The Architecture Of Matrix Large Scale Computation And Its Application To Doa Estimation And MIMO Receiver

Computation related to Matrix is the basic numeric computation in science or enginerring. It needs such computation in many case in communicaton system, such as MIMO receiver or array signal processing. In pratical system, it always needs the ability of real time processing, with the character of great amount of comptation and be complex to realize, one single processor is hard to satisfy such needs. Based on this reality, it needs accelerate the matrix computation by parallel processing. The most important aspects reside in parallel processing are architecture design, task allocation, corresponding the data to the processing elements(PE) and interconnection of PEs. Such that all the PEs can work in parallel, coordinately and efficiently to complete the whole comutation task with high speed.This chapter will based on the practical communication system to introduce parallel architecture of common matrix computation, it includes:1. The parallel architecture about basic matrix algorithm, such as matrix plus, matrix substraction, hardamard product, matrix-vectoring product. Especially, we introduce the matrix multiplication.2. The problems about matrix invertion and this algorithm is important prart of MIMO reiceiver.We first introduced some tradition methods, then especially introduce the methods based on matrix triangle decomposion, mainly about LU decomposition and QR decompositon. Last, gives the idear about the inversion of upper triangle matrix.At this part of the chapter, we realized the QR decomposition and the inversion of upper triangle matrix by hardware description language and give the simulation results.3. Singular value decomposition(SVD) of matrix. This computation related to the parallel decomposition about MIMO channel.firstly, we briefly introduced one-side Jacobi method and its one dimention linear systolic architecture. Then we mainly introduce the two-side Jacobi algorithm, which includes the theory of the algorithm, the architecture design, how the data flow among the PEs, and the processing procedure inside the PEs. Also, we realized the SVD of 4×4 matrix and give the simulation results and related performance analysis.4. The application of matrix parallel computation in MUSIC algorithm of direction estimation realization.we begin with array element and sequently introduce array singnal model and its statistical character and then is the most influential MUSIC algorithm in spatical estimation development. Also, we gives the performans analysis and the simulation results about the MUSIC algorithm. As the original MUSIC algorithm must implemented in plural domain, which will cause complexity of the hardware. So, subsequently, we introduce how to inplimented the MUSIC altorithm in real number through appropriate unitary transform. Then we will give how to realiz all parts of MUSIC altorithm combined with matrix parallel computation. At the same time, we gives another decomposition about the matrix, which is eigen value decomposition, also introduce the theory and realization architecture. At last, we improve the computation of MUSIC spectrum function, which will take only one multiplication cycle to complete one step computation.