IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR Toward Transparent Coexstence for Mult-hop econdary Cogntve Rado Networks Xu Yuan, tudent Member, IEEE, Canmng Jang, Y h, enor Member, IEEE, Y. Thomas Hou, Fellow, IEEE, Wenng Lou, enor Member, IEEE, astry Kompella, enor Member, IEEE, and cott F. Mdkff, enor Member, IEEE Abstract The domnate spectrum sharng paradgm of today s nterference avodance, where a secondary network can use the spectrum only when such a use s not nterferng wth the prmary network. However, wth the advances of physcal layer technologes, the mndset of ths paradgm s beng challenged. Ths paper explores a new paradgm called transparent coexstence for spectrum sharng between prmary and secondary nodes n a mult-hop network envronment. Under ths paradgm, the secondary network s allowed to use the same spectrum smultaneously wth the prmary network as long as ther actvtes are transparent (or nvsble ) to the prmary network. uch transparency s accomplshed through a systematc nterference cancelaton (IC) by the secondary nodes wthout any mpact on the prmary network. Although such a paradgm has been studed n the nformaton theory (IT) and communcatons (COMM) communtes, t s not well understood n the wreless networkng communty, partcularly for mult-hop networks. Ths paper offers an n-depth study of ths paradgm n a mult-hop network envronment and addresses ssues such as schedulng (both n frequency channels and tme slots) and IC (to/from prmary network and wthn the secondary network). Through a rgorous modelng and formulaton, problem formulaton, soluton development, and smulaton results, we show that transparent coexstence paradgm offers sgnfcant mprovement n terms of spectrum access and throughput performance as compared to the current prevalng nterference avodance paradgm. Index Terms pectrum sharng; coexstence; underlay; cogntve rado; mult-hop network; MIMO; nterference cancelaton I. INTRODUCTION Recent push by the government agences to share federal government rado spectrum wth non-government enttes has fueled the development of nnovatve technologes for spectrum sharng [2]. The current prevalng spectrum-sharng paradgm s that secondary nodes (typcally equpped wth cogntve rados (CRs)) are allowed to use a spectrum channel allocated to the prmary nodes only when such a use wll Ths paper was presented n part at IEEE ECON, June 24 27, 203, New Orleans, LA [9]. X. Yuan, Y.T. Hou, W. Lou, and.f. Mdkff are wth Vrgna Tech, Blacksburg, VA 2406, UA. e-mal: (thou@vt.edu, xuy0@vt.edu, wlou@vt.edu, mdkff@vt.edu). C. Jang s wth the hape ecurty n Mountan Vew, CA 94040, UA. e-mal: (cm@vt.edu). Y. h s wth the Intellgent Automaton Inc., Rockvlle, MD, 20855, UA. e-mal: (ysh@vt.edu).. Kompella s wth the U Naval Research Laboratory, Washngton, DC 20375, UA. e-mal: (sastry.kompella@nrl.navy.ml). Manuscrpt receved January 6, 204; revsed May 8, 204 and July 8, 204; accepted eptember, 204. For correspondence, please contact rof. Y.T. Hou (thou@vt.edu). not cause nterference to the prmary nodes [], [5], [8], [3]. Ths s also called nterweave paradgm n [6], whch we call nterference avodance paradgm n ths paper. Under ths paradgm, the wreless networkng communty has nvested sgnfcant research efforts n algorthm desgn and protocol mplementaton to optmze secondary CR users performance whle ensurng that ther actvtes wll not nterfere wth the prmary users. On the other hand, n the nformaton theory (IT) communty, there s a strong nterest n explorng nformaton theoretc lmt of CR [6]. In partcular, researchers have been explorng the potental of smultaneous actvaton of a secondary network wth the prmary network, as long as the nterference produced by secondary nodes can be properly controlled (e.g., canceled) by the secondary nodes. Here, secondary nodes are allowed to access the spectrum as long as they can cancel ther nterference to the prmary nodes n such a way that the prmary nodes do not feel the presence of the secondary nodes. In other words, actvtes by the secondary nodes are made transparent (or nvsble ) to the prmary nodes. We call ths transparent coexstence paradgm n ths paper. Under ths paradgm, secondary nodes are assumed to have powerful (physcal layer) capabltes to perform nterference cancelaton (IC), thereby, allowng them to access the spectrum n a much more aggressve manner than the nterference avodance paradgm. Although the dea of the transparent coexstence paradgm has been explored n the IT communty, results from the IT and communcatons (COMM) communtes have manly lmted to very smple network settngs, e.g., several nodes or lnk pars, all for sngle-hop communcatons [2], [7], [], [2], [22]. The more dffcult problem of how transparent coexstence can be acheved n a mult-hop secondary network remans open. As shown n [8], [3], the problem complexty assocated wth mult-hop CR networks s much hgher than sngle-hop CR networks. To date, there are no pror results on transparent coexstence for a mult-hop CR networks. The goal of ths paper s to advance the theoretcal foundaton of transparent coexstence paradgm for a mult-hop secondary CR network. We study how a mult-hop secondary CR network can co-exst wth a prmary network transparently. For IC, we assume that each secondary node s equpped wth multple transmt/receve antennas (MIMO). 2 For a set of Ths s also called underlay paradgm n [6]. 2 Other IC technques may also be employed and wll be explored n our future studes.
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 2 channels owned by the prmary networks, the prmary nodes may use them n whatever manner to sut ther needs. On the other hand, the secondary nodes are only allowed to use these channels f they can cancel ther nterference to the prmary nodes. Further, to ensure successful transmsson among the secondary nodes, the secondary nodes also need to perform IC to/from the prmary nodes as well as potental nterference among the secondary nodes. mply put, all IC burden should rest solely on the secondary nodes and reman nvsble to the prmary nodes. For ths paradgm, we offer a mathematcal modelng of channel/tme slot schedulng, IC between prmary and secondary nodes, and IC wthn the secondary network. Based on ths model, we study a throughput maxmzaton problem (wth the obectve of maxmzng the mnmum throughput among all sessons n the secondary network) wthout any mpact on the prmary users. nce the problem has a mxed-nteger lnear program (MIL) formulaton, we develop an effcent soluton based on a sequental fxng (F) technque. Through smulaton results, we demonstrate how the transparent coexstence paradgm can offer much mproved spectrum access and throughput performance than the current nterference avodance paradgm. The remander of ths paper s organzed as follows. In ecton II, we gve essental background on how IC may be performed by MIMO. ecton III descrbes our problem and key challenges. In ecton IV, we present a mathematcal model for the transparent coexstence paradgm where both the prmary and secondary networks are mult-hop. Based on ths model, n ecton V, we study a throughput maxmzaton problem and presents an effcent soluton algorthm. ecton VI presents smulaton results and demonstrates the sgnfcant mprovement n spectrum access and throughput performance under the transparent coexstence paradgm. ecton VII concludes ths paper and dscusses the further work. II. BACKGROUND AND MOTIVATION We gve a bref revew of MIMO n terms of ts spatal multplexng (M) and IC capabltes [4], [0], [7], [8]. Other capabltes such as spatal dversty [23] and nterference algnment [20] are not explored n ths paper and wll be consdered n our future work. A smple representaton of MIMO can be bult upon the so-called degree-of-freedom (DoF) concept [0], [8]. mply put, the total number of DoFs at a node (no more than the number of antenna elements) represents the avalable resources at the node. A DoF can be used for ether data transmsson/recepton or IC. Typcally, transmttng one data stream requres one DoF at a transmtter and one DoF at ts recever. M refers to the scenaro where multple DoFs are used to transmt multple data streams, thus substantally ncreasng data throughput between the two nodes. On the other hand, IC refers to a node s capablty to use some of ts DoFs to cancel nterference, ether as a transmtter or as a recever. Dependng on whether IC s done at a transmtter or recever, the number of requred DoF consumpton may be dfferent. IC by Tx. If a transmtter (Tx) s to cancel ts nterference to an unntended recever, the number of T p T s rmary node rmary lnk econdary lnk R p Interference R s econdary node Fg.. A smple example llustratng the benefts of usng MIMO to allow smultaneous actvaton of prmary and secondary nodes. DoFs requred at ths transmtter s equal to the number of data streams (or DoFs) that the unntended recever s tryng to receve from ts transmtter. IC by Rx. If a recever (Rx) s to cancel the nterference from an nterferng transmtter, the number of DoFs requred at ths recever s equal to the number of data streams (or DoFs) that the nterferng transmtter s tryng to transmt to ts ntended recever. At any node, the sum of DoFs used for M and IC cannot exceed the total number of DoFs at the node. A MIMO node s ablty to use a subset of ts DoFs to cancel nterference whle to use the remanng subset of DoFs for data transmsson allows the possblty of smultaneous actvaton of the secondary nodes wth the prmary nodes. We use a smple example to llustrate ths pont. In Fg., suppose T p and R p are a par of transmt and receve nodes n the prmary network, whle T s and R s are a par of transmt and receve nodes n the secondary network. Assume that all nodes share the same channel. uppose T p s transmttng data stream to R p. Under the nterference avodance paradgm, secondary transmt node T s s prohbted from transmsson on the same channel as t wll nterfere wth prmary receve node R p. However, when MIMO s employed on the secondary nodes, smultaneous transmssons can be acheved. Assume secondary nodes T s and R s are each equpped wth 4 antennas (4 DoFs). T s can use of ts DoFs to cancel ts nterference to R p so that R p can receve ts data stream correctly from T p. At node R s, R s can use of ts DoFs to cancel nterference from T p. After IC, both T s and R s stll have 3 DoFs remanng, whch can be used for M of 3 data stream from T s to R s. A. Channel tate Informaton As the above example shows, under transparent coexstence, all IC burden rests upon the secondary nodes. pecfcally, a secondary transmt node needs to cancel ts nterference to all neghborng prmary receve nodes who are nterfered by ths secondary transmtter; a secondary receve node needs to cancel nterference from all neghborng prmary transmt nodes that nterfere wth ths secondary recever. To acheve transparency to the prmary nodes, t s mportant for the secondary nodes to have accurate channel state nformaton (CI). The problem s: how can a secondary node obtan the CI between tself and ts neghborng prmary nodes whle remanng transparent to the prmary nodes? We propose the followng soluton to resolve ths problem. For each prmary node, t typcally sends out a plot sequence
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 3 3 (a) Tme slot t Fg. 2. CI estmaton at secondary node. 2 rmary node 3 econdary node (b) Tme slot t 2 Fg. 3. A mult-hop secondary network co-located wth a mult-hop prmary network. (tranng sequence) to ts neghborng prmary nodes so that those prmary nodes can estmate the CI. Ths s the practce for current cellular networks and we assume such a mechansm s avalable for a prmary network. nce we consder a multhop network, where each node wll act as a transmtter n one tme slot but as a recever n another tme slot. Then, each secondary node can overhear the plot sequence sgnal from the prmary node whle stayng transparent. For example, n Fg. 2(a), n tme slot t, when s transmttng the plot sequence, a secondary node can overhear ths sequence from. Lkewse, n Fg. 2(b), n tme slot t 2, when 2 s transmttng ts plot sequence, the secondary node can overhear ths plot sequence from 2. uppose the plot sequence from the prmary nodes s publcly avalable (as n cellular networks) and s known to the secondary nodes. Then the secondary node can use ths nformaton and the actual receved plot sequence sgnal from the prmary nodes for channel estmaton. Based on the recprocty property of a wreless channel [6], a secondary node wll be able to estmate the CI n both drectons to/from and 2. Lkewse, the CI among the secondary nodes may be derved followng a smlar approach. III. ROBLEM COE We consder a prmary mult-hop ad hoc network shown n Fg. 3, whch s co-located wth a secondary mult-hop network n the same geographcal regon. uppose that there s a set of channels B owned by the prmary network. For schedulng on each channel, we consder a tme frame wth T equal-length tme slots. The prmary nodes can use ths set of channels and tme slots freely as f they were the only nodes n the network. The prmary nodes are assumed to be sngle-antenna nodes. For the secondary nodes, they are 2 allowed to use a tme slot t ( t T ) on a channel only f ther nterference to the prmary nodes are canceled properly, wth complete transparency to the prmary nodes. For IC, we assume that the secondary nodes are equpped wth MIMO. ome key assumptons that we make n ths paper are the followng: In prmary network, we assume that each prmary node s a sngle-antenna node. 3 The secondary nodes need to know the prmary nodes transmsson behavor (lnk schedulng). We assume ths nformaton can be derved by the secondary nodes through montorng/sensng of the prmary nodes actvtes. The secondary nodes need to have CI to perform IC (to/from the prmary nodes and wthn the secondary nodes). A proposed soluton was gven n ecton II-A. We further assume that the CI obtaned at the secondary nodes s perfect. Ths assumpton allows us to develop an nformaton theoretc understandng on the potental benefts of transparent coexstence paradgm. In practce, perfect CI s hard to acheve and naccurate CI wll cause nterference leakage. Ths may be treated as addtonal nose and wll degrade lnk qualty. Just lke any other system, there s a gap between what a theoretcal lmt s and what can actually be acheved n practce. Investgaton of ths gap (between theoretcal lmt and achevable performance n practce) and how to close ths gap wll be deferred for future research. We assume each data stream s assocated wth the same constant rate. In practce, the data rate of a data stream depends on channel condton and many other factors. But for tractablty, we assume that we use a smple fxed rate codng and modulaton scheme for a data stream. In other words, we assume that there s a mnmum rate wth our fxed rate codng and modulaton for a data stream and we wll ust use ths mnmum rate for all data streams, despte that some streams wth better channels could n fact acheve hgher rates f an adaptve codng and modulaton scheme s used. We agree that such a smple fxed rate codng and modulaton scheme s not optmal. But ths assumpton allows us to keep the problem tractable when performng performance study. In our throughput optmzaton problem n the transparent coexstence paradgm, we assume to have global knowledge so that we can develop a centralzed soluton and use t to examne the benefts of such a paradgm. Based on these assumptons, we explore the followng challenges n the secondary network: Channel/tme slot schedulng In a secondary network, an ntermedate relay node s both a transmtter and a recever. Under the half-duplex, a node cannot transmt and receve on the same channel wthn the same tme slot. Therefore, schedulng (ether n tme slot or channel) s needed. Here, schedulng can be performed both n tme slot and channel allocaton (tme and frequency 3 The case where the prmary nodes also have multple antennas wll be left for further research.
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 4 domans). Note that schedulng transmsson/recepton at a secondary node wll lead to a partcular nterference relatonshp among the prmary and secondary nodes n the underlyng tme slot and channel. Ths ont tme/channel schedulng plays an ntegral role for IC n the network. Inter-netwrok IC We dscussed ths challenge n ecton II (see Fg. ), where a secondary transmtter needs to cancel ts nterference to ts neghborng prmary recevers whle a secondary recever needs to cancel the nterference from ts neghborng prmary transmtters. Intra-network IC In addton to nter-network IC, nterference from a secondary node may also nterfere wth another secondary node wthn ther own network (.e., ntra-network nterference). uch an nterference must also be canceled properly (ether by a secondary transmtter or recever) to ensure successful data communcatons nsde the secondary network. It s mportant to realze that the above three key challenges are not ndependent, but deeply ntertwned wth each other. In partcular, channel/tme slot schedulng at a secondary node s drectly ted to the nterference relatonshp between the prmary and secondary nodes as well as nterference among the secondary nodes. Therefore, a mathematcal modelng of transparent coexstence paradgm must capture all these components ontly. IV. MATHEMATICAL MODELING In ths secton, we develop a mathematcal model for the transparent coexstence paradgm under whch a mult-hop secondary network can access the same spectrum as a prmary network (see Fg. 3). Ths mathematcal model wll address the challenges outlned n the last secton through a ont formulaton. A. Notaton Table I lsts notaton n ths paper. uppose there s a set of sessons F wthn the prmary network. For a gven routng for each sesson, denote L as the set of lnks n the prmary network that are traversed by these sessons (shown n sold arrow lnes n Fg. 3). Denote z b (t) as the number of data ( l) streams over prmary lnk l L on channel b n tme slot t. nce a prmary node only has one antenna, z b (t) = f lnk ( l) l s actve (on channel b and tme slot t) and 0 otherwse. For the secondary network, we assume MIMO capablty at each node. Denote A as the number of antennas on a secondary node. uppose there s a set of mult-hop sessons F n. For a gven routng for each sesson, denote L as the set of secondary lnks (shown n dashed arrow lne n Fg. 3). To model schedulng at a secondary node for transmsson or recepton, we denote x b (t) and yb (t) (, b B and t T ) as whether node s a transmtter or recever on channel b n tme slot t, respectvely. We have x b (t) = f node s a transmtter on channel b n tme slot t; 0 otherwse. T B B F Ĩ L In L Out L z b (t) ( l) TABLE I NOTATION rmary Network The set of nodes n the prmary network The number of tme slots n a frame The sets of channels owned by the prmary network The number of channels n set B, B = B The set of sessons n the prmary network The set of prmary nodes wthn the nterference range of secondary node The set of ncomng lnks (from other prmary nodes) at node The set of outgong lnks (to other prmary nodes) at node The set of lnks n the prmary network The number of data streams over prmary lnk l on channel b n tme slot t econdary Network The set of nodes n the secondary network The number of secondary nodes n the network, = A The number of antennas at secondary node c The mnmum data rate carred by a data stream F The set of sessons n the secondary network I The set of node n that are wthn the nterference range of secondary node L In The set of ncomng lnks (from other secondary nodes) at node L Out The set of outgong lnks (to other secondary nodes) at node L The set of secondary lnks r(f) The data rate of the sesson f F r mn The mnmum data rate among all secondary sessons Rx(l) The recever of lnk l L Tx(l) The transmtter of lnk l L x b (t) = f node s a transmtter on channel b n tme slot t, and s 0 otherwse y b(t) = f node s a recever on channel b n tme slot t, and s 0 otherwse z(l) b (t) The number of data streams over lnk l L on channel b n tme slot t λ b, (t) The number of DoFs used by transmt node to cancel ts nterference to receve node on channel b n tme slot t µ b, (t) The number of DoFs used by receve node to cancel the nterference from transmt node on channel b n tme slot t θ, b (t) Bnary ndcator showng the relatonshp between nodes and n ordered lst on channel b n tme slot t,, π b (t) An orderng for IC among the secondary nodes on channel b n the tme slot t π b(t) The poston of node n πb (t) f node s a recever on channel b y b(t) = n tme slot t; 0 otherwse. Under half-duplex (a node cannot transmt and receve on the same channel n the same tme slot), we have the followng constrant on x b (t) and yb (t): x b (t) + y b (t) (, b B, t T ). () B. Node orderng for IC n secondary network Recall that the secondary network s solely responsble for nter-network IC (n addton to ntra-network IC). To avod unnecessary duplcaton n allocatng DoFs for IC, t was shown n [4] that node-orderng based IC s very effectve. Under ths scheme, all secondary nodes are put nto an ordered
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 5 lst. DoF allocaton at each secondary node for IC s based on the poston of the node n the lst. It was shown n [4] that such dscplned approach can ensure: () there s no duplcaton n IC (and thus no waste of DoF resources), and () the fnal DoF allocaton s feasble. We wll descrbe the specfc rules for DoF allocaton at a secondary node for IC (dependng on whether t s a transmtter or recever) n the followng two sectons. But frst, we gve a mathematcal model for the node orderng concept. Denote π b (t) as an ordered lst of the secondary nodes n the network on b B and t T, and denote π b (t) as the poston of node n π b (t). Therefore, π b (t), where =. For example, f π b (t) = 3, then t means that node s the thrd node n the lst π b (t). To model the relatve orderng between any two secondary nodes and n π b (t), we use a bnary varable θ, b (t) and defne t as follows: { f node s before node n π θ, b (t) = b (t); 0 otherwse. It was shown n [4] that the followng relatonshps hold among π b (t), πb (t) and θb, (t). π b (t) θ b,(t)+ π b (t) π b (t) θ b,(t)+, (2) where,, b B, and t T. We pont out that such a node orderng approach for DoF allocaton s the most effcent approach among all exstng DoF models that can guarantee feasblty. As ponted out n [4], an optmal node orderng can be found by nsertng the above orderng relatonshp as a constrant nto the overall formulaton of the optmzaton problem, as we shall do n ecton V. C. DoF allocaton at a secondary transmtter At a secondary transmtter, t needs to expend DoFs for () M, () IC to neghborng prmary recevers, and () IC to a subset of ts neghborng secondary recevers based on ther orders n the node lst. () DoF for M. For M, denote z(l) b (t) and LOut as the number of data streams on lnk l L and the set of outgong lnks from secondary node. Then the number of DoFs at secondary node for M s l L z b Out (l)(t) for b B and t T. () DoF for IC to neghborng prmary recevers. To ensure transparent coexstence, a secondary transmtter needs to cancel ts nterference to neghborng prmary recevers. Recall that f a prmary recever p s wthn the nterference range of node, the number of DoFs at node that s used for cancelng the nterference to node p s equal to the In number of data stream that are receved at node p. Denote L p as the set of ncomng prmary lnks to node p. Denote Ĩ as the set of prmary nodes that are located wthn the nterference range of secondary transmtter. For node p Ĩ, the number of DoFs used at node for cancelng nterference to node p s l LIn p z b ( l) (t) for b B and t T. Now for all prmary receve nodes n Ĩ, the number of DoFs used at node to ( ) cancel nterference to these nodes s p Ĩ l z b (t) LIn p ( l) for b B and t T. () DoF for IC to secondary recevers. For IC wthn the secondary network, ths secondary transmtter only needs to cancel ts nterference to a subset (nstead of all) of ts neghborng secondary recevers based on the node orderng lst [4]. pecfcally, ths secondary transmtter only needs to expend DoFs to null ts nterference to neghborng secondary recevers that are before tself n the ordered secondary node lst π b (t). Node does not need to expend any DoF to null ts nterference to those secondary recevers that are after tself n the ordered node lst π b (t). Ths s because the nterference from node to those secondary recevers (that are after ths node n π b (t)) wll be nulled by those secondary recevers later (when we perform DoF allocaton at those nodes). Ths s the key to avod duplcaton n IC. Recall that f a secondary recever s wthn the nterference range of secondary transmt node, the number of DoFs requred at transmt node to cancel ts nterference to node s equal to the number of data stream that are beng receved at node. Denote L In as the set of ncomng lnks to node. Denote I as the set of secondary nodes that are located wthn the nterference range of node. For secondary receve node I, the number of DoFs used at secondary ( transmt node for cancelng ts nterference to Tx(k) node s (t) z(k) ). b (t) Note that we are usng θ b, the ndcator varable θ, b (t) to consder only those secondary receve nodes that are before node n the ordered node lst π b (t). Now for all secondary receve nodes n I, the number of DoFs used at node to cancel nterference ) to these nodes s I (θ, b Tx(k) (t) z b (k) (t) for b B and t T. Total DoF consumpton. uttng all these DoF consumptons together at a secondary transmtter, we have the followng constrants: If ths secondary transmt node s actve,.e., x b (t) =, we have x b (t) z(l) b (t) + z b (t) ( l) + θ,(t) b I p Ĩ Tx(k) l LIn p z(k) b (t) A, (3) whch means that the DoF consumpton at node cannot be more that the total number of ts antennas. If node s not actve,.e., x b (t) = 0, we have z(l) b (t) = 0. (4) We can rewrte (3) and (4) nto the followng two mathematcal constrants: x b (t) z(l)(t) b b + z + I θ b,(t) Tx(k) p Ĩ z(k)(t) b A x b (t) + l LIn p ( l) (t) ( ) x b (t) M, (5)
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 6 z b (l) (t) xb (t) A, (6) where [ M s a large constant, whch s an upper bound ] of p Ĩ l z b (t)+ LIn p ( l) I θ, b Tx(k) (t) z b (k) (t) when x b (t) = 0. For example, we can set M = I A + p Ĩ l z b (t). LIn p ( l) To see that (5) and (6) can replace (3) and (4), note that () when x b (t) =, (5) becomes (3) and (6) holds trvally; () when x b (t) = 0, (4) and (6) are equvalent, and (5) holds trvally. ( Reformulaton. nce (5) has a nonlnear term θ, b Tx(k) (t) z (k) ), b (t) we can use Reformulaton Lnearzaton Technque (RLT) [9, Chapter 6] to reformulate ths nonlnear term by ntroducng new varables and addng new lnear constrants. We defne a new varable λ b, (t) as follows: Tx(k) λ b,(t) = θ,(t) b z(k) b (t), where, I, b B, and t T. For bnary varable θ, b (t), we have the followng assocated constrants: θ b,(t) 0, ( θ b,(t)) 0. For Tx(k) z (k) b (t), we have: Tx(k) z b (k) (t) 0, Tx(k) A z(k) b (t) 0. We can cross-multply the two constrants nvolvng θ, b (t) wth the two constrants nvolvng Tx(k) z (k) b (t), and replacng the product term θ, b Tx(k) ( ) (t) z b (k) (t) wth λ b, (t). Then (5) can be replaced by the followng lnear constrants: x b (t) z(l) b (t) + z b (t) ( l) + p Ĩ l LIn p λ b,(t) A x b ( (t) + x b (t) ) M, (7) I λ b,(t) λ b,(t) 0, (8) Tx(k) z(k) b (t), (9) λ b,(t) A θ b,(t), (0) Tx(k) λ b,(t) A θ,(t) b A + z(k) b (t), () where, I, b B, and t T. D. DoF allocaton at a secondary recever At a secondary recever, t needs to expend DoFs for () M, () cancelng nterference from neghborng prmary transmtters, and () cancelng nterference from a subset of ts neghborng secondary transmtters based on ther orders n the node lst. () DoF for M. For M, the number of DoFs consumed at a secondary recever s k L z b In (k)(t) for b B and t T. () DoF for IC from neghborng prmary transmtters. A secondary recever needs to cancel the nterference from neghborng prmary transmtters. If a prmary transmtter p s wthn the nterference range of secondary receve node, the number of DoFs at node requred for cancelng ths nterference from node p s equal to the number of data L Out p streams that are beng transmtted by node p. Denote as the set of outgong lnks from prmary node p. For p Ĩ, the number of DoFs used at node for cancelng nterference from node p s (t). Now for all prmary transmt nodes l LOut p z b ( l) n Ĩ, the number of DoFs ( used at node to cancel nterference ) from these nodes s p Ĩ l z b (t) for b B and LOut p ( l) t T. () DoF for IC from secondary transmtters. For IC wthn the secondary network, ths secondary recever only needs to null the nterference from a subset (nstead of all) of ts neghborng secondary transmtters based on node orderng lst. pecfcally, ths secondary recever only needs to expend DoFs to null the nterference from neghborng secondary transmtters that are before tself n the ordered secondary node lst π b (t). Node does not need to expend any DoF to null the nterference from those secondary transmtters that are after tself n the ordered node lst π b (t). Ths s because the nterference to node from those secondary transmtters wll be nulled by those secondary transmtters later (when we perform DoF allocaton at those nodes). Recall that f node s wthn the nterference range of a secondary transmt node, the number of DoFs at node that s used for cancelng the nterference from node s equal to the number of data stream that are beng transmtted at node. For a secondary transmt node I, the number of DoFs used at secondary( receve node for cancelng nterference from node s θ, b Rx(l) (t) z (l) ). b (t) Now for all other secondary transmt nodes n I, the number of DoFs used at node to cancel nterference ) from those nodes s I (θ, b Rx(l) (t) z b (l) (t) for b B and t T. Total DoF consumpton. We can put all DoF consumpton
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 7 at a secondary recever as follows: y b (t) z(k)(t)+ b I p Ĩ l LOut p z b ( l) (t) + Rx(l) ( ) θ,(t) b z(l)(t) b A y b (t)+ y b (t) N, (2) z b (k) (t) yb (t) A, (3) where [ N s a large constant, whch s an upper bound ] of p Ĩ l z b (t)+ LOut p ( l) I (θ, b Rx(l) (t) z b (l) (t) when y b(t) = 0. For example, we can set N = I A + z b (t). ( l) p Ĩ l LOut p Reformulaton. Followng the same token as n the last ( secton, we use RLT) to lnearze the nonlnear term θ, b Rx(l) (t) z b (l) (t) n (2). Denote µ b, (t) as ( θ, b Rx(l) (t) z (l) ). b (t) Then (2) can be replaced by the followng lnear constrants: y b (t) z(k)(t) b + z b ( l) (t) + p Ĩ p I µ b,(t) A y b (t) + µ b,(t) ( y b (t) ) N, (4) µ b,(t) 0, (5) Rx(l) z(l) b (t), (6) µ b,(t) A θ b,(t), (7) Rx(l) µ b,(t) A θ,(t) b A + z(l) b (t), (8) where, I, b B, and t T. V. CAE TUDY FOR A THROUGHUT MAXIMIZATION A. roblem Formulaton ROBLEM Usng the above mathematcal model for the transparent coexstence paradgm for a mult-hop secondary network, varous problems can be studed. In ths secton, we study a throughput optmzaton problem n the secondary network. Denote r(f) as the rate of sesson f F. Then at any lnk l L n the network, the aggregate throughput rate among the flows that traverse ths lnk cannot exceed the lnk s schedulng capacty (over a tme frame). That s, f traversng l f F r(f) c T T b B t= z(l) b (t) (l L), (9) where c s the data rate carred by a data stream. For the throughput maxmzaton problem, suppose we are nterested n maxmzng the mnmum throughput rate among all secondary sessons. Then the problem can be formulated as follows: OT max r mn s.t r mn r(f) (f F); Half-duplex constrants: (); Node orderng constrants: (2); Transmtter DoF constrants: (6) (); Recever DoF constrants: (3) (8); Lnk capacty constrants: (9). In ths formulaton, r mn, r(f), x b (t), yb (t), zb (l) (t), πb (t), λ b, (t), µb, (t) and θb, (t) are optmzaton varables, and A, M, N, z b (t) and c are gven constants. Ths optmzaton ( l) problem s n the form of a mxed-nteger lnear program (MIL), whch s N-hard n general. Although commercal solvers such as CLEX can be used, they are not scalable to address problems wth moderate to large-szed networks. In ths secton, we develop an effcent heurstc algorthm. B. Overvew of oluton Algorthm The algorthm that we propose s based on the so-called sequental fxng (F) technque n [9, Chapter 5]. F offers a general framework to handle nteger varables n a MIL problem, and has a polynomal tme complexty. The basc dea of F s as follows. For a MIL lke ours, f we were able to set the optmal values for all nteger varables, then the orgnal problem would be reduced to an L, whch can be solved n polynomal tme. o the key challenge n MIL s how to determne the values for all the nteger varables. Under F, ths can be done by studyng the lnear relaxaton of the orgnal problem, obtaned by relaxng all the nteger varables to contnuous varables. Although the soluton to ths lnear relaxaton may not have an nteger value for each nteger varable, we can fx the values of one or more nteger varables based on ther closeness to certan nteger values. Instead of determnng all the nteger varables n one teraton, we can fx only one or a few nteger varables n each teraton. For the remanng (unfxed) nteger varables, we can solve a new lnear relaxaton and then fx one or more remanng nteger varables. Ths F procedure termnates after all nteger varables are fxed. At ths pont, the MIL becomes an L. Any remanng contnuous varable n the L can be solved effcently. Although the dea of F s straghtforward, t requres a careful desgn to ensure ts performance. A nave applcaton of F, as we have experenced, may lead to ether nfeasble soluton or poor performance. Ths s because that fxng relaxed varables solely based on ther closeness to ntegers do not take nto consderaton of the physcal sgnfcance of dfferent varables n the partcular problem and ther ntrcate relatonshps. In our desgn, we propose to classfy nteger varables nto three groups: (π, θ), (x, y), and z. The frst group (π, θ), determnes the orderng among the secondary nodes n DoF allocaton and s consdered the structural foundaton of all nteger varables. Therefore, we wll determne
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 8 (π, θ) frst n our F algorthm. For the remanng (x, y) and z varables, (x, y) can be determned f we know the lnk status for the correspondng z. Therefore, we wll determne the lnk status (.e., whether z = 0 or z ) frst and then we can fx the correspondng (x, y). Note that n ths step, we only determne whether z = 0 (lnk nactve) or z (lnk actve). In the last step, we wll fx those z s wth z to exact nteger values teratvely. ome mportant detals of each step are gven n the followng secton. C. Algorthm Detals hase I: Fxng π and θ varables. In ths phase, for b B and t T, we wll fx one π b (t) varable, and further fx related θ, b (t) (or θb, (t)) varables durng an teraton. nce there are a total of of π b (t) s ( ) for b B and t T, there are teratons n hase I. pecfcally, n the frst teraton, for b B and t T, we dentfy node wth the smallest value of π b (t) among all π b(t) s ( ). We set πb (t) =. nce ths s the frst node on channel b n tme slot t, we set θ, b (t) = and θ, b (t) = 0 for. In the second teraton, another node k wth the smallest value πk b(t) among all un-fxed πb (t) s wll be chosen and we set πk b(t) = 2. Lkewse, we set θb k, (t) = and θ,k b (t) = 0 for, k. Ths process contnues tll the end of -th teraton, when all π b(t) and θb, (t) (, ) are fxed for b B, t T. hase II: Fxng x and y varables. In ths phase, we wll determne each lnk l s status (.e., actve or nactve) and fx x b (t) and yb (t) varables. In the case of an nactve lnk l, we set z(l) b (t) = 0; n the case of an actve lnk l, we wll leave the determnaton of z(l) b (t) to hase III. pecfcally, n each teraton, we choose the largest z(l) b (t) on channel b n tme slot t and determne the status of the correspondng lnk l (.e., actve or nactve). Ths lnk l s determned to be actve for b B and t T f t satsfes the followng condtons: () s satsfed, whch means that the transmtter and recever of ths lnk each meets half-duplex constrant. Lnk l s transmtter should satsfy (5) and ts recever should satsfy (2),.e., not exceedng DoF resources at both transmtter and recever. In the case that the status of another assocated lnk k s yet to be determned, we assume ts z(k) b (t) = 0. mlarly, n the case that the status of another assocated lnk k s actve, we assume z(k) b (t) =. Note that n ether case, we do not set the values for these z(k) b (t) s permanently, but rather, only a lower bound value so that we can test whether (5) and (2) can hold. If lnk l does not meet the above two condtons, t s consdered nactve. Dependng on whether lnk l s actve or nactve, we can fx (x b (t), yb (t)) and possbly some other z(k) b (t) varables based on the followng three rules: (a) If lnk l s actve for b B and t T, we can fx x b Tx(l) (t) = and yb Rx(l) (t) =. As a result of ths fxng, we can also fx ytx(l) b (t) = 0 and xb Rx(l) (t) = 0 by (). Otherwse (.e., lnk l s nactve for b B and Inactve 6 7 2 3 8 Inactve 4 5 Inactve 0 Fg. 4. An example llustratng how to fx x, y, and some z varables n hase II. t T ), we can fx z(l) b (t) = 0. Further, f all lnks n L Out Tx(l) are nactve for b B and t T, we set x b Tx(l) (t) = 0. mlarly, f all lnks n LIn Rx(l) are nactve for b B and t T, we set yrx(l) b (t) = 0. (b) If x b (t) = 0,.e., node does not transmt data for b B and t T, then we set all lnks k L Out to be nactve. Further, we set z(k) b (t) = 0 on these lnks. (c) If y b (t) = 0,.e., node does not receve data for b B and t T, then we set all lnk k L In to be nactve. Further, we set z(k) b (t) = 0 on these lnks. We use an example to llustrate the case when a lnk s determned to be actve. Referrng to Fg. 4, suppose the status on lnks 6, 8, and 0 are determned to be nactve on b and t n the last teraton. In ths teraton, suppose lnk s status s determned to be actve. Then, we can set x b Tx() (t) = and yrx() b (t) =. nce xb Tx() (t) =, we can set yb Tx() (t) = 0 and z(2) b (t) = 0, zb (3)(t) = 0. The lnk status of 2 and 3 can be set to be nactve. nce all outgong lnks from node Tx(3) are nactve, we can set x b Tx(3) (t) = 0. mlarly, snce yrx() b (t) =, we can set xb Rx() (t) = 0 and zb (4)(t) = 0, z(5) b (t) = 0. The lnk status of 4 and 5 can be set to be nactve. nce all ncomng lnks to Rx(4) are nactve, we can set x b Rx(4) (t) = 0. hase III: Fxng z varables. In hase II, we have fxed z(l) b (t) s to 0 for those nactve lnks. For those lnks that are actve, we have not yet determned the exact nteger values for z(l) b (t) s. In hase III, we wll fx these nteger values. On all actve lnks l, f there exsts some z(l) b (t) s that are not yet nteger, we use F to fx these z(l) b (t) s teratvely untl they are all ntegers. In partcular, durng each teraton, we dentfy lnk l wth the mn{z b l (l) (t) zb (l)(t) } for each for b B and t T and set z(l) b (t) = zb (l) (t). VI. ERFORMANCE EVALUATION The goal of ths secton s twofold. Frst, we want to use numercal results to llustrate how transparent coexstence can be acheved for a mult-hop secondary network. Note that we cannot compare our heurstc soluton to the global optmal soluton because a global optmal soluton s not avalable due to the exponental complexty of an MIL formulaton. But ths lmtaton does not prevent us from demonstratng the potental benefts of the transparent coexstence paradgm. Therefore, our second goal n ths secton s to show the 9
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 9 TABLE II LOCATION OF EACH NODE FOR THE 20-NODE RIMARY NETWORK AND 30-NODE ECONDARY NETWORK. rmary Network Node Locaton Node Locaton Node Locaton (0, 0) 8 (5, 50) 5 (20, 80) 2 (30, 30) 9 (40, 70) 6 (3, 48) 3 (50, 30) 0 (60, 90) 7 (35, 85) 4 (75, 50) (85, 90) 8 (90, 80) 5 (90, 20) 2 (40, 0) 9 (3, 35) 6 (90, 45) 3 (70,0) 20 (6, 97) 7 (75, 65) 4 (55, 55) econdary Network Node Locaton Node Locaton Node Locaton (23, 66) (55, 60) 2 (88, 62) 2 (3, 89) 2 (8, 56) 22 (70, 20) 3 (42, 4) 3 (3, 78) 23 (76, 74) 4 (9, 37) 4 (62, 2) 24 (84, 30) 5 (0, 70) 5 (92, 92) 25 (22, 92) 6 (29, 6) 6 (36, 94) 26 (60, 40) 7 (8, 25) 7 (82, 4) 27 (28, 6) 8 (5, 0) 8 (35, 60) 28 (99, 3) 9 (63, 75) 9 (76, 40) 29 (98, 38) 0 (65, 98) 20 (48, 2) 30 (47, 85) TABLE III OURCE AND DETINATION NODE OF EACH EION IN THE RIMARY AND ECONDARY NETWORK. rmary Network esson ource Node Destnaton Node 4 2 5 7 3 5 econdary Network esson ource Node Destnaton Node 7 25 2 2 7 3 4 3 4 30 23 tremendous benefts (n terms of spectrum access and throughput gan) of the transparent coexstent paradgm over the exstng nterference avodance paradgm. A. An Example Consder a 20-node prmary network and a 30-node secondary network randomly deployed n the same 00 00 area. For the ease of scalablty and generalty, we normalze all unts for dstance, bandwdth, and throughput wth approprate dmensons. The locaton for each node (both prmary and secondary) s generated at random and s lsted n Table II. We assume that there are four antennas on each secondary node, and all nodes transmsson range and nterference range are 30 and 50, respectvely. 4 There are two channels owned by the prmary network (B = 2). A tme frame s dvded nto four tme slots (T = 4). For smplcty, we assume the data rate of one data stream n a tme slot s unt (c = ). We assume there are three actve sessons n the prmary network and four actve sessons n the secondary network (see Table III). For smplcty, we assume that mnmumhop routng s used for the prmary and secondary sessons, 4 For an ndepth study on how to set nterference range, we refer readers to our prevous work n [5]. Fg. 5. 00 90 80 70 60 50 40 30 20 2 3 9 7 20 5 2 8 5 4 (, ) 25 (2, 2) 6 2 27 6 7 8 (, 4) (, 3) 9 3 30 (, 2) 20 0 2 8 3 6 28 4 7 0 0 0 20 30 40 50 60 70 80 90 00 3 0 4 26 9 22 0 (2, 4) 9 23 7 4 (2, 3) 24 8 2 6 5 5 29 (, 3) Actve sessons n the prmary and secondary networks. 00 20 6 0 25 0 5 (2, 4) 90 2 30 (, 3) [(, 3), (, 4), (2, ), (2, 2)] 80 7 8 3 5 [(, ), (, 2), (, 4), (2, 3)] 23 (2, 2) 9 70 5 [(, 3), (2, ), (2, 2), (2, 4)] 9 7 2 60 2 8 (2, 3) [(, ), (, 2), (2, 4)] 4 50 6 8 (, 2) [(, 2), (, 4), (2, 3)] 4 6 3 40 4 26 9 29 9 2 [(, ), (, 3), (2, ), (2, 2)] (, 4) 3 (, 3) 30 [(, 3), (2, ), (2, 2)] [(, ), (, 4), (2, 3)] 24 7 20 20 5 (, ) 22 27 [(, 2), (2, ), (2, 2), (2, 4)] 0 [(, 2), (2, 3), (2, 4)] 6 2 8 3 4 28 7 0 0 0 20 30 40 50 60 70 80 90 00 Fg. 6. Channel and tme slot schedulng on each lnk for the secondary sessons by our soluton algorthm. Channel and tme slot schedulng on each lnk for the prmary sessons are gven n Fg. 5. although other routng methods wll also work here. Further, the channel and tme slot allocaton on each hop for each prmary sesson s known a pror and s shown n Fg. 5, where (b, t) means ths lnk s transmttng on channel b n tme slot t. The sold arrows represent the lnks n the prmary network, whle the dashed arrows represent the lnks n the secondary network. For ths network settng, we apply our soluton algorthm to solve OT. The obtaned obectve value s.0. The channel and tme slot schedulng on each lnk for each secondary sesson s shown n the shaded box as n Fg. 6, where (b, t) on each secondary lnk represents that ths lnk transmts on channel b n tme slot t. The detals of DoFs used for M on each channel n each tme slot on each lnk n the secondary network are shown n Table IV. The lnk rate (.e., total number of DoFs used for M averaged over a 4-tme-slot frame) on a lnk s also shown n ths table. To see how the secondary node can be actve smultaneously wth the prmary nodes whle reman transparent, consder (b, t) = (, 2) (channel, tme slot 2) n Fg. 6. Here, lnk 3 4 n the prmary network s actve; lnks 4 20, 22 7, 2 9, 30 9 and 4 n the secondary network are also actve. Based on a node s
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 0 TABLE IV CHANNEL AND TIME LOT CHEDULING ON EACH LINK, DOF ALLOCATION FOR M, AND THROUGHUT ON EACH LINK FOR THE ECONDARY EION. esson 2 3 4 25 9 22 4 20 30 9 9 23 Lnk (channel, tme slot) DoF Lnk schedulng for M rate (2, )..0 (, 3) 2 7 4 (2, 2) (, 2).0 (, ) 4 (2, 4) 2 (, 4) (2, ).0 (, 3) (2, 2) (, 4) 2.0 (, 2) 2 9 (2, 3) (, 3).0 (2, ) (, ) (2, 2) (2, 3).0 (, 2) 22 7 (2, 4) 2 (2, ) (2, 2).0 (, 2) (2, 4) (, 4) 2.0 (, ) 2 20 3 (2, 3) (, 2) (, 4).0 (, ) (2, 3) (2, ) (2, 2).0 (, 3) (2, 4) TABLE V DOF ALLOCATION FOR M AND IC ON (b, t) = (, 2) AT EACH NODE IN THE ECONDARY NETWORK. Node TX/RX π (2) DoF DoF for IC to/from DoF for IC wthn for M prmary nodes secondary network 9 RX from 3 0 4 TX 2 0 to 9 22 TX 4 to 4 to 9 2 TX 5 to 4 0 7 RX 6 from 3 from 4 20 RX 8 from 3 from 22 30 TX 9 to 4 0 9 RX from 3 from 2 4 TX 2 to 4 to 20 RX 3 from 3 from 30 nterference range, the nterference relatonshps among the nodes assocated wth these actve lnks are shown n Fg. 7, where the dotted arrow lnes show the nterference from a (prmary or secondary) transmtter to an unntended (prmary or secondary) recever. Table V shows the DoF allocaton at each secondary node for M, IC to/from prmary nodes, and IC wthn the secondary network for (b, t) = (, 2). Frst, we check whether there s any nterference to prmary recever 4. Note that there are four potental nterference from secondary transmtters,.e., 4, 2, 22 and 30. nce each of these secondary transmtter uses one DoF to cancel ts nterference to prmary recever 4 (ffth column n Table V), all nterference on the prmary recever 4 s effectvely nulled. Therefore, the prmary recever 4 s not nterfered by the smultaneous actvaton of ts neghborng secondary transmtters. Next, we check whether the nterference from the prmary transmtter s nulled properly at ts neghborng secondary recevers ( nter-network nterference). Note that prmary transmt node 3 s nterferng ts neghborng secondary receve nodes, 20, 7, 9 and 9. nce each of these secondary receve nodes uses one DoF to cancel ths nterference (ffth column n Table V), ths nterference from prmary transmt node 3 s effectvely nulled at these secondary receve nodes. Fnally, we check whether the nterference wthn the secondary network ( ntra-network nterference) s nulled properly by the secondary nodes themselves. The IC wthn the secondary network follows the node orderng, whch s shown n the thrd column of Table V. The number of DoFs used for IC to/from other secondary nodes s shown n the last column of Table V. As an example, consder node 22, whch s a transmt node. Referrng to Table V, 22 only needs to cancel ts nterference to those receve nodes that are before tself n the ordered node lst and wthn 22 s nterference range,.e., node 9. Table V (last column) shows that 22 ndeed uses one DoF to cancel ts nterference to 9. For ts nterference to the secondary receve node 20 whch s also n 22 s nterference range, 22 does not need to do anythng as 20 s after node 22 n the ordered lst. Ths nterference to 20 wll be canceled by 20 (as shown n Table V, last column). It can be easly verfed that for all nterference among the actve secondary nodes are properly canceled. Further, at each actve secondary node, the DoFs used for M, IC to/from the prmary nodes, IC wthn the secondary network s not more than ts total DoFs (.e., 4). The above llustraton s for (b, t) = (, 2) (.e., channel, tme slot 2), the results for the other channel and tme slots (.e., (, ), (, 4), (, 3), (2, 2), (2, 3) and (2, 4)) are smlar and are omtted to conserve space. B. Comparson to Interference Avodance aradgm To see the benefts of the transparent coexstence paradgm, we compare t to the prevalng nterference avodance paradgm. Under the nterference avodance paradgm, a secondary node s not allowed to transmt (receve) on the same channel at the same tme when a nearby prmary recever (transmtter) s usng ths channel. Therefore, the set of avalable channel and tme slots that can be used by secondary nodes s smaller. The problem formulaton for ths paradgm s smlar to (but smpler than) OT. In partcular, we can remove the second term ( l z b (t) and p Ĩ LIn p Ĩ p ( l) l z b ) n constrants (5) and (2) n OT that LOut p ( l) are used for secondary nodes to cancel nterference to/from the prmary nodes. The problem formulaton remans an MIL
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 00 20 6 0 25 90 2 30 0 5 80 3 7 8 5 23 9 70 5 9 7 2 60 8 2 4 50 8 6 4 6 40 3 9 4 9 26 29 30 3 2 7 24 20 27 20 22 5 0 2 8 3 6 4 7 28 0 0 0 20 30 40 50 60 70 80 90 00 TABLE VI CHANNEL AND TIME LOT CHEDULING ON EACH LINK, DOF ALLOCATION FOR M, AND LINK RATE ON EACH LINK FOR THE ECONDARY EION UNDER THE INTERFERENCE AVOIDANCE ARADIGM. esson 2 3 4 Lnk (channel, tme slot) DoF Lnk schedulng for M rate 7 4 (2, 4) 2 0.5 4 (2, 3) 4.0 25 (2, ) 2 0.5 2 9 (2, ) 2 0.5 9 22 (2, 4) 2 0.5 22 7 (2, 2) 4.0 4 20 (2, ) 2 0.5 20 3 (2, 4) 2 0.5 30 9 (2, ) 2 0.5 9 23 (, ) 4.0 Fg. 7. Illustraton of nterference relatonshps among the prmary and secondary lnks on channel n tme slot 2 n the case study. 00 90 2 20 25 6 30 0 0 (2, 4) 5 (2, ) 80 7 8 3 (, 3) (2, ) 5 (2, 2) (, ) 23 9 70 5 9 7 2 60 8 2 (2, 3) (2, 3) 4 50 8 6 (2, ) 4 (, 2) 6 3 40 4 26 9 29 9 (2, 4) 2 (, 4) 3 (2, 4) (2, 4) (, 3) 30 7 24 20 20 22 5 (, ) 27 (2, ) (2, 2) 0 6 2 8 3 4 28 7 0 0 0 20 30 40 50 60 70 80 90 00 Fg. 8. Channel and tme slot schedulng on each lnk for the secondary sessons under the nterference avodance paradgm. and a soluton algorthm smlar to that n ecton V-C can be used to solve t. Followng the same settng as n the case study n ecton VI-A, we solve the above optmzaton problem under the nterference avodance paradgm. Note that the avalable channels and tme slot resources at each node are only a subset of 2 channels and 4 tme slots, versus full 2 channels and 4 tme slots for each secondary node n the transparent coexstence paradgm. The obtaned obectve value s 0.5 (compared to.0 n ecton VI-A). The channel and tme slot schedulng on each lnk of each secondary sesson s shown n Fg. 8. Comparng Fgs. 6 and 8, we fnd that the set of channels and tme slots used by each secondary lnk under nterference avodance paradgm s smaller. The detals for the DoF allocaton for M on each channel n each tme slot and lnk rate are shown n Table VI. Comparng Tables VI and IV, the rates on most lnks are smaller under the nterference avodance paradgm. C. Impact of Varous ystem arameters The results n ectons VI-A and VI-B show the soluton detals for a case study n the transparent coexstence paradgm and ts mprovement n obectve value over that n the nterference avodance paradgm. To show the robustness of our results, we further perform numercal study for the same network under dfferent system parameters, such as nterference range settng, the number of antennas on each node, and the number of sessons n the secondary network. Fg. 9(a) shows the obectve values under the transparent coexstence paradgm and the nterference avodance paradgm when the nterference range for the secondary network s vared from 40 to 90 (whle keepng the transmsson range at 30). As shown n the fgure, the performance under the transparent coexstence paradgm s always better than that under the nterference avodance paradgm for the same nterference range, although the performance under both paradgms degrades when the nterference range ncreases. Fg. 9(b) shows the comparson of obectve values wth dfferent antenna numbers for each secondary node under the two paradgms. Interference range for the secondary nodes s set to 50. For MIMO, the mnmum number of antennas on a node s 2. As shown n the fgure, the obectve value under the transparent coexstence paradgm s always better than that under the nterference avodance paradgm for the same number of antennas. Further, the obectve value ncreases under both paradgms. Fg. 9(c) shows the comparson of obectve values wth dfferent number of secondary sessons under the two paradgms. The number of antennas on each secondary node s 4. As shown n the fgure, the obectve value under the transparent coexstence paradgm s always better than that under the nterference avodance paradgm for the same number of secondary sessons, although the obectve value decreases under both paradgms when the number of secondary sessons ncreases. D. Complete Results for 50 Network Instances Followng the same settng as for the case study of one network nstance n the ecton VI-A, we randomly generate 50 nstances, each wth 20-node prmary network and 30-node secondary network. For each nstance, we randomly generate prmary and secondary sessons, and compare the obectve values obtaned by the transparent coexstence paradgm and nterference avodance paradgm. Table VII shows the results from 50 network nstances. The fourth column shows the percentage mprovement for transparent coexstence paradgm
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 2 2.8 4.5 4 2.8 Obectve Value.6.4.2 0.8 0.6 0.4 0.2 Interference Avodance Transparent Coexstence 0 40 45 50 55 60 65 70 75 80 85 90 Interference Range (a) Interference range Obectve Value 3.5 3 2.5 2.5 Transparent Coexstence 0.5 Interference Avodance 0 2 3 4 5 6 7 8 9 0 2 Number of Antennas (b) Number of antennas Obectve Value.6.4.2 0.8 0.6 0.4 Transparent Coexstence 0.2 Interference Avodance 0 2 3 4 5 6 7 8 9 0 2 Number of econdary essons (c) Number of secondary sessons Fg. 9. Impact of varous system parameters on the performance of transparent coexstence and nterference avodance paradgms. over nterference avodance paradgm. Note that some of the entres have, ndcatng that the achevable sesson throughput (n DoFs) n the nterference avodance paradgm s 0. Overall, we fnd that the achevable sesson throughput under the transparent coexstence paradgm s much hgher than that under the nterference avodance paradgm. VII. CONCLUION AND FURTHER WORK Ths paper explored the transparent coexstence paradgm for a mult-hop secondary network. Ths paradgm allows a secondary network to use the same spectrum smultaneously wth the prmary network as long as ts actvtes are transparent (or nvsble ) to the prmary network. uch transparency s accomplshed through a systematc nterference cancelaton (IC) by the secondary nodes wthout any mpact on the prmary network. The new techncal challenges n a mult-hop network nclude channel/tme slot schedulng, IC to/from prmary network by the secondary network, and IC wthn the secondary network. We developed a rgorous mathematcal modelng for a secondary mult-hop network n the transparent coexstence paradgm. As an applcaton, we appled ths model to study a throughput maxmzaton problem wth the obectve of maxmzng the mnmum throughput among all secondary sessons. For the optmzaton problem, we developed an effcent polynomal tme algorthm. Through smulaton results, we show that the transparent coexstence paradgm offers sgnfcant mprovement n spectrum access and throughput performance over the exstng prevalng nterference avodance paradgm. Although ths work shows the potental of transparent coexstence n terms of throughput mprovement for the secondary networks, much work remans to be done to transton ths dea nto realty. In partcular, the focus of ths paper has been on explorng performance gan of transparent coexstence under dealzed network settng (by gnorng many detals that may arse from practcal operatons). We brefly dscuss some of the practcal ssues that must be addressed n future work to acheve transparent coexstence n the real world. Ths dscusson s not meant to be exhaustve, as the transparent coexstence s a novel concept and ts path to adaptaton s bound to encounter many challenges, both known and unknown. The frst ssue s that the secondary nodes need to have accurate knowledge of the prmary nodes transmsson behavor (nformaton regardng transmtter, recever, tme slot, and channel). Ths ssue s easer to address n a snglehop envronment (cellular, TV tower, WF) but s a maor challenge n a mult-hop ad hoc network envronment. econd, we assume the schemes n ecton II-A to obtan CI would work perfectly and channel recprocty strctly holds. But n realty, the communcaton channel not only conssts of the physcal channel, but also the antennas, RF mxers, flters, A/D converters, etc., whch are not necessarly dentcal on all the nodes. Therefore, complex calbraton among the nodes s needed to acheve channel recprocty. uch calbraton s no smple task for a par of transmtter and recever and s even more complcated among a network of nodes. Thrd, zero-forcng based IC may not be perfect even f we have perfect CI. A consequence of non-perfect IC s nterference leakage, whch s undesrable for both prmary and secondary recevers. How to mtgate such nterference leakage to a mnmal acceptable level should be a key consderaton when deployng transparent coexstence for real applcatons. Fourth, the IC and DoF allocaton algorthm that we desgned for the secondary network s a centralzed one. uch a centralzed soluton serves our purpose of ntroducng a new concept. It bears smlar pros and cons of other centralzed algorthm for a wreless network. If a centralzed soluton s adopted n practce, those ssues must be carefully addressed. On the other hand, f a dstrbuted soluton s desred, then a dfferent set of ssues need to be addressed. These ssues nclude partal network knowledge, lmted nformaton sharng, communcaton overheard, ensurng IC feasblty at each secondary node, among others. Regardless centralzed or dstrbuted soluton, flow dynamcs (new sesson ntaton, exstng sesson termnaton) wll add addtonal complexty on nformaton update and algorthm executon. Clearly, there s a large landscape for further research on these mportant practcal operaton ssues. We expect to see more follow-up research n ths area n the near future. ACKNOWLEDGMENT Ths work was supported n part by the NF and ONR. The work of Dr.. Kompella was supported n part by the ONR. art of rof. W. Lou s work was completed whle she was servng as a rogram Drector at the NF. Any opnon, fndngs, and conclusons or recommendatons expressed n
IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR 3 TABLE VII ACHIEVABLE MINIMUM EION THROUGHUT UNDER TRANARENT COEXITENCE ARADIGM AND INTERFERENCE AVOIDANCE ARADIGM FOR 50 CAE. Network Transparent Interference ercentage Instance Coexstence Avodance Improvement.0 0.5 00% 2.0 0.5 00% 3.25 0.75 66.7% 4.0 0.5 00% 5.0 0 6.0 0.75 33.3% 7.0 0 8.0 0.5 00% 9.5 50% 0.0 0.5 50%.0 0.5 50% 2.0 0.75 33.3% 3.25 0.75 66.7% 4.0 0 5.0 0.5 00% 6.0 0.5 00% 7.0 0.75 33.3% 8 0.75 0.5 50% 9.0 0.5 00% 20 0.75 0 2.0 0 22 0.75 0.5 50% 23.0 0.5 00% 24.25 0.75 66.7% 25 0.5 0 26 0.5 0 27 0.75 0.5 50% 28.0 0.5 00% 29 0.25 0 30.0 0.75 33.3% 3.5 0.75 00% 32.25 0 33.0 0.5 00% 34.0 0.5 00% 35.25 0.75 66.7% 36 0.75 0.5 50% 37 0.5 0 38.0 0.25 300% 39 0.25 0 40.0 0.5 00% 4.25.0 25% 42.0 0.5 00% 43.0 0.5 00% 44 0.5 0 45.0 0.5 00% 46.0 0.5 00% 47 0.75 0.5 50% 48 0.25 0 49.0 0.5 00% 50.0 0.5 00% ths paper are those of the authors and do not reflect the vews of the NF. [4] L.-U. Cho and R.D. 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IEEE JOURNAL ON ELECTED AREA IN COMMUNICATION, VOL.??, NO.??, MONTH YEAR Xu Yuan ( 3) receved the B.. degree n Computer cence from Nanka Unversty, Tann, Chna, n 2009. nce the Fall 200, he has been pursung hs h.d. degree n the Bradley Department of Electrcal and Computer Engneerng at Vrgna Tech, Blacksburg, VA. Hs current research nterests focuses on algorthm desgn and optmzaton for cogntve rado networks. 4 astry Kompella ( 04 M 07 M 2) receved hs h.d. degree n computer engneerng from Vrgna Tech, Blacksburg, Vrgna, n 2006. Currently, he s the head of Wreless Network Theory secton, Informaton Technology Dvson at the U.. Naval Research Laboratory (NRL), Washngton, DC. Hs research focuses on complex problems n crosslayer optmzaton and schedulng n wreless and cogntve rado networks. Canmng Jang receved the B.E. degree from the Department of Electronc Engneerng and Informaton cence, Unversty of cence and Technology of Chna, Hefe, Chna, n 2004 and the M.. degree from the Graduate chool, Chnese Academy of cences, Beng, Chna, n 2007. He earned hs h.d. degree n computer engneerng from Vrgna Tech, Blacksburg, VA, n 202. He s currently a enor oftware Development Engneer at hape ecurty n Mountan Vew, CA. Y h ( 02 M 08 M 3) receved hs h.d. degree n Computer Engneerng from Vrgna Tech, Blacksburg, VA n 2007. He s currently a enor Research centst at Intellgent Automaton Inc., Rockvlle, MD, and an Adunct Assstant rofessor at Vrgna Tech. Hs research focuses on optmzaton and algorthm desgn for wreless networks. He was a recpent of IEEE INFOCOM 2008 Best aper Award and the only Best aper Award Runner-Up of IEEE INFOCOM 20. Y. Thomas Hou (F 4) s the Bradley Dstngushed rofessor of Electrcal and Computer Engneerng at Vrgna Tech, Blacksburg, VA. He receved hs h.d. degree from NYU olytechnc chool of Engneerng (formerly olytechnc Unv.) n 998. Hs current research focuses on developng nnovatve solutons to complex cross-layer optmzaton problems n wreless and moble networks. He has publshed two graduate textbooks: Appled Optmzaton Methods for Wreless Networks (Cambrdge Unversty ress, 204) and Cogntve Rado Communcatons and Networks: rncples and ractces (Academc ress/elsever, 2009). He s the teerng Commttee Char of IEEE INFOCOM conference. Wenng Lou (M 08) s a professor n the computer scence department at Vrgna Tech. he receved her h.d. n Electrcal and Computer Engneerng from the Unversty of Florda. Her research nterests are n the broad area of wreless networks, wth specal emphases on wreless securty and cross-layer network optmzaton. nce August 204, she has been servng as a program drector at the Natonal cence Foundaton. cott F. Mdkff ( 82 M 85 M 92) s rofessor & Vce resdent for Informaton Technology and Chef Informaton Offcer at Vrgna Tech, Blacksburg, VA. From 2009 to 202, rof. Mdkff was the Department Head of the Bradley Department of Electrcal and Computer Engneerng at Vrgna Tech. From 2006 to 20009, he served as a program drector at the Natonal cence Foundaton. rof. Mdkff s research nterests nclude wreless and ad hoc networks, network servces for pervasve computng, and cyber-physcal systems.