Interference Alignment Algorithms For Wireless Networks

The fifth-generation mobile communication system(5G)is now being gradually deployed,and the Beyond fifth-generation mobile communication system(B5G)is now also studied.The ultra-dense cellular network is an important technology for improving network throughput in 5G and B5G.However,due to the extreme scarcity of spectrum resources,extensive frequency reuse has caused serious interference in the network,which greatly restrains the performance of the network.Therefore,useing the effective interference management methods in the network has become an important means to improve network performance.As an effective interference management method,interference alignment technology has been extensively studied,and the difficulty of interference alignment is how to design a transmitters'precoding matrix and receivers'decoding matrix to meet the requirements of system degree of freedom.At present,there are two main directions in the research of interference alignment algorithms.One is the study of closed-form solutions of interference alignment in specific network scenarios,and the other is the study of iterative interference alignment algorithms in arbitrarily configured networks.For the former,it is only suitable for fixed network configurations,and has poor scalability and applicability.For the latter,the existing algorithms cannot achieve the maximum degree of freedom for arbitrarily configuring the network,which is still an open problem.This paper proposes an iterative interference alignment algorithm that can approach or even reach the maximum degree of freedom of the network for the Multiple Input Multiple Output(MIMO)Interference Channel(IC)system.The MIMO IC system studied in this paper is composed of multiple transmitter-receiver pairs.In addition to receiving the desired signal transmitted by the corresponding transmitter,each receiver also receives interference signals transmitted by other transmitters in the system.This paper first analyzes the mapping relationship between the degree of freedom of the system and the group sparse structure of the interference vector.This mapping relationship shows that the optimal interference alignment scheme can make all interference vectors have a group sparse structure,and then use the method that minimizes all interference vectors.The mixedl₁/l₂ norm limit the sparse structure of the interference vector,and then the problem of maximizing the degree of freedom of the system is transformed into a mixed l₁/l₂ norm problem of minimizing all the interference vectors,and the rank constraint required for interference alignment is transformed into a Stiefel manifold constraint,In this problem,because the two difficulties of mixedl₁/l₂ norm non-differentiable and rank-constrained non-convex are coupled with each other,it is extremely difficult to solve directly.Finally,this paper proposes an algorithm based on the Alternating Direction Method of Multipliers(ADMM),which couples the above two difficult points into two sub-problems,which are the classic group minimum absolute value convergence and selection algorithm.The Group Least Absolute Shrinkage and Selection Operator(Group Lasso)problem and the Frobenius norm problem of minimizing a matrix with manifold constraints.For these two problems,you can use Block Coodinate Descent(BCD)respectively.)Algorithm and trust region(Trust Region)algorithm to solve,so that the complexity of the solution is reduced.Compared with other iterative interference alignment algorithms,the algorithm in this paper obtains a higher degree of freedom,approximates or even reaches the maximum degree of freedom of the network,and can guarantee good performance when the transmit-receive pair increases.This reflects the superiority of this algorithm.