Abstract
Interference alignment (IA) is a key technology for achieving the capacity scaling required by next generation wireless networks, which is proved to obtain the maximum degrees of freedom (DoF). The aim of this paper is to propose interference alignment schemes through manifold optimization theory for K-user interference channel. We limit the optimization only at transmitters and relax the hypothesis of channel reciprocity to mitigate the overhead caused by alternation between the forward and reverse links significantly. Firstly, we introduce a classical algorithm based on the steepest descent (SD) algorithm in a multi-dimensional complex space to achieve feasible IA. Then, we reform the optimization problem on Stiefel manifold and propose a novel SD algorithm based on this manifold with lower dimensions. Moreover, aiming at further reducing the complexity, the Grassmann manifold is introduced to derive corresponding algorithm for reaching the perfect IA. Numerical simulations show that the proposed algorithms on manifolds have better performance both on system throughput and convergence than classical methods and also achieve the maximum DoF.
Highlights
Interference alignment (IA) has been envisioned as a promising technique [1, 2] to meet the overwhelming growth of data network traffic which is the main challenge of the wireless networks
There are three dominant interference alignment schemes: The first scheme is based on full channel state information (CSI), assuming the transmitters have the priori perfect CSI; the second one is based on limited CSI; and the third one do not need the CSI, which is called blind interference alignment
5 Conclusion and future work In this paper, we focus on the interference alignment schemes by employing manifold optimization theory
Summary
Interference alignment (IA) has been envisioned as a promising technique [1, 2] to meet the overwhelming growth of data network traffic which is the main challenge of the wireless networks. Several shortcomings are accompanied with the traditional constrained optimization techniques such as low-converging speed and high-complexity To overcome these limitations, in this paper, we introduce optimization on matrix manifolds into the precoding scheme for interference alignment and limit the optimization only at the transmitters’ side. For the sake of comparison, by employing classical constrained optimization method, a steepest descent (SD) algorithm in multi-dimensional complex space is provided to design the precoder of interference alignment. To further reduce the computation complexity in terms of dimensions of manifold, we explore the unitary invariance property of our cost function and solve the optimization problem on the complex Grassmann manifold, present the corresponding SD algorithm on the Grassmann manifold for interference alignment precoding design.
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