In millimeter-wave massive multiple input multiple output (MIMO) antenna systems, channel estimation is a crucial component. In this paper, we propose a virtual channel representation channel estimation method using out-of-band spatial information to reduce training overheads and a cooperative channel allocation method based on coalitional game framework. The proposed cooperative channel allocation method enhances throughput performance in mm-wave small cell networks.
Large antenna arrays (i.e. Massive MIMO) at both sides the eNodeB (eNB) and UE is a promising technology in order to achieve high-throughput services [Wan12]. Large antenna arrays deal with high pathloss in millimeter frequencies. Further, channel state information (CSI) in terms of channel matrix or beam alignment are needed at the eNB to point the beams in the UE direction. Both strategies are usually acquired by a training sequence [Has03].
In this work, we analyze a channel estimation method that leverages out-of-band measurements to decrease the training overheads for high-speed UEs in mm-wave massive MIMO systems. Therefore, the overlapped virtual beams provide a smaller search Copyright c by the paper's authors. Copying permitted for private and academic purposes.
In: Proceedings of the IV School of System and Networks (SSN 2018), Valdivia, Chile, October 29-31. Published at http://ceurws.org This work has been partially funded by Project FONDECYT 11160517 and Universidad de Las Americas (UDLA). space, resulting in reduced channel estimation overheads in mm-wave massive MIMO systems [Rap13]. Since the throughput performance achieved by the proposed channel estimation method inevitably decreases due to inter-cell interference in multiple small cell scenarios, we formulate a coalitional game framework to enhance the system throughput via cooperative channel allocation. 2
We consider a mm-wave MIMO uplink system with uniform linear arrays (ULAs) conformed by Nt transmitter antennas in the UE and Nr receiver antennas in the eNB. We consider that both the transmitter and the receiver have only one RF chain, hence, only analog beamforming/combining can be applied. We use f and q to denote the beamformer and combiner vector, respectively. The beamformer is de ned as follows:
f = p1Nt [1; :::; ej(Nr 1) 2 d cos ]T ; where 2 [ =2; =2]; is a quantized angle of departure, f has constant modulus entries, and random phase. In similar fashion the combiner is de ned as follows:
q = p1Nr [1; :::; ej(Nr 1) 2 d cos ]T ; where 2 [ =2; =2], is the quantized angle of arrival. Then considering a narrowband channel model H, the received signal in the eNB can be modeled as: y = p qH Hfx + qH v; (3) where p is the average transmit power in the training phase, x is the training symbol, and v is an i.i.d. vector, and CN (0; 02I) is the noise. A virtual channel representation (VCR) of H will provide spatial information uniformly spaced over the virtual angles, observed in Figure 1. (1) (2) (a) (b) where L is the number of paths, l represents the complex path gain of the l -th propagation path, l 2 [ =2; =2], and l 2 [ =2; =2] denotes the AoA and AoD of the L-th path at transmitter and receiver, respectively. The at( ) and ar( ) vectors denote the array response vectors for transmiting and receiving antenna arrays, respectively. 3
Lets consider an Orthogonal Frequency Division Multiple Access (OFDMA) multicell system, as is shown in Figure 2. We assume that in every cell there is a small microwave cell station and millimeter-wave small station located in the same position. Consider the multicell network architecture depicted in Figure 2 where the UE1 is located in the eNB2 coverage area border, such that this user must deal with hando management and interference from neighboring cells. In order to overcome these problems, we propose a method based on cooperative model using coalitional games between the concerned eNBs. eNB7 eNB2
UE1 eNB6 eNB3 eNB1 eNB4 eNB5 The main goal is to deal with interference from neighboring 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 coalitional game in partition form with transferable utility as the pair (N ; v) where N is the set of players in the game, and a value function v(S; GN ) assigning a real value to each coalition S. We also assume that v(;) = 0. The function describes how much collective payo a set of players can gain by forming a coalition, and the game is sometimes called a value game or a pro t game. Thus, the de nition above imposes a dependence on the coalitional structure N when evaluating the value of S N . Therefore the utility achieved by the coalition S can be expressed in terms of the channel rate as: U (S; GN ) = X X
il log2(1+ i2S l2 (5)
Given the power cost and utility function for any coalition S 2 N , we can de ne the value of any coalition, i.e., the total bene t as: i;lqiH;lHi;lfi;lfiH;lHiH;lqi;l ); o2 + ^IS v(S; GN ) = jSj U (S; GN ) if S lim 0 otherwise;
We can de ne the payo of a MMWSC i 2 S as: xi =
0 1 X v(fjg; GN )A + v(fig; GN ); j2S (6) (7) 3.2
For the stated coalitional game it is important to notice that due to power constraint requirements, the grand coalition seldom forms. Therefore, cooperation will occur when the interferring MMWSCs are closely Algorithm 1 Proposed MMWSC cooperation algorithm
Step 1: UE interference sensing
The UE sense the interference U Eint, once it overpass a threshold Ithr, the UE feedback the information 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 cooperating GN = f1; :::; N g = fS1; :::; SN g.
Three stages in each round of the algorithm Stage 1 - Discovering Neighbors:
Each MMWSC discovers the neighboring coalitions.
Stage 2 - Recursive Coalition Formation: repeat
Each MMWSC establishes negotiations with discovered neighboring FAPs. Each MMWSC create a list of the feasible coalitions which ensure S lim, Where S is the power cost needed to form a coalition S and lim is a maximum tolerable power cost for every coalition S. The payo for the feasible coalitions is computed and each MMWSC joins to the coalition which ensures the maximum payo .
until convergence to a stable partition in the recursive core.
Stage 3 - Inner-coalition scheduling:
The scheduling information is gathered by each MMWSC i 2 S from its coalitions members, and transmitted within the coalition S afterwards. end if Step 3: High Speed mmWave Communications located in a way that S lim. Finding an optimal coalitional structure for games in partition form has been studied in [Hua06] and [Pan11]. In this manuscript we will apply the concept of recursive core as it was done in [Pan11]. 3.3
In order to explore the performance of the proposed method, Sub 6-Ghz channel was set with 16 transmitter antennas and 16 receiver antennas, whereas for the mm-wave channel the systems was set with Nr = Nt = 64, Nr = Nt = 32, and Nr = Nt = 16 antennas. It can be seen in Figure 3 how the spectral
In this work, we proposed a channel estimation method based on coalitional game for a multicell case that improves the throughput. The prior based on an algorithm that improves intercell interference. As future works we will analyze in the single cell case how the analyzed method performs in di erent SNR scenarios, the computational complexity, user equipment (UE) mobility environment, and BER analysis.