Distributed Energy Spectral Efficiency Optimization for Partial/Full Interference Alignment in Multi-User Multi-Relay Multi-Cell MIMO Systems
aa r X i v : . [ c s . I T ] O c t ACCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 1
Distributed Energy Spectral Efficiency Optimizationfor Partial/Full Interference Alignment inMulti-User Multi-Relay Multi-Cell MIMO Systems
Kent Tsz Kan Cheung, Shaoshi Yang,
Member, IEEE , and Lajos Hanzo,
Fellow, IEEE
Abstract —The energy spectral efficiency maximization (ESEM)problem of a multi-user, multi-relay, multi-cell system is consid-ered, where all the network nodes are equipped with multiple an-tenna aided transceivers. In order to deal with the potentially ex-cessive interference originating from a plethora of geographicallydistributed transmission sources, a pair of transmission protocolsbased on interference alignment (IA) are conceived, which maybe distributively implemented in the network. The first, termedthe full-IA protocol, avoids all intra-cell interference (ICI) andother-cell interference (OCI) by finding the perfect interference-nulling receive beamforming matrices (RxBFMs). The secondprotocol, termed as partial-IA, only attempts to null the ICI.Employing the RxBFMs computed by either of these protocolsmathematically decomposes the channel into a multiplicity ofnon-interfering multiple-input–single-output (MISO) channels,which we term as spatial multiplexing components (SMCs). Theproblem of finding the optimal SMCs as well as their powercontrol variables for the ESEM problem considered is formallydefined and converted into a convex optimization form with theaid of carefully selected variable relaxations and transformations.Thus, the optimal SMCs and power control variables can bedistributively computed using both the classic dual decompositionand subgradient methods. The performance of both protocols ischaracterized, and the ESEM algorithm conceived is comparedto a baseline equal power allocation (EPA) algorithm. The resultsindicate that indeed, the ESEM algorithm performs better thanthe EPA algorithm in terms of its ESE. Furthermore, surprisinglythe partial-IA protocol outperforms the full-IA protocol in allcases considered, which may be explained by the fact that thepartial-IA protocol is less restrictive in terms of the numberof available transmit dimensions at the transmitters. Giventhe typical cell sizes considered in this paper, the path-losssufficiently attenuates the majority of the interference, and thusthe full-IA protocol over-compensates, when trying to avoid allpossible sources of interference. We have observed that, givena sufficiently high maximum power, the partial-IA protocolachieves an energy spectral efficiency (ESE) that is 2.42 timeshigher than that attained by the full-IA protocol.
I. I
NTRODUCTION
Future wireless cellular networks are required to satisfyever-increasing area spectral efficiency (ASE) demands in thecontext of densely packed heterogeneous cells, where bothrelay nodes (RNs) and small-cells [1], [2] are employed.However, these changes will result in severe co-channel in-terference (CCI), since future networks will aim for fullyexploiting the precious wireless spectrum by relying on a unityfrequency reuse factor [3]. Furthermore, owing to the growing
Copyright (c) 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected] research has been funded by the Industrial Companies who areMembers of the Mobile VCE, with additional financial support from the UKGovernment’s Engineering & Physical Sciences Research Council (EPSRC).The financial support of the Research Councils UK (RCUK) under the India-UK Advanced Technology Center (IU-ATC), of the EU under the auspices ofthe Concerto project, and of the European Research Council’s Senior ResearchFellow Grant is also gratefully acknowledged.The authors are with the School of Electronics and Computer Science,University of Southampton, Southampton, SO17 1BJ, UK (e-mail: {ktkc106,sy7g09, lh}@ecs.soton.ac.uk). energy costs, a system’s energy efficiency is becoming a majorconcern [4].
Against this backdrop, in this paper we aimfor maximizing the energy spectral efficiency (ESE) of thedownlink (DL) of a decode-and-forward (DF) [5] relay-aidedmultiple-input–multiple-output orthogonal frequency divisionmultiple access (MIMO-OFDMA) multi-cell network that em-ploys the technique of interference alignment (IA).
IA was first introduced in [6]–[8], and it was furtherpopularized in [9], [10]. In [10], Cadambe et al. describedthe main concept of IA and established the attainable degreesof freedom (DoF), when employing IA for completely avoid-ing interference in a network supporting K user-pairs. Theprinciple of IA is that, instead of dividing the wireless re-sources amongst all users (often termed as orthogonalization),each user aligns his/her transmissions into a predeterminedsubspace, referred to as the interference subspace, at all theother receivers, so that the remaining subspace at all receiversbecomes free of interference. Thus, the attainable DoFs in asystem supporting K user-pairs is K/ when employing IA,instead of /K obtained through orthogonalization [10]. Thisbecomes highly favorable, as K increases.Hence, IA has been advocated as a viable technique of man-aging the uplink (UL) co-channel interference of multi-cellnetworks [11], [12]. Explicitly, IA is suitable for the UL, sincethe number of receive antennas (RAs) at the basestation (BS)is typically higher than the number of transmit antennas (TAs)at each user equipment (UE). Thus, the potentially highernumber of signal dimensions available at the receiver can beexploited for aligning the CCI into a predetermined interfer-ence subspace, so that the BS can receive the transmissionsof its own UEs without CCI. However, this is not feasible inthe DL, since each UE has access to a low number of receivedimensions. This challenge was successfully tackled by theDL transmission scheme of [13], which relies on specificallydesigning transmit precoding (TP) matrices for reducing thenumber of transmit dimensions at the BSs, thus facilitatingDL IA at the UEs. In contrast to other IA techniques,such as [14]–[18], the technique presented in [13] does notrequire cooperation among the BSs for exchanging channelstate information (CSI), and IA is accomplished distributively.Furthermore, this technique facilitates IA in systems relyingon arbitrary antenna configurations with the aid of frequency-or time-extension, which is capable of substantially expandingthe total number of transmit and receive dimensions in amulticarrier system such as OFDMA. In [19], the techniqueof [13] was generalized to an arbitrary number of BSs andUEs, where each of them is equipped with an arbitrary numberof antennas. Furthermore, the authors of [19] employed thesemi-orthogonal user selection scheme of Yoo et al. [20] formaximizing the achievable SE. However, relaying was notconsidered in [19] and each UE was limited to receiving asingle spatial stream. CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 2
In this paper, we aim for maximizing the system’s attain-able ESE, defined as a counterpart of ASE [21], where thelatter has the units of (cid:2) bits/sec/Hz/m (cid:3) , while the former ismeasured in [ bits/sec/Hz/Joules ] . This ESE metric has alsobeen utilized in [22]–[27]. The authors of [22] considered ESEmaximization (ESEM) of both the UL and the DL of a cellularnetwork, while providing both the optimal solution method anda lower-complexity heuristic method. However, the effects ofinterference were not quantified in the system model of [22],since only a single cell was considered. Additionally, norelaying was employed. In [23], ESEM was performed in amulti-cell setting, where the CCI was eliminated with the aidof BS cooperation [28] and zero-forcing beamforming (ZFBF).However, the authors of [23] have not considered the benefitsof multiple antenna aided nodes or relaying. As a furtheradvance, the energy-efficiency of a relay aided system wasconsidered in [24], where the objective function (OF) of theoptimization problem considered was formulated by incorpo-rating both the spectral efficiency (SE) and the energy dissi-pated. Nevertheless, these two metrics must be appropriatelyweighted, which is still an open challenge. Thus, the ESEmetric was not formally optimized.In fact, the maximization of the ESE metric is typicallyformulated as a fractional (in this case, quasi-concave) pro-gramming problem [29]–[31], which relies on the classicsolution methods of the bisection search [31], and on Dinkel-bach’s method [29], as employed in [23], [25], [26]. However,the bisection search requires the solution of multiple convexfeasibility problems, while Dinkelbach’s method requires thesolution of multiple concave subtractive optimization prob-lems. The total number of algorithmic iterations may be-come prohibitive in both cases. Hence, we opt for employinga beneficial method based on the Charnes-Cooper variabletransformation [30], [32], allowing us to solve the ESEMproblem by solving a single concave optimization problemand to demonstrate its benefits to the wireless communicationscommunity.Let us now elaborate further by classifying the co-channelinterference as intra-cell interference (ICI) and other-cell inter-ference (OCI). In the DL considered, the former describes theinterference that a RN or UE may receive from the BS withinits own cell, where multiple concurrent transmissions are alsointended for other RNs or UEs, while the latter describes theinterference originating from sources located in other cells.We now provide a concise list of the contributions presentedin this paper. • We evaluate the ESEM of IA employed in a realisticMIMO-OFDMA system involving multiple cells, mul-tiple relays and multiple users. Although ESEM hasbeen studied intensely in recent years [22]–[24], thesecontributions typically consider single cells providingcoverage without the assistance of relaying, or do notexploit the benefits of multiple antenna aided transceivers.Additionally, although IA was employed recently in [14],[33]–[36], these contributions focus on user-pair net-works, rather than on multi-user cellular networks and theassociated challenges of implementing IA require furtherresearch in the latter scenario. More importantly, previouscontributions typically aim for investigating its SE bene-fits, while the achievable ESE of using IA-based protocolshas not been explored at all. Green communications has become increasingly important, but the quantitativebenefits of IA have not been documented in the contextof energy-efficient communications. Therefore, in thiscontribution we seek to deepen the research commu-nity’s understanding of IA from an ESE perspective.Furthermore, a more realistic multi-cell MIMO-OFDMArelay-aided network is considered in this treatise, wheremultiple users are supported by each BS and multiplerelays. Therefore, the system model considered inevitablybecomes challenging. As a beneficial result, the protocolsand solutions provided in this paper can be more readilyapplied to real network scenarios, when compared to theexisting IA literature, which focuses only on the K -user interference network. In contrast to our previouscontributions [25]–[27], this treatise investigates a multi-ple antenna aided multi-cell system. Although a multipleantenna assisted system was also studied in our previouscontribution [27], only a single macrocell was consideredand no IA was employed for avoiding the ICI imposedby both the simultaneously transmitting BS and RNs. • We provide a sophisticated generalization of the IAprotocol considered in [13]. Explicitly, in contrast to [13],the proposed IA protocol accounts for three cells, for anarbitrary number of users in each cell, for an arbitraryantenna configuration and for simultaneous direct aswell as relay-aided transmissions. This is accomplishedthrough the careful design of precoding-, transmit- andreceive- beamforming matrices in order to ensure thatIA is achieved. In particular, the number of guaranteedspatial dimensions available at the BSs, RNs and UEsmust be judiciously chosen. Furthermore, we conceive oftwo transmission protocols in this work, which may beimplemented distributively at each BS. The first protocolis termed as full-IA, which invokes IA for avoiding theinterference arriving from all transmitters. This is the in-tuitive choice, as advocated by the existing literature [11],[13], [19] highlighting its benefits in terms of achievingthe optimal DoF. For example, it was also employedin [13], but for a simpler system model having no relays.The second protocol proposed is unlike that of [13] andit is termed as partial-IA, which only aims for avoidingthe ICI using IA, while ignoring the effect of OCI whenmaking scheduling decisions. The partial-IA protocoltherefore reduces the computational burden of having toestimate the DL CSI of the other-cell channel matricesat the receivers, albeit this might be expected to reducethe system’s performance due to neglecting the OCI.We compared the performance of these two protocolsand found that, as a surprise, the reduced-complexitypartial-IA protocol is potentially capable of achievinga higher ESE than the full-IA protocol. Explicitly, thepartial-IA protocol achieves a higher ESE, since moresimultaneous transmissions may be scheduled due to itsrelaxed constraint on the number of transmit dimensionsavailable. Furthermore, in contrast to the protocol pro-posed in [19], ours is a two-phase protocol, which isspecifically designed for relay-aided networks and doesnot limit the number of spatial streams available to eachUE. • Employing the beamforming matrices calculated fromeither the full-IA or partial-IA protocols results in a
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Fig. 1: A multi-cell system is depicted on the left. Each cell is dividedinto three sectors, and one sector from each of the three neighboringcells are highlighted. This highlighted region is termed an OCI region.Through the use of directional antennas, it is assumed that the mainsource of OCI is caused when the neighboring BSs simultaneouslytransmit to a receiver located in its associated OCI region. On theright is a close-up view of the OCI region, with three BSs at thevertices of its perimeter. Furthermore, each sector is supported bytwo RNs and provides coverage for six UEs in this example. list of spatial multiplexing components (SMCs) , whichcorrespond to the specific data streams that the BSs canchoose to support. Finding the optimal SMCs as well asthe optimal power control variables associated with theseoptimal SMCs is formally defined as a network-wide opti-mization problem. Unlike in our previous work [25]–[27],we decompose the network-wide multi-cell optimizationproblem in order to formulate a subproblem for eachBS using the technique of primal decomposition [37],thus eliminating the need for the high-overhead backhaul-aided message passing amongst the BSs. Each of thesesubproblems is then converted into a convex form withthe aid of various variable relaxations and transforma-tions, which can then be optimally and distributivelysolved using the dual decomposition and subgradientmethods of [37].The organization of this paper is as follows. We introduceour system model in Section II and describe the proposedtransmission protocols in Section III. Subsequently, the ESEMoptimization problem considered is formulated in Section IV,where the solution method is developed as well. Our numericalresults along with our further discussions are presented inSection V. Finally, our conclusions are given in Section VIalong with our future research ideas.II. S YSTEM MODEL
In this work, a multi-cell DL MIMO-OFDMA network,relying on a radical unity frequency reuse factor is considered.The ubiquitous OFDMA technique is employed for avoidingthe severe frequency-selective fading encountered in widebandcommunication systems. Additionally, OFDMA allows fortransmission symbol extensions in the frequency-domain [13],which are required by the proposed IA-based transmissionprotocol described in Section III.As depicted in Fig. 1, each macrocell is divided into threesectors, and it is assumed that the employment of directionalantennas and the non-line-of-sight (NLOS) path-loss attenu-ates the interference power, with the exception of the OCIreceived from the first tier of interfering cells and the ICIfrom the serving BS and RNs of each macrocell. Therefore,we may focus our attention on the central region seen at the These SMCs are detailed further in Section III left of Fig. 1, which we term as an OCI region. Thus, eachDL transmission within an OCI region is subjected to OCIfrom two macrocells. Furthermore, each ◦ -sector of Fig. 1is supported by M RNs, which are located at a fixed distancefrom its associated BS and evenly spaced within the sector, asseen at the right of Fig. 1. The ratio of the BS-RN distanceto the cell radius is denoted by D r . Additionally, K UEsare uniformly distributed within each ◦ -sector. The systemhas access to L OFDMA subcarriers, each characterized by awireless bandwidth of W Hertz. The BSs, DF RNs, and UEsare respectively equipped with N B , N R and N U antennas. Itis assumed that all BSs and RNs are synchronized, and thatthe transceivers employ complex-valued symbol constellationsto convey their data.For each subcarrier l ∈ { , · · · , L } , the complex-valuedchannel matrix associated with the wireless link spanningfrom the BS of macrocell n ′ ∈ { , , } to RN m ∈{ , · · · , M } belonging to macrocell n ∈ { , , } is denotedby H BR,l,n ′ n,m ∈ C N R × N B . The channel matrix associatedwith the link spanning from the BS of macrocell n ′ to UE k ∈ { , · · · , K } and belonging to macrocell n on subcarrier l is denoted by H BU,l,n ′ n,k ∈ C N U × N B . Furthermore, the channelmatrix associated with the link between RN m ′ belongingto macrocell n ′ and UE k belonging to macrocell n onsubcarrier l is denoted by H RU,l,n ′ ,m ′ n,k ∈ C N U × N R . Allchannel matrices are assumed to have a full rank, as is oftenthe case for wireless DL channels. For simplicity, the channelmatrices associated with the same transceivers are combinedacross subcarriers to give the block-diagonal channel ma-trices H BR,n ′ n,m ∈ C LN R × LN B , H BU,n ′ n,k ∈ C LN U × LN B and H RU,n ′ ,m ′ n,k ∈ C LN U × LN R , respectively. For example, we have H BR,n ′ n,m := H BR, ,n ′ n,m . . .
00 0 H
BR,L,n ′ n,m . (1)The channel matrices account for both the small-scalefrequency-flat Rayleigh fading, as well as the large-scale path-loss between the corresponding transceivers. In this systemmodel, the transceivers are either stationary or moving suffi-ciently slowly for ensuring that the channel matrices can beconsidered time-invariant for the duration of a scheduled trans-mission period. However, the channel matrices may evolvebetween each transmission period. Furthermore, it is assumedthat the transceivers’ antennas are spaced sufficiently farapart for ensuring that the associated transmissions experiencei.i.d. small-scale fading, which are drawn from complex i.i.d.normal distributions having a zero mean and a unit variance.The system uses time-division duplexing (TDD) and hence theassociated channel reciprocity may be exploited for predictingthe CSI of the slowly varying DL channels from the receivedUL signal. Furthermore, by assuming the availability of low-rate error-free wireless backhaul channels, the CSI associatedwith the wireless intra-cell RN-UE links may be fed back tothe particular BS in control, so that it may make the necessaryscheduling decisions.Additionally, each receiver suffers from complex-valued ad-ditive white Gaussian noise (AWGN) having a power spectral Superscript indices refer to the transmitter, while subscript indices refer tothe receiver. Additionally, a prime symbol ′ refers to a potentially interferingtransmission source. CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 4 density of N . Due to both regulatory and safety concerns,the maximum instantaneous transmission power of each BSand each RN is limited, which are denoted by P Bmax and P Rmax , respectively. We stipulate the idealized simplifyingassumption that OFDMA modulation and demodulation isperformed perfectly for all the information symbols.III. T
RANSMISSION PROTOCOL DESIGN
Each BS may convey information to the UEs by either usinga direct BS-UE link, or by utilizing a RN to create a two-hop BS-RN and RN-UE link, which requires two transmissionphases. Thus, each transmission period is split into two halves.Due to the simultaneous transmissions from multiple sources,both the level of ICI and OCI in the network is likely tobe detrimental to the achievable ESE. In order to avoid bothtypes of interference, the technique of IA is employed, whichrequires the careful design of both the transmit beamformingmatrix (TxBFMs) of the BSs and of the RNs, as well as thereceive beamforming matrix (RxBFMs) of the RNs and of theUEs. As relaying links may be utilized in this system, thedesign of these matrices is different for the two transmissionphases. Hence they are described separately in the following.Additionally, both the full-IA and partial-IA protocols will bedescribed side-by-side. To elaborate a little further, the full-IAprotocol aims for completely avoiding both the ICI and OCIin both the first and second transmission phases by employingIA, while the partial-IA protocol only aims for avoiding the ICIin both transmission phases, thus dispensing with estimatingthe OCI channel matrices at each receiver.Furthermore, the proposed schemes crucially rely on thesingular value decomposition (SVD), where the columns ofthe left and right singular matrices are composed of the leftand right singular vectors of the associated matrix. These leftand right singular vectors may be further partitioned into theleftmost and rightmost parts, which correspond to the non-zero and zero singular values, respectively. This structure isillustrated in detail in Fig. 2.
A. Beamforming design for the first phase
In the first phase, only the BSs are transmitting to both theRNs and the UEs. Therefore, the only source of interference isconstituted by the neighboring BSs associated with the sameOCI region, which may be avoided by carefully designingthe TxBFMs at the BSs, as well as the RxBFMs at the RNsand the UEs in a distributive manner. Initially, a TP, denotedby A B,n,T ∈ C LN B × S B,T , is randomly-generated for eachBS n , where S B,T is the number of symbols transmitted byeach BS during the first phase, which is accurately defined inSection III-A3. The matrix A B,n,T has a full column rankand its entries are complex-valued. These TPs are invokedfor reducing the number of transmit dimensions for each BSfrom LN B to S B,T , thus facilitating IA at the receivers.Furthermore, the columns of these TP matrices are normalizedso that the power assigned to each transmission remainsunaffected. By employing these TPs, the precoded channelmatrices of the first phase are given by e H BR,n ′ ,T n,m := H BR,n ′ n,m A B,n ′ ,T ∈ C LN R × S B,T (2)and e H BU,n ′ ,T n,k := H BU,n ′ n,k A B,n ′ ,T ∈ C LN U × S B,T , (3) respectively for the BS-RN and BS-UE links.We now define S R and S U as the minimum number ofreceive dimensions at each RN and each UE, respectively,which are chosen by the network operator. Furthermore, onlythe specific values of S R and S U along with the number ofantennas at each network node and the number of availablesubcarrier blocks affect the feasibility of IA, while M and K have no effect.
1) Full-IA receiver design:
In order to completely avoid theinterference arriving from the neighboring BSs during the firstphase, it is necessary for the precoded OCI channel matricesgiven by (2) and (3), to have intersecting left nullspaces.Firstly, the precoded OCI channel matrices may be concate-nated for forming the interference matrices, for example b H R,T ,m := h e H BR, ,T ,m (cid:12)(cid:12)(cid:12) e H BR, ,T ,m i ∈ C LN R × S B,T (4)for RN m in macrocell , and b H U,T ,k := h e H BU, ,T ,k (cid:12)(cid:12)(cid:12) e H BU, ,T ,k i ∈ C LN U × S B,T (5)for UE k in macrocell . These matrices are associated witha left nullspace of at least S R and S U dimensions if LN R − S B,T ≥ S R (6)and LN U − S B,T ≥ S U , (7)respectively. Therefore, to guarantee S R and S U receivedimensions at the RNs and UEs, respectively, S B,T is derivedas S B,T = (cid:22) min (cid:18) LN R − S R , LN U − S U (cid:19)(cid:23) . (8)The intersecting left nullspace may be found using the SVDon b H R,T n,m and b H U,T n,k , for RN m and UE k in macrocell n ,respectively. For example, the SVD of b H R,T n,m may be writtenas U R,T n,m S R,T n,m (cid:0) V R,T n,m (cid:1) H , where U R,T n,m ∈ C LN R × LN R isthe left singular matrix containing, as its columns, the leftsingular vectors of b H R,T n,m , while S R,T n,m ∈ R LN R × S B,T + is a rectangular diagonal matrix whose diagonal entries arethe singular values of b H R,T n,m ordered in descending value,and V R,T n,m ∈ C S B,T × S B,T is the right singular matrixcontaining, as its columns, the right singular vectors of b H R,T n,m .The intersecting left nullspace may then be obtained as the (cid:0) LN R − S B,T (cid:1) rightmost columns of U R,T n,m (correspondingto the zero singular values), and this is used as the RxBFM, R R,T n,m , for RN m in macrocell n . A similar procedure isperformed for obtaining the RxBFM, R U,T n,k , for UE k inmacrocell n in the first phase, where the (cid:0) LN U − S B,T (cid:1) rightmost columns of the corresponding left singular matrixare selected.To summarize, the cost of implementing the full-IA protocolin the first transmission phase is the reduction of the number ofavailable spatial transmission streams at each BS from LN B to S B,T . Thus, if the RNs and UEs require a large numberof spatial streams, the BSs have to substantially reduce thenumber of transmitted streams in order to accommodate IA.However, it is clear that S B,T should be higher than toensure that the BSs become capable of transmitting. Followingthis procedure, the (cid:0) S B,T − S R (cid:1) and (cid:0) S B,T − S U (cid:1) totalinterference signal dimensions received at each RN and at eachUE respectively have each been aligned to S B,T dimensions, CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 5 u , u M, u , · · ·· · ·· · · ... ... u ,M u M,M · · ·· · ·· · · ... ... u ,M H = vectorsleft singularleftmost vectorsrightmostleft singular non-zerovaluessingular singularvalueszero right singularleftmostvectors rightmostright singularvectors v , v N, v , v ,N v ,N v N,N ... N × N · · ·· · · ... ... · · · · · ·· · · ... · · · s , . . .. . . 0 M × M M × NM × N Fig. 2: The structure of the SVD employed in this paper. The leftmost left and right singular vectors correspond to the non-zero singularvalues, while the rightmost left and right singular vectors correspond to the zero singular vectors. Therefore, the rightmost left singularvectors span the left nullspace of H . leaving LN R − S B,T ≥ S R and LN U − S B,T ≥ S U receive signal dimensions free from interference at the RNsand UEs, respectively. Thus, IA has been successfully em-ployed for reducing the number of spatial dimensions that theinterference signals occupy.
2) Partial-IA receiver design:
Using this design philosophy,the OCI encountered during the first phase is ignored whendesigning the RxBFMs. However, since there is no ICI in thefirst phase since only the BSs are transmitting, there is noneed to reduce the number of transmit dimensions at the BSs.Therefore, S B,T = LN B (9)is chosen. Furthermore, the matched filter receiver design isadopted for maximizing the achievable SE [38]. In this case,the SVD is performed on the intra-cell precoded channelmatrices, yielding for example e H BR,n,T n,m = U BR,n,T n,m S BR,n,T n,m (cid:0) V BR,n,T n,m (cid:1) H (10)and e H BU,n,T n,k = U BU,n,T n,k S BU,n,T n,k (cid:16) V BU,n,T n,k (cid:17) H , (11)respectively, and the S R (resp. S U ) leftmost left (thus corre-sponding to the highest singular values) singular vectors areselected as the RxBFM for the RNs (resp. UEs) in the firstphase.In summary, IA is not required during the first transmissionphase of the partial-IA protocol, since the only transmitterwithin the same cell is the associated BS. Therefore, it is notnecessary for the BSs to reduce the number of transmit dimen-sions available to them for the sake of avoiding interference.
3) Scheduling and transmitter design:
Having designed theRxBFMs, the effective DL channel matrices can be written as H BR,n,T n,m := (cid:0) R R,T n,m (cid:1) H e H BR,n,T n,m (12)or H BU,n,T n,k := (cid:16) R U,T n,k (cid:17) H e H BU,n,T n,k (13)for RN m and UE k in macrocell n , respectively. We termthe rows of these matrices as the SMCs of the associatedtransceivers, since each SMC corresponds to a distinct vir-tual multiple-input–single-output (MISO) channel between theassociated transmitter as well as receiver, and then mul-tiple MISOs can be multiplexed for composing a MIMOchannel. A set of SMCs is generated for each of the twotransmission phases, and each BS then distributively groups these SMCs according to the semi-orthogonal user selec-tion algorithm , as described in [20], [39], given a semi-orthogonality parameter α . For the first transmission phase,up to min (cid:0) S B,T , KLN U + M LN R (cid:1) SMCs may be servedsimultaneously by each BS, while avoiding ICI. The set ofgroupings available for BS n is denoted by G n . The SMCsbelonging to group j , which are denoted by E n,j , are thenthe rows of the effective scheduled DL matrix, denoted by H B,n,j,T for macrocell n . In order to avoid ICI betweenthese selected SMCs of group j , macrocell n applies theZFBF matrix, given in (14), by T B,n,j,T as the right channelinverse before using its TP, A B,n , where (cid:0) W B,n,j,T (cid:1) is areal-valued diagonal matrix, which normalizes the columnsof T B,n,j,T for ensuring that the power assigned to eachtransmission remains unaffected.The effective end-to-end channel power gains are then givenby the squares of the diagonal entries in (cid:0) W B,n,j,T (cid:1) . ForSMC e in group j of macrocell n corresponding to a directfirst phase BS-UE link, the effective channel power gain isdenoted by w BU,n,j,T n,e , while the effective channel power gainof the OCI link, originating from macrocell n ′ serving SMCgroup j ′ to UE k in macrocell n , is obtained from the elementof (cid:12)(cid:12)(cid:12)(cid:12)(cid:16) R U,T n,k (cid:17) H e H BU,n ′ ,T n,k T B,n ′ ,j ′ ,T (cid:12)(cid:12)(cid:12)(cid:12) (15)corresponding to SMC e at UE k of macrocell n , and isdenoted by w BU,n ′ ,j ′ ,T n,e . In the case of the full-IA protocol, allOCI is avoided, thus w BU,n ′ ,j ′ ,T n,e = 0 , ∀ n ′ = n . The effectivechannel power gains for the BS-to-RN links, corresponding toSMC-pair e , may be similarly obtained and are denoted by w BR,n,j,T n,e , whereas an OCI link is denoted by w BR,n ′ ,j ′ ,T n,e . B. Beamforming design for the second phase
During the second phase, both the BSs and the RNs maytransmit. Therefore, in a similar fashion to the first phase,the BS in cell n adopts the precoding matrix A B,n,T ∈ C LN B × S B,T , while RN m in cell n adopts the precoding ma-trix A R,n,m,T ∈ C LN R × S R , which are again complex-valuedmatrices having a full column-rank. Additionally, the columns This selection method aims for reducing the power loss imposed by thechannel inversion operation of the ZFBF matrix [20], [27]. N.B. Each group additionally contains the SMCs selected for the secondphase, as it will be discussed in Section III-B3. Relaying links contain both a SMC for the BS-RN link and a SMC forthe RN-UE link.
CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 6 T B,n,j,T = (cid:16) H B,n,j,T (cid:17) H (cid:20) H B,n,j,T (cid:16) H B,n,j,T (cid:17) H (cid:21) − (cid:0) W B,n,j,T (cid:1) (14)of these TP matrices are normalized. Due to the additionalinterference imposed by the transmissions of the RNs, it isnecessary to reduce the number of transmit dimensions at theBSs even further in order to facilitate IA at the DL receivers.Additionally, note that each TP matrix used at the RNs consistof S R columns, since the information received by each RNduring the first phase must be conveyed to the intended UE.The precoded channel matrices used during the second phaseare thus given by (note that the transmitter indices are n ′ and m ′ , since these may be inter-cell channel matrices) e H RU,n ′ ,m ′ ,T n,k := H RU,n ′ ,m ′ n,k A R,n ′ ,m ′ ,T ∈ C LN U × S R (16)and e H BU,n ′ ,T n,k := H BU,n ′ n,k A B,n ′ ,T ∈ C LN U × S B,T . (17)
1) Full-IA receiver design:
The receiver design used duringthe second phase depends on whether the BS or a RN isselected to serve each UE within the same macrocell. Eachof the (1 + M ) possible transmitters may be examined forthe sake of finding the most beneficial choice. For example,assuming that BS transmits to UE k during the second phase,the OCI and ICI channel matrices may be concatenated toform (18). However, when assuming for example, that RN of macrocell n transmits to UE k , the combined interferencematrix is defined by (19). Therefore, in order to guaranteehaving S U receive dimensions at each UE, we have S B,T = (cid:22) min (cid:18) LN U − S U − M S R ,LN U − S U − (3 M − S R (cid:19)(cid:23) . (20)In both cases described above, the SVD may again beemployed for finding the intersecting left nullspace ofthe precoded interference matrix. The RxBFM, R U,T n,k , atUE k in macrocell n used during the second phase isthen given by the rightmost (thus corresponding to itszero singular values) LN U − (cid:0) S B,T + 3 M S R (cid:1) numberof columns in the left singular matrix of b H BU, ,T ,k , whenthe BS is the activated transmitter. By contrast, when as-suming that RN is the activated transmitter, the right-most min (cid:0) S R , LN U − (cid:2) S B,T + (3 M − S R (cid:3)(cid:1) number ofcolumns in the ordered left singular matrix of b H RU,n, ,T n,k specify the RxBFM matrix.In conclusion, the BSs once again have to reduce thenumber of spatial transmission streams available to them inorder to facilitate IA. In this case, their number is reducedfrom LN B to S B,T . Additionally, each RN reduces thenumber of streams available for them to transmit from LN R to S R . On one hand, when the BS is selected as the activetransmitter for a particular UE using the full-IA protocol, atotal of (cid:0) S B,T + 3 M S R − S U (cid:1) interference signal dimen-sions are aligned to (cid:0) S B,T + 3 M S R (cid:1) signal dimensions,leaving LN U − (cid:0) S B,T + 3 M S R (cid:1) ≥ S U signal dimensionsfree from interference. Thus, IA has been successfully em-ployed. On the other hand, when a RN is selected as theactivated transmitter for a particular UE, there is a totalof (cid:0) S B,T + 3 M S R − S U (cid:1) interference signal dimensions, which are aligned to (cid:0) S B,T + 3 M S R − S R (cid:1) signal dimen-sions. Therefore, IA is only feasible at the UEs if we have S R > S U . The constraint given by LN U − (cid:0) S B,T + 3 M S R (cid:1) − S R > S R (21)is additionally enforced in the full-IA protocol, so that the CCIcan still be nulled when S R ≤ S U and a RN is selected as theactive transmitter. However, IA is not employed in this case.
2) Partial-IA receiver design:
Although the effects of OCIare ignored when using this protocol, the ICI must be avoided.Thus, the interference matrix, assuming for example that theBS is the selected transmitter for UE k in macrocell , is thengiven by b H BU, ,T ,k := h e H RU, , ,T ,k (cid:12)(cid:12)(cid:12) · · · (cid:12)(cid:12)(cid:12) e H RU, ,M,T ,k i ∈ C LN U × MS R . (22)By contrast, if RN of macrocell n is selected as thetransmitter for UE k , then the interference matrix is givenby b H RU,n, ,T n,k := h e H BU, ,T n,k (cid:12)(cid:12)(cid:12) e H RU,n, ,T n,k (cid:12)(cid:12)(cid:12) · · · (cid:12)(cid:12)(cid:12) e H RU,n,M,T n,k i ∈ C LN U × [ S B,T +( M − S R ] , (23)which implies that S B,T = LN U − S U − ( M − S R (24)is satisfied for ensuring that the UEs are capable of findingapproximate RxBFMs, which completely null the ICI.Thus, UE k may employ the LN U − M S R numberof rightmost left singular columns in b H BU, ,T ,k as itsRxBFM, when the BS is the activated transmitter. By con-trast, assuming that RN is the activated transmitter, the min (cid:0) S R , LN U − (cid:2) S B,T + ( M − S R (cid:3)(cid:1) number of right-most left singular columns in b H RU,n, ,T n,k specify the RxBFM.To summarize, the BSs reduce the number of spatial streamsavailable to them from LN B to S B,T , while the RNs reducethe number of their spatial streams from LN R to S R . On onehand, when the BS is selected as the active transmitter for thepartial-IA protocol, a total of (cid:0) S B,T + M S R − S U (cid:1) interfer-ence signal dimensions are aligned to M S R signal dimensions,leaving LN U − M S R ≥ S U signal dimensions free frominterference. Thus, IA has been successfully employed. On theother hand, when a RN is selected as the activated transmitter,there are a total of (cid:0) S B,T + M S R − S U (cid:1) interference signaldimensions, which are aligned to (cid:0) S B,T + M S R − S R (cid:1) sig-nal dimensions. Therefore, IA is only feasible for S R > S U .However, the aforementioned RxBFMs are still capable ofnulling the CCI, when a RN is selected as the active transmitterin the partial-IA protocol and we have S R ≤ S U . But in thiscase the constraint given by (21) is not required, since it isalready satisfied by (24).
3) Scheduling and transmitter design:
In a similar fashionto the first phase, the effective DL channel matrices are givenby H RU,n,m,T n,k := (cid:16) R U,T n,k (cid:17) H e H RU,n,m,T n,k (25)and H BU,n,T n,k := (cid:16) R U,T n,k (cid:17) H e H BU,n,T n,k , (26) CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 7 b H BU, ,T ,k : = h e H BU, ,T ,k (cid:12)(cid:12)(cid:12) e H BU, ,T ,k (cid:12)(cid:12)(cid:12) e H RU, , ,T ,k (cid:12)(cid:12)(cid:12) · · · (cid:12)(cid:12)(cid:12) e H RU, ,M,T ,k (cid:12)(cid:12)(cid:12) e H RU, , ,T ,k (cid:12)(cid:12)(cid:12) · · · (cid:12)(cid:12)(cid:12) e H RU, ,M,T ,k (cid:12)(cid:12)(cid:12) e H RU, , ,T ,k (cid:12)(cid:12)(cid:12) · · · (cid:12)(cid:12)(cid:12) e H RU, ,M,T ,k i ∈ C LN U × ( S B,T +3 MS R ) (18) b H RU,n, ,T n,k : = h e H BU, ,T n,k (cid:12)(cid:12)(cid:12) e H BU, ,T n,k (cid:12)(cid:12)(cid:12) e H BU, ,T n,k (cid:12)(cid:12)(cid:12) e H RU, , ,T n,k (cid:12)(cid:12)(cid:12) · · · (cid:12)(cid:12)(cid:12) e H RU, ,M,T n,k (cid:12)(cid:12)(cid:12) e H RU, , ,T n,k (cid:12)(cid:12)(cid:12) · · · (cid:12)(cid:12)(cid:12) e H RU, ,M,T n,k (cid:12)(cid:12)(cid:12) e H RU, , ,T n,k (cid:12)(cid:12)(cid:12) · · · (cid:12)(cid:12)(cid:12) e H RU, ,M,T n,k i ∈ C LN U × [ S B,T +(3 M − S R ] (19) T B,n,j,T = (cid:16) H B,n,j,T (cid:17) H (cid:20) H B,n,j,T (cid:16) H B,n,j,T (cid:17) H (cid:21) − (cid:0) W B,n,j,T (cid:1) (27) T R,n,m,j,T = (cid:16) H R,n,m,j,T (cid:17) H (cid:20) H R,n,m,j,T (cid:16) H R,n,m,j,T (cid:17) H (cid:21) − (cid:0) W R,n,m,j,T (cid:1) (28)when the BS or RN m is activated as the transmitter forUE k belonging to macrocell n , respectively. The rows ofthe DL TxBFMs corresponding to each transmitter form theSMCs for that transmitter, and they may be grouped at eachBS according to the semi-orthogonal user selection algorithmdescribed above. Furthermore, in the second phase, each BScan select up to min (cid:0) S B,T , KLN U (cid:1) number of SMCs toserve simultaneously while avoiding ICI, whereas each RNmay select min (cid:0) S R , KLN U (cid:1) number of SMCs. At BS n (orRN m of macrocell n ), the selected SMCs of group j formthe rows of its effective scheduled DL matrix, denoted by H B,n,j,T (or H R,n,m,j,T ). The ZFBF matrix employed byBS n or by RN m of macrocell n in the second phase isthen given by the right inverse (27) or (28), respectively,where the real-valued diagonal matrices of (cid:0) W B,n,j,T (cid:1) and (cid:0) W R,n,m,j,T (cid:1) are required for normalizing the columns of T B,n,j,T and T R,n,m,j,T , respectively.The effective channel power gains in the second phaseare thus given by the squares of the diagonal entries in (cid:0) W B,n,j,T (cid:1) and (cid:0) W R,n,m,j,T (cid:1) . The effective channelpower gain of a BS-UE SMC e of group j associated withmacrocell n and UE k is denoted by w BU,n,j,T n,e , while the RN-UE effective channel power gain of SMC-pair e associatedwith RN m of macrocell n and UE k may be denoted by w RU,n,m,j,T n,e . Similar to the first phase, the effective channelpower gain of the OCI link originating from the BS ofmacrocell n ′ serving group j ′ to UE k in macrocell n , isobtained from the specific element of (cid:12)(cid:12)(cid:12)(cid:12)(cid:16) R U,T n,k (cid:17) H e H BU,n ′ ,T n,k T B,n ′ ,j ′ ,T (cid:12)(cid:12)(cid:12)(cid:12) (29)corresponding to SMC e at UE k of macrocell n , whichis denoted by w BU,n ′ ,j ′ ,T n,e . On the other hand, the effectivechannel power gain of the OCI link, originating from RN m ′ of macrocell n ′ serving group j ′ to UE k of macrocell n , isobtained from the element of (cid:12)(cid:12)(cid:12)(cid:12)(cid:16) R U,T n,k (cid:17) H e H RU,n ′ ,m ′ ,T n,k T R,n ′ ,m ′ ,j,T (cid:12)(cid:12)(cid:12)(cid:12) (30)corresponding to SMC e at UE k of macrocell n , andis denoted by w RU,n ′ ,m ′ ,j ′ ,T n,e . In the case of the full-IAprotocol, all OCI is avoided, thus we have w BU,n ′ ,j ′ ,T n,e = w RU,n ′ ,m ′ ,j ′ ,T n,e = 0 , ∀ n ′ = n . C. Achievable spectral efficiency and energy efficiency
Since we have mathematically decomposed the MIMOchannels into effective SISO channels, we may directly employthe Shannon capacity bound for characterizing the achievableESE performance, rather than relying on bounds derived forMIMO channels [40]. We begin by defining the signal-to-interference-plus-noise-ratio (SINR) of the direct link SMCsbelonging to group j and intended for UE k of macrocell n during the first and the second phase as Γ BU,n,j,T n,e ( P , S ) = w BU,n,j,T n,e P B,n,j,T n,e ∆ γ (cid:16) N LW + I U,T n,e (cid:17) (31)and Γ BU,n,j,T n,e ( P , S ) = w BU,n,j,T n,e P B,n,j,T n,e ∆ γ (cid:16) N LW + I U,T n,e (cid:17) , (32)respectively, where the total received OCI in the first andsecond phase has been denoted by (33) and (34), respec-tively, where M ( e ) is a function of e , representing theRN index (similar to m used before) associated with theSMC-pair e . For simplicity , the interference that was notavoided using IA is treated as noise. The set P containsthe power control variables denoted by P B,n,j,T n,e , P B,n,j,T n,e , P B,n,j,T n,e , and P R,n,m,j,T n,e , ∀ n, e , e , e . On the other hand,the set S contains the group selection indicator variables, s n,j , ∀ n, j , where s n,j = 1 , when the SMC group j has beenselected for macrocell n , and s n,j = 0 otherwise. The totalnoise power across all subcarriers is given by N LW , while ∆ γ is the signal to noise ratio (SNR) difference betweenthe SNR at the discrete-input–continuous-output memorylesschannel (DCMC) capacity and the actual SNR required bythe specific modulation and coding schemes of the practicalphysical layer transceivers employed [41].The SINR of the BS-RN SMC e belonging to group j ofmacrocell n and intended for RN m may be expressed as Γ BR,n,j,T n,e ( P , S ) = w BR,n,j,T n,e P B,n,j,T n,e ∆ γ (cid:16) N LW + I R,T n,e (cid:17) , (35)while the SINR of the corresponding RN-UE link may be If the level of interference is strong enough, then more sophisticatedmethods, such as multiuser detection, may be employed.
CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 8 I U,T n,e ( P , S ) = X n ′ =1 n ′ = n X j ′ ∈G n ′ s n ′ ,j ′ w BU,n ′ ,j ′ ,T n,e X e ′ ∈E n ′ ,j ′ P B,n ′ ,j ′ ,T n ′ ,e ′ + X e ′ ∈E n ′ ,j ′ P B,n ′ ,j ′ ,T n ′ ,e ′ (33) I U,T n,e ( P , S ) = X n ′ =1 n ′ = n X j ′ ∈G n ′ s n ′ ,j ′ w BU,n ′ ,j ′ ,T n,e X e ′ ∈E n ′ ,j ′ P B,n ′ ,j ′ ,T n ′ ,e ′ + X e ′ ∈E n ′ ,j ′ w RU,n ′ , M ( e ′ ) ,j ′ ,T n,e P R,n ′ , M ( e ′ ) ,j ′ ,T n,e ′ (34)formulated as Γ RU,n,m,j,T n,e ( P , S ) = w RU,n,m,j,T n,e P R,n,m,j,T n,e ∆ γ (cid:16) N LW + I U,T n,e (cid:17) , (36)where the total received OCI of the BS-RN and RN-UE linksare given by (37) and (38), respectively.The achievable SE of the direct first and second phasetransmissions can be respectively written as C BU,n,j,T n,e ( P , S ) = 12 log (cid:0) BU,n,j,T n,e (cid:1) (39)and C BU,n,j,T n,e ( P , S ) = 12 log (cid:0) BU,n,j,T n,e (cid:1) , (40)where the pre-log factor of accounts for the fact that thetransmission period has been split into two phases. When usingthe DF protocol, the achievable SE of the relaying link islimited by the weaker of the BS-RN and RN-UE links [5],which is given by C BRU,n,m,jn,e ( P , S ) = min (cid:20)
12 log (cid:0) BR,n,j,T n,e (cid:1) ,
12 log (cid:0) RU,n,m,j,T n,e (cid:1)(cid:21) . (41)Thus the total achievable SE of macrocell n is given by (42).Furthermore, we simplified the energy dissipation modelof [42] in order to formulate the total energy dissipation inmacrocell n as (43). The effect of the number of TAs, ofthe energy dissipation of the RF as well as of the basebandcircuits, and the efficiencies of the power amplifier, feedercables, cooling system, mains power supply, and convertershas been accounted for in the fixed energy dissipation termsof P BC and P RC , while the transmit power dependent terms ξ B and ξ R are associated with the BS n and its RNs, respectively.Thus, the ESE of macrocell n is given by η nE ( P , S ) = C nT ( P , S ) P nT ( P , S ) . (44)In the sequel, our aim is to maximize (44) for each macrocell n by the careful optimization of the variables contained within P and S . We define the average ESE of the multicell systemas η E ( P , S ) = 13 X n =1 η nE ( P , S ) , (45)so that the average ESE of the system can be optimized byindividually maximizing each macrocell’s ESE, as it will bediscussed in the following. IV. O PTIMIZATION PROBLEM FORMULATION ANDSOLUTION ALGORITHM
In this section, our aim is to optimize the OF (45). Weformally describe the optimization problem as (46)–(52). Toelaborate, (45) is maximized by appropriately optimizing thedecision variables contained within the sets P and S . Theconstraint (47) ensures that each macrocell only serves asingle SMC group, thus the ICI is completely avoided. Theconstraints (48)–(50) require that none of the transmittersexceeds its maximum transmission power constraint. Observethat two constraints are needed for each BS, since each BStransmits in both phases, whereas the RNs only transmit duringthe second phase. Furthermore, the constraint (51) reflects thebinary constraint imposed on the s n,j variables, while theconstraints (52) ensures that the power control variables arenon-negative. A. Concave problem formulation
Observe that in both the full-IA and partial-IA protocols, theOCI terms are negligible or zero, if perfect CSI is available.Therefore, each macrocell’s ESE is independent of the decisionvariables associated with other macrocells, and the optimiza-tion problem can be decomposed and solved distributively,where each macrocell optimizes its own ESE. It can be readilyproven that the OF is nonlinear and involves binary variables.Thus, the optimization problem of (46)–(52) is a mixed integernonlinear programming (MINLP) problem, which are typicallysolved using high-complexity branch-and-bound methods [43].In order to mitigate the computational burden of finding asolution to (46)–(52), we relax the binary constraint imposedon the variables s n,j by replacing the constraint (51) with ≤ s n,j ≤ , ∀ n, j. (53)Additionally, we introduce the auxiliary variables e P B,n,j,T n,e = t n s n,j P B,n,j,T n,e , (55) e P B,n,j,T n,e = t n s n,j P B,n,j,T n,e , (56) e P B,n,j,T n,e = t n s n,j P B,n,j,T n,e , (57) In [44], such a relaxation results in a time-sharing solution regarding eachsubcarrier. In this work, this relaxation may be viewed as time-sharing ofeach subcarrier block, as multiple SMC groups can then occupy a fractionof each subcarrier block in time. Naturally, the relaxation means that we donot accurately solve the original problem of (46)–(52). In fact, since we haveexpanded the space of feasible solutions, solving the relaxed problem resultsin an upper bound of the optimal objective value of the original problem.However, the algorithm devised in this paper for obtaining the optimal solutionto the relaxed problem will only retain integer values of the relaxed variables.Therefore, the algorithm essentially maximizes a lower bound of the relaxedproblem. Having said that, as shown in [25], [45], [46], the optimal solutionto the original problem is still obtained with high probability when using thedual decomposition method on the relaxed problem (as in this work) as thenumber of subcarriers tends to infinity. It was shown that subcarriers issufficient for this to be true in the context of [47], while we have shown that subcarriers is sufficient in the context of [25]. CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 9 I R,T n,e ( P , S ) = X n ′ =1 n ′ = n X j ′ ∈G n ′ s n ′ ,j ′ w BR,n ′ ,j ′ ,T n,e X e ′ ∈E n ′ ,j ′ P B,n ′ ,j ′ ,T n ′ ,e ′ + X e ′ ∈E n ′ ,j ′ P B,n ′ ,j ′ ,T n ′ ,e ′ (37) I U,T n,e ( P , S ) = X n ′ =1 n ′ = n X j ′ ∈G n ′ s n ′ ,j ′ w BU,n ′ ,j ′ ,T n,e X e ′ ∈E n ′ ,j ′ P B,n ′ ,j ′ ,T n ′ ,e ′ + X e ′ ∈E n ′ ,j ′ w RU,n ′ , M ( e ′ ) ,j ′ ,T n,e P R,n ′ , M ( e ′ ) ,j ′ ,T n ′ ,e ′ (38) C nT ( P , S ) = X j ∈G n s n,j X e ∈E n,j C BU,n,j,T n,e + X e ∈E n,j C BU,n,j,T n,e + X e ∈E n,j C BRU,n, M ( e ) ,jn,e (42) P nT ( P , S ) = (cid:0) P BC + M P RC (cid:1) + 12 X j ∈G n s n,j ξ B X e ∈E n,j P B,n,j,T n,e + X e ∈E n,j P B,n,j,T n,e + X e ∈E n,j (cid:16) ξ B P B,n,j,T n,e + ξ R P R,n, M ( e ) ,j,T n,e (cid:17) (43)maximize P , S (45) (46)subject to X j ∈G n s n,j ≤ , ∀ n, (47) X j ∈G n s n,j X e ∈E n,j P B,n,j,T n,e + X e ∈E n,j P B,n,j,T n,e ≤ P Bmax , ∀ n, (48) X j ∈G n s n,j X e ∈E n,j P B,n,j,T n,e ≤ P Bmax , ∀ n, (49) X j ∈G n s n,j X e ∈E n,j M ( e )= m P R,n,m,j,T n,e ≤ P Rmax , ∀ n, m, (50) s n,j ∈ { , } , ∀ n, j, (51) P B,n,j,T n,e , P B,n,j,T n,e , P B,n,j,T n,e , P R,n,m,j,T n,e ≥ , ∀ n, j, e , e , e (52) t n = 1 (cid:0) P BC + M P RC (cid:1) + P j ∈G n " ξ B P e ∈E n,j e P B,n,j,T n,e + P e ∈E n,j e P B,n,j,T n,e + P e ∈E n,j ξ B e P B,n,j,T n,e + ξ R e P R,n,m,j,T n,e (54) e P R,n,m,j,T n,e = t n s n,j P R,n,m,j,T n,e , (58) e s n,j = t n s n,j , ∀ n, j, e , e , e, (59)where t n is given by (54). Note that we have applied theCharnes-Cooper variable transformation [30] using t n . Fur-thermore, the auxiliary SE variables e C BU,n,j,T n,e , e C BU,n,j,T n,e and e C BRU,n,m,jn,e are introduced, so that we may rewrite theoptimization problem of (46)–(52) in the hypograph form [31]given by (60)–(71), ∀ n , where e P n , e S n and e C n denote the vari-able sets containing the auxiliary variables that are associatedwith macrocell n . To elaborate further, the constraints (61)and (62) ensure that the auxiliary SE variables given by e C BU,n,j,T n,e and e C BU,n,j,T n,e do not exceed the direct linkSEs obtained from (39) and (40), respectively, while theconstraints (63) and (64) have to be combined to guaranteethat (41) is adhered to. The constraints (65)–(70) are simplythe equivalents of the constraints (47)–(52), when employingthe auxiliary variables, while the constraint (71) is the resultof the Charnes-Cooper variable transformation [30]. Finally,the OF (60) defines the ESE of macrocell n .Let us now aim for proving that (60)–(71) is a concave max- imization problem. It can be readily shown that the OF (60)is linear, hence concave. Similarly, the constraints (65)–(71)are all linear. Therefore, what remains for us to prove isthat the constraints (61)–(64) are all convex. Observe that theconstraints (61)–(64) are all of the form s log (cid:0) aPs (cid:1) ≥ C ,where the decision variables are s , P and C , while a issome constant. It is plausible that (1 + aP ) is linear. Thefunction composition of log (1 + aP ) is concave [31] andthe perspective transformation [31], giving s log (cid:0) aPs (cid:1) ,preserves concavity. Finally, rewriting the previous inequalityas C − s log (cid:0) aPs (cid:1) ≤ clearly shows that it is indeeda convex constraint. Thus, we have proven that (60)–(71) isa concave programming problem, which may be solved usingefficient algorithms. Let us now proceed with the portrayalof the algorithm employed in this work for solving the aboveproblem. B. Solution algorithm
Observe that the optimization problem of (60)–(71) is akinto a sum-rate maximization problem, which is optimally solvedusing the well-known water-filling method [21]. From our
CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 10 maximize e P n , e S n , e C n X j ∈G n X e ∈E n,j e C BU,n,j,T n,k,e + X e ∈E n,j e C BU,n,j,T n,k,e + X e ∈E n,j e C BRU,n, M ( e ) ,jn,k,e (60) e s n,j w BU,n,j,T n,e e P B,n,j,T n,e e s n,j ∆ γN LW ! ≥ e C BU,n,j,T n,e , ∀ j, e , (61) e s n,j w BU,n,j,T n,e e P B,n,j,T n,e e s n,j ∆ γN LW ! ≥ e C BU,n,j,T n,e , ∀ j, e , (62) e s n,j w BR,n,j,T n,e e P B,n,j,T n,e e s n,j ∆ γN LW ! ≥ e C BRU,n, M ( e ) ,jn,e , ∀ j, e, (63) e s n,j w RU,n, M ( e ) ,j,T n,e e P R,n, M ( e ) ,j,T n,e e s n,j ∆ γN LW ! ≥ e C BRU,n, M ( e ) ,jn,e , ∀ j, e, (64) X j ∈G n e s n,j ≤ t n , (65) X j ∈G n X e ∈E n,j e P B,n,j,T n,e + X e ∈E n,j e P B,n,j,T n,e ≤ t n · P Bmax , (66) X j ∈G n X e ∈E n,j e P B,n,j,T n,e ≤ t n · P Bmax , (67) X j ∈G n X e ∈E n,j M ( e )= m e P R,n,m,j,T n,e ≤ t n · P Rmax , ∀ m, (68) ≤ e s n,j ≤ t , ∀ j, (69) e P B,n,j,T n,e , e P B,n,j,T n,e , e P B,n,j,T n,e e P R,n,m,j,T n,e ≥ , ∀ j, e , e , e, (70) t n · (cid:0) P BC + M · P RC (cid:1) + 12 X j ∈G n ξ B X e ∈E n,j e P B,n,j,T n,e + X e ∈E n,j e P B,n,j,T n,e + X e ∈E n,j ξ B e P B,n,j,T n,e + ξ R e P R,n,m,j,T n,e = 1 (71)previous work [25]–[27] using dual decomposition [37], wemay deduce that the optimal (denoted by a superscript asterisk)values for e P B,n,j,T n,e and e P B,n,j,T n,e are respectively given by e P B,n,j,T ∗ n,e = e s n,j " ξ B µ ∗ + 2 λ n,T ∗ ) ln 2 − ∆ γN LWw
BU,n,j,T n,e + (72)and e P B,n,j,T ∗ n,e = e s n,j " ξ B µ ∗ + 2 λ n,T ∗ ) ln 2 − ∆ γN LWw
BU,n,j,T n,e + , (73)where e s n,j is yet to be determined, while [ · ] + is equivalentto max (0 , · ) . Furthermore, µ ∗ is the optimal Lagrangiandual variable [31] associated with the constraint (71), while λ n,T ∗ and λ n,T ∗ are respectively the optimal Lagrangiandual variables associated with the constraints (66) and (67)for macrocell n . The optimal Lagrangian dual variables arechosen to satisfy the constraints (66)–(68) with equality, andare found using the subgradient algorithm [37].It may be shown that the power control variables of therelaying links may be formulated as e P B,n,j,T n,e = e s n,j " ξ B µ ∗ + 2 λ n,T ∗ ) ln 2 − ∆ γN LWw
BR,n,j,T n,e + (74) and e P R,n, M ( e ) ,j,T n,e = e s n,j " (cid:0) ξ R µ ∗ + 2 ν n, M ( e ) ,T ∗ (cid:1) ln 2 − ∆ γN LWw
RU,n, M ( e ) ,j,T n,e + , (75)where ν n, M ( e ) ,T ∗ is the optimal Lagrangian dual variableassociated with the constraint (68) for RN M ( e ) belongingto macrocell n . Since the attainable SE of a relaying link islimited by the weaker of the BS-RN and RN-UE links, thereis no need to transmit at a higher power than necessary, ifthe other link is unable to support the higher SE. Thus, theoptimal power control variables for the relaying link are givenby e P B,n,j,T ∗ n,e = min w RU,n, M ( e ) ,j,T n,e w BR,n,j,T n,e · e P R,n, M ( e ) ,j,T n,e , e P B,n,j,T n,e ! (76)and e P R,n, M ( e ) ,j,T ∗ n,e = min w BR,n,j,T n,e w RU,n, M ( e ) ,j,T n,e · e P B,n,j,T n,e , e P R,n, M ( e ) ,j,T n,e ! . (77) CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 11 e C BRU,n, M ( e ) ,jn,e = e s n,j w BR,n,j,T n,e e P B,n,j,T n,e ∆ γN LW ! = e s n,j w RU,n, M ( e ) ,j,T n,e e P R,n, M ( e ) ,j,T n,e ∆ γN LW ! (78)Thus, the maximum values of e C BU,n,j,T n,e , e C BU,n,j,T n,e and e C BRU,n, M ( e ) ,jn,e are given by e C BU,n,j,T n,e = e s n,j w BU,n,j,T n,e e P B,n,j,T n,e ∆ γN LW ! , (79) e C BU,n,j,T n,e = e s n,j w BU,n,j,T n,e e P B,n,j,T n,e ∆ γN LW ! (80)and (78), where the value of e s n,j is not yet known. However,regardless of the exact value of e s n,j , macrocell n may choosethe specific SMC group j that obtains the highest value of X e ∈E n,j e C BU,n,j,T n,e + X e ∈E n,j e C BU,n,j,T n,e + X e ∈E n,j e C BRU,n, M ( e ) ,jn,e (81)in order to maximize the OF (60) by setting e s n,j = t n , wherethe value of t n is not yet known. As a result, the SMC groups j ′ = j are not chosen and we may set e s n,j ′ = e P B,n,j ′ ,T n,e = e P B,n,j ′ ,T n,e = e P B,n,j ′ ,T n,e = e P R,n, M ( e ) ,j ′ ,T n,e = e C BU,n,j ′ ,T n,e = e C BU,n,j ′ ,T n,e = e C BRU,n, M ( e ) ,j ′ n,e = 0 , ∀ e , e , e, j ′ = j .The optimal value of t n is then given by (82). Observethat this is possible, since (82) is only dependent on the dualvariables. Furthermore, determining the value of t n gives thevalues of e s n,j , e P B,n,j,T n,e , e P B,n,j,T n,e , e P B,n,j,T n,e and e P R,n,m,j,T n,e for the selected SMC group.By following the above derivations, the constraints (61)–(65) and (69)–(71) are implicitly satisfied and there is noneed to introduce dual variables for them. This ESEM solutionalgorithm may be implemented distributively, and iteratesbetween obtaining the optimal primal variables and applyingthe subgradient method [37] for updating the dual variables,until the change in the dual variable values becomes lessthan ǫ or the maximum number of iterations, I max , has beenreached. The ESEM algorithm is summarized in Table I, where λ n,T ( i ) , λ n,T ( i ) , ν n,m,T ( i ) and µ ( i ) indicate the value oftheir respective dual variables at the i th iteration.V. N UMERICAL RESULTS AND DISCUSSIONS
This section presents the numerical results obtained, whenthe solution algorithm presented in Section IV-B is employedfor the ESEM problem of (60)–(71), where the simulationparameters are given in Table II. Furthermore, we employedthe path-loss model of [49] and assumed that all BS-UEand RN-UE links are NLOS links, since they are typicallyblocked by buildings and other large obstructing objects, whileall BS-RN links may realistically be assumed to be line-of-sight links, since the RNs may be strategically positionedon tall buildings to create strong wireless backhaul links. In all cases, the step sizes and the initial values of the dual variablesdescribed in Section IV-B are empirically optimized so that the algorithmconverges in as few iterations as possible, although the exact analytical methodfor achieving this still remains an open issue. In our experience, the algorithmconverges within just iterations when carefully chosen step sizes areemployed, regardless of the size of the problem. TABLE I: The ESEM algorithm based on dual decomposition andthe subgradient method.
Algorithm 1
ESEM algorithm1: i ← do while | λ n,T ( i ) − λ n,T ( i − | > ǫ or | λ n,T ( i ) − λ n,T ( i − | > ǫ or | ν n,m,T ( i ) − ν n,m,T ( i − | > ǫ or | µ ( i ) − µ ( i − | > ǫ i ← i + 1 if i > I max break end if for n from to for each j in G n
9: Obtain the optimal power allocation using (72)–(77)10: Compute their achievable SE using (79)–(78)11: end for
12: Find the optimal SMC, which obtains the maximum (81)13: Compute the optimal t using (82)14: end for
15: Update the dual variables λ n,T ( i ) , λ n,T ( i ) , ν n,m,T ( i ) and µ ( i ) using the subgradient method [37]16: end do return TABLE II: Simulation parameters used to obtain all results in thissection unless otherwise specified.
Simulation parameter ValueSubcarrier block bandwidth, W [Hertz] kNumber of RNs per macrocell, M { , , , } Number of subcarriers blocks, N Number of UEs, K Antenna configuration, ( N B , N R , N U ) (4 , , Semi-orthogonality parameter, α . Inter-site distance (ISD), [km] { . , . , . , . } Minimum number of receive dimensionsat the RNs and UEs, S R and S U and Ratio of BS-to-RN distance to the cellradius, D r . SNR gap of wireless transceivers, ∆ γ [dB] 0Maximum total transmission power of the { , , , BS and RNs, P Bmax and P Rmax [dBm] , , } Fixed power rating of the BS, 32.306 N B P BC [Watts] [42], [48]Fixed power rating of RNs, 21.874 N R P RC [Watts] [42], [48]Reciprocal of the BS power amplifier’s 3.24 N B drain efficiency, ξ B [42], [48]Reciprocal of the RNs’ power amplifier’s 4.04 N R drain efficiency, ξ R [42], [48]Noise power spectral density, N [dBm/Hz] −174Convergence threshold, ǫ − Number of channel samples Furthermore, independently and randomly generated set of UElocations as well as fading channel realizations were used.Again, for benchmarking we employ a baseline algorithm,which relies on random SMC selections and equal powerallocation across the selected SMCs. This algorithm is termedas the EPA algorithm.The attainable performance of both the full-IA and partial-IA protocols is explored and these results are obtained byemploying the optimized power control variables and groupselection variables in the actual system model. Therefore,the results reflect the actual ESE achieved rather than theoptimized OF value of (60), which is optimistic, since it doesnot account for any potential OCI remaining after employing
CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 12 t n = P BC + M · P RC + X j ∈G n e s n,j ξ B X e ∈E n,j e P B,n,j,T n,e + X e ∈E n,j e P B,n,j,T n,e + X e ∈E n,j ξ B e P B,n,j,T n,e + ξ R e P R,n,m,j,T n,e − (82) A v e r ag e A S E [ b i t s / s / H z / k m ] Partial-IA w/EPAFull-IA w/EPAPartial-IA w/EEMFull-IA w/EEM P Rmax [dBm] P Bmax [dBm] A v e r ag e A S E [ b i t s / s / H z / k m ] (a) Surface plots of the achievable ASE when using the ESEM and EPAalgorithms. A v e r ag e E S E [ b i t s / s / H z / J ] P Rmax [dBm] P Bmax [dBm] A v e r ag e E S E [ b i t s / s / H z / J ] (b) Surface plots of the achievable ESE when using the ESEM and EPAalgorithms. Fig. 3: The average achievable ASE and ESE when using the ESEMand EPA algorithms with either full-IA or partial-IA, for varying P Bmax and P Rmax , and using the parameters in Table II with M = 2 and an ISD of . km. the partial-IA protocol. A. The variation of ASE and ESE for different values of P Bmax and P Rmax
The effects of varying both P Bmax and P Rmax are demon-strated in Fig. 3. Observe that the partial-IA protocol out-performs the full-IA protocol for all the power constraintsconsidered. This is due to the requirements of (8), (9), (20)and (24), which restrict the number of data streams that theBSs can transmit simultaneously in each phase. The full-IAprotocol imposes more restrictive constraints than the partial-IA protocol, since the partial-IA protocol only requires that theRx-BFMs has to eliminate the ICI, rather than both the ICI andOCI that the full-IA protocol has to null. Observe furthermorethat the EPA algorithms achieve higher ASE values thantheir ESEM algorithmic counterparts at high P Bmax values. A v e r ag e A S E [ b i t s / s / H z / k m ] S R S U A v e r ag e A S E [ b i t s / s / H z / k m ] (a) Surface plots of the achievable ASE when using the ESEM and EPAalgorithms. A v e r ag e E S E [ b i t s / s / H z / J ] S R S U A v e r ag e E S E [ b i t s / s / H z / J ] (b) Surface plots of the achievable ESE when using the ESEM and EPAalgorithms. Fig. 4: The average achievable ASE and ESE when using the ESEMand EPA algorithms with either full-IA or partial-IA, for varying S U and S R , and using the parameters in Table II with M = 2 , P Bmax = 30 dBm, P Rmax = 20 dBm and an ISD of . km. The legendis as presented in Fig. 3. However, this is achieved at a higher cost to the ESE obtainedfrom using the EPA algorithms, when compared to their ESEMcounterparts. In fact, in the low to medium P Bmax regime,both the SEM and ESEM correspond to the same solution, asdemonstrated in our previous works of [25]–[27]. This resultsin a higher ASE for the ESEM algorithm than for the heuristicEPA algorithm. As the value of P Bmax increases, the EPAcontinues to allocate more power, which increases the ASEobtained, without any cognizance to the ESE performance.However, the ASE and ESE obtained does not increasesignificantly upon increasing P Rmax . This can be attributed tothe low multiplexing gain specified in these experiments, giventhat S R = 1 . The results of the next subsection explore theeffects of varying the requirements imposed on S U and S R . CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 13
B. The variation of ASE and ESE for different values of S U and S R Fig. 4 shows the results obtained upon varying S U and S R .Once again, the partial-IA protocol outperforms the full-IAprotocol in terms of both its ASE and ESE performances.Additionally, we observe that the EPA algorithm performsworse than the ESEM algorithm for all cases. Increasing S U has a marginal effect on the ASE and ESE obtainedfor both protocols. However, increasing S R does lead to anincrease in SE, when employing the partial-IA protocol, albeitat a cost to ESE resulting from the fixed power dissipationcosts of the RNs. Observe that increasing S R reduces theASE attained when using the full-IA protocol. This maybe explained by the detrimental effects of the constraintsimposed on the multiplexing gain of the BSs’ transmissionswhen employing the full-IA protocol, because increasing S R imposes a substantial reduction on both (8) and (20), whenmultiple RNs are operated in each macrocell. This reductionin ASE is not so dominant for the partial-IA protocol, sincethe increase in the multiplexing gain of the RNs’ transmissionsoutweighs the detrimental effects of imposing a multiplexinggain restriction at the BSs due to (24). Additionally, thepotential multiplexing gain attained at the BSs in the firsttransmission phase, given by (9), is not affected by the increaseof S R . C. The variation of ASE and ESE for different values of M and inter-site distance As shown in Fig. 5, both the achievable ASE and ESEdecreases as the ISD is increased, indicating that the effectof a higher path-loss on the channel gains has a more gravedetrimental effect on both the ASE and ESE than the beneficialeffects of the reduced interference levels. Once again, theEPA algorithm performs worse than their ESEM algorithmiccounterparts. Additionally, the ASE attained, when using thefull-IA protocol is slightly reduced upon increasing M due toboth (8) and (20), while the ESE achieved is reduced, as thepower dissipation of the system is increased upon increasing M . Furthermore, the ASE obtained when using the partial-IA protocol peaks for M = 1 , but decreases slightly, uponincreasing M further, since then the multiplexing gain of theexperienced during the second phase is reduced as indicatedby (24). By contrast, the ESEM of the partial-IA protocol onlydecreases upon increasing M .VI. C ONCLUSIONS
In this paper, a multi-user, multi-relay, multi-cell MIMOsystem model is studied. In order to avoid the excessiveinterference inflicted by the multiple transmission sources,a pair of distributed IA protocols were designed. The first,termed as full-IA, completely avoids any interference byfinding RxBFMs, which entirely eliminate the interferenceimposed at the receivers. However, this comes at a cost to thespatial multiplexing gain of the BSs, which limits the numberof DL transmission streams. The second transmission protocol, In fact, when M = 0 or S R = 0 we arrive at a special case of the partial-IA protocol, which is similar to the conventional single cell multi-user ZFBFin the absence of RNs. However, the proposed partial-IA protocol representsa sophisticated extension of classic ZFBF to the broad class of multi-relayaided multi-cell networks, which have been combined with intelligent userselection. A v e r ag e A S E [ b i t s / s / H z / k m ] M ISD [km] A v e r ag e A S E [ b i t s / s / H z / k m ] (a) Surface plots of the achievable ASE when using the ESEM and EPAalgorithms. A v e r ag e E S E [ b i t s / s / H z / J ] M ISD [km] A v e r ag e E S E [ b i t s / s / H z / J ] (b) Surface plots of the achievable ESE when using the ESEM and EPAalgorithms. Fig. 5: The average achievable ASE and ESE when using the ESEMand EPA algorithms with either full-IA or partial-IA, for varying M and ISD, and using the parameters in Table II with P Bmax = 30 dBm, P Rmax = 20 dBm and an ISD of . km. The legend is as presentedin Fig. 3. namely partial-IA, aims for striking a balance between thespatial multiplexing gain and interference contamination byfinding RxBFMs, which only null the interference emerg-ing from sources within the same macrocell. Employing theRxBFMs created by either of these transmission protocolsresults in a list of SMCs, which correspond to data streamsthat may be conveyed by the BS. We formally defined theproblem of maximizing the ESE by optimally choosing theSMCs as well as by appropriately choosing their power controlvariables. The resultant non-convex optimization problem wasconverted into a convex optimization problem with the aidof carefully chosen variable relaxations and transformations,which was then solved using the classic dual decompositionand subgradient methods [37], that may be implementeddistributively at each BS. We characterized the attainable ASEand ESE performances of both protocols for a range of systemparameters, while comparing the performance of our ESEMalgorithm to that of a baseline EPA algorithm. To summarize,the ESEM algorithm outperforms the EPA algorithm in termsof ESE, while surprisingly the partial-IA protocol outperformsthe full-IA protocol in all cases. For the cell sizes considered,the path-loss mitigates the majority of the OCI, and thus thefull-IA protocol actually over-compensates, when reducing thenumber of available transmit dimensions at the transmitters to CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 14 facilitate IA. R
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CCEPTED TO APPEAR ON IEEE TRANSACTIONS ON SIGNAL PROCESSING, OCT. 2015 15
Kent Tsz Kan Cheung (S’09) received his B.Eng.degree (first-class honors) in electronic engineeringfrom the Univeristy of Southampton, Southampton,U.K., in 2009. In 2015, he completed his Ph.D.degree in wireless communications at the same insti-tution. He was a recipient of the EPSRC IndustrialCASE award in 2009, and was involved with theCore 5 Green Radio project of the Virtual Centre ofExcellence in Mobile and Personal Communications(Mobile VCE).His research interests include energy-efficiency,multi-carrier MIMO communications, cooperative communications, resourceallocation and optimization.
Shaoshi Yang (S’09-M’13) received his B.Eng.degree in Information Engineering from Beijing Uni-versity of Posts and Telecommunications (BUPT),Beijing, China in Jul. 2006, his first Ph.D. degreein Electronics and Electrical Engineering from Uni-versity of Southampton, U.K. in Dec. 2013, andhis second Ph.D. degree in Signal and Informa-tion Processing from BUPT in Mar. 2014. He isnow working as a Postdoctoral Research Fellow inUniversity of Southampton, U.K. From November2008 to February 2009, he was an Intern ResearchFellow with the Communications Technology Lab (CTL), Intel Labs, Beijing,China, where he focused on Channel Quality Indicator Channel (CQICH)design for mobile WiMAX (802.16m) standard. His research interests includeMIMO signal processing, green radio, heterogeneous networks, cross-layerinterference management, convex optimization and its applications. He haspublished in excess of 30 research papers on IEEE journals and conferences.Shaoshi has received a number of academic and research awards, in-cluding the prestigious Dean’s Award for Early Career Research Excel-lence at University of Southampton, the PMC-Sierra TelecommunicationsTechnology Paper Award at BUPT, the Electronics and Computer Science(ECS) Scholarship of University of Southampton, and the Best PhD ThesisAward of BUPT. He is a member of IEEE/IET, and a junior member ofIsaac Newton Institute for Mathematical Sciences, Cambridge University,U.K. He also serves as a TPC member of several major IEEE conferences,including
IEEE ICC, GLOBECOM, PIMRC, ICCVE, HPCC , and as a GuestAssociate Editor of
IEEE Journal on Selected Areas in Communications. (https://sites.google.com/site/shaoshiyang/)