1 Joint Network Optimization and Downlink Beamforming for CoMP Transmissions using Mixed Integer Conic Programming Yong Cheng, Student Member, IEEE, Marius Pesavento, Member, IEEE, and Anne Philipp Abstract—Coordinated multipoint (CoMP) transmission is a promising technique to mitigate intercell interference and to increase system throughput in single frequency reuse networks. Despite the remarkable benefits, the associated operational costs for exchanging user data and control information between multi- ple cooperating base stations (BSs) limit practical applications of CoMP processing. To facilitate wide usage of CoMP transmission, we consider in this paper the problem of joint network opti- mization and downlink beamforming (JNOB), with the objective to minimize the overall BS power consumption (including the operational costs of CoMP transmission) while guaranteeing the quality-of-service (QoS) requirements of the mobile stations (MSs). We address this problem using a mixed integer second- order cone program (MI-SOCP) framework and develop an extended MI-SOCP formulation that admits tighter continuous relaxations, which is essential for reducing the computational complexity of the branch-and-cut (BnC) method. Analytic studies of the MI-SOCP formulations are carried out. Based on the analyses, we introduce efficient customizing strategies to further speed up the BnC algorithm through generating tight lower bounds of the minimum total BS power consumptions. For practical applications, we develop polynomial-time inflation- and deflation procedures to compute high-quality solutions of the JNOB problem. Numerical results show that the inflation- and deflation procedures yield total BS power consumptions that are close to the lower bounds, e.g., exceeding the lower bounds by about 12.9% and 9.0%, respectively, for a network with 13 BSs and 25 MSs. Simulation results also show that minimizing the total BS power consumption results in sparse network topologies and reduced operational overhead in CoMP transmission, and that some of the BSs are switched off when possible. Index Terms—Coordinated Multipoint Transmission, Network Optimization, Downlink Beamforming, Mixed Integer Conic Programming, Low-complexity Heuristic Algorithms I. I NTRODUCTION Coordinated multipoint (CoMP) processing is widely rec- ognized as an effective mechanism for managing intercell Manuscript received Oct. 17, 2012; revised Mar. 2, 2013 and Apr. 19, 2013; accepted Apr. 21, 2013. The associate editor coordinating the review of this paper and approving it for publication was Prof. Anthony So. This work was supported by the European Research Council (ERC) Advanced Investigator Grants Program under Grant 227477-ROSE, and the LOEWE Priority Program Cocoon (www.cocoon.tu-darmstadt.de). Preliminary results of this work were presented at the conferences WSA’12 [1] and ICASSP’12 [2]. Copyright (c) 2012 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. Y. Cheng and M. Pesavento are with the Communication Systems Group, and A. Philipp is with the Dept. of Math., Technische Universit¨ at Darmstadt, 64283 Darmstadt, Germany. Emails: {pesavento, cheng}@nt.tu-darmstadt.de, [email protected]. interference (ICI) and improving system throughput in cel- lular networks with universal frequency reuse [3]–[20]. The potential of CoMP transmission has been validated in both theoretic studies [3]–[5] and field trials [3], [6], [7], and CoMP processing has therefore already been included in the emerging wireless communication standards, e.g., LTE- Advanced [8]. While CoMP operation with full cooperation between BSs that jointly serve users offers significant increases in network capacity and cell-edge throughput, it induces also considerable operational overhead, such as power expended in collecting and exchanging channel state information (CSI) among multiple BSs and MSs, signaling beamforming weights and forwarding user data to multiple cooperating BSs [3], [20]. To balance the benefits and the operational costs, CoMP processing shall be carried out among a limited number of cooperating BSs, resulting in the so-called partial BS coop- eration designs. Several partial BS cooperation schemes have been proposed in the literature, see, e.g., [3], [9]–[20]. Those existing contributions can roughly be categorized into two classes, namely coordinated beamforming [3], [9], [10] and clustered BS cooperation [3], [11]–[20]. In the coordinated downlink beamforming designs, the beamforming weights of the MSs are jointly designed across the network, but each MS is served by a single BS and therefore there is no need to route payload data or control information, e.g., beamforming weights, corresponding to one MS over the backhaul network to multiple BSs [3], [9], [10]. In the clustered BS cooperation frameworks, CoMP processing is implemented within clusters of BSs, with full BS cooperation inside each cluster and no cooperation between clusters [3], [11]–[20]. Since the CoMP operation is restricted to a small number of BSs in each cluster, the communication overhead of CoMP processing is bounded by the size of the BS clusters [3], [11]–[20]. While the existing approaches [3], [9]–[20] can alleviate the additional expenses in CoMP transmission to certain extent, several important issues remain open. For instance, in coordinated beamforming [3], [9], [10], the performance of cell-edge MSs may still suffer from ICI and large pathloss, as in conventional cellular systems. Even though cell-edge MSs can enjoy the performance gain from CoMP processing in the clustered BS cooperation frameworks [3], [11]–[20], the MSs located at the cluster edges still suffer from ICI and large pathloss. In addition, determining the optimal size of the BS clusters is a challenging open problem [3], [11]–[20]. More recently, mechanisms to optimize BS selection and multicell beamforming are proposed in [18]–[20] to reduce the overhead
16
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1
Joint Network Optimization and Downlink
Beamforming for CoMP Transmissions using Mixed
Integer Conic ProgrammingYong Cheng, Student Member, IEEE, Marius Pesavento, Member, IEEE, and Anne Philipp
Abstract—Coordinated multipoint (CoMP) transmission is apromising technique to mitigate intercell interference and toincrease system throughput in single frequency reuse networks.Despite the remarkable benefits, the associated operational costsfor exchanging user data and control information between multi-ple cooperating base stations (BSs) limit practical applications ofCoMP processing. To facilitate wide usage of CoMP transmission,we consider in this paper the problem of joint network opti-mization and downlink beamforming (JNOB), with the objectiveto minimize the overall BS power consumption (including theoperational costs of CoMP transmission) while guaranteeingthe quality-of-service (QoS) requirements of the mobile stations(MSs). We address this problem using a mixed integer second-order cone program (MI-SOCP) framework and develop anextended MI-SOCP formulation that admits tighter continuousrelaxations, which is essential for reducing the computationalcomplexity of the branch-and-cut (BnC) method. Analytic studiesof the MI-SOCP formulations are carried out. Based on theanalyses, we introduce efficient customizing strategies to furtherspeed up the BnC algorithm through generating tight lowerbounds of the minimum total BS power consumptions. Forpractical applications, we develop polynomial-time inflation- anddeflation procedures to compute high-quality solutions of theJNOB problem. Numerical results show that the inflation- anddeflation procedures yield total BS power consumptions that areclose to the lower bounds, e.g., exceeding the lower bounds byabout 12.9% and 9.0%, respectively, for a network with 13 BSsand 25 MSs. Simulation results also show that minimizing thetotal BS power consumption results in sparse network topologiesand reduced operational overhead in CoMP transmission, andthat some of the BSs are switched off when possible.
Coordinated multipoint (CoMP) processing is widely rec-
ognized as an effective mechanism for managing intercell
Manuscript received Oct. 17, 2012; revised Mar. 2, 2013 and Apr. 19, 2013;accepted Apr. 21, 2013. The associate editor coordinating the review of thispaper and approving it for publication was Prof. Anthony So. This work wassupported by the European Research Council (ERC) Advanced InvestigatorGrants Program under Grant 227477-ROSE, and the LOEWE Priority ProgramCocoon (www.cocoon.tu-darmstadt.de). Preliminary results of this work werepresented at the conferences WSA’12 [1] and ICASSP’12 [2].
Copyright (c) 2012 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].
Y. Cheng and M. Pesavento are with the Communication Systems Group,and A. Philipp is with the Dept. of Math., Technische Universitat Darmstadt,64283 Darmstadt, Germany. Emails: pesavento, [email protected],[email protected].
interference (ICI) and improving system throughput in cel-
lular networks with universal frequency reuse [3]–[20]. The
potential of CoMP transmission has been validated in both
theoretic studies [3]–[5] and field trials [3], [6], [7], and
CoMP processing has therefore already been included in
the emerging wireless communication standards, e.g., LTE-
Advanced [8]. While CoMP operation with full cooperation
between BSs that jointly serve users offers significant increases
in network capacity and cell-edge throughput, it induces also
considerable operational overhead, such as power expended
in collecting and exchanging channel state information (CSI)
among multiple BSs and MSs, signaling beamforming weights
and forwarding user data to multiple cooperating BSs [3], [20].
To balance the benefits and the operational costs, CoMP
processing shall be carried out among a limited number of
cooperating BSs, resulting in the so-called partial BS coop-
eration designs. Several partial BS cooperation schemes have
been proposed in the literature, see, e.g., [3], [9]–[20]. Those
existing contributions can roughly be categorized into two
classes, namely coordinated beamforming [3], [9], [10] and
clustered BS cooperation [3], [11]–[20]. In the coordinated
downlink beamforming designs, the beamforming weights of
the MSs are jointly designed across the network, but each MS
is served by a single BS and therefore there is no need to
route payload data or control information, e.g., beamforming
weights, corresponding to one MS over the backhaul network
to multiple BSs [3], [9], [10]. In the clustered BS cooperation
frameworks, CoMP processing is implemented within clusters
of BSs, with full BS cooperation inside each cluster and no
cooperation between clusters [3], [11]–[20]. Since the CoMP
operation is restricted to a small number of BSs in each cluster,
the communication overhead of CoMP processing is bounded
by the size of the BS clusters [3], [11]–[20].
While the existing approaches [3], [9]–[20] can alleviate
the additional expenses in CoMP transmission to certain
extent, several important issues remain open. For instance, in
coordinated beamforming [3], [9], [10], the performance of
cell-edge MSs may still suffer from ICI and large pathloss, as
in conventional cellular systems. Even though cell-edge MSs
can enjoy the performance gain from CoMP processing in the
clustered BS cooperation frameworks [3], [11]–[20], the MSs
located at the cluster edges still suffer from ICI and large
pathloss. In addition, determining the optimal size of the BS
clusters is a challenging open problem [3], [11]–[20]. More
recently, mechanisms to optimize BS selection and multicell
beamforming are proposed in [18]–[20] to reduce the overhead
2
of CoMP transmission, in which the BS selection is carried out
based on the solution of an optimization problem that gives
preference to sparse beamforming vectors [18]–[20]. However,
the sparsity patterns of the beamformers are more appropriate
for antenna selection, rather than for BS selection or network
topology optimization.
In contrast to the existing contributions [3]–[20], we propose
in this paper a systematic approach to find the optimal tradeoff
between the gain and the overhead of CoMP transmission.
Specifically, we consider the problem of joint network topol-
ogy optimization and downlink beamforming (JNOB), with
the objective to minimize the overall BS power consumption
(including the overhead of CoMP operation) while ensur-
ing the quality-of-service (QoS) requirements of the MSs.
The JNOB problem under consideration includes coordinated
beamforming [3]–[20], and full BS cooperation [3]–[5] as
special cases. In other words, in our systematic approach,
the number of cooperating BSs that transmit to each MS
is optimally determined on-the-fly according to the system
parameters and the channel conditions. In addition, we also
consider the possibility of switching off the power amplifiers
(PAs) of the BSs in the JNOB problem formulation to further
reduce BS power dissipations, which is not considered in the
previous works [3]–[20]. The major contributions of this paper
can be summarized as follows.
• In our JNOB approach we explicitly take into account the
operational overhead of CoMP transmission and consider
switching off the PAs of the BSs when minimizing the
total BS power consumption.
• We address the JNOB problem using a MI-SOCP ap-
proach [21] proposing a standard big-M MI-SOCP for-
mulation that supports the convex continuous relaxation
based BnC method [21]–[23].
• Based on the big-M formulation, we introduce auxiliary
variables and develop an extended MI-SOCP formula-
tion [23], also known as perspective formulation [23],
[24], which exhibits several appealing properties that are
exploited in the numerical algorithms.
• We conduct analytic studies to show that the extended
applying the BnC method to the big-M formulation (12). This
confirms that the extended formulation (22) admits less com-
putational complexity when applying the BnC method than
that of the big-M formulation (12) in large-scale networks.
TABLE IV: The percentage of solutions strictly better than the
initial solutions computed by the deflation procedure (Perct.),
the total BS power consumption (Power) [Watts], and the
algorithm runtime (Time) [seconds] vs. P (CMP), with K = 25MSs. Note that CPLEX terminates once a strictly better
solution than the initialization is found.
P(CMP) Deflation CPLEX on (12) CPLEX on (22)[dB] w/ (40) w/ priorities w/ priorities
2
Perct. – 0.0 84.4%
Power 264.1 264.1 260.0
Time 206.4 801.7 504.1
6
Perct. – 0.0 72.0%
Power 368.6 368.6 362.2
Time 197.8 801.8 622.9
VIII. CONCLUSION
We have considered in this paper the JNOB problem aiming
to balance the benefits and operational overhead of CoMP
transmission. The standard big-M MI-SOCP formulation (12)
and the extended MI-SOCP formulation (22) are developed
for the JNOB problem, and the advantages (e.g., admitting
tighter continuous relaxations) of the latter over the former
have been confirmed by analytic studies and numerical results.
Several techniques have been introduced to customize the BnC
algorithm implemented in CPLEX to solve the JNOB problem
and to compute tight lower bounds on the minimum total
BS power consumptions when optimality cannot be reached
due to runtime constraints. We have developed polynomial-
time inflation- and deflation procedures in Alg. 1 and Alg. 2,
respectively, to compute high-quality integer-feasible solutions
of the JNOB problem for practical applications. Simulations
results show that Alg. 1 and Alg. 2 yield with very low compu-
tational complexity the total BS power consumptions that are
close to the lower bounds, e.g., exceeding the lower bounds
by less than 12.9% and 9.0%, respectively, for a network
with L = 13 BSs and K = 25 MSs under the considered
settings. Numerical results have also confirmed the reduction
of computational complexity of the extended formulation (22)
over the big-M formulation (12) and the effectiveness of the
proposed branching priorities when applying the customized
BnC method. Finally, it has been observed in the simulations
that balancing the gain and operational overhead of CoMP
transmission results in partial BS cooperation designs and
sparse network topologies, and BSs are switched off when
possible to reduce the overall BS power consumptions in the
proposed partial BS cooperation design. The proposed MI-
SOCP approach can also be applied to other problems, e.g.,
joint beamforming and discrete rate adaptation [37], sparse
filter design [38], and sparse signal recovery [39], etc.
APPENDIX A
PROOF OF Theorem 1
Recall that the pointw
(bmi)k,l , a
(bmi)k,l , b
(bmi)l , ∀k ∈ K, ∀l ∈
L
represent an optimal solution of the JNOB problem (12).
The necessary conditions in Eqs. (16) can be proved by
contradicting argument.
Assuming that the necessary conditions (16) do not hold,
i.e., assuming that there exist two MSs with indices j, k ∈ Kand two BSs with indices m, l ∈ L such that
a(bmi)
j,l= a
(bmi)
k,l= a
(bmi)
k,m= 1. (49)
That is it is assumed that the lth BS serves the jth and the
kth MSs jointly, and the lth and the mth BSs collaboratively
serve the kth MS. Since∥∥w(bmi)
j,l
∥∥22> 0 when a
(bmc)
j,l= 1,
we know from the per-BS power constraints (12d) that:
∥∥w(bmi)
k,l
∥∥22< P
(MAX)
l= P
(MAX)
l
(a(bmi)
k,l
)2. (50)
We can then define the new variable a(bmi)
k,las: a
(bmi)
k,l,∥∥
w(bmi)
k,l
∥∥2√
P(MAX)
l
, which satisfies
0 < a(bmi)
k,l=
∥∥w(bmi)
k,l
∥∥2√
P(MAX)
l
< a(bmi)
k,l(51)
∥∥w(bmi)
k,l
∥∥22= P
(MAX)
l
(a(bmi)
k,l
)2(52)
∑
l∈L\m,l
a(bmi)
k,l+ a
(bmi)
k,l+ a
(bmi)
k,m> 1. (53)
We can then replace the variable a(bmi)
k,lin the optimal so-
lutionw
(bmi)k,l , a
(bmi)k,l , b
(bmi)l , ∀k ∈ K, ∀l ∈ L
of the JNOB
problem (12) with the variable a(bmi)
k,lto obtain a new feasible
solution of the SOCP (13), which, due to Eq. (51), achieves
a strictly smaller objective value than Φ(bmi). This, however,
contradicts with the fact that Φ(bmc) = Φ(bmi). Hence, the
lth BS cannot serve the jth and the kth MSs jointly when
Φ(bmc) = Φ(bmi). Following a similar contradicting argument,
we can prove that the mth BS must also serve exclusively the
kth MS. As a result, cooperating BSs must serve exclusively
a single MS when Φ(bmc) = Φ(bmi), i.e., the necessary
condition (16) must hold in the case that Φ(bmc) = Φ(bmi).
15
APPENDIX B
PROOF OF Theorem 2
We know from the constraints (22h), and (22j), which
are respectively the same as that of (12g) and (12h), and
Eqs. (32) and (33) that the pointw
(exc)k,l , a
(exc)k,l , b
(exc)l , ∀k ∈
K, ∀l ∈ L
, which is obtained from the projection of the pointw
(exc)k,l , a
(exc)k,l , b
(exc)l , t
(exc)k,l , ∀k ∈ K, ∀l ∈ L
, is a feasible
solution of the SOCP in (13). Hence, it holds that
Φ(bmc) ≤ f(
a(exc)k,l
,b(exc)l
,w
(exc)k,l
). (54)
Eq. (27) suggests that f(
a(exc)k,l
,b(exc)l
,w
(exc)k,l
)≤
Φ(exc). Hence, we have Φ(bmc) ≤ Φ(exc).
APPENDIX C
PROOF OF Theorem 3
Recall that the pointw
(exc)k,l , a
(exc)k,l , b
(exc)l , t
(exc)k,l , ∀k ∈
K, ∀l ∈ L
represent an optimal solution of the SOCP (24).
We first prove Eq. (35). If Φ(bmc) = Φ(exc), i.e., if∥∥w(exc)k,l
∥∥22= t
(exc)k,l , ∀k ∈ K, ∀l ∈ L, we know from Eq. (27)
that the relaxed binary variablesa(exc)k,l , ∀k ∈ K, ∀l ∈ L
take values in the discrete set 0, 1. Due to Eq. (22h), this
is also true for the relaxed binary variablesb(exc)l , ∀l ∈ L
.
Hence, Eq. (35) holds in the case that Φ(bmc) = Φ(exc).
We next prove Eq. (36). We know from Eq. (35) that the
pointw
(exc)k,l , a
(exc)k,l , b
(exc)l , t
(exc)k,l , ∀k ∈ K, ∀l ∈ L
is actu-
ally an optimal solution of the JNOB problem (22) [21]–[23]
and therefore the projected pointw
(exc)k,l , a
(exc)k,l , b
(exc)l , ∀k ∈
K, ∀l ∈ L
is an optimal solution of the JNOB problem (12).
Hence, Eq. (36) holds.
Finally, we know from Eqs (35) and (36) that the projected
pointw
(exc)k,l , a
(exc)k,l , b
(exc)l , ∀k ∈ K, ∀l ∈ L
is an optimal
solution of problem (12) and Φ(bmc) = Φ(bmi) in case that
Φ(bmc) = Φ(exc) holds. As a result, we can directly apply
the results of Theorem 1 to obtain the necessary conditions in
Eq. (37) for the special case of Φ(bmc) = Φ(exc).
REFERENCES
[1] Y. Cheng, S. Drewes, A. Philipp, and M. Pesavento, “Joint networktopology optimization and multicell beamforming using mixed integerprogramming,” in Proc. of International ITG Workshop on Smart An-
tennas (WSA), Mar. 2012, pp. 187–192.[2] ——, “Joint network optimization and beamforming for coordinated
multi-point transmission using mixed integer programming,” in Proc.
of IEEE International Conference on Acoustics, Speech and Signal
Processing (ICASSP), May 2012, pp. 3217–3220.
[3] P. Marsch and G. P. Fettweis, Coordinated Multi-Point in Mobile
Communications: From Theory to Practice. Cambridge UniversityPress, Jul. 2011.
[4] G. Foschini, K. Karakayali, and R. Valenzuela, “Coordinating multipleantenna cellular networks to achieve enormous spectral efficiency,” IEE
Proc. of Commun., vol. 153, no. 4, pp. 548–555, Aug. 2006.[5] S. Shamai and B. Zaidel, “Enhancing the cellular downlink capacity
via co-processing at the transmitting end,” in Proc. of IEEE Vehicular
Technology Conference Spring, May 2001.[6] R. Irmer, H. Droste, and et al., “Coordinated multipoint: Concepts,
performance, and field trial results,” IEEE Commun. Mag., vol. 49, no. 2,pp. 102–111, Feb. 2011.
[7] R. Irmer, H.-P. Mayer, and et al., “Multisite field trial for lte andadvanced concepts,” IEEE Commun. Mag., vol. 47, no. 2, pp. 92–98,Feb. 2009.
[8] 3GPP TR 36.814, “Further advancements for E-UTRA physical layeraspects,” Release 10, Mar. 2010.
[9] A. Tolli, H. Pennanen, and P. Komulainen, “Decentralized minimumpower multi-cell beamforming with limited backhaul signaling,” IEEE
[10] H. Dahrouj and W. Yu, “Coordinated beamforming for the multicellmulti-antenna wireless system,” IEEE Trans. Wireless Commun., vol. 9,no. 5, pp. 1748–1759, May 2010.
[11] J. Zhang, J. Andrews, A. Ghosh, and R. Heath Jr., “Networked MIMOwith clustered linear precoding,” IEEE Trans. Wireless Commun., vol. 8,no. 4, pp. 1910–1921, Apr. 2009.
[12] A. Papadogiannis, D. Gesbert, and E. Hardouin, “A dynamic clusteringapproach in wireless networks with multi-cell cooperative processing,”in Proc. of IEEE ICC’08, May 2008, pp. 4033–4037.
[13] S. Zhou, J. Gong, Y. Jia, and Z. Niu, “A decentralized clustering schemefor dynamic downlink base station cooperation,” IEICE Transactions,vol. 93-B, no. 12, pp. 3656–3659, 2010.
[14] Y.-F. Liu, Y.-H. Dai, and Z.-Q. Luo, “Coordinated beamforming forMISO interference channel: Complexity analysis and efficient algo-rithms,” IEEE Trans. Signal Process., vol. 59, no. 3, pp. 1142–1157,Mar. 2011.
[15] C. T. K. Ng and H. Huang, “Linear precoding in cooperative MIMOcellular networks with limited coordination clusters,” IEEE J. Sel. Areas
Commun., vol. 28, no. 9, pp. 1446–1454, Dec. 2010.
[16] J.-M. Moon and D.-H. Cho, “Inter-cluster interference managementbased on cell-clustering in network MIMO systems,” in Proc. of IEEE
73rd Vehicular Technology Conference, May 2011, pp. 1–6.
[17] A. Papadogiannis and G. C. Alexandropoulos, “The value of dynamicclustering of base stations for future wireless networks,” in Proc. of
IEEE International Conference on Fuzzy Systems, Jul. 2010, pp. 1–6.
[18] S.-J. Kim, S. Jain, and G. B. Giannakis, “Backhaul-constrained multi-cell cooperation using compressive sensing and spectral clustering,”in Proc of IEEE 13th International Workshop on Signal Processing
Advances in Wireless Communications, Jun. 2012, pp. 65–69.
[19] M. Hong, R. Sun, H. Baligh, and Z.-Q. Luo, “Joint base stationclustering and beamformer design for partial coordinated transmissionin heterogeneous networks,” IEEE J. Sel. Areas Commun., vol. 31, no. 2,pp. 226–240, Feb. 2013.
[20] Y. Zeng, E. Gunawan, Y. L. Guan, and J. Liu, “Joint base stationselection and linear precoding for cellular networks with multi-cellprocessing,” in Proc. of TENCON, Nov. 2010.
[21] S. Drewes, Mixed Integer Second Order Cone Programming. PhDdissertation, Darmstadt University of Technology, Germany, Jun. 2009.
[22] Y. Pochet and L. A. Wolsey, Production Planning by Mixed Integer
Programming. Springer (US), May 2006.
[23] J. Lee and S. Leyffer, Mixed Integer Nonlinear Programming. TheIMA Volumes in Mathematics and its Applications, Springer-US, Dec.2011.
[24] O. Gnlk and J. Linderoth, “Perspective reformulations of mixed integernonlinear programs with indicator variables,” Mathematical Program-
[26] G. Micallef, P. Mogensen, and H.-O. Scheck, “Cell size breathingand possibilities to introduce cell sleep mode,” in European Wireless
Conference (EW), Apr. 2010, pp. 111–115.
[27] E. Oh and B. Krishnamachari, “Energy savings through dynamic basestation switching in cellular wireless access networks,” in IEEE Global
Telecommunications Conference, Dec. 2010, pp. 1–5.
[28] A. Chatzipapas, S. Alouf, and V. Mancuso, “On the minimization ofpower consumption in base stations using on-off power amplifiers,” inProc. of IEEE Online Conference on Green Communications (Green-
Com), Sep. 2011, pp. 18–23.
[29] F. Richter, A. Fehske, and G. Fettweis, “Energy efficiency aspects ofbase station deployment strategies for cellular networks,” in Proc. of
IEEE 70th Vehicular Technology Conference Fall, Sep. 2009, pp. 1–5.
[30] O. Arnold, F. Richter, G. Fettweis, and O. Blume, “Power consumptionmodeling of different base station types in heterogeneous cellularnetworks,” in Proc. of Future Network and Mobile Summit, Jun. 2010,pp. 1–8.
[31] J. Gong, S. Zhou, and Z. Niu, “A dynamic programming approach forbase station sleeping in cellular networks,” IEICE Trans. Commun., vol.95-B, no. 2, pp. 551–562, 2012.
[32] M. Bengtsson and B. Ottersten, Optimal and Suboptimal Transmit
Beamforming. In: Handbook of Antennas in Wireless Communications,CRC Press, Aug. 2001.
16
[33] S. Boyd and L. Vandenberghe, Convex Optimization. CambridgeUniversity Press, Mar. 2004.
[34] E. Matskani, N. D. Sidiropoulos, Z.-Q. Luo, and L. Tassiulas, “Convexapproximation techniques for joint multiuser downlink beamforming andadmission control,” IEEE Trans. Wireless Commun., vol. 7, no. 7, pp.2682–2693, Jul. 2008.
[35] ——, “Efficient batch and adaptive approximation algorithms for jointmulticast beamforming and admission control,” IEEE Trans. Signal
Process., vol. 57, no. 12, pp. 4882–4894, Dec. 2008.[36] Y.-F. Liu, Y.-H. Dai, and Z.-Q. Luo, “Joint power and admission control
via linear programming deflation,” IEEE Trans. Signal Process., vol. 61,no. 6, pp. 1327–1338, Mar. 2013.
[37] Y. Cheng, A. Philipp, and M. Pesavento, “Dynamic rate adaptation andmultiuser downlink beamforming using mixed integer conic program-ming,” in Proc. of the 20th European Signal Processing Conference
(EUSIPCO), Aug. 2012, pp. 824–828.[38] D. Wei and A. V. Oppenheim, “A branch-and-bound algorithm for
quadratically-constrained sparse filter design,” IEEE Trans. Signal Pro-
cess., vol. 61, no. 4, pp. 1006–1018, Feb. 2013.[39] Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Appli-
cations. Cambridge University Press, May 2012.
Yong Cheng (S’09) received the B.Eng. (1st honors)and M.Phil. degrees from Zhejiang University (ZJU),Hangzhou, P.R. China, and the Hong Kong Uni-versity of Science and Technology (HKUST), HongKong, in 2006 and 2010, respectively. He is currentlya Ph.D. student at the Communication SystemsGroup, Dept. of Electrical Engineering and Informa-tion Technology, Technische Universitat Darmstadt,Darmstadt, Germany. His current research interestsmainly include mixed integer programming and con-vex optimization in signal processing and wireless
communications, multiple-antenna techniques in LTE/LTE-advanced, as wellas resource allocation and coordinated multipoint processing (CoMP) inheterogeneous networks.
Marius Pesavento (M’00) received the Dipl.-Ing.and M.Eng. degrees from Ruhr-Universitat Bochum,Germany, and McMaster University, Hamilton, ON,Canada, in 1999 and 2000, respectively, and in 2005the Dr.-Ing. degree in Electrical Engineering fromRuhr-Universitat Bochum, Germany. Between 2005and 2007, he was a Research Engineer at FAGIndustrial Services GmbH, Aachen, Germany. From2007 to 2009 he was the Director of the SignalProcessing Section at mimoOn GmbH, Duisburg,Germany. In 2010, he became a Professor for Robust
Signal Processing at the Department of Electrical Engineering and Informa-tion Technology, Darmstadt University of Technology, Darmstadt, Germany,and he is currently the Head of the Communication Systems Group. Hisresearch interests are in the area of robust signal processing and adaptivebeamforming, high-resolution sensor array processing, transceiver designfor cognitive radio systems, cooperative communications in relay networks,MIMO and multiantenna communications, space-time coding, multiuser andmulticarrier wireless communication systems (3+G), convex optimization forsignal processing and communications, statistical signal processing, spectralanalysis, parameter estimation and detection theory. Dr. Pesavento was arecipient of the 2003 ITG/VDE Best Paper Award, the 2005 Young AuthorBest Paper Award of the IEEE Transactions on Signal Processing, and the2010 Best Paper Award of the CROWNCOM conference. He is a member ofthe Editorial board of the EURASIP Signal Processing Journal, an AssociateEditor for the IEEE Transactions on Signal Processing, and a member ofthe Sensor Array and Multichannel (SAM) Technical Committee of the IEEESignal Processing Society (SPS).
Anne Philipp (S’09) received the Diploma degreein mathematics from Technische Universitat Darm-stadt, Darmstadt, Germany in 2011. From 2008 to2009, she studied mathematics at the University ofSaskatchewan, Saskatoon, Canada. She is currently aPh.D. student in the Nonlinear Optimization Group,Department of Mathematics, Technische Univer-sitat Darmstadt, Darmstadt, Germany. Her currentresearch interests include mixed integer nonlinearprogramming and semidefinite programming withapplications in signal processing and wireless com-