The Application Of Lagrange Multipliers Estimation For MIMO Detection

Multiple Input Multiple Output (MIMO) systems employ multiple antennas at the receiving and transmitting ends simultaneously which can get both multiplexing gains and diversity gains. MIMO technology is the key of making breakthrough in the area of wireless communications and becomes a hot topic of widely research. Meanwhile, MIMO systems request separation detection of the received multiple mixed signals at the receiving end, which leads the signal detection more difficult and greatly increases equipment costs. So, how to trade off the computational complexity and the detection performance under the channel noise and the mutual interference between the transmitted signals becomes an important problem which needs to be addressed urgently.Maximum likelihood (ML) detection is known as the optimal detection algorithm. However, due to its high computational complexity, it can’t meet requirement of real-time communication. For the MIMO system which is based on BPSK modulation, in order to achieve good detection performance with low computational complexity, we first convert the maximum likelihood detection problem into a quadratic programming problem with equality constraint which can be solved by the Lagrange multiplier method. In this paper, the main contents of research and innovations are concluded as follows:1. A novel MIMO detection method based on Lagrange multipliers estimation is proposed in this thesis. Firstly, we use Lagrange multiplier method to solve the quadratic programming problem with equality constraint and derive the relationship of the Lagrange multipliers, transmission signals and channel noise. Then, by utilizing the particularity of MIMO systems and the relationship between Lagrange multipliers and channel noise, we present an estimation method of Lagrange multipliers under the unknown sending signals and channel noise. What’s more, we use the sufficient conditions of binary quadratic programming problem to further constrain the estimated Lagrange multipliers and improve the estimation accuracy of the Lagrange multipliers.2. The asymptotic validity analysis is employed to evaluate the performance of the proposed detection method compared with those of the existing linear detectors, such as ZF, MMSE detector. The theoretical results show that the proposed method is superior to the conventional ZF, MMSE detector.3. The improved method of estimating Lagrange multipliers is presented in this thesis. The improved method can get more accurate Lagrange multipliers by using of the iterative method to gradually correct the estimated Lagrange multipliers and reduce the estimated errors of Lagrange multipliers. Compared with the non-iterative method, the iterative method can achieve the better detection performance.We conduct simulations of the MIMO detection method and its improved one based on Lagrange multipliers estimation in the MATLAB platform. The experiments results illustrate that the proposed detection methods can achieve good even nearly optimal detection performance with low computational complexity.