Large System Performance of Interference Alignment in Single-Beam MIMO Networks

Schmidt, David A.; Utschick, Wolfgang; Honig, Michael L.

doi:10.1109/glocom.2010.5684032

Cited by 23 publications

(31 citation statements)

References 10 publications

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“…Assuming the offsets are statistically independent and the number of sampled solutions L (as well as the system dimension N ) is reasonably large, we are able to approximate the expected value of r averaged over channel realizations. This analysis was presented in [7] and the approximation is summarized in the following section. We refer to this approach as "Maxof-L Alignment" (MLA).…”

Section: System Modelmentioning

confidence: 99%

“…In Section IV we summarize the performance approximation proposed in [7], in Section V we present a novel numerical method based on gradually increasing the SNR, and in Section VI we compare our new method with the state of the art and the analytical performance approximations by means of numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

“…The performance of this approach can be accurately approximated analytically as a function of L [7] assuming that the method for computing the different aligned solutions does not depend on the direct channels.…”

Section: Introductionmentioning

confidence: 99%

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Beamforming techniques for single-beam MIMO interference networks

Schmidt

Utschick

Honig

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We consider the joint optimization of beamformers and linear receivers in a MIMO interference network. Each transmitter transmits a single beam corresponding to a rankone precoder. When the number of users K is greater than the number of antennas at each terminal N , the maximum degrees of freedom is achieved via spatial interference alignment. Interference alignment is feasible for up to K = 2N −1 users, in which case there is a finite number of solutions to the alignment conditions. This number of solutions increases rapidly with N , and the solutions depend only on the cross-channel coefficients (i. e., they are independent of the direct channels). To maximize the achievable sum rate at high SNRs we therefore wish to select an aligned solution which is best matched to the direct channels. We evaluate the performance of this scheme for large K and N , assuming that the solution is the best out of a random subset of aligned solutions. We then compare numerically this performance with the performance of previously proposed numerical (e. g., forward-backward) techniques for optimizing beams, and a new technique which tracks the local optimum as the SNR is incrementally increased, similar to a homotopy method for improving convergence properties. We observe that the incremental technique typically achieves better performance than the previously proposed methods.

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Section: System Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Beamforming techniques for single-beam MIMO interference networks

Schmidt

Utschick

Honig

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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“…In the AMA, although the leakage interference can be perfectly canceled after convergence, its performance in terms of sum rate is not optimal. In fact, it is pointed out that for general interference channels the constructed LIM problem has a large number of different IA solutions obtained from different initial points, which lead to different achieved sum rate values [9]. The main reason is that the AMA only eliminates the interference in the desired signal space without considering the system sum rate, which results in a suboptimal sum rate achieved with finite signal power.…”

Section: Introductionmentioning

confidence: 99%

Low complexity interference alignment algorithms for desired signal power maximization problem of MIMO channels

Sun

Yang

Yuan

2012

EURASIP J. Adv. Signal Process.

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In this article, we investigate the interference alignment (IA) solution for a K-user MIMO interference channel. Proper users' precoders and decoders are designed through a desired signal power maximization model with IA conditions as constraints, which forms a complex matrix optimization problem. We propose two low complexity algorithms, both of which apply the Courant penalty function technique to combine the leakage interference and the desired signal power together as the new objective function. The first proposed algorithm is the modified alternating minimization algorithm (MAMA), where each subproblem has closed-form solution with an eigenvalue decomposition. To further reduce algorithm complexity, we propose a hybrid algorithm which consists of two parts. As the first part, the algorithm iterates with Householder transformation to preserve the orthogonality of precoders and decoders. In each iteration, the matrix optimization problem is considered in a sequence of 2D subspaces, which leads to one dimensional optimization subproblems. From any initial point, this algorithm obtains precoders and decoders with low leakage interference in short time. In the second part, to exploit the advantage of MAMA, it continues to iterate to perfectly align the interference from the output point of the first part. Analysis shows that in one iteration generally both proposed two algorithms have lower computational complexity than the existed maximum signal power (MSP) algorithm, and the hybrid algorithm enjoys lower complexity than MAMA. Simulations reveal that both proposed algorithms achieve similar performances as the MSP algorithm with less executing time, and show better performances than the existed alternating minimization algorithm in terms of sum rate. Besides, from the view of convergence rate, simulation results show that the MAMA enjoys fastest speed with respect to a certain sum rate value, while hybrid algorithm converges fastest to eliminate interference.

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“…The number of such solutions has been studied in [5], for the single-stream case. Despite its deceptively simple mathematical formulation, no general closed-form solution to the IA equations is available (although it exists for certain dimensions, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Interference alignment using variational mean field annealing

Badiu

Guillaud

Fleury

2014

2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)

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Abstract-We study the problem of interference alignment in the multiple-input multiple-output interference channel. Aiming at minimizing the interference leakage power relative to the receiver noise level, we use the deterministic annealing approach to solve the optimization problem. In the corresponding probabilistic formulation, the precoders and the orthonormal bases of the desired signal subspaces are variables distributed on the complex Stiefel manifold. To enable analytically tractable computations, we resort to the variational mean field approximation and thus obtain a novel iterative algorithm for interference alignment. We also show that the iterative leakage minimization algorithm by Gomadam et al. and the alternating minimization algorithm by Peters and Heath, Jr. are instances of our method. Finally, we assess the performance of the proposed algorithm through computer simulations.

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Large System Performance of Interference Alignment in Single-Beam MIMO Networks

Cited by 23 publications

References 10 publications

Beamforming techniques for single-beam MIMO interference networks

Beamforming techniques for single-beam MIMO interference networks

Low complexity interference alignment algorithms for desired signal power maximization problem of MIMO channels

Interference alignment using variational mean field annealing

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