Research On Multi-frequency Channel Interference Alignment Technology

Interference alignment theory is one of the most impressive researches in recent years. The classical interference alignment theory is based on multi an-tenna system, and has been extensive and in-depth researching. Unlike the multi antenna mutual interference network which have generalized random channel matrices, the channel matrix of multi frequency channel interference networks have diagonal random matrices. Therefore, the basic conclusion of multi an-tenna interference alignment system is no longer applicable to the multi fre-quency channel interference alignment systems. Based on the interference align-ment theory, this paper explores the multi frequency channel interference align-ment system, and completes the following innovative achievements:· If a multi frequency channel interference alignment system has M inde-pendent fading channels and single data stream transmitted by each user,then the degree of freedom for this system is proved to be 2M - 2, there-fore the user capacity of such an interference network is 2M-2 as well.Based on this conclusion, this paper proposes the concept of interference alignment multiplexing method. Compared with the traditional frequency division multiplexing, the proposed interference alignment multiplexing method can improve the spectrum utilization no more than double.· Based on the conclusion of degree of freedom, this paper researches the analytical solution of multi frequency channel interference alignment sys-tem with 3 channels and 4 users, and proves that the dimension of linear interference alignment solution space for a multi frequency channel inter-ference alignment system with M independent fading channels and 2M - 2 users is 2M - 2. Furthermore, this paper proves that the linear interference alignment solution space is a continuous manifold which is isomorphic to the Cartesian product space G(3,1) × G(3,1), and proposes the optimal linear interference alignment optimization model. At last, based on the simulated annealing idea, we proposed global search method to investi-gate the optimization model, and the optimal linear interference alignment solution is searched by this model.· A necessary condition for the iterative Max-SINR algorithm is proposed in this paper. Then by deduce the gradient function of sum rate function of interference alignment network, a necessary condition for a set of en-coding and decoding vectors to be the optimal solution with maximum sum rate is proposed. Based on such a necessary condition, this paper proves that the iterative Max-SINR algorithm is an asymptotically locally optimal solution for linear interference alignment, which means that the iterative Max-SINR algorithm cannot achieve even a local optimal sum rate solution. Even though, the converge solution of the iterative Max-SINR algorithm will approach towards a locally optimal sum rate solution with the increase of transmit signal power. At last, some numerical sim-ulations illustrate the approaching behavior of the convergent solution of the iterative Max-SINR algorithm.· The iterative Min-IL algorithm is proved to be the gradient descent method for the interference leakage function in this paper. Based on this conclu-sion, this paper explores the property of the optimal sum rate solution, and proposes the iterative gradient ascend with power increase algorithm. The iterative gradient ascends with power increase algorithm can efficiently track the process of the optimal sum rate solution, and overcome the sum rate performance degradation problem at moderate and high SNR regions for the iterative Max-SINR algorithm caused by locally convergence. At last, the numerical simulation results shows that the proposed iterative gra-dient ascends with power increase algorithm have an obvious advantage at high SNR regions.Finally, the full research works are summarized, and the continuous valu-able research directions of multi frequency channel interference alignment sys-tem are discussed.