INTERFERENCE MANAGEMENT FOR FEMTOCELL NETWORKS

The Pennsylvania State University The Graduate School Department of Electrical Engineering INTERFERENCE MANAGEMENT FOR FEMTOCELL NETWORKS A Thesis in Electrical Engineering by Basak Guler c 2012 Basak Guler Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2012

The thesis of Basak Guler was reviewed and approved* by the following: Aylin Yener Professor of Electrical Engineering Thesis Adviser Vishal Monga Assistant Professor of Electrical Engineering Kultegin Aydin Professor of Electrical Engineering *Signatures are on file in the Graduate School.

iii Abstract This thesis proposes methods for applying the idea of Interference Alignment (IA) in femtocell networks. In the first method, in order to manage the uplink interference caused by macrocell users (MU) at the femtocell base stations (FBS), cooperation between macrocell users with the closest femtocell base stations is used to align the received signals of macrocell users in the same subspace at multiple FBSs simultaneously. The proposed method achieves IA while providing the QoS requirements of macrocell users, in terms of minimum received SINR at the macrocell base station (MBS). With this approach, the BER performance of femtocell users is shown to improve, while maintaining the quality of the communication channel of macrocell users. In the second method, an interference limited multi-tier multiuser MIMO cellular uplink is considered. Specifically, an interference management scheme is proposed where interference from subsets of macrocell users is aligned at the femtocell base stations in order to ensure acceptable service for the femtocell users. The scheme employs interference alignment at each femtocell base station, to the set of macrocell users that are causing the high interference specifically at that FBS, and is termed selective IA. The proposed IA algorithm determines the interference subspaces at each FBS and precoders for each macrocell user in a distributed fashion.

iv Table of Contents List of Figures..................................... vi Acknowledgments................................... viii Chapter 1. Introduction................................ 1 Chapter 2. Background................................ 6 2.1 Femtocells: Home Base Stations..................... 7 2.2 Interference Alignment.......................... 11 2.2.1 Minimum Leakage Interference IA............... 18 2.2.2 Max SINR............................. 19 2.2.3 Alternating Minimization.................... 20 2.2.4 Minimum Mean Squared Error IA............... 22 2.2.5 Least Squares Approach for IA................. 22 Chapter 3. Interference Alignment for Cooperative MIMO Femtocell Networks. 25 3.1 Introduction................................ 25 3.2 System Model............................... 26 3.3 Interference Alignment with Successive SDP Relaxations....... 28 3.4 Minimum sum MSE with Coordinated Zero-Forcing......... 32 3.5 Minimum sum MSE without Zero Forcing............... 35 3.6 Simulation Results............................ 37

v Chapter 4. Distributed Multiuser MIMO Interference Alignment......... 41 4.1 Introduction................................ 41 4.2 Distributed Interference Alignment for the K-user Interference Channel 42 4.3 Distributed Interference Alignment with Imperfect Channel Information 52 4.4 Distributed Interference Alignment for Tiered Networks....... 58 Chapter 5. Selective Interference Alignment for MIMO Femtocell Networks... 68 5.1 Introduction................................ 68 5.2 System Model............................... 71 5.3 Macrocell User Selection for Interference Alignment.......... 73 5.4 Selective Distributed Interference Alignment for Tiered Networks.. 75 5.5 Convergence Analysis and Discussion.................. 80 5.6 Simulation Results............................ 82 Chapter 6. Conclusion................................. 85

vi List of Figures 2.1 A basic femtocell network.......................... 8 2.2 Comparison of coverage areas of various cell sizes............. 9 2.3 Spectrum access for femtocells....................... 10 2.4 Sources of Interference for a Tiered Network................ 12 2.5 Dominant macrocell interferer........................ 13 2.6 K user interference channel......................... 14 2.7 Interference Alignment in a 3 user interference channel.......... 15 2.8 Alternating Minimization.......................... 21 3.1 System model with a single MBS and 3 femtocell groups......... 27 3.2 Model for a case of 2 macrocell users and 2 FBSs, each with 2 users.. 27 3.3 Convergence results of the SDP-IA Algorithm............... 38 3.4 Average BER of the femtocell users with and without SDP-IA Algorithm 39 3.5 Number of macrocell users that can be aligned subject to min SINR requirement at the MBS........................... 39 3.6 Average BER of the femtocell users with SDP-IA Algorithm with MMSE precoding/decoding for femtocell users................... 40 4.1 Convergence of the Distributed IA Algorithm............... 52 4.2 Convergence of the Distributed IA Algorithm for Imperfect Channel Information................................... 57

vii 5.1 System model for a single MBS and multiple FBSs............ 72 5.2 Channel Model for 3 FBSs, with 2 FUs in each femtocell and 2 MUs.. 74 5.3 Convergence results of the Selective-IA Algorithm............ 83 5.4 Percentage of FUs with a particular BER with the proposed algorithm. 84 5.5 Average BER of the femtocell users wrt. number of macrocell interferers 84

viii Acknowledgments First, I would like to thank my advisor Dr. Aylin Yener for her guidance throughout my Master s studies. I want to thank her for introducing me to the exciting field of wireless communications. Her knowledge, experience and patience have been invaluable for the completion of this thesis. I would like to thank Dr. Vishal Monga for taking the time to serve on my thesis committee. I would also like to express my gratitude to the members of the Wireless Communications and Networking Laboratory for their help and their friendship, and for the valuable discussions. Thanks to all my friends who have been with me during the good and the difficult times, and for becoming my family away from home. I would like to thank Damien for his loving support. Many thanks to Peter Dinklage for turning the short breaks from work into an epic experience. I would like to thank my grandmothers, my grandfather and my brother. Lastly, I would like to say special thanks to my parents, Fatih and Hidayet Guler, for their love and support during my entire life.

1 Chapter 1 Introduction Next generation wireless networks are designed to provide high data rates to meet subscriber demands. Femtocells are a promising direction to increase the data rate for home users while reducing the load on the cellular (macrocell) network [1]. They require no infrastructure as they are plug and play devices that are connected to the conventional internet backhaul [2]. Femtocells operate in the licenced band, and consequently have to share the radio resources and coexist with the cellular network. Solutions proposed to guarantee coexistence range from partitioning the frequency resources between the two networks, to allowing cellular (macrocell) users to be served by femtocell base stations [1]. Management of cross interference in this two-tier network is of utmost importance. In the uplink, in particular, a macrocell user operating in the same band as femtocell users may cause unacceptably high interference levels, if it is close to the femtocell base station supporting the aforementioned femtocell users, and far away from its own macrocell base station. Additionally, the fact that femtocells can be deployed in an ad hoc fashion anywhere within a macrocell (and can be removed as easily) adds to the challenge of interference management and renders jointly optimal design of the two networks impractical. In order to manage the uplink interference caused by the macrocell users at the femtocell base stations (FBS), joint detection or interference cancellation may be used.

2 Joint detection may not be preferred due to privacy issues and the limited backhaul provided by the Internet service provider (ISP) to the femtocells. Interference cancellation methods such as zero forcing requires as many antennas at the FBS as the number of signals to be cancelled, which may be impractical in dense urban areas since only a limited number of antennas can be employed at the FBSs. We posit that a more viable alternative is by means of coordination between multiple FBS and the macrocell users that are causing high interference to this group of FBSs. Specifically, using the principle of interference alignment (IA), we can align the received signals from macrocell users in a lower dimensional subspace at multiple FBSs simultaneously, and use the remaining degree of freedoms to improve the performance of the femtocell users. While interference alignment helps the femtocell users to eliminate macrocell interference, this should not be at the expense quality of service (QoS) for the macrocell users. Our approach is that macrocell users apply interference alignment with individual SINR constraints at the MBS, thus making sure their QoS requirements are met. To solve this problem, in the first section, we propose an algorithm that uses successive semidefinite programming (SDP) relaxations, which will be referred as SDP-IA algorithm. After interference alignment, a precoding-decoding scheme is used at the FBSs which minimizes the sum MSE of the femtocell users with coordinated zero forcing to eliminate macrocell interference. Consequently, the quality of service/performance of the femtocell users is improved without diminishing the quality of service of the macrocell users. The numerical results demonstrate that the benefits of the proposed IA algorithm, and that these benefits increase as the number of interfering macrocell users increase. The number of macrocell users that can be aligned simultaneously depends on the minimum

3 SINR requirements at the MBS, more users can be aligned when the minimum SINR requirements are decreased. In the first algorithm, we used beamformers as precoders of mobile users to reduce the complexity of the interference alignment problem, in which all the precoders of the macrocell users are determined by solving a centralized problem. As a result, as the number of FBSs and the macrocell interferers in the network increased, the process time required for determining the precoders increased tremendously, and caused feasibility problems. In order to solve the centralized algorithm, the channel information from all the macrocell users to the MBS and to the FBSs they are interfering, has to be gathered by a central processor, and after solving the problem, the determined precoders should be sent back to the macrocell users, which is not preferred due to the excessive load it will cause on the macrocell network, as one of the main reasons for introducing femtocells was to reduce to load on the macrocell network. In order to reduce the complexity of the problem, in the second section we propose a distributed algorithm that is applicable for interference alignment in tiered networks. We do not have unitary assumptions on the precoders or the interference subspaces, and therefore the proposed IA problem can eaxily be turned into a QCQP, and applicable for adding extra constraints, such as minimum SINR constraints for the macrocell users. This algorthm is distributed in the sense that, the users will decide on their precoders individually and only partial amount of information exchange is necessary between macrocell users and the FBSs. In the last chapter, a selective interference alignment method is proposed. In this new method we again consider the uplink of a femtocell network. However, the area considered in this case is the whole macrocell coverage area with all the femtocell and

4 macrocell users, instead of a small group of femtocell base stations and the macrocell users close to them. The reason for this new approach is the fact that, in a real scenario where femtocell and macrocell users are distributed randomly around the macrocell coverage area, the set of high interferers at each FBS is different, and choosing a set of FBSs and macrocell users and applying IA at only this small group is suboptimal, as the macrocell users that are at the edge of the femtocell group may actually be causing higher interference to another neighboring FBS that is close to that macrocell user but not in the femtocell group. In order to solve this problem, at a specific FBS, we align the macrocell users that are causing very high interference at that FBS, which may be different then other femtocells. For this purpose, we have set two different thresholds, one is the minimum interference threshold defined for each FBS, and the second one is the maximum number of users that can be aligned at a FBS, which is limited by the number of dimensions, such as antennas. At each FBS, we choose the set of macrocell users that are causing higher interference then the predefined interference threshold, and call this the set of high interfering MUs for that femtocell. If the number of users to be aligned exceeds the number of dimensions available for interference alignment, we drop the user that is causing the least interference out of the set, which is continued until the number of MUs in the set is decreased to the maximum number of interferers allowed for interference alignment. Then the proposed distributed algorithm is applied to the macrocell users. The advantage of using the proposed algorithm in the tiered scheme is that, the proposed algorithm uses only the precoders of the macrocell users for achieving interference alignment, which in fact helps to increase the performance of the femtocell users, and the decoders of the macrocell users can be used to increase their

5 own performance. The results show that the proposed method helps the femtocell users to achieve better performance then they would have without the interference alignment, and there is no significant degrade on macrocell users performance. The performance criteria considered in this thesis is average bit error rate (BER).

6 Chapter 2 Background Interference management has been an important design element for multiuser systems in the past two decades. Judicious receiver design for CDMA systems provides effective interference cancellation [3]. Besides multiuser detection, power control [4], and joint design of transmitters and receivers [6, 5, 15] offer optimal interference mitigation in interference limited systems. While the aforementioned techniques have been primarily designed for multi-transmitter single receiver (multiple access) systems, interference alignment has recently been proposed for multi-transmitter multi-receiver (interference) networks and has been shown to achieve the maximum degrees of freedom for the K- user interference channel [7]. For practical scenarios, distributed algorithms have been proposed for interference alignment; these include minimizing the leakage interference and using channel reciprocity [8], minimizing MSE [9], or alternating minimization [10]. In this thesis, we take the viewpoint of managing the interference caused by the macrocell users to the uplinks of femtocells in their vicinity by aligning their signals. We leverage the recent advances in interference alignment and base station cooperation (for the femtocells) in order to put forward a practically relevant yet close to optimal design of this two-tier network.

7 2.1 Femtocells: Home Base Stations Femtocells are small base stations designed mainly for indoor use, to provide high data rates for next generation wireless cellular networks [1]. They emerged from the fact that next generation wireless networks should be designed to provide very high data rates, as data applications require higher data rates then the voice applications. They are low cost plug and play devices purchased by the subscribers, providing coverage to a small area where they are installed [2]. Decreasing the cell size will have the effect of increasing the capacity of the wireless network, and the load on the macrocell network will be reduced, and fewer macrocell base stations will be required in the wireless network, as the femtocell users will now be served by their femtocell base stations. In a basic femtocell network as given in Fig.2.1, the femtocell base station is connected to the internet broadband router. The fact that femtocell users (FU) utilize the internet backhaul reduces the load on the macrocell network, enabling the resources to be allocated to the truly mobile users. Another reason for employing femtocells is to increase the coverage, due to the poor indoor coverage experienced with current wireless standards and even no coverage in rural areas. As the femtocells are designed mainly for indoor use, and are connected to the internet backhaul instead of the macrocell network, they can operate and provide cellular coverage even in areas that has no cellular backhaul, but only the internet backhaul. Another reason for femtocells becoming popular among the wireless operators is that they require no infrastructure, as they are purchased and installed by the end user.

8 Fig. 2.1. A basic femtocell network

9 Fig. 2.2. Comparison of coverage areas of various cell sizes This fact reduces the construction and maintenance costs. The comparison of the coverage areas for different cell types [25] is given in Fig.2.2. The difference between the femtocells and other cell types is the fact that picocells, microcells and macrocells are constructed and maintained by the network operator, which makes it possible to employ centralized interference management and scheduling methods. The femtocells are installed by their own users, and the randomness of their locations require more sophisticated interference management methods to be employed, which should be adaptable to their environment. Femtocells are low power devices, and are designed to operate close to the mobile user they are serving. As a result the battery life of the mobile devices are higher when they are using femtocells for communication. It is preferred for the femtocells to share the frequency band with the existing macrocell network, as the licensed band is highly populated, and frequency is a scarce

10 Fig. 2.3. Spectrum access for femtocells resource. The spectrum access types for femtocells are shown in Fig.2.3. There are mainly three access types; dedicated, co-channel and hybrid [25]. In the dedicated access type, the femtocells and the macrocell have separate frequency bands, which increases the interference management performance, but it not preferred due to the inefficient use of the frequency spectrum. In the co-channel access type, the femtocells and the macrocell operate in the same frequencies, which increases the frequency reuse, but requires advanced interference management techniques to be employed due to co-channel interference. In the hybrid spectrum access, separate frequency bands are allocated to the femtocells and the macrocells as long as the load on the macrocell network is not very high. When there is excessive load in the macrocell network, some macrocell users are allowed to use the frequency bands of the femtocells. This notion brings another

11 idea for the access permissions for the femtocell and macrocell users, which is called the open and closed access. In the open access, all subscribers registered with an operator can access all base stations, whether it is a femtocell base station or a macrocell base station. In the closed access, only a limited number of users are permitted to access the access point. The performance of femtocell open and closed access from both femtocell owner and network operator s point of view is evaluated in [29]. The importance of sharing the frequency resources between the two tiers, combined with the ad hoc nature of femtocells, make cross tier interference management challenging, and the centralized solutions impractical. In this thesis, we consider this interference management problem, concentrating on the uplink interference caused by the macrocell users (MU) at the femtocell base stations (FBS), which may be destructive when the MU is far from the macrocell base station (MBS) and close to the FBS, thereby transmitting with high power as shown in Fig.2.4. MU close to a FBS is called a dominant interferer, as shown in Fig.2.5. 2.2 Interference Alignment The capacity characterizations of many distributed wireless channel models such as the interference channel in Fig.2.6 are still open problems in the literature. As a result, in order to approximate the capacity of these networks a notion called degrees of freedom is defined, which is also referred to as multiplexing gain [26]. In [28] it was shown that the sum capacity of the K-user interference channel with frequency-selective

12 Fig. 2.4. Sources of Interference for a Tiered Network

13 Fig. 2.5. Dominant macrocell interferer (or time varying) channel coefficients is as follows: C(SN R) = (K/2)log(SN R) + o(log(sn R)) (2.1) where K/2 denotes the degrees of freedom and SNR is defined as the total transmit power of all the transmitters in the network when the local noise power at each node is normalized to unity, and the achievable scheme is based on the idea of interference alignment [7]. The K user interference channel is as shown in Fig.2.6. In this channel model, each user is communicating with its intended receiver while interfering with K 1 other users. Each transmitter has N t transmit antennas and each receiver has N r receive antennas. The N r N t matrix H ij denotes the matrix of individual channel gains from transmitter j to receiver i. The aim at each receiver is to find a way to eliminate the effects of interfering users by sacrificing minimum number of dimensions

14 Fig. 2.6. K user interference channel so that it can correctly decode the data streams sent from the intended receiver. This is done by aligning all the interfering users signals in a lower dimensional subspace at each receiver simultaneously, as shown in Fig.2.7 for a 3 user interference channel. The importance of interference alignment lies in the fact that, as shown in [7], it enables to achieve the maximum degrees of freedom that can be achieved in a K user interference channel, which was shown to be K/2 in [28]. In the proposed interference alignment scheme, each transmitter uses a precoding matrix V j to enable interference alignment of its own transmitted signal at the nonintended receivers simultaneously. Each receiver uses a decoding matrix U i in order to eliminate the unintended signals received in the lower dimensional subspace (i.e. zero forcing) and allowing enough degrees of freedom to decode all of the data streams from the intended transmitter. The received signal at

15 Fig. 2.7. Interference Alignment in a 3 user interference channel

16 the i th receiver is as given in the following: K y i = H ij V j s j + n i (2.2) j=1 where V j denotes the N t d j precoding matrix, s j is the (d j 1) vector of independently encoded symbols, d j is the number of information bits transmitted by the j th user. The noise received at the i th receiver is represented by n i, which consists of independent zero mean Gaussian random variables with E{n i n H i } = σ 2 I, and ni H denotes the Hermitian transpose of the vector n i. The conditions at the receivers for interference alignment are given as: H 12 V 2 = H 13 V 3 =... = H 1K V K H 21 V 1 = H 23 V 3 =... = H 2K V K (2.3). H K1 V 1 = H K2 V 2 =... = H K(K 1) V (K 1) The signal at the i th receiver after the decoding matrix is applied is given as: Y i = U i Yi (2.4)

where U i denotes the conjugate transpose of the matrix Ui. For perfect interference alignment, the resulting system should ensure the following conditions: 17 U i Hij V j = 0 j i rank(u i Hii V i ) = d i (2.5) From these conditions it can be seen that, at each receiver the interference should be aligned into the null space of the decoding matrix and the rank of the resulting matrix should be equal to the number of symbols to be detected, in order to detect them properly. As a result the effective channel for user i can be represented as: Ỹ i = U i Hii V i s i + U i ni (2.6) The exact interference alignment scheme for a 3 user interference channel was proposed in [7]. However, the exact closed form solutions for channels with number of users K > 3 are not known. As a result, many distributed algorithms have emerged to find the approximate precoding and decoding matrices that take into account different objective functions, including minimizing the leakage interference [8], alternating minimization [10], maximizing the SINR [8], or minimizing MSE [9]. The common point of these algorithms is that they update the precoding/decoding matrices for a given decoding/precoding matrix set iteratively, and they are not jointly convex over all precoding and decoding matrices. As a result they cannot guarantee convergence to the global

18 optima, and may end up at a local optima. Some of these algorithms are discussed in the following sections. Recently it was shown that also the real-world performance of interference alignment outperforms conventional multiuser communication methods such as TDMA [27]. The measurements in [27] are done using practical MIMO channels and the exact interference alignment scheme for a 3 user interference channel and distributed algorithms were implemented using a 2 2 MIMO testbed. Since the distributed algorithms converge to the local optima due to their nonconvex nature, the algorithms were implemented for a number of different starting points and the one giving the best local minima was chosen. 2.2.1 Minimum Leakage Interference IA This algorithm seeks the perfect interference alignment by minimizing the leakage interference [8], calculated as the trace of the interference covariance matrix, given in the following equation: min (U k ) U k =I trace(u k Qk U k ) (2.7) where Q k = K j=1 P s H kj V j V j Hkj and Ps is the transmitted symbol power. j k denotes the identity matrix. I The algorithm aims to align all the interfering signals in a lower dimensional subspace at each receiver simultaneously. At each iteration the coding matrices are updated in such a way that the signal is transmitted along the n smallest eigenvectors, i.e. in the directions of the n smallest eigenvalues of the leakage interference matrix. Then the roles of the transmitters and receivers are changed by exploiting channel reciprocity,

the precoders now become decoders and the decoders now become precoders, and the same procedure is applied to the new precoder/decoders. 19 This algorithm was shown to converge in [8]. However, due to the nonconvex nature of the problem, one cannot assure the algorithm converges to the global optima, it will possibly converge only to a local optima. Although the algorithm provides good performance in high SINR (Signal to Interference plus Noise Ratio), for low to moderate SNR values, it was shown in [8] that the performance is poor since the objective function does not aim to maximize the received SINR at the intended receiver. 2.2.2 Max SINR Max SINR algorithm was developed in [8] due to the fact that Minimum Leakage Interference algorithm only seeks perfect interference alignment and does not consider about the received SINR values. Max SINR algorithm aims to maximize the received SINR at each receiver, by find the unit vector U l k that maximizes the SINR in the lth stream of the k th user, which is given as: max SINR kl = (Ul k ) H kk V l k (Vl k ) H kk U l k P s U l k B kl Ul k (2.8) where B kl = K j=1 P s d j d=1 H kj Vd j (Vd j ) H kj P s H kk + I N t and I Nt is the N t N t identity matrix. P s is the transmitted symbol power. Again the precoder and decoders are updated iteratively and the role of the precoder and decoders are changed at each iteration.

20 2.2.3 Alternating Minimization Alternating minimization is the technique to tackle the optimization problems in which finding an exact solution over two variables is difficult, but optimizing over one variable while fixing the others is relatively easy. In this method the aim is to find the minimum of d(a, B) where d denotes the distance in any metric space. And A and B denote the sets of optimization variables. Here the sequence {A k } (k=0) and {B k } (k=0) are obtained by an iterative algorithm, that is first fixing B k and optimizing over A and then fixing A k and optimizing over B. The algorithm, illustrated in Fig.2.8, is given as follows: A k+1 = argmin A A B k+1 = argmin B B d(a, B k ) d(b k+1, A) (2.9) A A, B B k (2.10) The idea of using alternating minimization for interference alignment was proposed in [10]. The received signals are projected onto a subspace which is called the interference subspace. The objective of the algorithm is to minimize the sum of the distances between the projected signals to the interference subspace, in which the sum is done over the interfering users. The precoding and orthogonal projection matrices F l and C k for the l th transmitter and k th receiver are find via alternating minimization, which is shown to converge, but whether it converges to the global optima is unknown. The received

21 Fig. 2.8. Alternating Minimization signal at the k th receiver is given as follows: y k = H kk F k s k + l k H kl F l s l + n k (2.11) The objective function is represented as: min F l F l =I, l C k C k =I, k K K H kl F l C k C k H kl F l 2 F k=1 l=1 l k (2.12) In this approach the optimization is done over 2K variables, where 2K 1 variables are temporarily fixed and the optimization is done over the remaining variable.

22 2.2.4 Minimum Mean Squared Error IA Another distributed algorithm [9] aims to minimize the sum mean squared-error by using precoding/decoding matrices at each transmitter/receiver, which is given as: min v 1,...,v k g 1,...,g k K ϵ k (2.13) k=1 where ϵ k = E{ ŝ k s k 2 }, v k is the precoding vector of the k th user, g k is the decoding vector for the k th user, and ŝ k is the estimated symbol of the k th user. 2.2.5 Least Squares Approach for IA Least squares approach [11] uses an alternative representation for interference alignment given as: C(H 12 w 2 ) = C(H 13 w 23 ) = = C(H 1K w K ) (2.14) C(H 21 w 1 ) = C(H 23 w 3 ) = = C(H 2K w K ) (2.15). C(H K1 w 1 ) = C(H K2 w 2 ) = = C(H K(K 1) w (K 1) ) (2.16) where C(.) represents that the interfering signals span the same subspace. For each specific receiver, each interfering signal is represented by a linear combination of the

23 remaining interfering signals using scalar coefficients, which is given as: H 12 w 2 = α 13 H 13 w 23 = = α 1K H 1K w M (2.17) H 21 w 1 = α 23 H 23 w 3 = = α 2K H 2K w K (2.18). H K1 w 1 = α K2 H K2 w 2 = = α K(K 1) H K(K 1) w (K 1) (2.19) Using the precoders and the associated coefficients, the interference alignment expressions can be combined in a single matrix representation as: Hw = 0 (2.20) where w = [w T 1 w T 2... wt K ]T and 0 H 12 α 13 H 13 0... 0 0 H 12 0 α 14 H 14... 0........ 0 H 12 0... 0 α 1K H 1K H =........ H K1 α K2 H K2 0... 0 0........ H K1 0 0... 0 α K(K 1) H K(K 1)

24 The proposed approach for finding the precoding matrices is making the norm of this expression as close to zero as possible, from which follows the notion of least squares approach for interference alignment [11]: min w w=1 Hw (2.21) As a result of the unitary assumption on w, the solution for w is the eigenvector of Hw that corresponds to its smallest eigenvalue.

25 Chapter 3 Interference Alignment for Cooperative MIMO Femtocell Networks 3.1 Introduction In this chapter, we propose a method for mitigating the uplink interference caused by the macrocell users (MU) at the femtocell base stations (FBS). The proposed method uses interference alignment for restricting the received interference from MUs to a lower dimensional subspace at multiple FBSs simultaneously. Our approach considers improving the performance of femtocell users by aligning the macrocell interference, while satisfying the QoS requirements of the macrocell users, in terms of the minimum SINR required at the macrocell base station. As a solution, we propose to use SDP relaxations with eigenvector approximation for interference alignment in tiered networks with SINR constraints. The remainder of the chapter is organized as follows: In Section II, we introduce the system model. Interference alignment for macrocell users is presented in Section III. Section IV describes the precoding and decoding scheme for femtocell users. In Section V, the numerical results and simulations are discussed. We conclude the chapter in Section VI. The notation used in this chapter is as follows: We use lower (upper) bold case letters for vectors (matrices). X H is used to denote the Hermitian transpose, X

as the pseudo-inverse of matrix X, and for the Kronecker product. Finally, trace(x) represents the trace of matrix X. 26 3.2 System Model We consider an uplink femtocell network as shown in Fig. 3.1 consisting of a macrocell base station (MBS) at the center with N o receive antennas. The macrocell coverage area is partitioned into smaller cells of fixed radius in which the mobile users and base stations can cooperate with each other. Suppose such a group consists of F femtocell base stations (FBS), with U f users in the f th femtocell (FU) and M macrocell users (MU). We have N t transmit antennas at each mobile device and N f receive antennas at the f th FBS. Then the signal received at the k th FBS is given by U k y k = H k ki wk i sk i i=1 U F f + H f ku wf u sf u + M H o km wo m so m + n k (3.1) f=1 u=1 m=1 f k where H f ku denotes the channel from the uth user of the f th femtocell to the k th FBS, H o km is the channel from the mth MU to the k th FBS, w f u and sf u are the precoding vector and the message bit of the u th user of the f th femtocell, w o m and so m are the precoding vector and message bit of the m th MU, n k is a vector of independent zero mean Gaussian random variables with E{n k n H k } = σ 2 I. The channels considered are Rayleigh fading channels and the path loss is modeled using the ITU-R channel model [23]. We used rank 1 precoders to reduce the complexity of the algorithm and to avoid

27 Macrocell User Femtocell User Macrocell Base Station Femtocell Base Station Fig. 3.1. System model with a single MBS and 3 femtocell groups Fig. 3.2. Model for a case of 2 macrocell users and 2 FBSs, each with 2 users

28 feasibility problems due to the large number of users. We assume s f u and so m = ±1 for u = 1,..., U f, f = 1,..., F, and m = 1,..., M. An example model is given in Fig.3.2 for 2 macrocell users and 2 FBSs, each with 2 users. 3.3 Interference Alignment with Successive SDP Relaxations For simplicity, we will neglect the uplink interference caused at a FBS by the users of other femtocells, and consider only the (dominant) interference caused by the macrocell users. We will use the condition for interference alignment proposed in [11]: H o 11 wo 1 = α 12 Ho 12 wo 2 = = α 1M Ho 1M wo M (3.2) H o 21 wo 1 = α 22 Ho 22 wo 2 = = α 2M Ho 2M wo M (3.3). H o F 1 wo 1 = α F 2 Ho F 2 wo 2 = = α F M Ho F M wo M (3.4) where α fm is a constant and the equations denote that all interfering users span the same column space at each FBS. That is, each interfering signal is represented by a linear combination of other interfering signals, represented by different coefficients. Using the precoders and the associated coefficients, expressions (3.2)-(3.4) can be combined in a single matrix representation as in (3.5), as proposed in [11]. Then the condition of perfect interference alignment is equal to the expression being equal to zero (3.5). Therefore, one approach for finding the interference aligning precoding matrices is to make the norm of this expression as close to zero as possible as in (3.6), from which follows the notion of

29 least squares approach for interference alignment, proposed in [11]. Hw = 0 (3.5) where H o 11 H o 11. H o 11 H =. H o F 1 H o F 1. H o F 1 α 12 H o 0... 0 12 0 α 13 H o... 0 13...... 0 0... α 1M H o 1M...... α F 2 H o 0... 0 F 2 0 α F 3 H o... 0 F 3...... 0 0... α F M H o F M ] T w = [w o1 T w o2 T w o3 T... w om 1 T w om T We will follow this definition for interference alignment, however, our solution follows a SDP relaxation method to solve the norm minimization problem that satisfies the individual minimum SINR requirements for each macrocell user, which incorporates successive SDP relaxations [20] and rank-one approximation. The interference alignment problem in (3.5) can be regarded as a least squares (LS) problem [11]. In fact, (3.5)

30 denotes a set of linear equations and the LS approach is a conventional method to approximate the solution. In order to satisfy QoS requirements, we define an individual SINR constraint for each macrocell user. The problem is thus given by: minimize w o 1,...,wo M Hw subject to SINR i γ i (3.6) (w o i )H w o i Po i i = 1,..., M where P o i denotes the maximum transmit power of the ith macrocell user, γ i denotes the minimum SINR threshold of the i th macrocell user, and SINR i is given as in (3.8). SINR i = (w i o )H (H o oi )H H o oi wo i Mn=1 (w n o )H (H o on )H H o on wo n + B + (3.7) σ2 n i where U F f B = (w f u )H (H f ou )H H f ou wf u f=1 u=1 (3.8) where H o on denotes the channel from the nth macrocell user to the MBS. Then the equivalent problem can be written as: minimize w o 1,...,wo M subject to trace(rw) trace(( R oi γ i R on )W) γ i σ 2 n i

31 trace((diag(e i ) I (Nt N t ) )W) Po i rank(w) = 1 (3.9) W 0, i = 1,..., M where R = H H H, W = ww H, R on = (H o on )H H o on, Ron = diag(e n ) R on, and e n = [0... 010... 0] T is an (M 1) unit vector with 1 as the n th element and zeros elsewhere. I (Nt N t ) denotes the (N t N t ) identity matrix. By relaxing the rank 1 constraint, we obtain the semidefinite relaxation [19] of the problem: minimize w o 1,...,wo M subject to trace(rw) trace(( R oi γ i R on )W) γ i σ 2 n i (3.10) trace((diag(e i ) I (Nt N t ) )W) Po i W 0, i = 1,..., M The SDP in (3.9) can be solved efficiently by software such as SeDuMi[13]. In case the resulting solution has a higher rank than one, we can use eigenvector approximation [12], in which the vector w is approximated as the eigenvector q 1 corresponding to the largest eigenvalue of W, scaled by the square root of the largest eigenvalue of W, λ 1, i.e., W = ww H = i λ i q i q H i (3.11) w = λ 1 q 1 (3.12)

After this step, the coefficients are determined using the conditions in (3.2)-(3.4) [11], as given by: 32 α km = (H o km wo m ) (H o k1 wo 1 ) (3.13) (H o km wo m ) = ((H o km wo m )H (H o km wo m )) 1 (H o km wo m )H (3.14) 3.4 Minimum sum MSE with Coordinated Zero-Forcing Femtocell users can either cooperate and contribute interference alignment, which may increase the load on the backhaul or they can try to improve their own performance. As a suitable precoding-decoding scheme for the second case, each FBS may try to minimize the sum MSE of its own users, by zero-forcing the aligned macrocell users. A coordinated zero-forcing beamforming for SINR maximization was proposed in [14], which uses the ideas from [15] and [16]. We will use a precoding-decoding scheme that minimizes the sum MSE at the FBSs while zero-forcing the aligned interference from the macrocell users. The estimated bit of the j th user of the k th femtocell is given as: U k ŝ k j = (g k j )H H k F U ki wk i sk i + f (g k j )H H f ku wf u sf u i=1 f=1 u=1 f k M + (g k j )H H o km wo m so m + (gk j )H n k (3.15) m=1 where g k j is the decoding vector for the jth user of the k th femtocell. Since the interference caused by other femtocells are very small compared to the intracell interference,

for simplicity we will regard intercell femtocell interference as noise, which is given as: 33 U F f ñ k = H f ku wf u sf u + n k (3.16) f=1 u=1 f k Using the conditions in (3.2)-(3.4) and (3.15), the minimum sum MSE at the FBS problem can be formulated as: minimize w k 1,...,wk U k U k ŝ k j sk j 2 j=1 g k 1,...,gk U k (3.17) subject to (g k j )H H o k1 wo 1 = 0 (w k j )H w k j Pk j j = 1,..., U k or equivalently minimize w k 1,...,wk U k U k j=1 [ (g k j )H H k kj wk j 1 2 g k 1,...,gk U k U k ] + (g k j )H H k ki wk i 2 + g k j 2 2 σ2 i=1 i j (3.18) subject to (g k j )H H o k1 wo 1 = 0 (w k j )H w k j Pk j j = 1,..., U k

where P k j is the maximum transmit power of the jth user of the k th femtocell, and 34 E{ñ k (ñ k ) H } = σ 2 I. The zero forcing constraint in (3.18) implies that g k j should be in the null space of (H o k1 wo ) [17], from which we can define a decoding vector such as: 1 g k j = Uo k vk j (3.19) where [U 0 k U1 k ]Λ k V k is obtained from the SVD of Ho k1 wo 1 and the columns of Uo k is a nullspace basis of H o k1 wo 1. If we let (U0 k )H H k kj = H k, the problem in (3.18) is equal kj to: minimize w k 1,...,wk U k U k j=1 [ (v k j )H Hk kj wk j 1 2 v k 1,...,vk U k U k + i=1 i j (v k j )H Hk ki wk i 2 + v k j 2 2 σ2 ] (3.20) subject to (w k j )H w k j Pk j j = 1,..., U k The problem in (3.20) is convex in w k j if the all other vk j are fixed, and convex in vk j if all other w k j are fixed. Using this property, we can use an iterative algorithm by first fixing the decoding matrices and obtaining the precoding matrices, then fixing the precoding matrices to obtain the decoding matrices. An iterative procedure for obtaining the optimal coding vectors is used in [18] where the transmit precoding vector had unit norm. After writing the Lagrangian for the problem in (3.20), from the KKT conditions

35 we have the optimal precoding and decoding vectors as: ( U k ) 1 v k j = ( H k ki wk i )( H k ki wk i )H + σ 2 I Hk kj wk j i=1 ( U k ) 1 w k j = ( H k kj )H v k i (vk i )H Hk kj + µk j I ( H k kj )H v k j i=1 (3.21) (3.22) for j = 1,..., U k. We determine µ k j such that (wk j )H w k j = Pk j. 3.5 Minimum sum MSE without Zero Forcing In this section we apply MMSE precoding/decoding for the femtocell users, without zero forcing the aligned interference from the macrocell users first. For the new approach, the problem in (3.17) becomes: Using the conditions in (3.2)-(3.4) and (3.15), the minimum sum MSE at the FBS problem can be formulated as: minimize w k 1,...,wk U k g k 1,...,gk U k U k ŝ k j sk j 2 j=1 (3.23) subject to (w k j )H w k j Pk j j = 1,..., U k

where the zero forcing requirement for the macrocell users is removed from the problem in (3.17). The problem can also be represented in the following form: 36 minimize w k 1,...,wk U k g k 1,...,gk U k U k [ U k (g k j )H H k kj wk j 1 2 + (g k j )H H k ki wk i 2 j=1 i=1 i j M ] + (g k j )H H o km wo m 2 + g k j 2 2 σ2 m=1 (3.24) subject to (w k j )H w k j Pk j j = 1,..., U k where the problem in (3.24) is convex in w k j if the all other gk j are fixed, and convex in g k j if all other wk j are fixed. We can again make use of this to obtain an iterative algorithm by first fixing the decoding matrices and determining the precoding matrices, then fixing the precoding matrices determining the decoding matrices. An iterative procedure is used in [18] to obtain the coding vectors where the transmit precoding vector had unit norm. After writing the Lagrangian and using the KKT conditions, the resulting expressions for the optimal precoders and decoders of the femtocell users are found to be as follows: ( U k g k j = (H k M ) 1 ki wk i )(Hk ki wk i )H + (H o km wo m )(Ho km wo m )H + σ 2 I H k kj wk j i=1 m=1 (3.25) ( U k ) 1 w k j = (H k kj )H g k i (gk i )H H k kj + µk j I (H k kj )H g k j i=1 (3.26)

37 for j = 1,..., U k. We determine µ k j such that (wk j )H w k j = Pk j. 3.6 Simulation Results Simulations are performed to compare the performance of the proposed macrocell interference alignment with that of the setting where macrocell users (MU) minimize their sum MSE at the MBS, without regard to femtocell users (FU). The MBS has a coverage radius of 2km, the group of FBSs close to each other is denoted by an area of 150m radius, placed randomly according to a uniform distribution within the coverage radius of the MBS, and the MUs within this area apply interference alignment jointly. We consider 3 FBSs each with a radius of 30m coverage. Each FBS has 3 users, and each mobile user has 4 transmit antennas. FBSs have 4 receive antennas. Noise power is assumed to be 110dB. Power control at both FBS and MBS is used to compensate for the path loss. The maximum transmit power of each user is 1W. The convergence of the SDP-IA algorithm for 10 macrocell users and a minimum SINR requirement of 0.1 at the MBS is presented in Fig.3.3. The comparison of the SDP- IA with coordinated zero forcing scheme with the one with no interference alignment in terms of average BER versus the number of MUs interfering to the femtocell group is given in Fig.3.4. For the case when no interference alignment is applied, the only objective for the MUs is to minimize the sum MSE at the MBS. The number of MUs that can be aligned for different minimum SINR requirements at the MBS is depicted in Fig.3.5 for the SDP-IA with coordinated zero forcing algorithm. The results show that the performance of the FUs in terms of average BER is significantly better when compared to the case when the interfering MUs only consider

38 2.5 x 10 6 2 leaked interference 1.5 1 0.5 1 2 3 4 5 6 7 8 9 10 iteration Fig. 3.3. Convergence results of the SDP-IA Algorithm their own performance and minimize the sum MSE at the MBS. It was observed in the simulations that, the received SINR constraints of the MUs in the second case do not satisfy a minimum and may cause an outage in voice applications. The feasibility of the minimum SINR constraints is a main limitation in this system: as the minimum SINR constraints of MUs are increased, the maximum number of MUs that can be aligned simultaneously decreases significantly. The average BER of the femtocell users with respect to the number of interfering macrocell users for the SDP-IA without zero forcing algorithm is given in Fig.3.6 for a single femtocell group. From Fig.3.6 it can be seen that the average BER of the femtocell users have decreased, correspondingly their performances have improved.

39 0.7 0.6 with SDP IA Algorithm without SDP IA Algorithm 0.5 Average BER 0.4 0.3 0.2 0.1 0 2 3 4 5 6 7 8 9 10 Number of interfering macrocell users Fig. 3.4. Average BER of the femtocell users with and without SDP-IA Algorithm 1 0.9 Min SINR required at the MBS 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 2 3 4 5 6 7 8 9 10 Number of aligned macrocell users Fig. 3.5. Number of macrocell users that can be aligned subject to min SINR requirement at the MBS

40 4.5 x 10 4 4 3.5 3 Average BER 2.5 2 1.5 1 0.5 0 3 4 5 6 7 8 9 10 Number of interfering macrocell users Fig. 3.6. Average BER of the femtocell users with SDP-IA Algorithm with MMSE precoding/decoding for femtocell users

41 Chapter 4 Distributed Multiuser MIMO Interference Alignment 4.1 Introduction In the previous chapter, a method for dealing with large number of macrocell users in a femtocell network was proposed. This method combined the ideas of interference alignment and semidefinite relaxation in order to restrict the macrocell interference in a lower dimensional subspace, simultaneously at multiple base stations, so that the macrocell interference could be cancelled at each femtocell base station, using a relatively small number of antennas compared to the number of interfering macrocell users. Since the femtocell devices have an ad-hoc nature, unlike the microcell and picocell networks, the interference management and scheduling cannot be done in a centralized manner. Therefore adaptive schemes should be proposed that can adjust to the current specifications of the tiered cellular network. For this purpose, in this chapter, we first define a new interference alignment algorithm that determines the precoders and the aligned subspaces iteratively. This is because using one dimensional precoders or beamformers will cause feasibility problems if we want to align a larger number of interferers. Another reason for introducing the new distributed algorithm is that the interference alignment algorithm with semidefinite relaxation operated in a centralized manner, which requires a processing unit to gather information from both tiers, and to send the resulting information back to the users, which may not be desirable in a tiered network, due to the load

42 it will add to the network and for security and privacy reasons. Therefore, a distributed algorithm is highly desirable in these networks, especially when we are designing schemes that consider the whole femtocell network, instead of a smaller part of it, as we have considered in the previous chapters. This chapter is organized as follows. In the next section the iterative interference alignment algorithm is described for a K-user interference channel. In Section 4.3, this algorithm is considered for the case when the channel information available at the transmitters is imperfect. We generalize the distributed interference alignment algorithm for the tiered networks in Section 4.4. 4.2 Distributed Interference Alignment for the K-user Interference Channel In this section, the proposed multiantenna distributed interference alignment algorithm is described for a K-user interference channel as shown in Fig.2.6, with K transmitters and K receivers. The transmitter and receivers are assumed to have perfect Channel State Information (CSI). The aim is to determine the precoder of each transmitter and the interference subspace at each receiver such that the received signals from all the interfering users are restricted in a lower dimensional subspace simultaneously at each receiver. The channel considered in this section is a K-user interference channel, but the results can be extended to the two-tier systems such as femtocell networks, as will be done in Section 4.4.