JOINT MULTICAST BEAMFORMING AND ADMISSION CONTROL E. Matskani, N.D. Sidiropoulos ∗ Dept. of ECE Tech. Univ. of Crete 73100 Chania - Crete, Greece Z.-Q. Luo † Dept. of ECE Univ. of Minnesota Minneapolis, MN 55455, U.S.A. L. Tassiulas ‡ Dept. of CE & T Univ. of Thessaly 38221 Volos, Greece ABSTRACT Wireless multicasting is quickly emerging as an important enabling technology for mass content distribution to mobile hand-held de- vices. With channel state information at the transmitter, it is possi- ble to tailor transmissions by selective beamforming towards specific user groups, thereby harnessing the wireless ‘broadcast advantage’ and managing co-channel interference. Wireless (physical layer) multicasting options are currently being debated in the emerging UMTS-LTE standard. A key problem in this context is admission control: it is often infeasible or impractical to serve all subscribers from a single access point, due to mutual interference or power lim- itations. This paper considers the joint multicast beamforming and admission control problem, aiming to maximize the number of sub- scribers that can be served and minimize the power required to serve them. The joint problem is NP-hard, yet suitable reformulation re- veals that it can be naturally relaxed to a semidefinite program (SDP), leading to an approximation by deflation over SDP. Experimental re- sults using measured channels indicate that the proposed approxima- tion approach is fast and efficient. Index terms: Multicasting, transmit beamforming, admission con- trol, UMTS-LTE. 1. INTRODUCTION Wireless multicasting is becoming increasingly important as mass content distribution (network TV, streaming media, software updates, network management) starts permeating the celluler wireless market. Emerging standards such as UMTS-LTE provision wireless multi- casting [7] in addition to network-layer packet multicast routing. Wireless multicasting can boost spectral efficiency by taking advan- tage of the spatial dimension. With channel state information at the transmitter (CSI-T), it is possible to tailor transmissions by selec- tive beamforming towards specific user groups, thereby harnessing the wireless ‘broadcast advantage’ and simultaneously managing co- channel interference. Consider a downlink scenario comprising an access point with N antenna elements, and K single-antenna receivers. The case of an isolated subcarrier with full CSI-T will be considered for simplicity. The approach can be generalized in various ways, e.g., to use sta- tistical CSI-T. Let h i denote the N × 1 complex vector that models the propagation loss and phase shift of the frequency-flat quasi-static ∗ Tel: +302821037227, Fax: +302821037542, E-mail: (matskani,nikos)@telecom.tuc.gr. Supported in part by ARL/ERO contract N62558-06-0340 and E.U./FP6 COOPCOM, WIP. † E-mail: luozq@ece.umn.edu. Supported in part by U.S. NSF grants DMS-0312416 and DMS-0610037. ‡ E-mail: leandros@uth.gr. Supported in part by E.U./FP6 Netrefound and WIP. channel from each transmit antenna to receiver i, i ∈{1, ··· ,K}. Assuming a total of 1 ≤ G ≤ K multicast groups, {G 1,... , GG}, where Gm contains the indices of receivers participating in multi- cast group m, m ∈{1,... ,G}. Each receiver listens to a single multicast; thus G m ∩G l = ∅, l  = m, ∪mGm = {1,... ,K}, and, denoting Gm := |Gm|, ∑ G m=1 Gm = K. Let w H m denote the 1 × N weight vector applied to the N trans- mitting elements to beamform towards group m, m ∈{1, ··· ,G}. The joint (co-channel) multicast beamformer design problem under individual Signal to Interference plus Noise Ratio (SINR) constraints and an overall power constraint can be expressed as min {wm∈C N } G m=1 G  m=1 ‖wm‖ 2 2 (1) subject to : G  m=1 ‖wm‖ 2 2 ≤ P, (2) |w H m hi | 2 ∑ ℓ =m |w H ℓ hi | 2 + σ 2 i ≥ ci , ∀i ∈Gm, ∀m ∈{1, ··· ,G} , (3) where σ 2 i is the additive noise power at receiver i and ci stands for the associated minimum SINR requirement. The above has been considered in [5], and it includes the broadcasting problem (a single multicast group, G =1) [11], and the multiuser downlink problem (G = K) [3, 1] as special cases. An important concern is that (1)-(3) is often infeasible, in which case some form of admission control is necessary. This entails user selection, and it is natural to ask that the number of users served should be maximized, and the power required to serve them should be minimized. Mathematically, the problem can be described in two stages. In the first stage, S o = argmax S⊆{1,··· ,K},{wm∈C N } G m=1 |S| (4) subject to :  m |Gm∩S =∅ ‖wm‖ 2 2 ≤ P, (5) |w H m hi | 2 ∑ ℓ |G ℓ ∩S =∅,ℓ =m |w H ℓ hi | 2 + σ 2 i ≥ ci , ∀i ∈Gm ∩ S, ∀m, (6) where |S| denotes the cardinality of S. Note that if Gm ∩ S = ∅, then no constraints are imposed for the given m. Given So, we then wish to min {wm∈C N } m |Gm∩So=∅  m |Gm∩So =∅ ‖wm‖ 2 2 (7)