Fast Rank-Revealing QR Factorization for Two-Dimensional Frequency Estimation

Abstract

It is well known that the singular value decomposition (SVD), as the best rank-revealing factorization, furnishes the best rank- $k$ approximation to a dense matrix with expensive computational cost of $\mathcal O(M^{2}N+N^{2}M+\min (M,N)^{3})$ . Moreover, it is hard to implement in parallel, which challenges the memory storage in wireless communications data-driven system. In this letter, a fast rank-revealing technique, namely, bilateral random projections (BRP) with $\mathcal O(MN)$ operations, is exploited for two-dimensional (2-D) frequency estimation of a complex sinusoid in noisy environment. Based on the resulting data matrix, whereafter, two-stage QR factorization frequency estimation method with the weighted least squares (WLS) as solver, is proposed to reduce the computational complexity of those SVD-based frequency estimators. Simulation results demonstrate the efficiency of the proposed algorithm in comparison with several frequency estimation approaches and the Cramer-Rao lower bound (CRLB) as benchmark.