Power Efficient Resource Allocation for Downlink OFDMA Relay Cellular Networks

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 60, NO. 5, MAY 2012 2447

Power Efficient Resource Allocation for DownlinkOFDMA Relay Cellular Networks

Jingon Joung, Member, IEEE, and Sumei Sun

Abstract—Resource allocation in orthogonal frequency divisionmultiple access (OFDMA) relay cellular networks (RCN) has beeninvestigated. We introduce an orthogonal frequency-and-timetransmission (OFTT) protocol, in which orthogonal frequencyand time resources are allocated to different communicationmodes and phases, respectively, and propose a simple algorithmfor resource allocation. Communication modes (one- and two-hopmodes), subchannels, and relay transmit power are sequentiallyallocated to enhance the power efficiency of the OFDMARCN.Weshow an achievable quality-of-service tradeoff between one- andtwo-hop users. Furthermore, we show that the relays consume pro-portional power to their own second hop channel gains, whereas asingle selected relay uses its full available power. Network powerand system throughput are evaluated to confirm that the proposedOFTT protocol with the sequential resource allocation is powerefficient in OFDMA RCN.

Index Terms—Orthogonal frequency division multiple access(OFDMA), orthogonal frequency-and-time transmission protocol,power efficiency, relay cellular networks (RCN), resource alloca-tion.

I. INTRODUCTION

R ELAYING strategies have been applied to interference-limited cellular networks to extend coverage, achieve di-

versity gain, and/or increase system capacity [1]–[5]. In down-link cooperative cellular networks, using both signals trans-mitted from base station (BS) and relay stations (RSs) can be apower inefficient strategy because BS or RS may consume highpower to compensate relatively weak link gain. To reduce powerefficiency loss, various orthogonal transmission of one-hop userequipment (denoted by UE1) and two-hop user equipment (de-noted by UE2) have been studied [2]–[5]. In the orthogonaltransmission, UE1s communicate directly with BS without anysupport from RSs, while UE2s communicate with BS throughRSs without using a direct link to BS. These communicationnetworks are henceforth referred to as relay cellular network(RCN) to be distinguished from the general cooperative cellularnetworks.A half-duplex (HD) relay that receives and transmits data

separately is easier to implement as it does not suffer fromcross 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 publicationFebruary 13, 2012; date of current version April 13, 2012. The associate editorcoordinating the review of this manuscript and approving it for publication wasProf. Min Dong.The authors are with the Institute for Infocomm Research Institute for Info-

comm Research I2R, A*STAR, Singapore 138632 (e-mail: [email protected]; [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]. Avariable 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 referencestherein). The HD RCN requires at least two phases includinga relay-receiving phase (first phase) and a relay-transmittingphase (second phase). We categorize the interferences duringtwo phases into five types as shown in Table I. To maximizethe benefit of the HD relays, various methods that meticulouslymanage the interferences have been studied vigorously. Someexamples [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 fororthogonal frequency division multiple access (OFDMA) sys-tems as illustrated in Fig. 1. An orthogonal time transmissionprotocol achieves lower spectral efficiency compared to a si-multaneous transmission protocol because it uses three phasesas reported in [12]. On the other hand, the simultaneous trans-mission protocol suffers from intracell interferences, namely

and in the second phase, in addition tointercell interferences. To the best of our knowledge, there isno work in the literature which has considered a relay protocolsimultaneously with the management of all correspondinginterferences in the downlink OFDMA HD RCN. This hasmotivated 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 illus-trated in Fig. 2. For the OFTT protocol in OFDMA HD RCN(simply OFDMA RCN), we formulate a multicell networkpower minimization problem with three constraints: an orthog-onal subchannel assignment constraint, a relay transmit powerconstraint, and a quality-of-service (QoS) constraint, i.e., alower 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 multicellproblem into multiple single cell problems and split each singlecell problem into outer and inner problems. The outer problem

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2448 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 60, NO. 5, MAY 2012

TABLE IINTERFERENCES IN HD-RCNFOR TWO PHASES

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

is to assign the subchannels with communication modes andthe inner problem is to design the relay processing. Then, wedevise a simple heuristic strategy solving the outer and the innerproblem sequentially. Consequently, throughout the proposedsequential resource allocation, the network power consumptioncan be reduced efficiently while achieving throughput as highas possible. The main contributions of our work regarding theOFDMA RCN are summarized as follows:• Transmit protocol; we introduce a power efficient OFTTprotocol in OFDMA RCN (Section II).

• Resource allocation algorithm; we formulate resource al-location problem (Section III), and propose a simple andsequential algorithm to allocate subchannels, communica-tion modes, and relay transmit power (Section IV).

• Effective link gain; for simple mode selection, we devise anew metric, i.e., an effective link gain consisting of instan-taneous signal-to-noise-ratios (SNRs), which represents allinvolved link gains in the communication (Section IV-A).

• Analysis; from the solution for the aforementioned algo-rithm, we show that: i) there is a tradeoff between achiev-able QoSs of one- and two-hop users; ii) the multiple re-lays consume proportional power to their own second hopchannel gains; and iii) a single selected relay uses its fullavailable power (Section IV-B).

• Performance evaluation; we evaluate network power andsystem throughput to assess the performance of the OFTTprotocol with various relaying strategies: multiple amplify-and-forward (AF) relay set, one AF relay selection, andone decode-and-forward (DF) relay selection. Based on thenumerical results, we observe that the most power efficientstrategy is a single DF relay selection for each subchannelin OFDMA RCN (Section V).

Notation: The superscripts ’ ’ and ’ ’ denote transpositionand complex conjugate transposition, respectively; , , and

denote the absolute value, the Euclidean norm, and thenorm, respectively; is an -by- identity matrix; is an

TABLE IINOTATION AND MODEL FOR SUBCHANNELS BETWEEN CELL AND

-by- zero matrix or vector; means the element of avector ; denotes a diagonal matrix with the elements ofthe vector as its diagonal entries; is a column vectorcontaining the diagonal entries of a square matrix ; and isthe 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 rep-resents AF or DF type of RSs) support UEs (denoted by

) through subchannels. A tradeoffbetween multiuser diversity (high throughput) and fairness interms of the data rate can be achieved by scheduling users overmultiple channel realizations in time domain. Since the sched-uling is outside the scope of this study, throughout the paper, wefocus on allocating resources for a single snapshot of channelrealizations 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) repre-sented as , we summarize the notation of sub-channel in Table II. The channel is divided into a path lossterm generally depending on distance between Tx and Rx anda small scale fading term modeled as an i.i.d. and zero-meancomplex Gaussian random variable with a unit variance. Thesecond-order statistics for the channels thus are represented as

,

and , respectively. Throughout

the paper, we use index sets, , , , and defined inTable III.

A. OFTT Protocol

Refer to the OFTT protocol in Fig. 2. In the first phase ofcell , with duration , transmits signals to and

JOUNG AND SUN: DOWNLINK OFDMA RCN 2449

TABLE IIIINDEX SETS USED IN THE PAPER

by using frequency resources1 and , respectively, whereand are orthogonal subchannels in , and represents a-hop user, i.e., . In the second phase, with duration

where , transmits a signal with new informa-tion to through , and at the same time, retrans-mits the received signals to through . Note thatis a logical representation of the users, i.e., generally a practicaluser can communicate as both UE1 and UE2 simultaneously ifthe subchannels in and are allocated in resource alloca-tion. Due to the orthogonal frequency resource allocation be-tween UE1 and UE2, intracell interferences, namelyand , can be avoided. However, intercell interferences

, , and occur in the OFTT protocol.The corresponding SINRs in the OFTT protocol are derived inthe following sections.

B. SINR in First Phase

Let a data symbol at the subchannel of be with. A received signal of on subchannel in

the first phase is written as

(1)

where is a fixed amount of transmit power2 of andis ’s zero-mean additive white Gaussian noise

(AWGN) with a variance . In (1), the second term of the righthand side (RHS) is an intercell direct interference .The instantaneous SINR of one-hop user in the first phase isderived from (1) as

(2)

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

1Each frequency resource consists of a single subcarrier or a group of subcar-riers (subband or chunk of subcarriers). Frequency resource granularity issue isnot covered in this paper; henceforth, we call the frequency resources as sub-channels 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 canbe shared through two phases to further improve system performance, it makesa resource allocation problem more complex. Thus, we leave it as further work.

(3)

where is ’s received signal;

is a first hop channel

vector; isrelays’ AWGN vector with ;andis a vector whose elements are sum of an AWGNand a first hop intercell interference , i.e.,

.Since the first hop channels from BS to different RSsare independent of one another, i.e., andare independent if , we can model asan AWGN with . Here,

. Also, sinceis independent of the channel vector , we can derive aninstantaneous SINR at as

(4)

C. SINR in Second Phase

In the second phase, BS transmits new information signalsto UE1s, and at the same time, RSs forward the received in-formation in the previous phase to UE2s after processing withtheir own weight denoted by for . Thus, the re-ceive signals in the second phase are modeled according to theforwarding types, AF and DF. Letting a weight vector on sub-channel befor all fwd-relays in the cell, we show the receive signal andSINR models for both AF and DF cases.1) AF Case: In the second phase, transmits new infor-

mation signal to UE1. The receive signal of one-hop user(note that from the orthogonal frequency allocation

described later) is written as

(5a)

(5b)

(5c)

(5d)

where is a

second hop channel vector andis a diagonal matrix with the elements of a relay weight

vector . Here, the RHS of (5a) is an intended signal from; (5b) is a direct intercell interference from all BSs


in cell where ; (5c) is a second hop intercellinterference from all AF RSs in cell ; and (5d)is a total noise. One-hop user’s instantaneous SINR is derivedfrom (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-hopuser ’s receive signal is written as

(7a)

(7b)

(7c)

(7d)

where the RHS of (7a) is an intended signal from ; (7b) is asecond hop intercell interference from all AF RSs incell 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

(9a)

(9b)

(9c)

(9d)

where the RHS of (9a) is an intended signal from at thesecond phase; (9b) is a direct intercell interferencefrom all BSs in cell where ; (9c) is a second hopintercell interference from all DF RSs in cell ;and (9d) is an AWGN. One-hop user’s instantaneous SINR isderived 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 signalof two-hop is written as

(11a)

(11b)

(11c)

(11d)

If all relays correctly detect , i.e., , the RHSof (11a) is an intended signal from ; (11b) is a second hopintercell interference from all DF RSs in cell

(6)

(8)

(10)


where ; (11c) is a direct intercell interferencefrom all BSs in cell ; and (11d) is an AWGN. From (11),two-hop user’s instantaneous SINR is derived as (12), shown atthe bottom of the page.

III. PROBLEM FORMULATION FOR NETWORKPOWER MINIMIZATION

We are aiming at minimizing the average power consumptionof multicell networks. In the mean time, the direct and secondhop interferences in the second phase, namely those in (5), (7),(9), and (11), will be carefully managed by determining anddesigning .The average network power is defined as

(13)

where is the network power transmitted on subchannelduring two phases. Let a transmitted signal from be

. Then,

ifif

(14)

and in (13) is expressed as

(15)

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

(16)

where

if

if(17)

In (16), we assume that every relay is deployed to obtain almostidentical received-signal-power from its BS, i.e.,

. This assumption enables RSs tofairly support users who are distributed uniformly throughoutthe cell.After introducing three constraints on subchannel allocation,

relay transmit power, and average SINR lower bound, we for-mulate an optimization problem which minimizes the networkpower under the constraints.

A. Constraints on Subchannel Allocation

To describe subchannel allocation, we define the assignmentvariable as

ifotherwise.

(18)Here, two constraints on are required

and (19a)

and (19b)

The first constraint (19a) means that a subchannel is occupiedby only one user to prevent co-channel intracell interfer-ences among the users in the same cell, namely and

, and the second constraint (19b) implies that everyuser occupies at least one subchannel to achieve its own targetperformance.Again, the communication mode index is defined as

if subchannel is allocated for -hop communication to .Combining assignment variable and communicationmode index , we define the indicator representing bothfrequency allocation and communication mode as

(20)

and its vector representation

If , subchannel is not allocated to . On theother hand, if , subchannel is allocated tofor -hop communication.

(12)


B. Constraint on Relay Transmit Power

Average transmit power per-subchannel of RSs is boundedby as

and (21)

Instead of a sum power constraint, we use the per-subchannelpower constraint in (21). The per-subchannel power constraintis stricter than the sum power constraint; therefore, the powerallocation satisfying the per-subchannel power constraint al-ways satisfies the sum power constraint, yet it yields a lossof degree-of-freedom at power allocation, resulting in powerefficiency reduction. However, the per-subchannel power con-straint enables us to handle a relay weight design problem forindividual subchannel separately as shown in (36) later. As aconsequence, we can easily handle the problem. Furthermore, apeak-to-average-power ratio (PAPR) can be reduced [24].Using (3) and (14) in (21), a constraint on relay weights is

derived as

and (22)

where a maximum value of relay amplification factor is denotedby .

C. Constraints on Average SINR Lower Bound

Since the allocation and the relay processing affect not onlythe network power but also the system performance, the networkpower minimization problem should include a constraint for re-liable communications; otherwise, it yields an obvious solutionthat every node becomes silent to minimize network power. Theintercell direct interferences in the first phase in (1) are unman-ageable because of the fixed broadcasting power of BSs. Also,the direct interferences are relatively smaller than the secondhop interferences in the second phase due to the longer distancefrom the interference sources. We thus focus on the strong in-terferences in the second phase. The constraints on the secondphase performance is written with QoS required for the-hop user as

and and (23)

where is a lower bound3 of the average SINR of

-hop user , 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 interfer-ence-plus-noise power are positive and independent of each other and ii)

is a convex function, we can show that fromJensen’s inequality. In our problem, the lower bound constraints (23) performwell, especially, when the interferences are strong. This is because the boundbecomes tight as a denominator increases.

where is a second hop intercell interferenceon subchannel of derived as

(25)

and represents a direct intercell interferenceon subchannel of derived as

Here, a diagonal matrix

Similarly, for UE2, we get from (8) and (12) as

(26)

D. Optimization Formulation

Let a multicell-multiuser indicating vector be

,where is a multiuser indicating vector definedas ;and let a multicell-multiuser relay weight vector be

, where is a multiuser(multiple subchannels) expression of the relay processing vectoras . Withthe constraints in (19), (22), and (23), we eventually formulatean optimization problem that minimizes the network powerin (13) as follows:

(27a)

s.t. and (27b)

where is a set of all candidates of vector .

IV. SIMPLE AND SEQUENTIAL STRATEGY PER CELL

Noting two facts that: i) is directly mapped from the indi-cator vector ; and ii) the network power is a functionof and as represented in (16), we express the networkpower as a function of and as .Then, without any loss of optimality, we rewrite the objectivefunction in (27a) as

(28)

In (28), the minimization problems outside and inside thebracket are called as an outer and an inner problems, respec-tively. To find the optimal solution, we have to solve the outerproblem with all candidates from assignments .


Since there is tremendously large number of candidates of, around , it is intractable to directly solve

the original problem (27); thus, the problem simplification isinevitable. Furthermore, we acknowledge a difficulty in solvingthe inner problem itself due to the intertwined variables amongthe cells. To circumvent these problems and to reduce thecomplexity and network overhead, we divide (27) into multiplesingle cell problems. Accordingly, we rewrite the objectivefunction (28) for given as

(29)

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

(30)

Now, a heuristic strategy, in which the inner and outer prob-lems with the single cell objective function in (29) are sequen-tially solved, is proposed to efficiently find a close approxi-mation to the optimal solution and to significantly reduce thecomplexity. Firstly, we modify the outer problem to a linearassignment problem with an effective link gain. Under a con-straint on orthogonal subchannel allocation, we find the sub-channel allocations and communication modes, which maxi-mize the effective link gain and equivalently minimize the net-work power [23]. Secondly, for the subsequent inner problemwith the allocated subchannels and communication modes fromthe outer problem, the relay processing has been designed underconstraints on relay transmit power and on a QoS. The QoSconstraint is relaxed to guarantee the feasibility of the innerproblem; as a result, the transmit rates are maximized in fea-sible region.

A. Outer Problem: Communication Mode and SubchannelAllocation

The communication modes and subchannels are assigned bysolving a modified outer problem

s.t. (31)

In (31), identical transmit power is assumed for all relays todecouple the outer problem objective function from (29), i.e.,

where is an arbitrary positive real number.The performance degradation from this assumption can be com-pensated 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 derivedfrom (30) as

(32)

From the fact that the network power in (32) is a function ofonly and communication modes, we see that in (31) isan assignment problem.To apply a simple linear assignment algorithm that matches

between two separate vertex groups [25] into (31), we determinebeforehand the communication mode. To that end, we introducean effective link gain of that is a represen-tative gain of -links including two-hop links andone direct link of subchannel . At the end of this section, wewill provide examples of the effective link gains. Using the ef-fective link gains allows the communication mode tobe determined implicitly. If the direct-link gain is chosen as theeffective link gain, , otherwise, . As aconsequence, the problem in (31) is simplified to a linear as-signment 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 asan effective link gain increases [23], is eventually modifiedas

s.t. (33)

In (33), assignment variables, , are determined tominimize the cost, equivalently to maximize a sum of effectivelink gains. The modified problem is a linear assignmentproblem and it can be readily solved by using any linear assign-ment algorithms, such as the Hungarian, Edmonds-and-Karp’s,and network flow algorithms [25]. Also, there are many effi-cient suboptimal algorithms to solve (33), e.g., a best-fit algo-rithm assigning the best available resource to a user sequentially[26]. The number of candidates for all cells, i.e., combinationsof , is reduced to . The optimization is per-formed in distributed manner. In other words, each obtains

for all and from (33), and gets the indicatorvector denoted by , locally.Three effective link gains are introduced according to a re-

laying strategy.1) Multiple AF Relay Set: Since a two-hop link gain of AF

relay systems is represented by a multiplication of the first andsecond hop gains, the effective link gain of multiple AF relaysystems is represented by

where the instantaneous link-SNRs are defined as

; ; and

. Here, we get two-hop link gain by averagingtwo-hop link gains because the multiple forwarded signals arecombined at the destination.2) One AF Relay Selection: Though one relay selection is a

suboptimal strategy for the Gaussian parallel AF relay networks


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

where the selected AF relay index is obtained from the max-imum two-hop link gain as

3) One DF Relay Selection: For one DF relay selection, weemploy a strategy in [23] as follows:

ifotherwise

where the selected DF relay index is obtained as

Here, is the useful relay set defined as

This strategy is known as an optimal strategy for minimizingnetwork power with a throughput constraint and also for max-imizing throughput with a power constraint in Gaussian par-allel-relay networks [23].

B. Inner Problem: Relay Processing Design

The inner problem is solved with the given obtainedfrom (33) to determine the relay processing as follows:

s.t. and (34)

Note that the network power in (34) is a function of onlysince is given. Due to the orthogonal frequency allocationin (33), the problem can be independently solved for eachsubchannel . Thus, subchannel index is henceforthomitted 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)

where positive values

(37a)

(37b)

and the -by-1 vector

(38)

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

(39)

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)

where

(41)

The relay processing in (40) controls relay’s transmit power.Each relay magnifies a retransmit signal according to its secondhop channel gain . Since scales up or downthe weights of subchannel of all RSs in cell , we call it as acommon 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 thenoise 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 con-ditions, in (42) decreases as well, resulting in the reduc-tion of relays’ transmit power. iii) As the second hop channelgains increase when other values are given, decreases sothat the relays reduce their transmit power. These phenomenamatch well with our strategy. For example, the relays decrease


their transmit power to reduce network power when the secondhop 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. Inthis case, i.e., if there is no feasible solution of (36), we have twooptions to support the user. One is to wait until the poor channelbecomes better, so that the user can be served. The other is torelax its target average SINR. The first option requires a sched-uling. In the current paper, we chose the second option to guar-antee the feasible solution of (36) and relax the infeasible targetto 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 asthe performance measure in our simulation later. To the end, weneed to know a maximum achievable QoS value. In the sub-sequent sections, we will show the maximum achievable QoSvalues from the feasibility conditions and provide the feasiblerelay weights.1) Achievable QoS Region: The conditions to obtain the

feasible solution in (40) are derived from the conditions fornon-empty intersection of (36c)–(36d) as

(43a)

(43b)

From the QoS feasibility conditions in (43), we can verify atradeoff between achievable QoSs of one- and two-hop users asshown.• As increases in (37a), decreases, resulting in vi-olation of (43a) if is fixed. In such a case, shouldbe reduced to increase and satisfy (43a) since isfixed. This scenario is reasonable because UE1’s perfor-mance in the second phase is affected by the second hopintercell interferences, , from all relays which arein other cells and use UE1’s subchannels.

• On the other hand, as increases in (37b), increasesas well; as a result, (43a) can be violated if is fixed,though (43b) is still satisfied. In such a case, shouldbe reduced to satisfy (43a). This scenario is also reason-able because UE2’s performance is affected by the directintercell interferences, , from all BSs which arein other cells and use UE2’s subchannels.

Under the assumption that is large enough to satisfy aninequality which is typi-cally true in the considered system configuration in Section V-B,(43a) is always satisfied if (43b) is satisfied. Thus, we focus onthe critical constraint (43b). By substituting (37b) for in(43b), we get an achievable region of UE2’s QoS as

(44)

where is the normalized second hop channel gain definedas

(45)

The upper bound in (44) is achievable only when all relays incell know , which is unrealistic. This is be-cause enormous signaling is required for the relays to estimatethe second hop intercell interferences of all users in other cells,i.e., where and [see (37b) and (39)]. There-fore, we are motivated to derive a new QoS bound indicating apractically achievable QoS region for given and . Under thestrongest second hop interference assumption, namely isits maximum value satisfying (43b) and forall in (44) where , we can derive the practically achiev-able QoS bound as

(46)

2) Relay Weights: Since in (46) is derived under thestrongest interference (worst case) scenario, anyis achievable in cell without knowledge of . As a con-sequence, we can design a relay processing weight satisfyingthe feasible QoSs. Substituting QoS in (37a) with in(46), and again using the strongest interference assumption that

where , we can derive the upper boundof , and then obtain the upper bound of in (41) as

(47)

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

if

otherwise.(48)

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 dis-

tributed manner.R3: Transmit weight of one selected relay be-

comes since , i.e., a single selected relayuses its full available power for retransmission.

The third remark above implies that a transmit power controlis not required for one-relay selection strategies in IV-A2 andIV-A3. From R3, we can see that the strategy selecting one relayfor each subchannel is significant for practical implementation


Fig. 3. Block diagrams of procedure. (a) Problem decomposition. (b) Signalingwith feedback (broadcasting) and/or training signals.

of RCN because a relay can avoid much signaling and com-puting procedure. Furthermore, these pragmatic one-relay se-lection strategies cause more null subchannels and reduce PAPRat the relay like an antenna selection method in [27]. A simula-tion result, which is omitted in this paper, indicates that one-relay selection strategy can reduce PAPR by about 2 dB com-pared to other strategies using multiple AF relays.

C. Summary of Sequential Procedure and Signaling

The sequential procedure to solve the original problem issummarized in a block diagram illustrated in Fig. 3(a). The orig-inal problem is divided into multiple single cell problems.Each single cell problem is then split into the outer and innerproblems. In the outer problem, instantaneous channel state in-formation is used to maximize the diversity gain from the sub-channel allocation as commonly assumed in literature. In theinner problem, on the other hand, the original constraints onlower bound of average SINR are taken into consideration. Asa consequence, the relay processing is designed based on thesecond-order statistics as shown in (48), resulting in the reduc-tion of a network overhead. Note that the relays require infor-mation of only which is broadcasted from as

described in Step 3.Before the data transmission, we naturally consider a sig-

naling period for the resource allocation as illustrated inFig. 3(b). In time division duplex (TDD) systems, for example,the signaling procedure in cell is as follows:

Step. 1 UE broadcasts a training signal. and

estimate and , respectively.Step. 2 RS broadcasts a training signal and

. estimates and the feed-

back information .

Step. 3 BS solves a linear assignment problem (33)by using the channel reciprocity of TDD systems, and ob-tains and broadcasts it to and . At the same

time, the information is also broadcasted to

’s.Step. 4 RS estimates feedback information and deter-mines its transmit power , from (48).

A bottleneck procedure on computational complexity in anoptimization is to solve (33). If the optimal linear assignment al-gorithm such as a maximum-weighted matching [25] is appliedto (33), can find the optimal assignment withtime complexity when is dominantly large.

V. PERFORMANCE EVALUATION AND DISCUSSION

We evaluate the average system throughput and networkpower of OFDMA RCN employing the OFTT protocol withthree relaying strategies: multiple AF relay set (Orth-AF-Set),one AF relay selection (Orth-1-AF-Sel), and one DF relay se-lection (Orth-1-DF-Sel). Time sharing coefficients and arefixed at 0.5. Accordingly, the average throughput is evaluatedfrom the instantaneous SINR’s in (2), (4), (6), (8), (10), and (12)as

for AF RCN and

for DF RCN. Here, weassume that each user’s data is coded independently and eachuser decodes only its own data, and the interferences are treatedas white noise. To solve (33), Hungarian algorithm is used inour simulation.For benchmarking, we evaluate the performance of direct

communication without relays (depicted by Di-Comm), inwhich all users perform one-hop communications regardlessof their locations and SNRs. The simultaneous transmissionprotocol with a single DF relay selection strategy [12] (de-picted by Sim-1-DF-Sel) is also included in our simulation. It isdifficult to fairly and exactly compare the suboptimal methodsto the optimum method because the optimality is not valid ifthe 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. Twentyusers are uniformly generated throughout each cell times.Large-scale path loss with shadowing is generated from a log-normal model with a 3.76 path loss exponent and a 8.9 dB shad-owing standard deviation (STD). Multipath fading is modeledas Rayleigh for the direct and second hop channels and as Ri-cian with for the first hop channel. Refer to Table IV formore detailed parameters. Both BSs and UEs are equipped witha single omnidirectional antenna, while RSs have two antennas:a directional receive antenna focusing on BS and an omnidirec-tional transmit antenna broadcasting signals to UE2s.We assume a perfect signaling, in which the frequency-do-

main channel of the first OFDM symbol and the requiredsecond-order statistics are accurately estimated. The channelgain of the first OFDM symbol in each frame is used to allocateresources for the frame.


TABLE IVSIMULATION 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 relaysystems, each cell has 10 relays located 0.5 Km apart fromthe BS. The average network power consumption and achiev-able rate have been computed from the CDFs and depictedin the figures. An average network power of Sim-1-DF-Selincreases by 3% compared to Di-Comm, while that of OFTTprotocol decreases. Namely, Orth-AF-Set, Orth-1-AF-Sel,and Orth-1-DF-Sel achieve the power reduction compared toDi-Comm by 3.2%, 22.7%, and 24.5%, respectively. Sinceno power is allocated at for two-hop subchannelduring the second phase, network power can be further reducedwith the OFTT protocol.Because Sim-1-DF-Sel employs a distance based communi-

cation mode selection, in which UEs located near BS (within 0.5Km) are selected for direct communications, one- and two-hopusers coexist in the same subchannel in most cases with a prob-ability of 0.8. In other words, BS transmits twice and the se-lected RS transmits once on subchannels around 80% (due to theprobability of 0.8 in CDF which is a step function) during twophases, resulting in a high probability of power consumption by

. On the other hand, from the CDFfunction of Orth-1-DF-Sel, we observe that two-hop communi-cation is assigned by around 70% (i.e., the probability of 0.7in the step CDF). In this case, the subchannel power consumeddominantly is about , resulting innetwork power reduction.Fig. 4(b) confirms that RCN can improve a system

throughput. We observe that Orth-1-DF-Sel outperformsother methods in terms of an average achievable rate withimprovement of Di-Comm, Sim-1-DF-Sel, Orth-AF-Set, andOrth-1-AF-Sel by around 114%, 18%, 72%, and 41%, respec-tively.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 apartfrom BS. (a) Subchannel power (dBm/phase) CDF. (b) Rate (bits/sec/Hz) CDF.

factor means a number of transmitted bits per unit power con-sumption. Fig. 5(a) shows over when RSs are located 0.5Km apart from BS, and Fig. 5(b) shows it over the relay po-sition when . From the results, it is confirmed thatOrth-1-DF-Sel always achieves the highest power efficiencycompared to the others. The efficiency provides vital informa-tion for deployingmultiple relays inmulticell environments. Forexample, if Sim-1-DF-Sel and Orth-1AF-Sel schemes are em-ployed to RCN, the efficient way is to locate relays as many aspossible and as close as possible to BS. On the other hand, tolocate small number of relays less than six at about halfway be-tween 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 as-signment, communication mode selection, and relay processingdesign, is proposed. From the numerical results in RCN, it isverified that the OFTT protocol improves the power efficiencywith the proposed resource allocation and the relaying strategyselecting one decode-and-forward relay per-subchannel.


Fig. 5. Power efficiency comparison. (a) Over when RSs are located 0.5Km apart from BS. (b) Over relay position when .

APPENDIXDERIVATION OF (36)

Using (24) in the QoS constraint (23), we get

(A.1)

and again using (25) in (A.1), we arrive at a underdeterminedinequality

(A.2)

Noting thatis a singular matrix, we get a singular value decomposi-tion (SVD) of as

, where is a right singular

vector and is a matrix having null vectorcolumns spanned from null space of . Multiplying

to both sides of (A.2) and using the SVD, we canderive

(A.3)

Now, (A.3) is divided into two inequalities as

(A.4a)

(A.4b)

From the fact that any arbitrary satisfies (A.4b), we canrewrite (A.3) as

(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) asa minimum-distance least squares solution for the underdeter-mined equality. Consequently, we can show (36c) from (A.6)as

Similarly, using (26) in the QoS constraint (23), we can show(36d).

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Jingon Joung (S’04–M’07) received the B.S. degreein electrical engineering from Yonsei University,Seoul, Korea, in 2001, and the M.S. and Ph.D. de-grees in electrical engineering and computer sciencefrom 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 Departmentof Electrical Engineering, KAIST. From April 2007to August 2008, he worked as a Commissioned Re-searcher at Lumicomm, Inc., Daejeon. From October

2008 to September 2009, he was a Postdoctoral Fellow with the Department ofElectrical Engineering at the University of California, Los Angeles (UCLA).Since October 2009, he has been a Scientist with the Institute for InfocommResearch , Singapore. His current research has focused on the studyof 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 fromPeking University, China, the M.Eng. degree fromNanyang Technological University, and the Ph.D. de-gree from the National University of Singapore.She has been with the Institute for Infocomm

Research (formerly Centre for Wireless Commu-nications) since 1995 and is currently Head ofModulation and Coding Department, developingphysical layer-related solutions for next-generationcommunication systems. Her recent research inter-ests are in energy efficient multiuser cooperative

MIMO systems, joint source-channel processing for wireless multimediacommunications, and wireless transceiver design.Dr. Sun has served as the TPC Chair of 12th IEEE International Confer-

ence on Communications in 2010 (ICCS 2010), General Co-Chair of 7thand 8th IEEE Vehicular Technology Society Asia Pacific Wireless Com-munications Symposium (APWCS), and Track Co-Chair of TransmissionTechnologies, IEEE VTC 2012 Spring. She has also been an Associate Editorof the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, and an Editor ofIEEE WIRELESS COMMUNICATION LETTERS. She is a corecipient of IEEEPIMRC’2005 Best Paper Award.

Power Efficient Resource Allocation for Downlink OFDMA Relay Cellular Networks

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