Design of Jacobi EVD Processor Based on CORDIC for DOA Estimation with MUSIC Algorithm

Minseok KIM
Hiroyuki ARAI

IEICE TRANSACTIONS on Communications   Vol.E85-B    No.12    pp.2648-2655
Publication Date: 2002/12/01
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on Software Defined Radio Technology and Its Applications)
adaptive antenna,  FPGA implementation,  DOA estimation,  MUSIC,  EVD,  

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Computing the Eigen Value Decomposition (EVD) of a symmetric matrix is a frequently encountered problem in adaptive (or smart or software) antenna signal processing, for example, super resolution DOA (Direction Of Arrival) estimation algorithms such as MUSIC (MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique). In this paper the hardware architecture of the fast EVD processor of symmetric correlation matrices for the application of an adaptive antenna technology such as DOA estimation is proposed and the basic idea is also presented. Cyclic Jacobi method is well known for the simplest algorithm and easily implemented but its convergence time is slower than other factorization algorithm like QR-method. But if considering the fast parallel computation of the EVD with a hardware architecture like ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array), the Jacobi method can be a appropriate solution, since it offers a quite higher degree of parallelism and easier implementation than other factorization algorithms. This paper computes the EVD using a Jacobi-type method, where the vector rotations and the angles of the rotations are obtained by CORDIC (COordinate Rotation DIgital Computer). The hardware architecture suitable for ASIC or FPGA with fixed-point arithmetic is presented. Because it consists of only shift and add operations, this hardware friendly feature provides easy and efficient implementation. In this paper, the computational load, the estimate of circuit scale and expected performance are discussed and the validation of fixed-point arithmetic for the practical application to MUSIC DOA estimation is examined.