Welch bounds for cross correlation of subspaces and generalizations

Datta, Somantika

doi:10.1080/03081087.2015.1091437

Cited by 14 publications

(12 citation statements)

References 21 publications

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“…The measurement matrix Φ will be helpful for signal reconstruction when restricted isometry property (RIP) criteria is satisfied. In other words, each column is a unit vector, and the sum of squares of all columns meets the Welch bound [24,25]…”

Section: Code-domain Compression Acquisitionmentioning

confidence: 99%

GNSS Signal Acquisition Algorithm Based on Two-Stage Compression of Code-Frequency Domain

Zhou

Zhao

et al. 2022

Applied Sciences

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The recently-emerging compressed sensing (CS) theory makes GNSS signal processing at a sub-Nyquist rate possible if it has a sparse representation in certain domain. The previously proposed code-domain compression acquisition algorithms have high computational complexity and low acquisition accuracy under high dynamic conditions. In this paper, a GNSS signal acquisition algorithm based on two-stage compression of the code-frequency domain is proposed. The algorithm maps the incoming signal of the same interval to multiple carrier frequency bins and overlaps the mapped signal that belongs to the same code phase. Meanwhile, the code domain compression is introduced to the preprocessed signal, replacing circular correlation with compressed reconstruction to obtain Doppler frequency and code phase. Theoretical analyses and simulation results show that the proposed algorithm can improve the frequency search accuracy and reduce the computational complexity by about 50% in high dynamics.

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Section: Code-domain Compression Acquisitionmentioning

confidence: 99%

GNSS Signal Acquisition Algorithm Based on Two-Stage Compression of Code-Frequency Domain

Zhou

Zhao

et al. 2022

Applied Sciences

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“…Therefore it is desirable to improve Theorem 1.2.and to get a continuous version of Inequality (1) by replacing maximum by supremum. For the sake of completeness, we note that there are some further refinements of Theorem 1.1, see [9,13,37]. The goal of this article is to derive Theorem 1.1 for arbitrary measure spaces (Theorem 2.7).…”

Section: Introductionmentioning

confidence: 99%

Continuous Welch bounds with Applications

Krishna

2021

Preprint

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Let (Ω, µ) be a measure space and {τ α } α∈Ω be a normalized continuous Bessel family for a finite dimensional Hilbert space H of dimension d. If the diagonal ∆ := {(α, α) : α ∈ Ω} is measurable in the measure space Ω × Ω, then we show that supThis improves 47 years old celebrated result of Welch [IEEE Transactions on Information Theory, 1974 ].We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

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“…There are several theoretical and practical applications of Theorem 1.1 such as in the study of root-meansquare (RMS) absolute cross relation of unit vectors [57], frame potential [7,12,15], correlations [56], codebooks [25], numerical search algorithms [71,72], quantum measurements [58], coding and communications [61,67], code division multiple access (CDMA) systems [41,42], wireless systems [53], compressed sensing [64], 'game of Sloanes' [37], equiangular tight frames [62], etc. Some improvements of Theorem 1.1 has been done in [18,23,68,69]. It is in the paper [22] where the following generalization of Theorem 1.1 has been done for continuous collections.…”

Section: Introductionmentioning

confidence: 99%