TY - JOUR
T1 - Unitary PUMA Algorithm for Estimating the Frequency of a Complex Sinusoid
AU - Qian, Cheng
AU - Huang, Lei
AU - So, Hing Cheung
AU - Sidiropoulos, Nicholas D.
AU - Xie, Junhao
PY - 2015/10/15
Y1 - 2015/10/15
N2 - One-dimensional (1-D) and two-dimensional (2-D) frequency estimation for a single complex sinusoid in white Gaussian noise is a classic signal processing problem with numerous applications. It is revisited here through a new unitary principal-singular-vector utilization modal analysis (PUMA) approach, which is realized in terms of real-valued computations. The 2-D unitary PUMA is first formulated as an iteratively weighted least squares optimization problem. Recognizing that only one iteration is sufficient when 2-D unitary PUMA is initialized using least squares, a computationally attractive closed-form solution is then obtained. A variant of 2-D unitary PUMA is also developed for the 1-D case. Due to the real-valued computations and closed-form expression for the frequency estimate, the unitary PUMA is more computationally efficient than a number of state-of-The-Art methods. Furthermore, the asymptotic variances of 1-D and 2-D unitary PUMA estimators are theoretically derived, and numerical results are included to demonstrate the effectiveness of the proposed methods.
AB - One-dimensional (1-D) and two-dimensional (2-D) frequency estimation for a single complex sinusoid in white Gaussian noise is a classic signal processing problem with numerous applications. It is revisited here through a new unitary principal-singular-vector utilization modal analysis (PUMA) approach, which is realized in terms of real-valued computations. The 2-D unitary PUMA is first formulated as an iteratively weighted least squares optimization problem. Recognizing that only one iteration is sufficient when 2-D unitary PUMA is initialized using least squares, a computationally attractive closed-form solution is then obtained. A variant of 2-D unitary PUMA is also developed for the 1-D case. Due to the real-valued computations and closed-form expression for the frequency estimate, the unitary PUMA is more computationally efficient than a number of state-of-The-Art methods. Furthermore, the asymptotic variances of 1-D and 2-D unitary PUMA estimators are theoretically derived, and numerical results are included to demonstrate the effectiveness of the proposed methods.
KW - Complex sinusoid
KW - frequency estimation
KW - subspace method
KW - weighted least squares
UR - http://www.scopus.com/inward/record.url?scp=84959419421&partnerID=8YFLogxK
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U2 - 10.1109/TSP.2015.2454471
DO - 10.1109/TSP.2015.2454471
M3 - Article
AN - SCOPUS:84959419421
VL - 63
SP - 5358
EP - 5368
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
IS - 20
M1 - 7152983
ER -