MIMO Millimeter-Wave Channel Estimation Using Coalitional Games Pablo Palacios Cesar A. Azurdia-Meza Nicolás Ortega Universidad de Las Américas Universidad de Chile Universidad de Chile Quito, Ecuador Santiago, Chile Santiago, Chile pablo.palacios@udla.edu.ec cazurdia@ing.uchile.cl nicolas.ortegas@usach.cl space, resulting in reduced channel estimation over- heads in mm-wave massive MIMO systems [Rap13]. Abstract Since the throughput performance achieved by the pro- posed channel estimation method inevitably decreases In millimeter-wave massive multiple input due to inter-cell interference in multiple small cell sce- multiple output (MIMO) antenna systems, narios, we formulate a coalitional game framework to channel estimation is a crucial component. enhance the system throughput via cooperative chan- In this paper, we propose a virtual channel nel allocation. representation channel estimation method us- ing out-of-band spatial information to reduce 2 System Model training overheads and a cooperative channel We consider a mm-wave MIMO uplink system with allocation method based on coalitional game uniform linear arrays (ULAs) conformed by Nt trans- framework. The proposed cooperative chan- mitter antennas in the UE and Nr receiver antennas in nel allocation method enhances throughput the eNB. We consider that both the transmitter and performance in mm-wave small cell networks. the receiver have only one RF chain, hence, only ana- log beamforming/combining can be applied. 1 Introduction We use f and q to denote the beamformer and com- biner vector, respectively. The beamformer is defined Large antenna arrays (i.e. Massive MIMO) at both as follows: sides the eNodeB (eNB) and UE is a promising tech- 1 2π nology in order to achieve high-throughput services f = √ [1, ..., ej(Nr −1) λ d cos φ ]T , (1) [Wan12]. Large antenna arrays deal with high path- Nt loss in millimeter frequencies. Further, channel state where φ ∈ [−π/2, π/2], is a quantized angle of de- information (CSI) in terms of channel matrix or beam parture, f has constant modulus entries, and random alignment are needed at the eNB to point the beams in phase. In similar fashion the combiner is defined as the UE direction. Both strategies are usually acquired follows: by a training sequence [Has03]. 1 2π q = √ [1, ..., ej(Nr −1) λ d cos θ ]T , (2) In this work, we analyze a channel estimation Nr method that leverages out-of-band measurements to where θ ∈ [−π/2, π/2], is the quantized angle of ar- decrease the training overheads for high-speed UEs rival. Then considering a narrowband channel model in mm-wave massive MIMO systems. Therefore, the H, the received signal in the eNB can be modeled as: overlapped virtual beams provide a smaller search √ y = ρqH Hfx + qH v, (3) Copyright c by the paper’s authors. Copying permitted for √ where ρ is the average transmit power in the training private and academic purposes. phase, x is the training symbol, and v is an i.i.d. vec- In: Proceedings of the IV School of System and Networks (SSN 2018), Valdivia, Chile, October 29-31. Published at http://ceur- tor, and ∼ CN (0, σ02 I) is the noise. A virtual channel ws.org representation (VCR) of H will provide spatial infor- This work has been partially funded by Project FONDECYT mation uniformly spaced over the virtual angles, ob- 11160517 and Universidad de Las Américas (UDLA). served in Figure 1. eNB3 UE1 eNB4 eNB2 eNB1 eNB5 eNB7 eNB6 (a) Figure 2: Multicell network architecture. 3.1 Coalitional Game: System Model The main goal is to deal with interference from neigh- boring millimeter-wave small cells (MMWSC) in the border coverage area by forming coalitions. Using coalitional game theory, we denote as B the set of all partitions GN of N , this problem can be modeled as (b) coalitional game in partition form with transferable utility as the pair (N , v) where N is the set of players Figure 1: Virtual channel matrix for: (a) Sub-6 Ghz in the game, and a value function v(S, GN ) assigning with Nr=Nt=16, (b) Mmwave with Nr=Nt=64. a real value to each coalition S. We also assume that v(∅) = 0. The function describes how much collective 2.1 Millimeter-wave Channel model payoff a set of players can gain by forming a coalition, and the game is sometimes called a value game or a We adopt a geometric channel model with L scatterers, profit game. Thus, the definition above imposes a de- where each scatterer contributes to one propagation pendence on the coalitional structure N when evaluat- path. Accordingly, the channel matrix H, is expressed ing the value of S ⊆ N . Therefore the utility achieved as: by the coalition S can be expressed in terms of the L p X channel rate as: H = Nt Nr αl ar (θl )aH t (φl ), (4) l=1 H H XX ρi,l qH i,l Hi,l fi,l fi,l Hi,l qi,l where L is the number of paths, αl represents the U(S, GN ) = αil log2 (1+ ), complex path gain of the l -th propagation path, θl ∈ i∈S l∈Γ σo2 + ÎS [−π/2, π/2], and φl ∈ [−π/2, π/2] denotes the AoA (5) and AoD of the L-th path at transmitter and receiver, Given the power cost and utility function for any respectively. The at (·) and ar (·) vectors denote the coalition S ∈ N , we can define the value of any coali- array response vectors for transmiting and receiving tion, i.e., the total benefit as: antenna arrays, respectively.  |S| U(S, GN ) if ρS ≤ ρlim v(S, GN ) = (6) 3 Multicell Analysis 0 otherwise, Lets consider an Orthogonal Frequency Division Mul- We can define the payoff of a MMWSC i ∈ S as: tiple Access (OFDMA) multicell system, as is shown   in Figure 2. We assume that in every cell there is a 1  X small microwave cell station and millimeter-wave small xi = v(S, πN ) − v({j}, GN ) + v({i}, GN ), |S| j∈S station located in the same position. Consider the mul- ticell network architecture depicted in Figure 2 where (7) the UE1 is located in the eNB2 coverage area border, 3.2 Proposed Algorithm such that this user must deal with handoff manage- ment and interference from neighboring cells. In or- For the stated coalitional game it is important to no- der to overcome these problems, we propose a method tice that due to power constraint requirements, the based on cooperative model using coalitional games grand coalition seldom forms. Therefore, cooperation between the concerned eNBs. will occur when the interferring MMWSCs are closely Algorithm 1 Proposed MMWSC cooperation algo- rithm Step 1: UE interference sensing The UE sense the interference U Eint , once it over- pass a threshold Ithr , the UE feedback the infor- mation to its attached eNB in order to initiate the cooperation process, thus: if U Eint ≥ Ithr then Step 2: Coalitional Game Starts At the beginning when players are not cooper- ating GN = {1, ..., N } = {S1 , ..., SN }. Figure 3: Rate achieved by CE training-based over Three stages in each round of the algorithm different SNR values. Stage 1 - Discovering Neighbors: efficiency changes according to different SNR values. • Each MMWSC discovers the neighboring coalitions. 4 Conclusions and Future Work Stage 2 - Recursive Coalition Formation: In this work, we proposed a channel estimation method repeat based on coalitional game for a multicell case that im- proves the throughput. The prior based on an algo- • Each MMWSC establishes negotiations rithm that improves intercell interference. As future with discovered neighboring FAPs. Each works we will analyze in the single cell case how the MMWSC create a list of the feasible coali- analyzed method performs in different SNR scenarios, tions which ensure ρS ≤ ρlim , Where ρS is the computational complexity, user equipment (UE) the power cost needed to form a coalition mobility environment, and BER analysis. S and ρlim is a maximum tolerable power cost for every coalition S. The payoff for References the feasible coalitions is computed and each [Wan12] J. Wang, H. Zhu, and N. J. Gomes. Dis- MMWSC joins to the coalition which ensures tributed antenna systems for mobile commu- the maximum payoff. nications in high speed trains. IEEE J. Sel. until convergence to a stable partition in the Area Commun., vol 30, no. 4, pp 675-683, recursive core. May. 2012. Stage 3 - Inner-coalition scheduling: [Has03] B. Hassibi and B. M. Hochwald. How much • The scheduling information is gathered by training is needed in multiple-antenna wire- each MMWSC i ∈ S from its coalitions mem- less links?. IEEE Trans. Inf. Theory, vol.49, bers, and transmitted within the coalition S no.4, pp. 951-963, Apr. 2003. afterwards. [Rap13] T. S. Rappaport, S. Sun, R. Mayzus, end if H. Zhao, Y. azar, K. Wang, G. N. Wong, Step 3: High Speed mmWave Communica- J. K. Schulz, M. Samini, and F. Gutierrez. tions Millimeter wave mobile communications for 5G cellular: It will work. IEEE Access, vol.1, located in a way that ρS ≤ ρlim . Finding an opti- pp.335-349, 2013. mal coalitional structure for games in partition form [Hua06] C.-Y. Huang and T. Sjostrom, Implementa- has been studied in [Hua06] and [Pan11]. In this tion of the recursive core for partition func- manuscript we will apply the concept of recursive core tion form games. Journal of Mathematical as it was done in [Pan11]. Economics, 42, 2006. 3.3 Preliminary Numerical Results [Pan11] F. Pantisano, M. Bennis, W. Saad, R. Ver- done, and M. Latva-aho, Coalition forma- In order to explore the performance of the proposed tion games for femtocell interference manage- method, Sub 6-Ghz channel was set with 16 trans- ment: a recursive core approach. Proc. 2011 mitter antennas and 16 receiver antennas, whereas IEEE Wireless Commun. Netw. Conf., Can- for the mm-wave channel the systems was set with cun, Quintana Roo, Mexico, pp.2831, March. Nr = Nt = 64, Nr = Nt = 32, and Nr = Nt = 16 2011. antennas. It can be seen in Figure 3 how the spectral