Distributed Resource Allocation Assisted by Intercell Interference Mitigation in Downlink Multicell MC DS-CDMA Systems

Transcription

1 1 Distributed Resource Allocation Assisted by Intercell Interference Mitigation in Downlin Multicell MC DS-CDMA Systes Jia Shi, Zhengyu Song, IEEE Meber, and Qiang Ni, IEEE Senior Meber Abstract This paper investigates the allocation of resources including subcarriers and spreading codes, as well as intercell interference (ICI) itigation for ulticell downlin ulticarrier direct-sequence code division ultiple-access (MC DS-CDMA) systes, which ai to axiize the syste s spectral efficiency (SE). The analytical benchar schee for resource allocation and ICI itigation is derived by solving or closely solving a series of ixed integer non-convex optiization probles. Based on the optiization objectives sae as the benchar schee, we propose a novel distributed resource allocation assisted by ICI itigation schee referred to as RAIM, which requires very low ipleentation coplexity and deands little bachaul resource. Our RAIM algorith is a fully distributed algorith, which consists of the subcarrier allocation (SA) algorith naed RAIM-SA, spreading code allocation (CA) algorith called RAIM-CA and the ICI itigation algorith tered RAIM-IM. The advantages of the RAIM include that, its CA only requires liited binary ICI inforation of intracell channels, and it is able to ae itigation decisions without any nowledge of ICI inforation. Our siulation results show that, the proposed RAIM schee with very low coplexity required achieves significantly better SE perforance than other existing schees, and its perforance is very close to that obtained by the benchar schee. Index Ters Resource allocation, ulticell, MC DS-CDMA, intercell interference itigation. I. INTRODUCTION Dynaic resource allocation has becoe ore and ore iportant in future broadband ulticarrier counications by exploiting tie-varying characteristics of wireless channels and aing use of ultiuser diversity. However, resource allocation also faces a lot of challenges, including the possible huge signaling overhead, liited bachaul resources, high-coplexity bachaul operations, expansive servicing area, highly diverse services, etc. Resource allocation in single-cell ulticarrier systes has been widely investigated in [1 4]. However, it becoes very challenging in ulticell systes due to severe intercell interference (ICI) caused by frequency reuse. Resource allocation in ulticell ulticarrier systes can be categorized into two classes, naely centralized and distributed approaches. Specifically, centralized resource allocation has been widely investigated and studied in ulticell scenarios, such as [5, 6]. Despite exploiting various degrees of freedo This wor is supported by EU H00 TWEETHER project under grant agreeent nuber J. Shi and Q. Ni are with School of Coputing and Counications, Lancaster University, LA1 4WA, UK. Z. Song is with the School of Electronic and Inforation Engineering, Beijing Jiaotong University, Beijing , China. (E-ail: j.shi@lancaster.ac.u, z.song91@gail.co, q.ni@lancaster.ac.u). in ters of allocation, centralized approach usually deands a very high ipleentation coplexity and bachaul resources. By contrast, when distributed approach is used, resources can be anaged and assigned independently by each base station (BS). In coparison with centralized approach, distributed resource allocation requires a significantly lower coplexity, and it can also release huge burden on the bachaul syste and reduce assive signaling overhead. Furtherore, distributed approach is able to quicly respond to the dynaic and fast varying channel environents of wireless counication systes. Exploiting the above advantages, distributed resource allocation will be ore and ore useful and desirable in future wireless systes considering a large nuber of cells. Hence, distributed resource allocation has attracted intensive attentions, e.g. [7 10] in ulticell orthogonal frequency division ultiple access (OFDMA) systes. However, soe distributed schees, such as those in [8, 9], still need BSs to exchange channel state inforation (CSI) of their users, as a result, these schees are less copetitive for practical ipleentation. On the other hand, due to lac of ICI inforation, cobating ICI for distributed resource allocation is ore challenging than that for centralized resource allocation. In the literature, BS cooperation is an efficient ICI itigation approach, which shifts the processing burden fro obile terinals to BSs. The authors in [11, 1] have studied the scheduling and power-allocation in the ulticell downlin OFDMA networs, which handles ICI via BS coordination supported by CSI exchange aong BSs. By contrast, the researches in [13, 14] have studied the resource allocation in the ulticell systes with full BS cooperation requiring both CSI and data inforation exchanged aong BSs, which is however not allowed in any practical scenarios. In coparison with the other ulticarrier schees without using direct-sequence (DS) spreading, such as OFDMA and MC-CDMA, ulticarrier DS code division ultiple-access (MC DS-CDMA) eploys a high nuber of degrees-offreedo for high-flexibility design and reconfiguration [15]. With the aid of DS spreading, MC DS-CDMA is able to eploy a significant lower nuber of subcarriers than OFDMA [16], and, hence, can itigate the pea to average power ratio (PAPR) proble. Wireless signals in ulticarrier schees ay experience severe frequency-selective fading, which significantly degrades syste perforance if it is not properly handled. MC DS-CDMA eploys the flexibility to configure its nuber of subcarriers according to the frequency-selectivity of wireless channels. As a result, each subcarrier experiences independent fading, and frequency diversity ay be attained by conveying

2 the sae inforation using different subcarriers, which are then coherently cobined at receiver. In this case, the nuber of subcarriers of MC DS-CDMA will be at the order of the nuber of tie doain resolvable paths of wireless channels and, hence, will usually be low [16]. By exploiting the aboveentioned advantages, MC DS-CDMA can be a proising solution for supporting ubiquitous wireless counications in diverse environents, such as indoor, rural, and urban areas. It is feasible for accessing a large and possibly discontinuous bandwidth. This property is especially beneficial to the cognitive radio systes, where the bandwidth for supporting ultiuser counications is obtained fro the spectru holes of priary radio systes. However, very liited researches, such as [17 ], have been devoted to resource allocation in MC DS-CDMA systes. In [17, 18], the joint allocation of subcarrier and non-orthogonal spreading codes have been studied in the single-cell MC DS-CDMA systes. Moreover, a code assignent schee with ultiple-access interference avoidance has been proposed for the generalized MC DS-CDMA systes in [19, 0]. Recently, with the aid of non-cooperative gae approach, the paper in [1] has addressed the resource allocation including only transit power and subchannels for the ulticell distributed MC DS-CDMA networ. The authors in [] have proposed a joint spreading code allocation and subcarrier scrabling schee to reduce the PAPR in the singlecell MC CDMA syste, where the interference issue has not been addressed. In our paper [3], we have investigated lowcoplexity subcarrier allocation in the single-cell MC DS- CDMA systes. However, efficient resource allocation in ulticell scenarios will be very challenging due to existence of strong ICI as well as high ipleentation coplexity. To the best of our nowledge, there are no published references that have studied resource allocation and interference itigation together for the ulticell MC DS-CDMA systes. Against the bacground, in this paper, we investigate how to efficiently allocate resources including subcarriers and spreading codes, while effectively itigating ICI for ulticell downlin MC DS-CDMA systes, which ais to axiize the syste s spectral efficiency (SE). The ain contributions of our paper can be suarized as follows. We derive a novel benchar schee for the distributed resource allocation and ICI itigation in the ulticell MC DS-CDMA systes. The benchar schee proposes an efficient approach to allocate subcarriers and codes, while itigating ICI, which can be obtained by solving and closely solving a series of ixed integer non-convex optiization probles. As proposed, the distributed subcarrier allocation (SA) is first carried out, then the distributed spreading code allocation (CA) is ipleented, aiing to axiize the su rate of each cell. After that, the ICI itigation is operated for axiizing the su rate of celledge users. Inspired by the benchar schee, we propose a novel low-coplexity schee, naely distributed resource allocation assisted by ICI itigation (RAIM), for the ulticell downlin MC DS-CDMA systes. Based on the optiization objectives sae as the benchar schee, our RAIM schee is designed to be of very low ipleentation coplexity and sall bachaul resource deanded. The RAIM first operates the distributed SA algorith naed RAIM-SA, then runs the CA algorith called RAIM- CA. In contrast to the benchar, after the SA and CA the RAIM carries out the fully distributed ICI itigation algorith tered RAIM-IM. We analyze the characteristics and coplexity of the RAIM and the benchar schees eployed by our ulticell MC DS-CDMA systes. The proposed schees have a range of advantages, including quic response to wireless channel environents, requring iniu bachaul burden and iniu load on feedbac channels, as well as easily applicable for large syste, etc. According to the coplexity analysis, the RAIM schee requires uch lower coplexity than the benchar schee, which iplies the RAIM is very advantegeous in practical ipleentation. We carry out coprehensive perforance analysis for the proposed RAIM and benchar schees eployed by the ulticell systes. It is shown that, the proposed RAIM schee achieves significantly better SE perforance than other existing distributed resource allocation algoriths, and its perforance is very close to that obtained by the benchar schee. Therefore, the MC DS-CDMA associated with the RAIM schee ay constitute a proising candidate that facilitates practical ipleentation in future counication systes. The rest of this paper is organized as follows. Section II introduces the syste odel, and states our optiization probles. Section III derives the benchar for our resource allocation. Section IV proposes the novel RAIM schee. Section V analyzes the characteristics and coplexity of the proposed schees. Perforance results are shown in Section VI. Finally, we suarize the ain conclusions in Section VII. II. SYSTEM MODEL AND PROBLEM FORMULATION In this section, we present the syste odel followed by describing the ain optiization probles for the resource allocation and ICI itigation in the ulticell MC DS-CDMA systes. A. Syste Model To reflect the ain features of ulticell systes, we consider the classical three-cell syste odel, which has been widely studied in [14, 4, 5]. As shown in Fig. 1, a BS locates at the center of a hexagonal cell, and its K users uniforly distribute in the cell. Each of the counication terinals is equipped with one antenna for signal transission and reception. Furtherore, signals transitted fro BSs to obile users are MC DS- CDMA signals eploying length-n orthogonal DS spreading codes (or, siply, codes) and in total M orthogonal subcarriers. We assue that each cell supports K = MN users and, hence, each user can be allocated one subcarrier and one code. Note that, we consider this extree case for both the SA and CA in the systes, as it is the ost challenging one while avoiding considering different trivial cases.

3 3 Intracell Lin Intercell Interference (ICI) Lin Fig. 1: Conceptual structure of the downlin ulticell MC DS- CDMA systes. In order to avoid intracell interference, users in the sae cell are allocated either different subcarriers or different codes, or both are different. However, the co-subcarrier-code users in different cells assigned the sae subcarrier and code, such as users, 0 and 1 of cells 0, 1 and in Fig. 1, will cause ICI to each other. Furtherore, in each cell we assue for siplicity ideal power control as in [1, 13, 6], for aintaining the sae average received power of one unit per user when there are no SA and CA. In that case, we define an ICI factor α, considering the cobined effects of propagation pathloss and shadowing, as [7] α = (d0 d 1 ) µ 10 ζ 0 ζ 1 10 (1) where d 0 and d 1 represent the distances fro a BS to its intracell and intercell users respectively. In (1), µ is the pathloss exponent, and (ζ 0 ζ 1 ) (in db) obeys the log-noral distribution with standard deviation Υ (in db), which accounts for the shadowing effect [7]. In addition, each transission also experiences fast fading, which is assued to be the independent Rayleigh flat fading. Let us assue that the data sybols transitted by BS u (u U = {0, 1, }) to its K intracell users are expressed as x (u) = [x (u) 0, x(u) 1,..., x(u) K 1 ]T, where x (u) is the data sybol to user, and is assued to satisfy E[x (u) ] = 0 and E[ x(u) ] = 1. Assue that users, in cells u, u are co-subcarrier-code users, which are assigned subcarrier and code n. The signals received by user can be written by y (u), =h(u), V W (u) x (u) + u U,u u h (u ), α(u ), V W (u ) x (u ) + n (u), K(u), M () where K (u) contains the indexes of users in cell u, and M includes the indexes of subcarriers of the syste. In (), y (u), is a length-n observation vector, and h (u), is the fast fading channel gain fro BS u to user of subcarrier. As defined in (1), α (u ), characterizes the ICI fro BS u to user. We assue V is a (N K)-diensional atrix with coluns consisting of the spreading sequences taen fro a (N N) orthogonal spreading code atrix. Hence, V is a (N K)- diensional atrix fored fro V by setting those coluns for the subcarriers other than to zero vectors. The vector n (u) = [n (u),0,..., n(u), ]T is a coplex Gaussian noise vector at user, which has zero ean and a variance of σ = 1/γ s. We define γ s as the average signal-to-noise ratio (SNR) per sybol, when there is no SA/CA. We assue that a BS is capable of acquiring the CSI of its intracell channels. Hence, the preprocessing atrix can be set as W (u) = diag{w (u) 0, w(u) 1,..., w(u) ( ) / K 1 } with w (u) = h (u), h (u),, where ( ) denotes the conjugate operation. However, to iniize bachaul burden and ipleentation coplexity, BSs are not allowed to exchange the inforation about both intracell and ICI channels of the users. After despreading, the decision variable of user becoes z (u), = h (u), x (u) + u U,u u h (u ) ), α(u, w (u ) x (u ) } {{ } ICI + n (u), K(u), M (3) Fro (3), we now the signal-to-interference-plus-noise ratio (SINR) of user, given by γ (u), = h (u), ) ) u U,u u h(u, α(u, w (u ) + σ 1 = (A (u), ) 1 + (η, (u) K(u), M (4), ) 1 where A (u), and η(u), are respectively the SNR and signalto-interference (SIR) for user of subcarrier. They can be written as A (u), = h(u), σ = γ s h (u),, η (u), = h (u),, ) u U,u u I(u,, K (u), K (u ), M (5) where I (u ) received fro BS u.,, = ) ) h(u, α(u, w (u ) B. Proble Forulation is the ICI power of user This section discusses the general theories and forulates the optiization probles for the distributed resource allocation and ICI itigation in the ulticell systes. First, the distributed resource allocation including SA and CA ais to axiize the su rate of each cell, described as {S (u), C (u) } = arg ax {S (u),c (u) } R (u) K (u), u U (6)

4 4 R (u) = log ( 1 + u U,u u K (u ) n N M s(u), h(u), M c(u) ),n c(u,n s(u) ) ), s(u, I(u,, + σ ) (7) subject to s (u), = {0, 1}, M, K(u), (8) K (u) s (u), M = N, M, (9) s (u), = 1, K(u), (10) c (u),n = {0, 1}, K(u), n N, (11) c (u),n = 1, K(u), (1) n N K (u) c (u),n = M, n N. (13) Above, R (u), given by (7), is the achievable rate of user in cell u. In (6), S (u) = {s (u),,, } and C(u) = {c (u),n,, n} contain the SA and CA variables, while {S (u), C (u) } denotes the final results of cell u. The indicator s (u), = 1 if subcarrier is allocated to user in cell u, otherwise s (u), = 0. Siilarly, the indicator c (u),n = 1 if code n is assigned to user in cell u, otherwise c (u),n = 0. In above equations, N contains the indexes of codes in the syste. Note that, the constraints of (9) and (10) follow the assuption that each subcarrier is assigned to N users in one cell, while each user is allocated one subcarrier. By contrast, (1) and (13) constrain that each user is only allocated one code, and each code is assigned to M users. To solve proble (6), the BSs are required to share the full ICI inforation of all users, which is however not allowed by our assuption for achieving iniu bachaul burden and low ipleentation coplexity. Therefore, liited by this assuption, each BS first independently carries out the SA for solving proble (14), then operates CA for solving proble (16) which can approxiate proble (6). After that, ICI itigation is ipleented based on the optiization proble of (19), which ais to axiize the su rate of the cell-edge users for further iproving the syste throughput. First, the distributed SA ais to axiize the su rate of each cell, described as {S (u), } = arg ax, u U (14) {S (u), } K (u) R (u) subject to (8), (9), and (10). In (14), the achievable rate of user, i.e. R (u), becoes ( ) M R (u) = log 1 + s(u), h(u), I + σ. (15) In (14), S (u) = {s (u),, } contains the SA variables of cell u. Note that in (15), I denotes the su of the ICI experienced by user, and it can be given by the first ter of the SINR s denoinator in (7). However, we focus on studying distributed resource allocation, and the BSs are not allowed to share the full ICI inforation of all users and, hence, I in (15) cannot be nown. Furtherore, each user s ICI only coes fro its co-subcarrier-code users, which can be nown after the SA and CA. Hence, users ICI cannot be deterined when carrying out the SA based on (14). After SA, each BS independently carries out CA, which ais to axiize the su rate of each cell. In order to avoid intracell interference, the co-subcarrier users in a cell are distinguished by different codes. Therefore, based on the SA results, axiizing the su rate of a cell is equivalent to independently axiizing the su rate of every co-subcarrier user group in a cell. Correspondingly, the CA proble can be expressed as } =arg ax {C (u) {C (u) } subject to (11), (1), and F (u) R (u) {S (u) }, M, u U (16) F (u) c (u),n = 1, n N. (17) In (16), C (u) = {c (u) (u),n, F, n} contains the CA variables for the users allocated subcarrier, where F (u) includes the indexes of the users assigned to subcarrier in cell u. For avoiding intracell interference, (17) constrains the users in a co-subcarrier user group are assigned different codes. In (16), the rate of user can be expressed by = log 1 + h R (u) u U,u u F (u ) n N (u), c (u),n c(u ),n I(u ),, + σ. (18) Note that, (18) is derived by reoving all the SA variables in (7), since SA has been done. In addition, seen fro (18), each user s potential ICI can only coe fro its co-subcarrier users in the other cells. Finally, based on the SA and CA, our ICI itigation is attepted for cell-edge users suffering fro strong ICI. Let us define ˆK (u) = { η < η t, K (u) } as the set of users in cell u, whose SIRs are below the SIR threshold η t, which can be set according to various counication objectives. Then, cell-edge users are collected into K (u), which includes both the users in ˆK (u) as well as the users in (K (u) ˆK (u) ) that share the sae subcarriers and codes as the users in ˆK (u ) and ˆK (u ). Therefore, the ICI itigation for cell-edge users ais to axiize the su rate of every cell-edge user group containing three co-subcarrier-code users. The optiization proble can be expressed as {D,n } = arg ax {D,n } u U B (u),n R (u) {S, C}, M, n N (19)

5 5 subject to d (u),n = {,,, 1}, if B,n (u) & B (u ),n & B (u ),n, u U, (0) U 1 u=0 d (u),n, (1) d (u),n d (u ),n, if d (u),n = d (u ),n =, u. () Above, B,n (u) = K (u) F (u) V n (u) is the set of indexes of the cell-edge users assigned subcarrier and code n, in which V n (u) contains the indexes of the users assigned to code n in cell u. Siilarly, B (u ),n = K (u ) F (u ) V (u ) n and B (u ),n = K (u ) F (u ) V (u ) n. Further, we define ICI itigation decision (IMD) variable set as D,n = {d (u),n, u U} for subcarrier and code n. As described by (0), variable d (u),n can be defined as BS u transits x (u) to user on subcarrier and code n, d (u) 1 BS u turns off its transission on subcarrier,n = and code n, (or ) BS u helps to send x (u ) (or x (u ) ) to user (or ) on subcarrier and code n, if B (u),n, B (u ),n, B (u ),n. (3) As shown by (3), two strategies, i.e. power off and cooperation, are jointly utilized for ICI itigation. The syste s SE ay be significantly iproved by switching off soe transissions which ipose strong ICI on other transissions [8]. Furtherore, when cooperation is available between two BSs, the space tie bloc coding (STBC) [9] aided BS cooperation can be a proising schee, which only needs to exchange data sybols, but no CSI, between the two BSs. (1) and () constrains that at ost two users are allowed to switch off, and only two BSs can cooperate for a user in a cell-edge group. So far, we can readily now that the optiization probles in (14), (16) and (19) for the SA, CA and the ICI itigation are ixed integer non-convex probles, which are extreely hard to solve. In Section III, we otivate to solve the probles in (14), (16) and (19) respectively, resulting in a benchar schee. Furtherore, aiing to obtaining proising sub-optiu solutions, we propose a novel low-coplexity schee, naely RAIM, which follows the design objectives of the benchar schee. III. BENCHMARK ANALYSIS OF RESOURCE ALLOCATION AND ICI MITIGATION In this section, we derive a novel benchar schee for the resource allocation and ICI itigation in ulticell downlin MC DS-CDMA systes. The benchar schee is obtained by closely solving the probles in (14) and (16), as well as solving proble (19). The benchar schee consists of the distributed SA algorith referred to as the benchar-sa, the distributed CA algorith tered as benchar-ca and the centralized ICI itigation algorith called as benchar-im. In order to solve the proble of (19), the BSs are only allowed to exchange the ICI inforation of cell-edge users. A. Benchar of Distributed Subcarrier Allocation: Benchar-SA Our distributed SA ais to axiize the su rate of the users in each cell, as shown in (14). However, to solve (14) it requires all users ICI inforation exchanged aong the BSs, which is not allowed in our assuption and in ost of practical systes. In this case, as done in [3, 30] and the references therein, the best sub-optiu solution to proble (14) can be achieved by axiizing every user s SNR without considering ICI effect, having the distributed SA proble of {S (u), } = { arg ax {S (u), } M s (u), A(u),, K(u) }, u U (4) subject to (8), (9) and (10). However, the proble of (4) is still a cobinatorial proble, which is very hard to solve. By contrast, in [, 31], the authors have proved that the Hungarian algorith is the optiu SA solutions for axiizing the SNR of all users in the single-cell OFDMA syste eploying the channel-inverse power-allocation. Furtherore, as shown in [3, 30], the Hungarian algorith is able to closely solve the proble of (4). Therefore, the benchar for our SA can be obtained by independently operating the Hungarian algorith at each BS, which corresponds to the benchar-sa. However, the Benchar- SA algorith still has very high coplexity, especially, when the nuber of users in the syste is large. B. Benchar of Distributed Spreading Code Allocation: Benchar-CA After the SA, our distributed CA is carried out in each cell, aiing at axiizing the su rate of every co-subcarrier user group, as shown in (16). However, the proble of (16) for the CA is a ixed integer nonlinear non-convex proble, which is hard to find the optiu solution. Moreover, directly solving (16) requires the BSs to exchange the full ICI inforation of users in different cells, which is not practical in real systes. Because of the above issues, we convert the proble in (16) to the concave probles of (5) and (7) by relaxing the constraint of (11) and reforing the users rate expressions in (18), in order to study the benchar perforance of the syste eploying distributed CA. Specifically, the benchar for our distributed CA, i.e. benchar-ca, can be obtained by solving the relaxed probles of (5) and (7), which, for our three-cell syste, is ipleented in three stages by BSs u, u and u (u u u U) successively, when users ICI inforation is not exchanged aong the BSs. In detail, during the first stage, BS u randoly allocates the codes to its users due to its lac of the nowledge about the CA results of the other cells. After the CA in the uth cell, the users in cells u and u are able to easure the ICI fro cell u, which are infored to their BSs. Then, during the second stage, BS u can carry out the CA based on the CA results of cell u, by solving the optiization proble

6 6 given by {C (u ) } = arg ax {C (u ) } F (u ) R (u ) {C (u), S (u ) }, M (5) subject to the constraints of (1), (13) with superscript u substituted by u, and the relaxed constraint of 0 c (u ),n 1, F (u ), n N. (6) Following the CA in cell u, the users in cell u can now infor BS u the ICI fro the other two BSs. Therefore, during the last stage, BS u can operate its CA with the nowledge of the ICI fro both BSs u and u, by solving the optiization proble of {C (u ) } = arg ax {C (u ) } F (u ) R (u ) {C (u), C (u ), S (u ) }, M (7) subject to the constraints in (1), (13) with superscript u substituted by u, and the relaxed constraint of 0 c (u ),n 1, F (u ), n N. (8) Furtherore, in order to ae the probles in (5) and (7) the concave probles, the rates R (u ) and R (u ) are evaluated by the forulas of (9) and (30), which are equivalent to (18) by our siulation under the successive CA. In (30), Ĩ(u),,n is the ICI fro BS u to user in cell u assigned subcarrier and ) code n assigned. Ī(u is the average ICI fro BS u, which ) is evaluated as Ī(u = ( j F (u ) I (u ),j,)/n, since the CA in cell u has not been done yet. Siilarly, in (30), Ĩ(u),n and Ĩ (u ),n count the ICI fro BSs u and u. The CA probles in (5) and (7) are concave probles associated with the constraints in (1), (13), and the rates in (9), (30). The corresponding proofs are given in the Appendix. Therefore, there are any ethods, such as the interior point ethod [3], that can be eployed to solve the probles of (5) and (7). However, in order to solve the probles in (5) and (7), BSs u and u need to now the analog ICI inforation of their users, which ay becoe challenging for the feedbac channels in practice if there are a lot of users. In order to itigate this deand, in this paper, we propose the RAIM schee including the heuristic CA algorith, which only requires the bit-valued ICI inforation by the BSs. C. Benchar of Intercell Interference Mitigation: Benchar-IM After the SA and CA, we can derive the centralized benchar-im algorith, which can find the optiu solution to the proble of (19). In order to derive the optiu solution, the benchar-im carries out the exhaustive search with the nowledge of full ICI inforation for cell-edge users, and its principles can be suarized in Algorith 1. (Algorith 1) Benchar of ICI Mitigation: Benchar-IM 1: Initialization: B,n = { K (u) F (u) V n (u), u}, d (u),n = if F (u) V n (u) = {}, M, u U; : For subcarrier = 0,..., M 1 & code n = 0,..., N 1 3: If B,n 4: Copute su rates of all optional decisions (OPs) with power off only: OP(1) Power off for one user: ˆd (u),n = 1, ˆd (u ),n = d (u ),n, ˆd (u ),n = d (u ),n, u, OP() Power off for two users: ˆd (u),n = ˆd (u ),n = 1, ˆd (u ),n = d (u ),n, u; 5: Copute su rates of all the OPs with cooperation only: OP(3) Cooperation between two BSs: ˆd (u),n = ˆd (u ),n = d (u),n, ˆd (u ),n = d (u ),n, u, OP(4) Cooperation aong three BSs: ˆd (i),n = d (u),n, i {u, u, u }, u; 6: Copute su rates of all the OPs with both power off and cooperation: OP(5) Power off for one user, cooperation for one user: ˆd (u),n = ˆd (u ),n = d (u),n, ˆd (u ),n 7: Identify the best decision: {d (u),n, u} = ax { ˆd(u) 8: End 9: End,n, u} = 1, u; { B,n R } ; In detail, under the benchar-im, we assue that a control unit (CU) collects the ICI inforation of all cell-edge users in the three cells. Then, the CU aes the best ICI itigation decisions, which are infored to the BSs. The decisions are ade independently for the cell-edge user groups of each containing three co-subcarrier-code users. For a cell-edge user group, the CU finds the best itigation decision achieving the highest su rate by exhaustively searching the 1 possible decisions, as stated in lines 3-8 of Algorith 1. However, the benchar-im requires analog ICI inforation of all cell-edge users for decision aing, which is required to be sent to the CU. In this case, the benchar-im ay ipose a heavy coplexity burden on the bachaul networ, especially when there is a big nuber of cell-edge users. Therefore, in Section IV, we propose the distributed ICI itigation algorith under the RAIM schee, which does not require the BSs to now any ICI inforation of users. IV. NOVEL DISTRIBUTED RESOURCE ALLOCATION ASSISTED BY ICI MITIGATION In this section, we propose a novel low-coplexity heuristic schee, naely RAIM, which can approxiate the benchar schee in Section III. The proposed RAIM is a fully distributed schee for the resource allocation and ICI itigation in the considered ulticell syste, and it does not require the BSs to share any channel inforation. The fully distributed RAIM schee consists of the SA, CA and ICI itigation algoriths, which are referred to as the RAIM-SA, the RAIM-CA and the RAIM-IM. Let us now first discuss the RAIM-SA algorith. A. RAIM s Subcarrier Allocation: RAIM-SA The RAIM-SA algorith otivates to find a proising suboptiu solution to the proble of (4), by axiizing the best SNR of users as well as the worst SNR of users. The

7 7 R (u ) R (u ) = n N = n N,n log 1 + c (u ) c (u ),n log 1 + h (u ), ) n N c(u,nĩ(u),,n + ) Ī(u + σ h (u ), n N c(u ),n (Ĩ(u),,n + Ĩ(u ),,n ) + σ, F (u ), (9), F (u ). (30) (Algorith ) Stage I of RAIM-SA: Candidate Searching (For BS u, u U) 1: Initialization: F (u) = U (u) =, M; Q (u) =, M (u) = M, K (u) ; : Repeat 3: Each user identifies an unselected subcarrier having the best subchannel quality as a candidate: (E.1): 4: Update: (D.1): = arg ax M (u) {A (u), }, K(u) ; U (u) U (u) {}, Q (u) Q (u) { }, K (u), (D.): M (u) M (u) { }, K (u) ; 5: Condition chec: (C.1): U (u) N, M; 6: Until C.1=true RAIM-SA has two stages, and is independently operated by each BS. During Stage I, the algorith searches the candidates (including the subcarriers and users) having the best subchannel qualities. During Stage II, it allocates the candidates in the way that copletes the allocation with the iniu nuber of candidates required. The principles of the RAIM-SA are suarized in Algoriths and 3. In Stage I given by Algorith, it iteratively searches the best candidates in each cell. During an iteration, each user in cell u identifies a candidate subcarrier which has not been selected and has the best subchannel quality. For the exaple in (E.1), user finds that subcarrier is a candidate, and user is also seen as a candidate of subcarrier. Then in line 4, BS u updates the candidate sets U (u) and Q (u), which contain the candidate indexes, respectively, for subcarrier and user in cell u. At the end of each iteration, the algorith checs if enough candidates are found, i.e. Condition (C.1) is satisfied. The algorith proceeds to Stage II when each subcarrier has at least N candidate users, which is required by our allocation. In Stage II, one candidate subcarrier is allocated to one candidate user in each iteration. The RAIM-SA algorith otivates to coplete the allocation in Stage II with the iniu nuber of candidates. As shown in Algorith 3, during an iteration it first tries to finds the candidate which only has the fixed allocation option/options but no other options, as shown in lines 3-6. For instance, in line 3, it finds that subcarrier has to be assigned to its candidate user. This is because, as shown in (E3.1), the nuber of the candidate users for subcarrier is equal to its possible nuber of allocations. Siilarly, in line 5, user has the only one candidate, i.e. subcarrier. When the fixed allocation is unavailable, the allocation of the candidates having ore than one allocation options follows the ax-in ethod, which ais to axiize the iniu subchannel quality of the candidate assigned. In (Algorith 3) Stage II of RAIM-SA: Candidate Assigning (For BS u, u U) 1: Initialization: M = M, K(u) = K (u) ; : Repeat (Fixed Allocation) 3: Identify subcarrier with fixed allocation option/options and find its candidate user : (E3.1): ˇM = { U (u) = N F (u), M}, U (u) ; 4: If ˇM = 5: Identify user having candidate subcarrier only: (E3.): Ǩ(u) = { Q (u) = 1, K (u) }, U (u) ; 6: End (Max-Min Allocation) 7: If ˇM = & Ǩ (u) = 8: Identify user having the iniu worst candidate subchannel quality: { (E3.3): = arg in in K(u) (u) Q {A (u), }; } 9: Find user the best candidate subcarrier having the highest subchannel quality: (E3.4): = arg ax (u) Q {A (u), }; 10: End 11: Allocate subcarrier to candidate user : F (u) F (u) { }; 1: Update: (D3.1): U (u) U (u) { }; Q (u) (D3.): K(u) K (u) { }, M M { } if F (u) = N; 13: Condition chec: (C3.1): U (u) N F (u), M & Q (u) 1, K (u) ; 14: Until M = or (C3.1)=false 15: Go bac to line of Stage I if (C3.1)=false; Q(u) { }, (E3.3), aong the reaining users in K (u), user is identified since it has the iniu worst candidate subchannel quality. Then it finds the best candidate subcarrier for user, which is subcarrier having the highest subchannel quality. Once having identified the candidates, it carries out the corresponding allocation, which is given in line 11. The algorith copletes the candidate allocation when allocation requireent is et. However, when there are not enough candidates for reaining allocation, i.e. Condition (C3.1) is unsatisfied, the algorith goes bac to Stage I to add ore candidates. B. RAIM s Code allocation: RAIM-CA After carrying out the SA, the RAIM schee operates the distributed CA, i.e. the RAIM-CA algorith. The RAIM-CA otivates to approach the perforance of the benchar-ca algorith. It can find the low-coplexity sub-optiu solutions to the probles of (5) and (7) by iniizing the ICI

8 8 of each co-subcarrier user group in each cell. The RAIM-CA is carried out in three stages successively and independently by the three BSs. Siilar to the benchar-ca, during the first stage, BS 0 randoly allocates codes to its users. During the second and third stages, the CAs of cells 1 and follows the principles in Algorith 4 based on the nowledge of the bitvalued ICI (bici) inforation of intracell users. Shown by Algorith 4, the CA is carried out independently for each co-subcarrier user group containing N users, and one code is allocated to a user during each of N iterations. First of all, the users estiate their ICI fro the cell/cells whose CA has/have been done in previous stage/stages. Then the users infor its BS the bici for the allocation. For the exaple shown in (E4.1), Î(u),, is the bici received by user fro BS u, when assuing both users and in cells u and u are assigned subcarrier. The bici Î(u),, Î (u),, = { 0 if I (u),, < I t, 1 if I (u),, I t can be given by (31) where I t is the threshold that defines if the ICI is sall (Î(u),, = 0) or strong (Î(u),, = 0). Known fro (E4.1), during the second stage, BS u (u = 1) only aes use of its users bici fro BS 0, which is evaluated as Ĩ(u) Î (u),,,, = = {0, 1}. By contrast, during the third stage, BS u (u = ) eploys the cobined bici fro both BSs 0 and 1, which is evaluated as Ĩ(u),, = {0, 1, }. Specifically, when Ĩ (u),, =, it eans that user suffers strong ICI fro the other two BSs, which is the case that the RAIM-CA otivates to avoid. As shown in lines 5-10, the RAIM-CA identifies a co-code user pair for allocating a code during each iteration. In line 1, when the pair (u, u ) is identified, user u is allocated code n which has been allocated to user u in a previous stage. Note that, during the third stage, it actually finds a pair of co-code users for the user in cell, since the CAs of cells 0 and 1 have been done in previous stages. The algorith otivates to find the user pair of sall ICI, which contains the co-code user generating the sall ICI to the user. Therefore, the algorith first tries to identify a user pair of sall ICI for fixed allocation. As the exaple shown in line 5, when the pair (, ) in Θ (u,u ),0 is identified, it eans user has only one co-code user available, i.e. user, generating sall ICI to user. By contrast, when the pair (, ) in Θ (u,u ),1 is identified, user generates strong ICI to all the users of subcarrier in cell u except user (u. Note that, in (E4.), F ) contains the indexes of the users with subcarrier allocated in cell u but without codes assigned, and Ṽ(u) contains the indexes of available co-code users in cell u for the users in F (u ). When the fixed allocation of sall ICI is unavailable, i.e. Θ (u,u ) =, the RAIM-CA selects the user pair of sall ICI that can avoid the axiu nuber of the allocation of strong ICI in future allocation, which is described by line 6. Furtherore, when there is no co-code user pair of sall ICI found, i.e. Θ (u,u ) =, the RAIM-CA tries to identify a desired user pair containing the user, which suffers strong ICI fro only one BS. The identification process for this given in lines 8-9 is (Algorith 4) RAIM s Code Allocation: RAIM-CA (For BS u = 1, ) 1: Initialization: V (u ) u = 0, M; : For =, Ṽ(u) = V (u), F (u ) = F (u ), For Subcarrier = 0,..., M 1 3: Users allocated subcarrier infor BS u bici inforation {Î(u),,,, }, BS u fors inforation {Ĩ(u),,,, }: (E4.1): Ĩ(u),, = u i=0 Î(i), i,, F (u), i F (i), F (u ) ; 4: Repeat 5: Identify a co-code user pair of sall ICI (u, u ) Θ (u,u ) for fixed allocation, and Θ (u,u ) = Θ (u,u ),0 Θ (u,u ),1 which are defined in (E4.), (E4.3) and (E4.4); 6: Find the co-code user pair of sall ICI (u, u ) that avoids the axiu nuber of strong ICI assignents if Θ (u,u ) = & Θ (u,u ) : (E4.5):(u, u ) = arg ax (, ) Θ (u,u ) { Ǩ(u) + ) Ǩ(u }, (E4.6):Ǩ(u) }, Ǩ (u ) = {j Ĩ(u) j,, 0, j F (u ) = {j Ĩ(u),j, 0, j Ṽ(u) }; 7: If Θ (u,u ) = 8: Identify a desired co-code user pair of strong ICI (u, u ) Λ (u,u ) for fixed allocation, and Λ (u,u ) = Λ (u,u ),0 Λ (u,u ),1, which are defined in (E4.7), (E4.8) and (E4.9); 9: Identify a desired co-code user pair of strong ICI (u, u ) ) Λ(u,u if Λ (u,u ) = ; 10: Select a co-code user pair of strong ICI (u, u ), where Ṽ(u), F (u ) if Λ (u,u ) = ; 11: End 1: Allocate code n to user u : ) V(u V (u ) (n ) { u }, where V (u) (n ) = {u}; 13: Update: Ṽ(u) 14: Until F (u ) 15: End Ṽ(u) {u}, (u F ) F (u ) = 16: Update: u u + 1; { u }; siilar to that for a user pair of sall ICI shown in lines 5-6. Finally, when a desired co-code user pair cannot be identified, as in line 10, the algorith is forced to select a co-code user pair including the user, which suffers strong ICI fro two BSs. C. RAIM s ICI Mitigation: RAIM-IM After the SA and CA, the RAIM schee carries out the distributed ICI itigation, naely RAIM-IM. The RAIM-IM algorith otivates to find a proising sub-optiu solution to the proble of (19) in order to approach the perforance of the benchar-im. The BSs successively and independently carry out the RAIM-IM for their cell-edge users, but they do not share any channel inforation. For the sae of coparison, we also extend the existing on-off power (OOP) ICI itigation algorith [8, 33] to our ulticell systes. Let us first briefly discuss the principles of the OOP algorith under our systes. The OOP algorith [8, 33] eployed by the OFDMA systes can efficiently itigate ICI, which however does not eploy BS cooperation. In a little ore detail, the core principle of the OOP is to allow BSs to switch off the transissions suffering strong ICI. In our three-cell MC DS-CDMA systes, the OOP is scheduled to be carried out by the BSs in three

9 9 { (E4.) : Θ (u,u ) = (, ) Ĩ(u) { (E4.4) : Θ (u,u ),1 = (E4.7) : Λ (u,u ) = (E4.9) : Λ (u,u ),1 =,, = 0, Ṽ(u), F } (u ), (E4.3) : Θ (u,u ) },0 = (, ) j F (u ),j Ĩ(u) j,, 0, (, ) Θ (u,u ). { (, ) Ĩ(u),, = 1, Ṽ(u), F } (u ), (E4.8) : Λ (u,u ) { (, ) Ĩ(u) j,, =, j, j F } (u ), (, ) Λ (u,u ).,0 = { (, ) j Ṽ(u),j } Ĩ (u),j, 0, (, ) Θ (u,u ), { } (, ) Ĩ(u),j, =, j, j Ṽ(u), (, ) Λ (u,u ), (Algorith 5) RAIM s ICI itigation: RAIM-IM (For Subcarrier, M and Code n, n N ) 1: Initialization: d (u),n =, d (u ),n =, d (u ),n =, where V (u) (n) =, V (u ) (n) =, V (u ) (n) = ; u u u, u, u U; : For Stage u = 0, 1, 3: User estiates its SIR η (u),, if η (u), < η t & d,n (u) =, execute: 4: User infors BS u the requireent of the cooperation fro BS u (or u ) if (C5.1)=true (or (C5.)=true), (C5.1): η (u), η t & I (u ),, < I c I (u ),,, (C5.): η (u), η t & I (u ),, < I c I (u ),, ; 5: BS u requests BS u (or u ) for the cooperation for user ; 6: BS u (or u ) accepts the cooperation for user : d (u ),n = (or d (u ),n = ), if BS u (or u ) is available d (u ),n = (or d (u ),n = ); 7: If ((C5.1)=false and/or d (u ),n = ) & ((C5.)=false and/or d (u ),n = ) 8: BS u broadcasts essage that it can provide cooperation; 9: BSs u (or u ) confirs that user (or ) requires the cooperation fro BS u if (C5.3)=true (or (C5.4)=true), (C5.3): d (u ),n = & η (u ), η t & I (u),, < I c I (u),,, (C5.4): d (u ),n = & η (u ), η t & I (u),, < I c I (u),, ; 10: BS u accepts the cooperation for user : d (u),n =, if < ηt. Otherwise, BS u accepts the cooperation for user : d (u),n = ; 11: BS u switches off the transission to user : d (u),n = 1, if (C5.3)=false & (C5.4)=false; 1: End 13: End η (u ), stages. The OOP algorith aes the ICI itigation decisions independently for the cell-edge user groups. During stage u (u U = {0, 1, }), BS u turns off the transission to the user with poor SIR, such as user (η (u) < η t ), where η t is the SIR threshold. By turning off the transissions having poor SIR, it saves power for future transissions, when the transissions counication qualities becoe iproved. In addition, the ICI iposed by these transissions with poor channel conditions on the other cells can also be reoved. By contrast, our RAIM-IM algorith eploys STBC based BS cooperation in addition to the strategy of power off, in order to achieve iproved perforance. However, the cooperation cost is ainly the increase of the coplexity for exchanging users data aong BSs, and that the BSs have to stop transitting inforation to soe of their own users. Therefore, the RAIM-IM ais to axiize the pay-off fro BS cooperation, while iniizing the cost. The principles of the RAIM-IM are suarized in Algorith 5. The RAIM-IM aes the ICI itigation decisions for the cell-edge user groups of each containing three co-subcarriercode users within three stages. As the exaple of Algorith 5, subcarrier and code n are assued in line 1 to allocate to users, and in cells u, u and u. During stage u, user infors BS u the requireent of ICI itigation if it finds that its SIR is below the threshold, i.e. η (u), < η t. Then the itigation decision can be ade by lines The RAIM- IM algorith otivates to axiize the benefit fro using BS cooperation. Hence, in line 4 user first checs if the conditions for cooperation are et, i.e. (C5.1) and/or (C5.) are satisfied. User requests the cooperation fro BS u when (C5.1) is true. There are two conditions included in (C5.1). First, the new SIR of user after the cooperation, i.e. η (u),,n, should exceed the SIR threshold, which is η (u),,n η t η (u),,n. Second, only one neighboring iposes strong ICI on user, i.e. I (u ),, < I c I (u ),, or ) I(u,, < I c I (u ),,. The philosophy behind the second condition can be explained as follows. If BSs u and u set up the cooperative transission for user, the SIRs of the three users becoe η (u), = h(u), + I (u ) I (u ),,,,, η (u ), = 0, η (u ), = h (u, I (u),, +. (3) ) I(u,, Known fro (3), the SIR of user can be significantly iproved, when I (u ),, is large but ) I(u,, is sall. In this case, the su rate of the three users is ost probably increased owing to aing use of the strong ICI of I (u ),,. By contrast, when both I (u ),, and ) I(u,, are very wea or very strong, the su rate of the three users contributed by this BS cooperation is insignificant. As stated in line 6, BS u accepts the cooperation request for user when it is available d (u ),n =, in other words, when it has not established a cooperation with another BS. Note that, when two BSs agree on a cooperation, the BS sends its user s data inforation to the cooperating BS. For the exaple, BS u sends the data sybol of user to BS u so that the two BSs carry out the STBC transission to user. When the conditions in line 7 are et, it eans that neither BS u nor BS u can provide the cooperation for user. Then the RAIM-IM algorith requests BS u to provide cooperation for users or in the other cells, which follows the process in lines In line 9 BS u broadcasts the essage of the availability of cooperation fro itself. Then BSs u and u as their users to chec if the conditions for the cooperation, i.e. (C5.3) or (C5.4), can be satisfied. Note that, the conditions of (C5.3) and (C5.4) are siilar to those of (C5.1) and (C5.), and the philosophies have been explained above. It is worth noting )

10 10 that, when both the BSs request the cooperation fro BS u, the algorith always prefers to set up the cooperation for the user with poor SIR. As shown in line 10, BS u accepts the cooperation for user, since η (u ), < η t. However, when no cooperation can be set up, BS u has to turn off the transission to user, shown by line 11. V. CHARACTERISTIC AND COMPLEXITY ANALYSIS In this section, we analyze the characteristics and the coplexity of the RAIM schee as well as the benchar schee. A. Characteristic Analysis The proposed benchar schee is obtained by solving and closely solving the forulated probles in (14), (16) and (19), which are respectively for the distributed SA and CA, as well as the ICI itigation. For the considered ulticell DS-CDMA syste, the benchar schee proposes a novel strategy of resource allocation and ICI itigation. It proposes that distributed SA is first carried out for axiizing intracell subchannel quality, then distributed CA is operated for axiizing the su rate of the co-subcarrier users, and ICI itigation is finally ipleented for axiizing the su rate of cell-edge users. The proposed strategy can be efficiently eployed by practical ulticell counication systes owing to the various advantages suarized as follows. First, the strategy eploys distributed resource allocation which can quicly respond to various wireless environents, and it can also be easily extended to large systes with the iniu aount of cost needed. Second, the proposed strategy otivates to eep bachaul burden as low as possible. Third, the proposed strategy also ais to iniize the load on intracell feedbac channels, where very liited ICI inforation is only required to transit. The RAIM schee follows the novel strategy proposed by the benchar schee, and it also otivates to achieve the optiization objectives of the benchar. By contrast, the RAIM schee is designed to approach the perforance of the benchar schee, while lowering ipleentation coplexity and further iniizing bachaul burden as well as decreasing the cost of feedbac channels. Let us now discuss the characteristics of the RAIM s SA, CA and ICI itigation algoriths, and copare the with those of the benchar schee. The RAIM-SA is a fully distributed SA algorith, which requires uch lower coplexity than the benchar-sa and the other existing SA algoriths as analyzed in Section V-B. The coplexity required by the RAIM-SA is directly proportional to the nuber of ties S for operating Stage II to coplete allocation. Hence, in Table I, we suarize the average values of Ŝ according to the siulation considering the various cases. Seen fro Table I, S is always very sall even when the values of M and N are big. In contrast to the benchar- SA and the other existing SA algoriths, the RAIM-SA only requires each BS to now the intracell CSI of a part of its users, which guarantees very sall signaling burden on feedbac channels and very low ipleentation coplexity. Fro Table I, we also observe the RAIM-SA algorith requires a BS to now the intracell CSI of less than 50% users, i.e. ρ < 0.5, for ost scenarios. Due to the above advantages, the RAIM- SA can be efficiently used for the SA in other ulticarrier systes which eploy very high nuber of subcarriers, such as OFDMA systes. As suggested by the benchar-ca, the RAIM-CA independently and successively operate the CA for the cells in two stages, which guarantees very low ipleentation coplexity. By contrast, the RAIM-CA otivates to axiize the su rate of co-subcarrier users by avoiding strong ICI as any as possible in order to efficiently itigate ICI. Furtherore, for iniizing the signal burden on intracell feedbac channels, the RAIM-CA only requires a BS to carry out the CA based on the binary inforation about a part of ICI for its users. Both the benchar-im and RAIM-IM algoriths ai to axiize the su rate of the cell-edge users with the aid of BS cooperation and power off. The two algoriths establish the cooperation between two BSs instead of that aong three BSs in the considered three-cell systes, which eeps the cooperation cost and ipleentation coplexity as low as possible. The benchar-im requires the BSs to exchange the ICI inforation of cell-edge users, which can be avoided by the RAIM-IM in order to further lower the bachaul resources. Moreover, the benchar-im is able to find the optial ICI itigation solutions by eans of the exhaustive search with a relatively high coplexity required. By contrast, the distributed RAIM-IM algorith ainly otivates to iniize the ipleentation coplexity, while finding the suboptial ICI itigation solutions by axiizing the benefit of BS cooperation. The proposed benchar and RAIM schees can be odified for deployent in practical systes which ay have a large nuber of cells and users. First, the proposed SA algoriths will be directly used in practical systes, since they are fully distributed algoriths based on the intracell CSI only. Note that in practical systes, the RAIM-SA algorith can find better suboptial SA solutions, since ore nuber of subcarriers eployed by practical systes allows the SA to exploit higher selecting diversity. Second, siilar to the three-cell case, the CA is also carried out cell by cell in practical scenarios. The CA for a cell needs to consider the ICI effect fro the cells that have done CA in previous stages. Owing to the structure of the practical cellular systes, one user can usually siultaneously receive strong ICI fro two neighboring cells at ost, which happens when a user is located near the borders of three cells. Hence, the cells operating the CA after the second stage can consider the strongest two ICI effects only on each user, which will release a lot signal burden on feedbac channels. Third, the proposed ICI itigation algoriths can be directly applied to practical systes, where each cell-edge user group contains only three co-subcarrier-code users generating strong ICI to each other. However, there is still a possibility that one user is siultaneously a eber of two or ore cell-edge user groups. In this case, the ICI itigation algoriths can be odified to siply switch off the transission to a user belonging to two or ore cell-edge user groups. B. Coplexity Analysis In this section, we analyze the coplexity of the benchar and the RAIM schees. The coplexity ainly reflects the