Statistical analysis of the product high-order ambiguity function
Scaglione, A.; Barbarossa, S.
Information Theory, IEEE Transactions on
Volume 45, Issue 1, Jan 1999 Page(s):343 - 356
Digital Object Identifier 10.1109/18.746840
Summary:The high-order ambiguity function (HAF) was introduced for the
estimation of polynomial-phase signals (PPS) embedded in noise. Since
the HAF is a nonlinear operator, it suffers from noise-masking effects
and from the appearance of undesired cross terms and, possibly, spurious
harmonics in the presence of multicomponent (mc) signals. The product
HAF (PHAF) was then proposed as a way to improve the performance of the
HAF in the presence of noise and to solve the ambiguity problem. In this
correspondence we derive a statistical analysis of the PHAF in the
presence of additive white Gaussian noise (AWGN) valid for high
signal-to-noise ratio (SNR) and a finite number of data samples. The
analysis is carried out in detail for single-component PPS but the
multicomponent case is also discussed. Error propagation phenomena
implicit in the recursive structure of the PHAF-based estimator are
explicitly taken into account. The analysis is validated by simulation
results for both single- and multicomponent PPSs
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