Research On The Capacity Of Dual-hop Beamforming Relay Networks

In the field of wireless communication,the network capacity,transmission efficiency and anti-jamming ability are the important indicators for wireless transmission.The relay network is an effective method to expand the coverage of signal transmission,improve transmission efficiency and save network resources Beamforming can obtain the diversity gain and improve the transmission performance by weighting the signals of the antenna array.Moreover,because of its directional beam transmission and spatial filtering,Beamforming has a good anti-jamming ability.Therefore,it is of great theoretical and application value to study beamforming on the relay network to improve capacity and anti-jamming performance.Dual-hop multi-access multi-antenna relay network is a basic multi-user communication models.Combing with this network,it is very important to discuss the ability of beamforming to improve capacity.The existing researches only discuss the transmission sum-rate,but does not characterize the network capacity region.This paper presents a method to characterize the capacity region of Dual-hop multi-access multi-antenna relay network on beamforming.In recent years,the research of the anti-jamming in the network obtain a lot of attention.This paper consider a new jamming mode.The jammer can randomly select a code word from the codebook of the source to disturb the transmission.Then,it is difficult for the receiver to distinguish whether the received signals are from the source or the jammer.In this paper,the anti-jamming performance and the ability to improve capacity for beamforming are studied.This paper mainly deals with four network models which are dual-hop multi-access multi-antenna relay network,dual-hop distributed relay network with a jammer,dual-hop distributed relay energy harvesting network with a jammer,and dual-hop multi-antenna relay network with a jammer.The main work of this paper can be summarized three parts as following.First,consider a dual-hop multi-access multi-antenna beamforming relay network,we investigate the achievable rate region of a dual-hop two sources multi-access multi-antenna beamforming relay network.Under the criterion of maximizing transmission rate,we establish an optimization problem with beamforming matrix,and present a method to characterize the capacity region.In order to reduce the computational complexity,we give the structure of the optimal beamforming matrix,and reduce the number of variables of the optimization problem to no more than 9.We use a suitable transformation technique and combine with semi-definite relaxation to transform this non-convex optimization problem into an equivalent semi-positive definite optimization problem.Then,the optimal beamforming matrix can be solved in polynomial time.In addition,we give the mathematical closed-form expressions for the two maximum individual rate and sum-rate of the two sources.Meanwhile,we give the mathematical closed expressions of two beamforming matrices corresponding to the maximum individual rate.The beamforming matrix corresponding to the maximum sum-rate can be determined by solving a simple linear equation.We show that the outer bound determined by maximizing the two individual rates and the sum-rate is not tight.The simulation results show this conclusion is correctSecond,we consider dual-hop distributed beamforming relay network with a jammer and dual-hop distributed relay energy harvesting network with a jammer.These two network can be equivalent to Gaussian arbitrarily varying channels with the beamforming vectors.According to the relevant conclusions in information theory,we give the necessary and sufficient conditions for the capacity is positive,and the capacity formula.Under the criterion of maximizing transmission rate,we establish two non-convex optimization problem with beamforming vector.We propose a method to transform these two non-convex optimization problems into standard second-order cone programming problems,which can be solved in polynomial time.Thus we can obtain the maximum capacities and the corresponding beamforming vectors of the two networks.The simulations confirm that the beamforming can improve the system performance and has good anti-jamming ability.Third,we consider a dual-hop multi-antenna beamforming relay network in presence of a jammer.Similarly,we give the necessary and sufficient conditions for the capacity is positive,and the capacity formula.The goal is to determine the beamforming matrix so that the maximum rate can be achieved.This problem can be modeled as a non-convex optimization problem with the beamforming matrix in terms of maximizing capacity.In order to reduce the computational complexity,we propose an ingenious method to transform this non-convex optimization problem into a standard second-order cone programming problem,which can be solved in polynomial time.Thus we can obtain the maximum capacity and the corresponding beamforming matrix.For the two special cases,we give the mathematical closed-form expressions of the maximum capacity and the corresponding optimal beamforming matrix.For the general cases,we propose a beamforming scheme with low complexity,and give the suboptimal rate and the corresponding suboptimal beamforming matrix.The simulations show that the suboptimal beamforming scheme is an optimal zero-forcing.The rate under the optimal beamforming scheme will approach suboptimal scheme when the jamming power is large.Beamforming can improve the system performance and has good anti-jamming ability.