## Product high-order ambiguity function for multicomponent polynomial-phase signal modeling (1998)

Venue: | IEEE Trans. on Signal Processing |

Citations: | 14 - 1 self |

### BibTeX

@ARTICLE{Barbarossa98producthigh-order,

author = {Sergio Barbarossa and Anna Scaglione and Student Member and Georgios B. Giannakis},

title = {Product high-order ambiguity function for multicomponent polynomial-phase signal modeling},

journal = {IEEE Trans. on Signal Processing},

year = {1998},

pages = {691--708}

}

### OpenURL

### Abstract

Abstract—Parameter estimation and performance analysis issues are studied for multicomponent polynomial-phase signals (PPS’s) embedded in white Gaussian noise. Identifiability issues arising with existing approaches are described first when dealing with multicomponent PPS having the same highest order phase coefficients. This situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomialphase signals through channels affected by multipath and is thus worthy of a careful analysis. A new approach is proposed based on a transformation called product high-order ambiguity function (PHAF). The use of the PHAF offers a number of advantages with respect to the high-order ambiguity function (HAF). More specifically, it removes the identifiability problem and improves noise rejection capabilities. Performance analysis is carried out using the perturbation method and verified by simulation results. I.

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Citation Context ...he number of multiple paths in the communication case. The analysis of PPS’s has received considerable attention in the recent signal processing literature [1], [3], [6], [11], [12], [14]–[18], [20], =-=[23]-=-–[25], [30], [32], [34]–[36]. In particular, the polynomial-phase transform (PPT) [18], which was later Manuscript received July 25, 1996; revised September, 26, 1997. This work was supported by the “... |

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Citation Context ...s useful to note an artifact arising under some particular circumstances. Sequence , with , where and are co-prime integers, is a periodic sequence of period , as can be proved by direct substitution =-=[37]-=- so that the HAF (or PHAF) of such sequences would exhibit spurious peaks due to periodicity. However, if comes from sampling a continuous-time signal , where as before and , with sampling period , it... |

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Citation Context ...lity problem related to the HAF and propose a method for resolving it based on the so-called product HAF (PHAF). A multilag HAF was originally introduced in [1] and subsequently used in [3], [6], and =-=[7]-=-. However, the transformation proposed in [7] is computationally demanding. In contrast, the transformation herein improves the performance with respect to HAF-based techniques with a slight increase ... |

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Citation Context ...CESSING, VOL. 46, NO. 3, MARCH 1998 APPENDIX PERFORMANCE ANALYSIS BY PERTURBATION METHOD In this section, we compute the expected value and variance of (56), extending the methodology already used in =-=[19]-=-. As far as the denominator of (56) is concerned, we have [cf. (51)] (57) To compute the derivatives of the PHAF, we need to compute the derivatives of the ml-HAF. Starting from (40), we have which, f... |

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Citation Context ...HIM’s obtained using different sets of lags by multiplying the corresponding ml-HAF’s. This leads to what we call the PHAF, which will be defined next. An alternative subspace approach is proposed in =-=[2]-=-, based on the intersection of the signal subspaces obtained using different sets of lags. A. Definition Given sets of lags with , we compute the ml-HAF’s for and then define the product ambiguity fun... |

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Citation Context ...nt scatterers in the radar case or to the number of multiple paths in the communication case. The analysis of PPS’s has received considerable attention in the recent signal processing literature [1], =-=[3]-=-, [6], [11], [12], [14]–[18], [20], [23]–[25], [30], [32], [34]–[36]. In particular, the polynomial-phase transform (PPT) [18], which was later Manuscript received July 25, 1996; revised September, 26... |

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Citation Context ...alid for finite length sequences. We also introduce the ml-HAF for infinite length sequences as (7) (8) (9) (10) The multilag definition was originally introduced in [1] and subsequently used in [3], =-=[4]-=-, and [6]. B. Properties We derive first a closed-form expression for the ml-HIM of mc-PP’s and then prove a series of corollaries that will provide the basis for parameter estimation. Theorem: Given ... |

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Citation Context ...e definition given in [18] is not ( and so on) so that, for the same value of the lags, the duration of the HIM, in our case, is half the duration of the HIM defined in [18]. Indeed, it can be proved =-=[8]-=- that the symmetric definition should be preferred because it leads to smaller estimation variances for all phase coefficients, except the highest order one, whose variance is the same in both cases. ... |

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Citation Context ...lready been applied to the analysis of radar signals in [5] and [28] as an autofocusing method for synthetic aperture radar imaging and to the demodulation of continuos-phase modulation (CPM) signals =-=[9]-=-, where it offers some new possibilities for blind equalization.s704 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 46, NO. 3, MARCH 1998 APPENDIX PERFORMANCE ANALYSIS BY PERTURBATION METHOD In this sec... |

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Citation Context ...ly proposed for chirp signals in [15]. The HAF-based approach provides a simple order-recursive algorithm for estimating the polynomial-phase coefficients. Simpler methods were also proposed in [11], =-=[16]-=-, and [32] based on the computation of the instantaneous phase followed by phase unwrapping and polynomial fitting. Those methods are indeed simpler but are able to deal only with monocomponent PPS’s.... |

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Citation Context ...mber of multiple paths in the communication case. The analysis of PPS’s has received considerable attention in the recent signal processing literature [1], [3], [6], [11], [12], [14]–[18], [20], [23]–=-=[25]-=-, [30], [32], [34]–[36]. In particular, the polynomial-phase transform (PPT) [18], which was later Manuscript received July 25, 1996; revised September, 26, 1997. This work was supported by the “Minis... |

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Citation Context ...es, leading to possible further enhancements of the useful terms with respect to spurious sinusoids and noise. The proposed method has already been applied to the analysis of radar signals in [5] and =-=[28]-=- as an autofocusing method for synthetic aperture radar imaging and to the demodulation of continuos-phase modulation (CPM) signals [9], where it offers some new possibilities for blind equalization.s... |