Woodward's ambiguity function: From foundations to applications

Eustice, Dylan; Baylis, Charles; Marks, Robert J.

doi:10.1109/wmcas.2015.7233208

Cited by 17 publications

(6 citation statements)

References 34 publications

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“…In order to take the radial velocity (i.e., the Doppler effect) into account, it is necessary to introduce the ambiguity function (AF) which represents the output of the matched filter when the echo is affected by a Doppler shift f [16,17]:…”

Section: Deterministic Waveformsmentioning

confidence: 99%

Signal design and processing for noise radar

Galati

Pavan

Wasserzier

2022

EURASIP J. Adv. Signal Process.

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An efficient and secure use of the electromagnetic spectrum by different telecommunications and radar systems represents, today, a focal research point, as the coexistence of different radio-frequency sources at the same time and in the same frequency band requires the solution of a non-trivial interference problem. Normally, this is addressed with diversity in frequency, space, time, polarization, or code. In some radar applications, a secure use of the spectrum calls for the design of a set of transmitted waveforms highly resilient to interception and exploitation, i.e., with low probability of intercept/exploitation capability. In this frame, the noise radar technology (NRT) transmits noise-like waveforms and uses correlation processing of radar echoes for their optimal reception. After a review of the NRT as developed in the last decades, the aim of this paper is to show that NRT can represent a valid solution to the aforesaid problems.

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Section: Deterministic Waveformsmentioning

confidence: 99%

Signal design and processing for noise radar

Galati

Pavan

Wasserzier

2022

EURASIP J. Adv. Signal Process.

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“…[84], Table 2). Woodward is known for first mentioning the sinc function [32,43,100,152,153] and his time-frequency ambiguity function [46,51,56,[154][155][156][157][158][159][160][161][162]. We now let g be the Dirac comb, it leads us to the following lemma [82,142].…”

Section: Definition 1 (Periodization and Discretizationmentioning

confidence: 99%

On the Reversibility of Discretization

Fischer

Stens

2020

Mathematics

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“Discretization” usually denotes the operation of mapping continuous functions to infinite or finite sequences of discrete values. It may also mean to map the operation itself from one that operates on functions to one that operates on infinite or finite sequences. Advantageously, these two meanings coincide within the theory of generalized functions. Discretization moreover reduces to a simple multiplication. It is known, however, that multiplications may fail. In our previous studies, we determined conditions such that multiplications hold in the tempered distributions sense and, hence, corresponding discretizations exist. In this study, we determine, vice versa, conditions such that discretizations can be reversed, i.e., functions can be fully restored from their samples. The classical Whittaker-Kotel’nikov-Shannon (WKS) sampling theorem is just one particular case in one of four interwoven symbolic calculation rules deduced below.

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“…Signal ambiguity function is [7,8,9]: is the ambiguity function of a rectangular sub-pulse, which is …”

Section: Ds-psk System Model and Analysismentioning

confidence: 99%

The Research on Anti-interference Performance of Ambiguity Function Based Digital Communication System

Han¹,

Gao²,

Fang³

2016

Proceedings of the 2015 4th National Conference on Electrical, Electronics and Computer Engineering

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Abstract. Ambiguity function describes the measurement accuracy, resolution capability and ambiguity degree of signal delay and Doppler frequency shift, which can be used to analyze the resolution of adjacent targets and anti-interference performance of the system. In this paper, the binary digital modulation communication systems are considered, ambiguity function of the Direct Sequence -Binary Phase Shift Keying (DS-BPSK) is derived, and the performance of the signal interference is measured by the size of cutting area for ambiguity function. For 31 and 255 bits m-sequence spread-spectrum codes, the ambiguity functions are simulated. We conclude that the narrower the cutting area of ambiguity function the sharper the main lobe, the larger the resolution signal, and the stronger the anti-interference ability.

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Woodward's ambiguity function: From foundations to applications

Cited by 17 publications

References 34 publications

Signal design and processing for noise radar

Signal design and processing for noise radar

On the Reversibility of Discretization

The Research on Anti-interference Performance of Ambiguity Function Based Digital Communication System

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