Power Efficient Resource Allocation for Downlink ... - IEEE Xplore

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 60, NO. 5, MAY 2012

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Power Efficient Resource Allocation for Downlink OFDMA Relay Cellular Networks Jingon Joung, Member, IEEE, and Sumei Sun

Abstract—Resource allocation in orthogonal frequency division multiple access (OFDMA) relay cellular networks (RCN) has been investigated. We introduce an orthogonal frequency-and-time transmission (OFTT) protocol, in which orthogonal frequency and time resources are allocated to different communication modes and phases, respectively, and propose a simple algorithm for resource allocation. Communication modes (one- and two-hop modes), subchannels, and relay transmit power are sequentially allocated to enhance the power efficiency of the OFDMA RCN. We show an achievable quality-of-service tradeoff between one- and two-hop users. Furthermore, we show that the relays consume proportional power to their own second hop channel gains, whereas a single selected relay uses its full available power. Network power and system throughput are evaluated to confirm that the proposed OFTT protocol with the sequential resource allocation is power efficient in OFDMA RCN. Index Terms—Orthogonal frequency division multiple access (OFDMA), orthogonal frequency-and-time transmission protocol, power efficiency, relay cellular networks (RCN), resource allocation.

I. INTRODUCTION

R

ELAYING strategies have been applied to interferencelimited cellular networks to extend coverage, achieve diversity gain, and/or increase system capacity [1]–[5]. In downlink cooperative cellular networks, using both signals transmitted from base station (BS) and relay stations (RSs) can be a power inefficient strategy because BS or RS may consume high power to compensate relatively weak link gain. To reduce power efficiency loss, various orthogonal transmission of one-hop user equipment (denoted by UE1) and two-hop user equipment (denoted by UE2) have been studied [2]–[5]. In the orthogonal transmission, UE1s communicate directly with BS without any support from RSs, while UE2s communicate with BS through RSs without using a direct link to BS. These communication networks are henceforth referred to as relay cellular network (RCN) to be distinguished from the general cooperative cellular networks. A half-duplex (HD) relay that receives and transmits data separately is easier to implement as it does not suffer from cross interferences between retransmit signals from itself and Manuscript received March 21, 2011; revised July 26, 2011, November 02, 2011, and January 29, 2012; accepted February 02, 2012. Date of publication February 13, 2012; date of current version April 13, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Min Dong. The authors are with the Institute for Infocomm Research Institute for Infocomm Research I2R, A*STAR, Singapore 138632 (e-mail: [email protected]. edu.sg; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2012.2187643

Fig. 1. Relaying protocols in HD RCN with occurred interferences [12]. A variable stands for frequency. Variables , , and are period for the first, second, and third phases, respectively.

receive signals from BS (see, e.g., [6] and the references therein). The HD RCN requires at least two phases including a relay-receiving phase (first phase) and a relay-transmitting phase (second phase). We categorize the interferences during two phases into five types as shown in Table I. To maximize the benefit of the HD relays, various methods that meticulously manage the interferences have been studied vigorously. Some examples [7]–[22] including multiple-input multiple-output (MIMO) techniques, relay selection and sharing techniques, and resource allocation techniques are summarized in Table I. Various transmission protocols have also been studied for orthogonal frequency division multiple access (OFDMA) systems as illustrated in Fig. 1. An orthogonal time transmission protocol achieves lower spectral efficiency compared to a simultaneous transmission protocol because it uses three phases as reported in [12]. On the other hand, the simultaneous transmission protocol suffers from intracell interferences, namely and in the second phase, in addition to intercell interferences. To the best of our knowledge, there is no work in the literature which has considered a relay protocol simultaneously with the management of all corresponding interferences in the downlink OFDMA HD RCN. This has motivated our work. In this paper, we propose a power efficient resource allocation algorithm for an orthogonal frequency-and-time transmission (OFTT) protocol consisting of two consecutive phases as illustrated in Fig. 2. For the OFTT protocol in OFDMA HD RCN (simply OFDMA RCN), we formulate a multicell network power minimization problem with three constraints: an orthogonal subchannel assignment constraint, a relay transmit power constraint, and a quality-of-service (QoS) constraint, i.e., a lower bound of average signal-to-interference-plus-noise ratio (SINR). To solve the intractable original multicell problem, due to the tremendous complexity, we divide the multicell problem into multiple single cell problems and split each single cell problem into outer and inner problems. The outer problem

1053-587X/$31.00 © 2012 IEEE

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TABLE I INTERFERENCES IN HD-RCNFOR TWO PHASES

TABLE II NOTATION AND MODEL FOR SUBCHANNELS BETWEEN CELL

AND

and Fig. 2. Proposed OFTT protocol for OFDMA HD RCN. Variables represent orthogonal frequencies, and and are orthogonal phases.

is to assign the subchannels with communication modes and the inner problem is to design the relay processing. Then, we devise a simple heuristic strategy solving the outer and the inner problem sequentially. Consequently, throughout the proposed sequential resource allocation, the network power consumption can be reduced efficiently while achieving throughput as high as possible. The main contributions of our work regarding the OFDMA RCN are summarized as follows: • Transmit protocol; we introduce a power efficient OFTT protocol in OFDMA RCN (Section II). • Resource allocation algorithm; we formulate resource allocation problem (Section III), and propose a simple and sequential algorithm to allocate subchannels, communication modes, and relay transmit power (Section IV). • Effective link gain; for simple mode selection, we devise a new metric, i.e., an effective link gain consisting of instantaneous signal-to-noise-ratios (SNRs), which represents all involved link gains in the communication (Section IV-A). • Analysis; from the solution for the aforementioned algorithm, we show that: i) there is a tradeoff between achievable QoSs of one- and two-hop users; ii) the multiple relays consume proportional power to their own second hop channel gains; and iii) a single selected relay uses its full available power (Section IV-B). • Performance evaluation; we evaluate network power and system throughput to assess the performance of the OFTT protocol with various relaying strategies: multiple amplifyand-forward (AF) relay set, one AF relay selection, and one decode-and-forward (DF) relay selection. Based on the numerical results, we observe that the most power efficient strategy is a single DF relay selection for each subchannel in OFDMA RCN (Section V). Notation: The superscripts ’ ’ and ’ ’ denote transposition and complex conjugate transposition, respectively; , , and denote the absolute value, the Euclidean norm, and the norm, respectively; is an -by- identity matrix; is an

-by- zero matrix or vector; means the element of a denotes a diagonal matrix with the elements of vector ; the vector as its diagonal entries; is a column vector containing the diagonal entries of a square matrix ; and is the cardinality of a set . II. OFTT PROTOCOL AND SIGNAL MODELS The OFDMA RCN consists of cells. In cell , one BS (denoted by ) and HD RSs (denoted by , where represents AF or DF type of RSs) support UEs (denoted by ) through subchannels. A tradeoff between multiuser diversity (high throughput) and fairness in terms of the data rate can be achieved by scheduling users over multiple channel realizations in time domain. Since the scheduling is outside the scope of this study, throughout the paper, we focus on allocating resources for a single snapshot of channel realizations to the users, which are less than or equal to . Let a subchannel index be . With a channel gain from a transmitter (Tx) to a receiver (Rx) represented as , we summarize the notation of subchannel in Table II. The channel is divided into a path loss term generally depending on distance between Tx and Rx and a small scale fading term modeled as an i.i.d. and zero-mean complex Gaussian random variable with a unit variance. The second-order statistics for the channels thus are represented as , and the paper, we use index sets, Table III.

,

, respectively. Throughout , , and defined in

A. OFTT Protocol Refer to the OFTT protocol in Fig. 2. In the first phase of cell , with duration , transmits signals to and

JOUNG AND SUN: DOWNLINK OFDMA RCN

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TABLE III INDEX SETS USED IN THE PAPER

(3) where

is

’s received signal; is a first hop channel

by using frequency resources1 and , respectively, where and are orthogonal subchannels in , and represents a -hop user, i.e., . In the second phase, with duration where , transmits a signal with new information to through , and at the same time, retransthrough . Note that mits the received signals to is a logical representation of the users, i.e., generally a practical user can communicate as both UE1 and UE2 simultaneously if the subchannels in and are allocated in resource allocation. Due to the orthogonal frequency resource allocation between UE1 and UE2, intracell interferences, namely and , can be avoided. However, intercell interferences , , and occur in the OFTT protocol. The corresponding SINRs in the OFTT protocol are derived in the following sections.

vector; is ; relays’ AWGN vector with and is a vector whose elements are sum of an AWGN and a first hop intercell interference , i.e., . Since the first hop channels from BS to different RSs are independent of one another, i.e., and are independent if , we can model as . Here, an AWGN with . Also, since is independent of the channel vector , we can derive an instantaneous SINR at as (4)

B. SINR in First Phase

C. SINR in Second Phase

Let a data symbol at the subchannel of be with . A received signal of on subchannel in the first phase is written as

In the second phase, BS transmits new information signals to UE1s, and at the same time, RSs forward the received information in the previous phase to UE2s after processing with their own weight denoted by for . Thus, the receive signals in the second phase are modeled according to the forwarding types, AF and DF. Letting a weight vector on subchannel be for all fwd-relays in the cell, we show the receive signal and SINR models for both AF and DF cases. 1) AF Case: In the second phase, transmits new information signal to UE1. The receive signal of one-hop user (note that from the orthogonal frequency allocation described later) is written as

(1) is a fixed amount of transmit power2 of and is ’s zero-mean additive white Gaussian noise (AWGN) with a variance . In (1), the second term of the right . hand side (RHS) is an intercell direct interference The instantaneous SINR of one-hop user in the first phase is derived from (1) as where

(5a) (2)

(5b)

On the other hand, a vector representation of multiple relays’ received signal is written as

(5c)

(5d) 1Each frequency resource consists of a single subcarrier or a group of subcar-

riers (subband or chunk of subcarriers). Frequency resource granularity issue is not covered in this paper; henceforth, we call the frequency resources as subchannels which is typical in a frequency resource allocation. 2The

fixed amount of transmit power at BS has been currently applied in many standards such as 3GPP-LTE [19], [20]. Though BSs’ transmit power can be shared through two phases to further improve system performance, it makes a resource allocation problem more complex. Thus, we leave it as further work.

where

is a

second hop channel vector and is a diagonal matrix with the elements of a relay weight vector . Here, the RHS of (5a) is an intended signal from from all BSs ; (5b) is a direct intercell interference

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in cell where ; (5c) is a second hop intercell interference from all AF RSs in cell ; and (5d) is a total noise. One-hop user’s instantaneous SINR is derived from (5) as (6), shown at the bottom of the page. At the same time, multiplies the receive signal in (3) by the weight and forwards it to UE2. The two-hop ’s receive signal is written as user (7a)

(7b) (7c)

(9b) (9c) (9d) where the RHS of (9a) is an intended signal from at the second phase; (9b) is a direct intercell interference from all BSs in cell where ; (9c) is a second hop intercell interference from all DF RSs in cell ; and (9d) is an AWGN. One-hop user’s instantaneous SINR is derived from (9) and shown in (10) at the bottom of the page. The DF relay detects from the receive signal in (3), and retransmits it to . The receive signal is written as of two-hop

(7d)

(11a)

; (7b) is a where the RHS of (7a) is an intended signal from second hop intercell interference from all AF RSs in cell where ; (7c) is a direct intercell interference from all BSs in cell ; and (7d) is a total noise. Two-hop user’s instantaneous SINR is derived from (7) as (8), shown at the bottom of the page. 2) DF Case: If the DF relays are employed in the second phase, the receive signal of one-hop user is written as

(11b)

(9a)

(11c) (11d) , i.e., , the RHS If all relays correctly detect of (11a) is an intended signal from ; (11b) is a second hop intercell interference from all DF RSs in cell

(6)

(8)

(10)


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where ; (11c) is a direct intercell interference from all BSs in cell ; and (11d) is an AWGN. From (11), two-hop user’s instantaneous SINR is derived as (12), shown at the bottom of the page. III. PROBLEM FORMULATION FOR NETWORK POWER MINIMIZATION We are aiming at minimizing the average power consumption of multicell networks. In the mean time, the direct and second hop interferences in the second phase, namely those in (5), (7), (9), and (11), will be carefully managed by determining and designing . The average network power is defined as (13) is the network power transmitted on subchannel where during two phases. Let a transmitted signal from be . Then, if if and

In (16), we assume that every relay is deployed to obtain almost identical received-signal-power from its BS, i.e., . This assumption enables RSs to fairly support users who are distributed uniformly throughout the cell. After introducing three constraints on subchannel allocation, relay transmit power, and average SINR lower bound, we formulate an optimization problem which minimizes the network power under the constraints. A. Constraints on Subchannel Allocation To describe subchannel allocation, we define the assignment variable as if otherwise. Here, two constraints on

(18) are required and

(19a)

and

(19b)

(14)

in (13) is expressed as

(15) . In the RHS of where a vector (15), the first term is the average transmit power of all BSs for one-hop communications and the factor two appears since BSs transmit twice during two phases for one-hop communications; the second and the third terms are the average transmit power of all BSs in the first phase and of all RSs in the second phase, respectively, for two-hop communications. Since the data symbols, channel elements, and noises are independent of one another, we can further simplify (15) as

The first constraint (19a) means that a subchannel is occupied by only one user to prevent co-channel intracell interferences among the users in the same cell, namely and , and the second constraint (19b) implies that every user occupies at least one subchannel to achieve its own target performance. Again, the communication mode index is defined as

if subchannel is allocated for -hop communication to . Combining assignment variable and communication mode index , we define the indicator representing both frequency allocation and communication mode as (20)

(16)

and its vector representation

(17)

If , subchannel is not allocated to . On the , subchannel is allocated to other hand, if for -hop communication.

where if if

(12)

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B. Constraint on Relay Transmit Power by

Average transmit power per-subchannel of RSs is bounded as and

where on subchannel

is a second hop intercell interference of derived as

(25)

(21)

Instead of a sum power constraint, we use the per-subchannel power constraint in (21). The per-subchannel power constraint is stricter than the sum power constraint; therefore, the power allocation satisfying the per-subchannel power constraint always satisfies the sum power constraint, yet it yields a loss of degree-of-freedom at power allocation, resulting in power efficiency reduction. However, the per-subchannel power constraint enables us to handle a relay weight design problem for individual subchannel separately as shown in (36) later. As a consequence, we can easily handle the problem. Furthermore, a peak-to-average-power ratio (PAPR) can be reduced [24]. Using (3) and (14) in (21), a constraint on relay weights is derived as

represents a direct intercell interference and on subchannel of derived as

Here, a diagonal matrix

Similarly, for UE2, we get

from (8) and (12) as (26)

and

(22)

where a maximum value of relay amplification factor is denoted . by C. Constraints on Average SINR Lower Bound Since the allocation and the relay processing affect not only the network power but also the system performance, the network power minimization problem should include a constraint for reliable communications; otherwise, it yields an obvious solution that every node becomes silent to minimize network power. The intercell direct interferences in the first phase in (1) are unmanageable because of the fixed broadcasting power of BSs. Also, the direct interferences are relatively smaller than the second hop interferences in the second phase due to the longer distance from the interference sources. We thus focus on the strong interferences in the second phase. The constraints on the second phase performance is written with QoS required for the -hop user as and

and

(23)

D. Optimization Formulation Let

a

multicell-multiuser

indicating

vector

be

, where is a multiuser indicating vector defined ; as and let a multicell-multiuser relay weight vector be , where is a multiuser (multiple subchannels) expression of the relay processing vector . With as the constraints in (19), (22), and (23), we eventually formulate an optimization problem that minimizes the network power in (13) as follows: (27a)

s.t. where

and

is a set of all candidates of vector

(27b) .

IV. SIMPLE AND SEQUENTIAL STRATEGY PER CELL where -hop user

is a lower bound3 of the average SINR of , i.e.,

From (6) and (10), we can derive

. of UE1 as

(24) 3From the facts that i) an average signal power and an average interferare positive and independent of each other and ii) ence-plus-noise power is a convex function, we can show that from Jensen’s inequality. In our problem, the lower bound constraints (23) perform well, especially, when the interferences are strong. This is because the bound becomes tight as a denominator increases.

Noting two facts that: i) is directly mapped from the indi; and ii) the network power is a function cator vector of and as represented in (16), we express the network power as a function of and as . Then, without any loss of optimality, we rewrite the objective function in (27a) as (28) In (28), the minimization problems outside and inside the bracket are called as an outer and an inner problems, respectively. To find the optimal solution, we have to solve the outer problem with all candidates from assignments .


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Since there is tremendously large number of candidates of , around , it is intractable to directly solve the original problem (27); thus, the problem simplification is inevitable. Furthermore, we acknowledge a difficulty in solving the inner problem itself due to the intertwined variables among the cells. To circumvent these problems and to reduce the complexity and network overhead, we divide (27) into multiple single cell problems. Accordingly, we rewrite the objective function (28) for given as (29) where

is a set of -by-1 vector ’s, and is cell ’s network power derived as

(30) Now, a heuristic strategy, in which the inner and outer problems with the single cell objective function in (29) are sequentially solved, is proposed to efficiently find a close approximation to the optimal solution and to significantly reduce the complexity. Firstly, we modify the outer problem to a linear assignment problem with an effective link gain. Under a constraint on orthogonal subchannel allocation, we find the subchannel allocations and communication modes, which maximize the effective link gain and equivalently minimize the network power [23]. Secondly, for the subsequent inner problem with the allocated subchannels and communication modes from the outer problem, the relay processing has been designed under constraints on relay transmit power and on a QoS. The QoS constraint is relaxed to guarantee the feasibility of the inner problem; as a result, the transmit rates are maximized in feasible region.

A. Outer Problem: Communication Mode and Subchannel Allocation The communication modes and subchannels are assigned by solving a modified outer problem s.t.

(31)

In (31), identical transmit power is assumed for all relays to decouple the outer problem objective function from (29), i.e., where is an arbitrary positive real number. The performance degradation from this assumption can be compensated during a subsequent optimization of the inner problem, which will be verified through numerical results in Section V. Under the assumption, the network power in (31) is derived from (30) as

(32)

From the fact that the network power in (32) is a function of and communication modes, we see that in (31) is only an assignment problem. To apply a simple linear assignment algorithm that matches between two separate vertex groups [25] into (31), we determine beforehand the communication mode. To that end, we introduce an effective link gain of that is a representative gain of -links including two-hop links and one direct link of subchannel . At the end of this section, we will provide examples of the effective link gains. Using the effective link gains allows the communication mode to be determined implicitly. If the direct-link gain is chosen as the effective link gain, , otherwise, . As a consequence, the problem in (31) is simplified to a linear assignment problem to find a matching from user to subchannel , i.e., instead of since is given in (20). Furthermore, from the fact that the required power decreases as an effective link gain increases [23], is eventually modified as

s.t.

(33)

, are determined to In (33), assignment variables, minimize the cost, equivalently to maximize a sum of effective link gains. The modified problem is a linear assignment problem and it can be readily solved by using any linear assignment algorithms, such as the Hungarian, Edmonds-and-Karp’s, and network flow algorithms [25]. Also, there are many efficient suboptimal algorithms to solve (33), e.g., a best-fit algorithm assigning the best available resource to a user sequentially [26]. The number of candidates for all cells, i.e., combinations of , is reduced to . The optimization is performed in distributed manner. In other words, each obtains for all and from (33), and gets the indicator , locally. vector denoted by Three effective link gains are introduced according to a relaying strategy. 1) Multiple AF Relay Set: Since a two-hop link gain of AF relay systems is represented by a multiplication of the first and second hop gains, the effective link gain of multiple AF relay systems is represented by

where the instantaneous link-SNRs are defined as ;

; and

. Here, we get two-hop link gain by averaging two-hop link gains because the multiple forwarded signals are combined at the destination. 2) One AF Relay Selection: Though one relay selection is a suboptimal strategy for the Gaussian parallel AF relay networks

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as studied in [23], it outperforms the strategy employing a multiple AF relay set if RSs have only second-order statistics as observed in Section V. The effective link gain for one AF relay selection is expressed as follows:

where positive values

(37a) where the selected AF relay index imum two-hop link gain as

is obtained from the max-

3) One DF Relay Selection: For one DF relay selection, we employ a strategy in [23] as follows: if otherwise where the selected DF relay index

Here,

is obtained as

(37b) and the

-by-1 vector (38)

Note the facts that: i) the decomposition among cells is performed only on the objective function in (36a); ii) constraint (36b) is identical to (22); iii) constraints (36c) and (36d) sustain the constraint in (23); and iv) the constraints still include the intercell interferences as shown in (37). For the detailed derivation, see the Appendix. If there exists an intersection of (36b)–(36d), we can find the solution of (36) as

is the useful relay set defined as

(39)

This strategy is known as an optimal strategy for minimizing network power with a throughput constraint and also for maximizing throughput with a power constraint in Gaussian parallel-relay networks [23].

otherwise, there is no feasible solution. If a feasible solution of (36) exists, from the definition in (35), we get ’s weight for given subchannel as

(40)

B. Inner Problem: Relay Processing Design The inner problem is solved with the given obtained from (33) to determine the relay processing as follows:

where (41)

s.t.

and

(34)

Note that the network power in (34) is a function of only since is given. Due to the orthogonal frequency allocation in (33), the problem can be independently solved for each . Thus, subchannel index is henceforth subchannel omitted in this section when it is convenient for notation. Define the vector of squared magnitude of relay weights as (35) Using (35), we equivalently rewrite (34) as (36a) (36b) (36c) (36d)

The relay processing in (40) controls relay’s transmit power. Each relay magnifies a retransmit signal according to its second . Since scales up or down hop channel gain the weights of subchannel of all RSs in cell , we call it as a common scaling factor. Using (37b) in (41), we can show Second hop channel gains

(42)

and interpret it as follows: i) As the interferences and/or the noise increase with a given QoS, in (42) increases as well; as a result, relays’ transmit power increases to achieve the QoS. ii) As a QoS of two-hop users decreases for given channel conditions, in (42) decreases as well, resulting in the reduction of relays’ transmit power. iii) As the second hop channel gains increase when other values are given, decreases so that the relays reduce their transmit power. These phenomena match well with our strategy. For example, the relays decrease


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their transmit power to reduce network power when the second hop channel gains are large enough to achieve their QoSs. For fixed location of users, sometimes a user cannot achieve its target average SINR because of the limited power budget. In this case, i.e., if there is no feasible solution of (36), we have two options to support the user. One is to wait until the poor channel becomes better, so that the user can be served. The other is to relax its target average SINR. The first option requires a scheduling. In the current paper, we chose the second option to guarantee the feasible solution of (36) and relax the infeasible target to a maximum achievable target according to the environment. Consequently, instead of outage performance with a fixed target, we have evaluated the achievable rates without target QoSs as the performance measure in our simulation later. To the end, we need to know a maximum achievable QoS value. In the subsequent sections, we will show the maximum achievable QoS values from the feasibility conditions and provide the feasible relay weights. 1) Achievable QoS Region: The conditions to obtain the feasible solution in (40) are derived from the conditions for non-empty intersection of (36c)–(36d) as (43a) (43b) From the QoS feasibility conditions in (43), we can verify a tradeoff between achievable QoSs of one- and two-hop users as shown. • As increases in (37a), decreases, resulting in violation of (43a) if is fixed. In such a case, should be reduced to increase and satisfy (43a) since is fixed. This scenario is reasonable because UE1’s performance in the second phase is affected by the second hop intercell interferences, , from all relays which are in other cells and use UE1’s subchannels. • On the other hand, as increases in (37b), increases as well; as a result, (43a) can be violated if is fixed, should though (43b) is still satisfied. In such a case, be reduced to satisfy (43a). This scenario is also reasonable because UE2’s performance is affected by the direct intercell interferences, , from all BSs which are in other cells and use UE2’s subchannels. Under the assumption that is large enough to satisfy an inequality which is typically true in the considered system configuration in Section V-B, (43a) is always satisfied if (43b) is satisfied. Thus, we focus on the critical constraint (43b). By substituting (37b) for in (43b), we get an achievable region of UE2’s QoS as

(44) where as

is the normalized second hop channel gain defined (45)

The upper bound in (44) is achievable only when all relays in cell know , which is unrealistic. This is because enormous signaling is required for the relays to estimate the second hop intercell interferences of all users in other cells, i.e., where and [see (37b) and (39)]. Therefore, we are motivated to derive a new QoS bound indicating a practically achievable QoS region for given and . Under the strongest second hop interference assumption, namely is for its maximum value satisfying (43b) and all in (44) where , we can derive the practically achievable QoS bound as

(46) 2) Relay Weights: Since in (46) is derived under the strongest interference (worst case) scenario, any is achievable in cell without knowledge of . As a consequence, we can design a relay processing weight satisfying the feasible QoSs. Substituting QoS in (37a) with in (46), and again using the strongest interference assumption that where , we can derive the upper bound , and then obtain the upper bound of in (41) as of

(47)

in (40) as For the maximum achievable QoS, we set in (47), and consequently we get ’s weight for subchannel as

if

(48)

otherwise. Some remarks of interest from the feasible solution in (48) are as follows: R1: The relays consume proportional power to their own second hop channel gains. R2: The relays compute their processing weights in distributed manner. R3: Transmit weight of one selected relay besince , i.e., a single selected relay comes uses its full available power for retransmission. The third remark above implies that a transmit power control is not required for one-relay selection strategies in IV-A2 and IV-A3. From R3, we can see that the strategy selecting one relay for each subchannel is significant for practical implementation

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Step. 3 BS solves a linear assignment problem (33) by using the channel reciprocity of TDD systems, and obtains and broadcasts it to and . At the same time, the information is also broadcasted to ’s. estimates feedback information and deterStep. 4 RS mines its transmit power , from (48). A bottleneck procedure on computational complexity in an optimization is to solve (33). If the optimal linear assignment algorithm such as a maximum-weighted matching [25] is applied to (33), can find the optimal assignment with time complexity when is dominantly large. V. PERFORMANCE EVALUATION AND DISCUSSION We evaluate the average system throughput and network power of OFDMA RCN employing the OFTT protocol with three relaying strategies: multiple AF relay set (Orth-AF-Set), one AF relay selection (Orth-1-AF-Sel), and one DF relay selection (Orth-1-DF-Sel). Time sharing coefficients and are fixed at 0.5. Accordingly, the average throughput is evaluated from the instantaneous SINR’s in (2), (4), (6), (8), (10), and (12) as Fig. 3. Block diagrams of procedure. (a) Problem decomposition. (b) Signaling with feedback (broadcasting) and/or training signals.

of RCN because a relay can avoid much signaling and computing procedure. Furthermore, these pragmatic one-relay selection strategies cause more null subchannels and reduce PAPR at the relay like an antenna selection method in [27]. A simulation result, which is omitted in this paper, indicates that onerelay selection strategy can reduce PAPR by about 2 dB compared to other strategies using multiple AF relays. C. Summary of Sequential Procedure and Signaling The sequential procedure to solve the original problem is summarized in a block diagram illustrated in Fig. 3(a). The original problem is divided into multiple single cell problems. Each single cell problem is then split into the outer and inner problems. In the outer problem, instantaneous channel state information is used to maximize the diversity gain from the subchannel allocation as commonly assumed in literature. In the inner problem, on the other hand, the original constraints on lower bound of average SINR are taken into consideration. As a consequence, the relay processing is designed based on the second-order statistics as shown in (48), resulting in the reduction of a network overhead. Note that the relays require information of only which is broadcasted from as described in Step 3. Before the data transmission, we naturally consider a signaling period for the resource allocation as illustrated in Fig. 3(b). In time division duplex (TDD) systems, for example, the signaling procedure in cell is as follows: broadcasts a training signal. and Step. 1 UE estimate and , respectively. broadcasts a training signal and Step. 2 RS . estimates and the feed. back information

for AF RCN and for DF RCN. Here, we assume that each user’s data is coded independently and each user decodes only its own data, and the interferences are treated as white noise. To solve (33), Hungarian algorithm is used in our simulation. For benchmarking, we evaluate the performance of direct communication without relays (depicted by Di-Comm), in which all users perform one-hop communications regardless of their locations and SNRs. The simultaneous transmission protocol with a single DF relay selection strategy [12] (depicted by Sim-1-DF-Sel) is also included in our simulation. It is difficult to fairly and exactly compare the suboptimal methods to the optimum method because the optimality is not valid if the original problem is infeasible, i.e., if the QoS constraints in (23) are infeasible. A. Simulation Environment Each cell is modeled as a hexagonal array with 1 Km radius. Interference cells are generated up to the second-tier. Twenty users are uniformly generated throughout each cell times. Large-scale path loss with shadowing is generated from a lognormal model with a 3.76 path loss exponent and a 8.9 dB shadowing standard deviation (STD). Multipath fading is modeled as Rayleigh for the direct and second hop channels and as Rician with for the first hop channel. Refer to Table IV for more detailed parameters. Both BSs and UEs are equipped with a single omnidirectional antenna, while RSs have two antennas: a directional receive antenna focusing on BS and an omnidirectional transmit antenna broadcasting signals to UE2s. We assume a perfect signaling, in which the frequency-domain channel of the first OFDM symbol and the required second-order statistics are accurately estimated. The channel gain of the first OFDM symbol in each frame is used to allocate resources for the frame.


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TABLE IV SIMULATION PARAMETERS

B. Simulation Results and Discussion Fig. 4(a) and (b) show a cumulative distribution function (CDF) of power consumption and transmit rate. For the relay systems, each cell has 10 relays located 0.5 Km apart from the BS. The average network power consumption and achievable rate have been computed from the CDFs and depicted in the figures. An average network power of Sim-1-DF-Sel increases by 3% compared to Di-Comm, while that of OFTT protocol decreases. Namely, Orth-AF-Set, Orth-1-AF-Sel, and Orth-1-DF-Sel achieve the power reduction compared to Di-Comm by 3.2%, 22.7%, and 24.5%, respectively. Since no power is allocated at for two-hop subchannel during the second phase, network power can be further reduced with the OFTT protocol. Because Sim-1-DF-Sel employs a distance based communication mode selection, in which UEs located near BS (within 0.5 Km) are selected for direct communications, one- and two-hop users coexist in the same subchannel in most cases with a probability of 0.8. In other words, BS transmits twice and the selected RS transmits once on subchannels around 80% (due to the probability of 0.8 in CDF which is a step function) during two phases, resulting in a high probability of power consumption by . On the other hand, from the CDF function of Orth-1-DF-Sel, we observe that two-hop communication is assigned by around 70% (i.e., the probability of 0.7 in the step CDF). In this case, the subchannel power consumed dominantly is about , resulting in network power reduction. Fig. 4(b) confirms that RCN can improve a system throughput. We observe that Orth-1-DF-Sel outperforms other methods in terms of an average achievable rate with improvement of Di-Comm, Sim-1-DF-Sel, Orth-AF-Set, and Orth-1-AF-Sel by around 114%, 18%, 72%, and 41%, respectively. Fig. 5 compares power efficiency defined as an average achieved rate over average consumed power. The efficiency

Fig. 4. Simulation results when and RSs are located 0.5 Km apart from BS. (a) Subchannel power (dBm/phase) CDF. (b) Rate (bits/sec/Hz) CDF.

factor means a number of transmitted bits per unit power conwhen RSs are located 0.5 sumption. Fig. 5(a) shows over Km apart from BS, and Fig. 5(b) shows it over the relay position when . From the results, it is confirmed that Orth-1-DF-Sel always achieves the highest power efficiency compared to the others. The efficiency provides vital information for deploying multiple relays in multicell environments. For example, if Sim-1-DF-Sel and Orth-1AF-Sel schemes are employed to RCN, the efficient way is to locate relays as many as possible and as close as possible to BS. On the other hand, to locate small number of relays less than six at about halfway between BS and cell boundary is efficient for Orth-AF-Set scheme.

VI. CONCLUSION An OFTT protocol is introduced in downlink OFDMA RCN. Power efficient resource allocation including subchannel assignment, communication mode selection, and relay processing design, is proposed. From the numerical results in RCN, it is verified that the OFTT protocol improves the power efficiency with the proposed resource allocation and the relaying strategy selecting one decode-and-forward relay per-subchannel.

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Now, (A.3) is divided into two inequalities as (A.4a) (A.4b) From the fact that any arbitrary rewrite (A.3) as

satisfies (A.4b), we can

(A.5) where

is a

-by-1 arbitrary vector. Here, is invertible. Thus, (A.5) can be de-

rived as (A.6) , Noting that the object function in (36) is to minimize without loss of generality, we can set in (A.6) as a minimum-distance least squares solution for the underdetermined equality. Consequently, we can show (36c) from (A.6) as

Similarly, using (26) in the QoS constraint (23), we can show (36d). Fig. 5. Power efficiency comparison. (a) Over Km apart from BS. (b) Over relay position when

when RSs are located 0.5 .

APPENDIX DERIVATION OF (36) Using (24) in the QoS constraint (23), we get (A.1) and again using (25) in (A.1), we arrive at a underdetermined inequality (A.2) Noting that is a singular matrix, we get a singular value decomposition (SVD) of as , where

is a right singular

is a matrix having null vector vector and columns spanned from null space of . Multiplying to both sides of (A.2) and using the SVD, we can derive (A.3)

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Jingon Joung (S’04–M’07) received the B.S. degree in electrical engineering from Yonsei University, Seoul, Korea, in 2001, and the M.S. and Ph.D. degrees in electrical engineering and computer science from the Korea Advance Science and Technology (KAIST), Daejeon, in 2003 and 2007, respectively. From March 2007 to August 2008, he was a Postdoctoral Research Scientist with the Department of Electrical Engineering, KAIST. From April 2007 to August 2008, he worked as a Commissioned Researcher at Lumicomm, Inc., Daejeon. From October 2008 to September 2009, he was a Postdoctoral Fellow with the Department of Electrical Engineering at the University of California, Los Angeles (UCLA). Since October 2009, he has been a Scientist with the Institute for Infocomm , Singapore. His current research has focused on the study Research of energy efficient systems with multiuser multiple-input multiple-output (MIMO) and cooperative techniques. Dr. Joung was the recipient of a Gold Prize at the Intel-ITRC Student Paper Contest in 2006.

Sumei Sun received the B.Sc. (Honours) degree from Peking University, China, the M.Eng. degree from Nanyang Technological University, and the Ph.D. degree from the National University of Singapore. She has been with the Institute for Infocomm Research (formerly Centre for Wireless Communications) since 1995 and is currently Head of Modulation and Coding Department, developing physical layer-related solutions for next-generation communication systems. Her recent research interests are in energy efficient multiuser cooperative MIMO systems, joint source-channel processing for wireless multimedia communications, and wireless transceiver design. Dr. Sun has served as the TPC Chair of 12th IEEE International Conference on Communications in 2010 (ICCS 2010), General Co-Chair of 7th and 8th IEEE Vehicular Technology Society Asia Pacific Wireless Communications Symposium (APWCS), and Track Co-Chair of Transmission Technologies, IEEE VTC 2012 Spring. She has also been an Associate Editor of the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, and an Editor of IEEE WIRELESS COMMUNICATION LETTERS. She is a corecipient of IEEE PIMRC’2005 Best Paper Award.