Lower Bounds on Parameter Modulation-Estimation under Bandwidth Constraints

Nir Weinberger; Neri Merhav

doi:10.1109/TIT.2017.2677461

Lower Bounds on Parameter Modulation-Estimation under Bandwidth Constraints

Nir Weinberger, Neri Merhav

Research output: Contribution to journal › Article › peer-review

Abstract

The problem of modulating the value of a parameter onto a band-limited signal to be transmitted over a continuous-time, additive white Gaussian noise (AWGN) channel, and then estimating this parameter at the receiver, is considered. The performance is measured by the mean power-α error (MPαE), which is defined as the worst case αth-order moment of the absolute estimation error. The optimal exponential decay rate of the MPαE as a function of the transmission time is investigated. Two upper (converse) bounds on the MP αE exponent are derived, on the basis of known bounds for the AWGN channel of inputs with unlimited bandwidth. The bounds are computed for typical values of the error moment and the signal-to-noise ratio (SNR), and the SNR asymptotics of the different bounds are analyzed. The new bounds are compared with known converse and achievability bounds, which were derived from channel coding considerations.

Original language	English
Article number	7869423
Pages (from-to)	3854-3874
Number of pages	21
Journal	IEEE Transactions on Information Theory
Volume	63
Issue number	6
DOIs	https://doi.org/10.1109/TIT.2017.2677461
State	Published - Jun 2017
Externally published	Yes

Keywords

Additive white Gaussian noise (AWGN)
bandwidth constraints
error exponents
modulation
parameter estimation
reliability function

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10.1109/TIT.2017.2677461

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abstract = "The problem of modulating the value of a parameter onto a band-limited signal to be transmitted over a continuous-time, additive white Gaussian noise (AWGN) channel, and then estimating this parameter at the receiver, is considered. The performance is measured by the mean power-α error (MPαE), which is defined as the worst case αth-order moment of the absolute estimation error. The optimal exponential decay rate of the MPαE as a function of the transmission time is investigated. Two upper (converse) bounds on the MP αE exponent are derived, on the basis of known bounds for the AWGN channel of inputs with unlimited bandwidth. The bounds are computed for typical values of the error moment and the signal-to-noise ratio (SNR), and the SNR asymptotics of the different bounds are analyzed. The new bounds are compared with known converse and achievability bounds, which were derived from channel coding considerations.",

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Lower Bounds on Parameter Modulation-Estimation under Bandwidth Constraints

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Keywords

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