiate optial position Siulated optial position =,=,= Fig Outage probability against the distance antenna equient when S is 079dB and P P P =,=,= =,=,= d S with various S S =,=,= =,=,= Overall Outage Probability 0-0 -3 0-4 =,=,= 0-5 =,=3,= 0-6 0 4 6 8 0 4 6 8 0 S Fig 4 Outage probability when the relay is deployed at the proposed position and the actual optial position with P P P S S =,=,=3 =,=3,= Fig 3 Outage probability against the distance antenna equient when S is 079dB, P S d S with various P /3 and P S P / 3 Fig and Fig 3 show the overall outage probability against the distance d with various antenna equipent, S both analytical approxiations and Monte-Carlo siulations are presented when S is 079dB, the transitting power is P P P and P P /3, P S S S P / 3, respectively As expected, Fig and Fig 3 all confir that, the optial position of the relay is independent of the ner of the relay since (,, ) (,,) and (,3,) share the sae optial position Further observation fro Fig finds that when the antenna configuration of the two sources is syetric, ie,, the outage-optial relay deployent solution is to put the relay in the half-way between the two sources; while when the antenna configuration of the two sources is asyetric, ie,, the optial relay location will be closer to the source with less antennas -- this coincides with the analytical results in () On the other hand, we can also observe fro Fig 3 that when the transitting power of the two sources are in-equivalent, the optial relay location will have a slight difference with the situation in Fig S Overall Outage Probability 0 0 0-0 - 0-3 0-4 Approxiate optial position Siulated optial position =,=,= =,=,= 0 4 6 8 0 4 6 8 0 S Fig 5 Outage probability when the relay is deployed at the proposed position and the actual optial position with P S =P /3 and P S =P /3 In Fig 4 and Fig 5, the outage probability of the developed approxiate relay position is presented copared with Monte-Carlo siulation with different S Fig 4 shows that the outage probability of the proposed relay deployent schee is very close to the actual optial one when the transitting power of the two sources and relay are the sae For exaple, when the S is around 0dB, the approxiate relay position is alost the sae as the actual globally optial one when the antenna configuration of the two sources and the relay is, and, respectively Moreover, the sae conclusion also stands when the transitting power is allocated unequally in Fig 5, the transitting power of the two sources and relay are P P /3, P P / 3, respectively The observations S S 04 Engineering and Technology Plishing 560

Journal of Counications Vol 9, o 7, July 04 above verify that the developed schee only brings negligible perforance loss thus is applicable in practice To further reveal the perforance gain achieved by the proposed relay deployent schee, Fig 6 presents the outage probability for different relay positions when the transitting power of the two sources and relay are P P P for the antenna configuration of the two S S sources and the relay are, and 3, respectively It can be observed fro Fig 6 that the proposed relay deployent schee significantly outperfors other relay deployent solutions in ters of outage behavior For exaple, when the outage probability is 0-3, the proposed relay deployent schee achieves about 4dB and 7dB gain copared to the position randoly when d 03 and d 0, S S respectively Therefore, Fig 6 also indicates that even in a network with ultiple potential relays, the proposed deployent schee can also help with quick relay selection by choosing the relay closest to the developed approxiate position Overall Outage Probability 0 0 0-0 - 0-3 0-4 0-5 optial d S rando d S d 0 d 03 0-6 0 5 0 5 0 5 S Fig 6 Outage probability for the proposed and other relay postion when P P P S S V COCLUSIOS In this paper the relay deployent for AF MIMO twoway relaying was studied An approxiation of the outage probability was utilized to reveal the existence of the outage-optial relay location and developed a nearoptial relay deployent schee The near-optial relay position was expressed in closed for, showing that the optial relay position is affected by the ner of antennas and the transitting power at sources but independent of the ner of antennas at the relay Siulations confired theoretical analysis and showed the achieved perforance gain EFEECES [] P Popovski and H Yoo, Wireless network coding by aplifyand-forward for bi-directional traffic flows, IEEE Coun Lett, vol,no, pp 6 8, 007 S S [] B ankov and A Wittneben, Spectral efficient protocols for half-duplex fading relay channels, IEEE J Sel Areas Coun, vol 5, no, pp 379 389, 007 [3] Y Han, et al, Perforance bounds for two-way aplify-andforward relaying, IEEE Trans Wireless Coun, vol 8, pp 43 439, 009 [4] J Joung and A Sayed, Multiuser two-way aplify-and-forward relay processing and power control ethods for beaforing systes, IEEE Trans on Signal Process, vol 58, no 3, pp 833 846, Mar 00 [5] A F Molisch and M Z Win, MIMO systes with antenna selection, IEEE Microwave, vol 5, no, pp 46 56, 004 [6] C Li, L Yang, and W-P Zhu, Two-way MIMO relay precoder design with channel state inforation, IEEE Trans Coun, vol 58, no, pp 3358 3363, 00 [7] Zhang, et al, Optial beaforing for two-way ultiantenna relay channel with analogue network coding, IEEE J Sel Areas Coun, vol 7, no 5, pp 699 7, 009 [8] A Y Panah and W Heath, MIMO two-way aplify-andforward relaying with iperfect receiver CSI, IEEE Trans Veh Technol, vol 59, no 9, pp 4377 4387, 00 [9] M Eslaifar, C Yuen, W H Chin, and Y L Guan, Max-in antenna selection for bi-directional ulti-antenna relaying, in Proc IEEE 7st Veh Tech Conf, 00, pp 5 [0] G Aarasuriya, C Tellabura, and M Ardakani, Two-way aplify-and-forward ultiple-input ultiple-output relay networks with antenna selection, IEEE J Sel Areas Coun, vol 30, no 8, Sept 0 [] C Li, L Yang, and W-P Zhu, Two-way MIMO relay precoder design with channel state inforation, IEEE Trans on Coun, vol 58, no, pp 3358-3363, Dec 00 [] C Li, L Yang, and W-P Zhu, "Miniu ean squared error design of single-antenna two-way distributed relays based on full or partial channel state inforation," IET Coun, vol 5, no 5, pp 78-735, Mar 0 [3] Lertwira, G K Tran, K Sakaguchi, and K Araki, An efficient relay node placeent schee for two-way MIMO ultihop networks in practical indoor environents, IEEE Trans on Wireless Coun, vol, no 6, pp 977-987, June 03 [4] P K Upadhyay and S Prakriya, Joint power and location optiization for analog network coding with ulti-antenna sources, in Proc IEEE Wireless Coun and etw Conference, 03, pp 05-09 [5] Q Sun, L H Li, and M Juntti, Energy efficient transission and optial relay location for two-way relay systes, in Proc IEEE Wireless Coun and etw Conference, 03, pp 88-83 [6] Y Li, X Zhang, M G Peng, and W B Wang, Power provisioning and relay positioning for two-way relay channel with analog network coding, IEEE Signal Proces Lett, vol 8, no 9, pp 57-50, Sept 0 [7] Handbook of Matheatic-al Functions, Dover Plications, Inc, M Abraowitz and I Stegun, ew York, 970 Yi-zhen Zhang was born in Henan Province, China, in 990 She received the BS degree in inforation and counication engineering fro Xi an Shiyou University, in 0 She is currently a aster student in the School of Electronics and Inforation Engineering, Xi an Jiaotong University Her research interests include wireless relay and physical layer network coding 04 Engineering and Technology Plishing 56

Journal of Counications Vol 9, o 7, July 04 Guo-bing Li is currently an assistant professor in the School of Electronic and Inforation Engineering, Xi an Jiaotong University, Xi an, China He received the BS and MS degree both in Electrical Engineering fro Xidian University, Xi an, China, in 00 and 004, respectively, and the PhD degree in Electrical Engineering fro Xi an Jiaotong University in 0 His research interests include wireless relay network, physical layer network coding and spectru sensing in cognitive radio systes Guo-ei Zhang is currently a lecturer in School of Electronics and Inforation Engineering, Xi an Jiatong University, Xi an, PChina She received the BS, MS, and PhD degrees in inforation and counication engineering fro Xi an Jiaotong University, in 000, 003 and 00 respectively Her research interests include odulation and coding, signal detection, interference suppression and siulation ethods in wireless counication systes systes Gang-ing Lv is currently an assistant professor in the School of Electronic and Inforation Engineering, Xi an Jiaotong University, Xi an, China He received the PhD degree in Electrical Engineering fro Xi an Jiaotong University in 00 His research interests include obile counications, assive MIMO and QoS guarantee in wireless counications Chao Zhang is currently an associate professor in the School of Electronic and Inforation Engineering, Xi an Jiaotong University, Xi an, China PhD degrees fro University of Science and Technology of China, in 005 and 00, respectively His current research interests include wireless counication, relay networks, and UWB 04 Engineering and Technology Plishing 56