A Feasibility Test for Linear Interference Alignment in MIMO Channels With Constant Coefficients

González, Óscar; Beltrán, Carlos; Santamarı́a, Ignacio

doi:10.1109/tit.2014.2301440

Cited by 72 publications

(97 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In each step of the ICI cancelation, considering that each receiver cannot resolve and cancel all ICIs, we divide the ICIs into resolvable and irresolvable ICIs: the ICIs that can be canceled by the receiver are called resolvable ICIs and the remaining ICIs are called irresolvable ICIs. 9 To help the receiver resolve all ICIs, we construct the genie to resolve the irresolvable ICIs. Then, the tightest upperbound is obtained by constructing genies to help each node eliminate the maximal number of irresolvable ICIs.…”

Section: Proof Of Dof Upper-boundmentioning

confidence: 99%

“…The degrees of freedom (DoF) can reflect the potential of interference networks, which are the first-order approximation of sum capacity at high signal-to-noise ratio (SNR) regime [1,2]. Recently, significant research efforts have been devoted to find the DoF for MIMO interference channel (MIMO-IC) [1][2][3][4][5][6][7][8][9], MIMO interfering broadcast channel (MIMO-IBC) [10][11][12], and MIMO interfering multiple access (MIMO-IMAC) [13] have M and N antennas, respectively, when the channels are time/frequency varying and M = N , the information theoretic maximal DoF per user are M/2. This implies that the sum DoF can linearly increase with G, and the performance of the interference network is not interference-limited [3].…”

mentioning

confidence: 99%

“…The study in [8] investigated the sufficient conditions of linear IA feasibility for the asymmetric 1 The configurations are summarized in Table II. MIMO-IC. In [9], the authors developed a polynomial complexity test that allows a complete characterization of the achievable DoF region by the linear IA for the symmetric MIMO-IC with arbitrary antenna configuration. For the MIMO-IBC network with generic channels, the proper condition was proved to be necessary in [18,19] and to be sufficient for two cases: 1) M = N + (K − 1)d by extending the result in [16] and 2) either M or N is divisible by d in [19].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Genie Tree and Degrees of Freedom of the Symmetric MIMO Interfering Broadcast Channel

Liu

Yang

2016

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-In this paper, we study the information theoretic maximal degrees of freedom (DoF) for the symmetric multiinput-multi-output (MIMO) interfering broadcast channel (IBC) with arbitrary antenna configurations. For the G-cell K-user M × N MIMO-IBC network, we find that the information theoretic maximal DoF per user are related to three DoF bounds: 1) the decomposition DoF bound d Specifically, for most configurations in Region I, the information theoretic maximal DoF are the decomposition DoF bound and can be achieved by the asymptotic IA. For all configurations in Region II, the information theoretic maximal DoF are the quantity DoF bound and can be achieved by the linear IA.To obtain the tight upper-bound, we propose a unified way to construct genies, where the genies help each base station or user resolve the maximal number of interference. According to the feature that the designed genies with the same dimension can derive identical DoF upper-bound, we convert the information theoretic DoF upper-bound problem into a linear algebra problem and obtain the closed-form DoF upper-bound expression. Moreover, we develop a non-iterative linear IA transceiver to achieve the DoF upper-bound for the networks with antenna configurations in Region II, which means that the derived DoF upper-bound is tightest. The basic principles to derive the DoF upper-bound and design the linear IA transceiver to achieve the DoF upper-bound can be extended into general asymmetric networks.Index Terms-Interference alignment (IA), interfering broadcast channel (IBC), degrees of freedom (DoF), genie tree, irresolvable and resolvable inter-cell interferences (ICIs)

show abstract

Section: Proof Of Dof Upper-boundmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Genie Tree and Degrees of Freedom of the Symmetric MIMO Interfering Broadcast Channel

Liu

Yang

2016

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…Although there are still many open problems regarding this technique, different studies carried out over the last years have provided many interesting theoretical results [6]- [9], as well as many different algorithms to perform IA [10]- [17]. Among those, it is worth highlighting the interference leakage minimization algorithm (MinIL) proposed in [10].…”

Section: Introductionmentioning

confidence: 99%

Interference shaping constraints for underlay MIMO interference channels

Lameiro

Santamarı́a

Utschick³

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

In this paper, a cognitive radio (CR) scenario comprised of a secondary interference channel (IC) and a primary point-to-point link (PPL) is studied, when the former interferes the latter. In order to satisfy a given rate requirement at the PPL, typical approaches impose an interference temperature constraint (IT). When the PPL transmits multiple streams, however, the spatial structure of the interference comes into play. In such cases, we show that spatial interference shaping constraints can provide higher sum-rate performance to the IC while ensuring the required rate at the PPL. Then, we extend the interference leakage minimization algorithm (MinIL) to incorporate such constraints. An additional power control step is included in the optimization procedure to improve the sum-rate when the interference alignment (IA) problem becomes infeasible due to the additional constraint. Numerical examples are provided to illustrate the effectiveness of the spatial shaping constraint in comparison to IT when the PPL transmits multiple data streams.Index Terms-Cognitive radio, interference alignment, interference channel, interference temperature

show abstract

“…The feasibility of linear IA in this scenario, which is closely related to the problem treated in this work, has been an active research topic during the last years [7]- [12]. Here, we study the problem of how many different IA solutions exist for a feasible system, which is relevant as a diversity metric.…”

Section: Introductionmentioning

confidence: 99%

Finding the number of feasible solutions for linear interference alignment problems

González

Santamarı́a

Beltrán

2013

2013 IEEE International Symposium on Information Theory

View full text Add to dashboard Cite

In this paper, we study how many different solutions exist for a feasible interference alignment (IA) problem. We focus on linear IA schemes without symbol extensions for the K-user multiple-input multiple-output (MIMO) interference channel. When the IA problem is feasible and the number of variables matches the number of equations in the polynomial system, the number of solutions is known to be finite. Unfortunately, the exact number of solutions is only known for a few particular cases, mainly single-beam MIMO networks. In this paper, we prove that the number of IA solutions is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of solutions is the scaled average over a subset of the solution variety (formed by all triplets of channels, precoders and decoders satisfying the IA polynomial equations) of the determinant of certain Hermitian matrix related to the geometry of the problem. Our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas and streams per user.

show abstract

A Feasibility Test for Linear Interference Alignment in MIMO Channels With Constant Coefficients

Cited by 72 publications

References 30 publications

Genie Tree and Degrees of Freedom of the Symmetric MIMO Interfering Broadcast Channel

Genie Tree and Degrees of Freedom of the Symmetric MIMO Interfering Broadcast Channel

Interference shaping constraints for underlay MIMO interference channels

Finding the number of feasible solutions for linear interference alignment problems

Contact Info

Product

Resources

About