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

Abstract

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.

Low complexity high throughput algorithms for MIMO AF relay networks

“…Shown in simulations, the consideration of P S provides significant improvement of system sum rate. In [12] similar techniques are used. First C is set as a small positive scalar (for example C = 1), then after each iteration we update it as…”

“…Because the computational complexity of the SQP algorithm is only O(n 3 ) while the Semi-definite Programming (SDP) relaxation algorithm [9] requires O(n 6 ), with n as the dimension of the variable x, we use SQP rather than SDP to solve (12). Although SQP algorithm can only guarantee to achieve a local optimal solution, we start the algorithm from the previous feasible precoder, to get sufficient reduction of the objective function value.…”

Distributed Transceiver Design and Power Control for Wireless MIMO Interference Networks

“…To investigate the complexity of the proposed algorithm, we follow the approach in [40] and use the number of complex multiplications as the complexity criterion to evaluate the proposed algorithms. For the sake of simplicity we consider a symmetric network where d k = d, n D k = n D , and n S k = n S , ∀k ∈ {1, ..., K}.…”

Multi-stream sum rate maximization for MIMO af relay networks

“…With Interference Alignment (IA) technique [4], we are able to eliminate the interference and achieve the required DoFs. In MIMO networks, IA technique as well as the IA algorithms have been deeply investigated [5][6][7][8]. There are also some related works for two-hop networks.…”