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As one of the most promising future fundamental devices, memristor has its unique advantage on implementing low-power high-speed matrix multiplication. Taking advantage of the high performance on basic matrix operation and flexibilitys of memristor crossbars, in this paper, we investigate both discrete Fourier transformation (DFT) and miltiple-input and multi-output (MIMO) detection unit in baseband processor. We reformulate the signal processing algorithms and model structures into a matrix-based framework, and present a memristor crossbar based DFT module design and MIMO detector module design. For both designs, experimental results demonstrate significant gains in speed and power efficiency compared with traditional CMOS-based designs. 

A memristor crossbar, which is constructed with memristor devices, has the unique ability to change and memorize the state of each of its memristor elements. It also has other highly desirable features such as high density, low power operation and excellent scalability. Hence the memristor crossbar technology can potentially be utilized for developing low-complexity and high-scalability solution frameworks for solving a large class of convex optimization problems, which involve extensive matrix operations and have critical applications in multiple disciplines. This paper, as the first attempt towards this direction, proposes a novel memristor crossbar-based framework for solving two important convex optimization problems, i.e., second-order cone programming (SOCP) and homogeneous quadratically constrained quadratic programming (QCQP) problems. In this paper, the alternating direction method of multipliers (ADMM) is adopted. It splits the SOCP and homogeneous QCQP problems into sub-problems that involve the solution of linear systems, which could be effectively solved using the memristor crossbar in O(1) time complexity. The proposed algorithm is an iterative procedure that iterates a constant number of times. Therefore, algorithms to solve SOCP and homogeneous QCQP problems have pseudo-O(N) complexity, which is a significant reduction compared to the state-of-the-art software solvers (O(N3.5)-O(N4)).