Minimax Duality for MIMO Interference Networks

Dotzler, Andreas; Riemensberger, Maximilian; Utschick, Wolfgang

doi:10.3390/info7020019

Cited by 8 publications

(6 citation statements)

References 35 publications

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“…The feasible set of the worst-case noise minimization contains as the only element, i.e., the noise statistics are fixed. However, the formulation as a minimax problem enables us to apply the minimax uplink-downlink duality from [56], [57]. This duality was shown in [56] for proper complex signals, but by repeating the derivation from [56] for real-valued systems, we obtain that the above optimization has the same optimal value as the following composite real minimax uplink problem.…”

Section: Optimality Of Proper Signaling In Gaussian Mimo Broadcastmentioning

confidence: 84%

“…However, until recently, it had not been shown that the optimality of proper signals also holds under a shaping constraint, i.e., a constraint on the sum transmit covariance matrix instead of on the sum power. 7 In our recent works [34], [35], we used the minimax duality with linear conic constraints from [56], [57] in combination with a power shaping matrix and an impropriety matrix to show this more general result. As discussed in Section III.D, these matrices fit into the framework proposed in this paper.…”

Section: Optimality Of Proper Signaling In Gaussian Mimo Broadcastmentioning

confidence: 99%

“…For this minimax uplink problem, the optimal transmit strategy can easily be shown to consist of proper signals ( [34], Lemma 4). Transforming this strategy back to the downlink as described in [56] leads to a proper strategy in the downlink as well.…”

Section: Optimality Of Proper Signaling In Gaussian Mimo Broadcastmentioning

confidence: 99%

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Block-Skew-Circulant Matrices in Complex-Valued Signal Processing

Utschick

2015

IEEE Trans. Signal Process.

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Two main lines of approach can be identified in the recent literature on improper signals and widely linear operations. The augmented complex formulation based on the signal and its complex conjugate is considered as more insightful since it leads to convenient mathematical formulations for many considered problems. Moreover, it allows an easy distinction between proper and improper signals as well as between linear and widely linear operations. On the other hand, the composite real representation using the real and imaginary parts of the signal is closer to the actual implementation, and it allows to readily reuse results that have originally been derived for real-valued signals or proper complex signals. In this work, we aim at getting the best of both worlds by introducing mathematical tools that make the composite real representation more powerful and elegant. The proposed approach relies on a decomposition of real matrices into a block-skew-circulant and a block-Hankel-skew-circulant component. By means of various application examples from the field of signal processing for communications, we demonstrate the usefulness of the proposed framework.

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Section: Optimality Of Proper Signaling In Gaussian Mimo Broadcastmentioning

confidence: 84%

Section: Optimality Of Proper Signaling In Gaussian Mimo Broadcastmentioning

confidence: 99%

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Block-Skew-Circulant Matrices in Complex-Valued Signal Processing

Utschick

2015

IEEE Trans. Signal Process.

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“…[19]). Since (18) was shown to have zero duality gap for C ≻ 0 [30], we can consider the Lagrangian dual problem of the maximization in ( 16) and express R ⋆ A (C) as…”

Section: Approximation and Primal Decompositionmentioning

confidence: 99%

Maximizing the Partial Decode-and-Forward Rate in the Gaussian MIMO Relay Channel

Gest¹,

Wiegart²,

Utschick³

2019

Preprint

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It is known that circularly symmetric Gaussian signals are the optimal input signals for the partial decode-andforward (PDF) coding scheme in the Gaussian multiple-input multiple-output (MIMO) relay channel, but there is currently no method to find the optimal covariance matrices nor to compute the optimal achievable PDF rate since the optimization is a non-convex problem in its original formulation. In this paper, we show that it is possible to find a convex reformulation of the problem by means of an approximation and a primal decomposition. We derive an explicit solution for the inner problems as well as an explicit gradient for the outer problem, so that the efficient cutting-plane method can be applied for solving the outer problem. As the accuracy of this provably convergent algorithm might be impaired by the previous approximation, we additionally propose a modified algorithm, for which we cannot give a converge guarantee, but which provides rigorous upper and lower bounds to the optimum of the original rate maximization. In numerical simulations, these bounds become tight in all considered instances of the problem, showing that the proposed method manages to find the global optimum in all these instances.

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“…The proposed algorithm aims at maximizing the tolerable interference power, but without exploiting the cross-CSI. A more general scenario is considered in [29], where an uplinkdownlink duality is introduced for minimax problems with linear matrix inequality constraints, which usually appear in robust optimization under worst-case interference.…”

Section: Introductionmentioning

confidence: 99%

Spatial interference shaping for underlay MIMO cognitive networks

2017

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Interference temperature (IT) is a widely-used approach for protecting primary users (PUs) from the secondary users (SUs) in underlay cognitive radio. However, when multiple antennas are available at the transmitters and receivers, the spatial structure of the interference comes into play, strongly affecting the performance of the primary network. In this work, we propose interference shaping constraints as an alternative to IT-based approaches. Spatial shaping constraints take account of the structure of interference and exploit it in benefit of the secondary network. Moreover, they can be designed dynamically based on the channel conditions and performance requirements of the PUs. We first show that spatial shaping constraints generalize IT, in that the latter can be expressed as a set of isotropic shaping constraints on each interference dimension. Then, we exemplary consider a PU that has a rate requirement, and propose an algorithm for obtaining suitable shaping matrices, which can be easily modified to include primary transmitter cooperation. This algorithm is performed at the primary receiver using only local channel state information. Afterwards, we address the transceiver optimization of the SU, modeled as a multiple-input multiple-output point-to-point link, and provide optimal and suboptimal transmit covariance designs under the proposed shaping constraints.

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Minimax Duality for MIMO Interference Networks

Cited by 8 publications

References 35 publications

Block-Skew-Circulant Matrices in Complex-Valued Signal Processing

Block-Skew-Circulant Matrices in Complex-Valued Signal Processing

Maximizing the Partial Decode-and-Forward Rate in the Gaussian MIMO Relay Channel

Spatial interference shaping for underlay MIMO cognitive networks

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