Opportunistic User Selection for Interference Alignment

Jongpil Seo, Jaeyoung Kim, Chamsol Yang and Jaehak ChungDep. Of Electronic Engineering, Inha University

Wireless Mobile Communication LaboratoryIncheon, Korea

Abstract—An opportunistic user selection method for inter-ference alignment is proposed. The proposed scheme selects aspace between desired signal and interference spaces according to received signals from all base stations. An additional selective diversity gain is obtained in addition to a multi-user diversity gain. Simulation examples show that the proposed method achieves higher sum capacity than that of conventional opportunistic interference alignment.

Keywords; Interference alignment, opportunustic user selection, Selective diversity gain.

I. INTRODUCTION

In future wireless communication systems, interference managements become a key issue. As one of interference management methods, interference alignment(IA) scheme has been studied[1]. The basic idea of the IA is that the IA aligns all interferences to a subspace at each receiver. Then, the degrees of freedom (DoF) of K user interference channel is kept to 2K . To achieve the IA in practice, iterative algorithm for the IA is proposed for K user MIMO interference channels[2].

For perfect IA, all and accurate channel state information isrequired at all transmitters. Practically, however, the feedback of all channel state information causes enormous system overheads and inaccurate channel state information degrades alignment performance. Computational complexity is also one of obstacles since transmitters and receivers require iterative computations.

To combat these problems, an opportunistic IA(OIA)[3] has been proposed which is motivated by opportunistic beam-forming[4]. In the OIA scheme, each transmitter broadcasts a random beam and each user feeds back the correlation between interfering signals. As increasing the number of users, the chance of interference alignment increases. The OIA, however, is hard to obtain the benefit of the IA with the small number of users. If the correlation between the desired signal and theinterfering signal is larger than the correlation of interferences, the performance of the OIA may degrade.

In this paper, we propose an opportunistic user selection for interference alignment. The proposed scheme selects a space between desired signal and interference spaces of the received

signals among all base stations. Since the proposed schemeextends spaces selected by users, an additional selective diversity gain can be obtained compared with that of the conventional OIA.

The rest of this paper is organized as follow. In Section II, system model is described. The opportunistic user selectionmethod for interference alignment is proposed in Section III. Numerical example is shown in Section IV and conclusion is followed in Section V.

II. SYSTEM MODEL

We consider a multi-cell MIMO downlink system of Bcells and K users per cell. Each base station and user are equipped with M transmit antennas and N receive antennas, respectively. All users are located at cell edge region for maximizing the effect of the IA. Each transmitter transmits min( , ) / 2M N spatial streams among available min( , )M Nindependent streams to guarantee desired signal spaces for the IA.

Let jV be a random unitary beamforming matrix at BS jthat satisfies H

j j d�V V I . Then, received signal at the -k th user in the -b th cell is given by

( ) ( ) ( )

1

,b b b

B

j jk k j kj�

� ��y H V x n (1)

where ( )bN M

k j��H � denotes a channel matrix from the

-j th BS to the -k th user in the -b th cell and all elements areindependent and identically distributed(i.i.d) complex Gaussian random variables with zero mean and unit variance. jx denotes a transmit signal at the -j th BS and satisfies the powerconstraint 2{ }jE P�x . Additive Gaussian noise is denoted by ( )

1b

Nk

��n � and ( )2~ ( , )bk �n 0 I�� . We do not consider

path loss since all users are located at cell edge. Therefore,signal-to-noise ratio(SNR) is equal to interference-to-noise ratio(INR). In the next section, we describe the proposed opportunistic selection method for the interference alignment.

III. OPPORTUNISTIC USER SELECTION FOR INTERFERENCE ALIGNMENT

In the conventional OIA, each transmitter at BSs oppor-tunistically selects a user among all users whose correlation between interferences is the smallest. Then, the BSs and the

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selected users construct a B -user MIMO interference channel. Therefore, as increasing the number of users, the probability ofinterference alignment increases.

For few users, however, it is difficult to obtain the benefit of the IA. If a correlation between a desired signal vector and a certain interfering vector is larger than other interfering vectors, the channel gain of the desired signal is attenuated largely. Toovercome this problem, the proposed method provides a chance to switch the signal and interference space of the received signal from all BSs, i.e., the serving BS can be switched. Thus, the proposed method acquires an additional selection diversity gain from B to BK compared with that of the conventional scheme. Following describes our oppor-tunistic user selection scheme for the IA in detail.

Assume that each BS is connected to others with backhaul. As a selection method, we measure the leakage interference of each user. For the first step, each BS broadcasts a random beam. For the second step, each user calculates the leakage interference from the sum of the -d smallest eigenvalues of interference covariance matrix, which is given by

( ) ( ) ( )

1,

.b b b

BH H

m mk j k m k mm m j� �

� �Q H V V H (2)

Then, the leakage interferences at each user is calculated by the eigenvalue decomposition and given by

( ) ( )

1

( ),b b

d

ik j k ji

L ��

� � Q (3)

where ( )i� � denotes the i th eigenvalue and 1 N� � � .For the third step, the leakage interferences of users are fed back to their BSs and the BSs select the user whose ( )bk jL is minimum among all users as following.

( )( )

,argmin .bb

j k jb k

k L� � (4)

The information of the leakage interferences of other BSs are shared using backhaul. For the last step, the selected users calculate the interference suppression matrix in (2) using eigenvectors of the d smallest eigenvalues similarly in [2, Eq.(22)]. Then, the effective interference for users is equal to (3). The proposed method considers all signal and interference spaces from all BSs. Therefore, the proposed method achieves an additional selective diversity gain compared with that of the conventional scheme.

IV. NUMERICAL EXAMPLE

In this section, we evaluated the sum-rate performance of the proposed scheme. We assumed three cells and each BS and user are equipped with four transmit antennas and two receive antennas, respectively. We assumed that all users are located at cell edge, the path losses of all links are set to 0dB. Sum capacity is computed via Monte Carlo simulations using 1000 random channel generations.

Figure 1 shows the sum capacity of the proposed and the conventional OIA according to the number of users in each cell when 15dBSNR INR� � . For precise comparison, we utilized min-INR in the conventional scheme. Since both

schemes have multi-user diversity gain, sum capacity increases as the number of users increases. The proposed method,however, provides higher sum capacity than that of the conventional scheme at the same number of users because the proposed scheme has an additional selective diversity gain.

V. CONCLUSION

In this paper, we proposed an opportunistic user selection method for the IA. The proposed scheme selects the user whose leakage interference is minimum among all users. If the number of users increases, the probability of interferencealignment increases compared with that of the conventional scheme. Thus, the proposed scheme exhibits an additional selective diversity gain. Numerical example shows that the proposed scheme achieves higher sum capacity than that of the conventional scheme.

ACKNOWLEDGMENT

This research was supported by the KCC(Korea Communications Commission), Korea, under the R&D program supervised by the KCA(Korea Communications Agency)(KCA-2012-[12-911-01-107]).

REFERENCES

[1] V. R. Cadambe and S. A. Jafar, “Interference alignment and the degrees of freedom for the K-user interference channel,” IEEE Transactions on Information Theory, vol. 54, no.8, pp.3424-3441, Aug. 2008.

[2] K. Gomadam, V. R. Cadambe and S. A. Jafar, “A distributed numerical approach to interference alignment and applications to wireless interference networks,” IEEE Transactions on Information Theory, vol. 57, no, 6, Jun. 2011.

[3] J. Lee and W. Choi, “Opportunistic interference aligned user selection in multiuser MIMO interference channels,” Proceedings of Global Telecommunication Conference 2010, Dec. 2010.

[4] P. Viswanath, D. N. C. Tse and R. Laroia, “Opportunistic beamforming using dumb antenna,” IEEE Transactions on Information Theory, vol. 48, no. 6, Jun. 2002.

0 2 4 6 8 10 12 14 16 18 205

6

7

8

9

10

11

12

13

Number of users in each cell

Sum

-rate

[bps

/Hz]

OIA based on DCSConventional OIA

Figure 1. Sum capacity performance according to the number of users when SNR=INR=15dB

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