806,697 research outputs found
Sequential joint signal detection and signal-to-noise ratio estimation
The sequential analysis of the problem of joint signal detection and
signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model
is considered. The problem is posed as an optimization setup where the goal is
to minimize the number of samples required to achieve the desired (i) type I
and type II error probabilities and (ii) mean squared error performance. This
optimization problem is reduced to a more tractable formulation by transforming
the observed signal and noise sequences to a single sequence of Bernoulli
random variables; joint detection and estimation is then performed on the
Bernoulli sequence. This transformation renders the problem easily solvable,
and results in a computationally simpler sufficient statistic compared to the
one based on the (untransformed) observation sequences. Experimental results
demonstrate the advantages of the proposed method, making it feasible for
applications having strict constraints on data storage and computation.Comment: 5 pages, Proceedings of IEEE International Conference on Acoustics,
Speech, and Signal Processing (ICASSP), 201
Signal-to-noise ratio of Gaussian-state ghost imaging
The signal-to-noise ratios (SNRs) of three Gaussian-state ghost imaging
configurations--distinguished by the nature of their light sources--are
derived. Two use classical-state light, specifically a joint signal-reference
field state that has either the maximum phase-insensitive or the maximum
phase-sensitive cross correlation consistent with having a proper
representation. The third uses nonclassical light, in particular an entangled
signal-reference field state with the maximum phase-sensitive cross correlation
permitted by quantum mechanics. Analytic SNR expressions are developed for the
near-field and far-field regimes, within which simple asymptotic approximations
are presented for low-brightness and high-brightness sources. A high-brightness
thermal-state (classical phase-insensitive state) source will typically achieve
a higher SNR than a biphoton-state (low-brightness, low-flux limit of the
entangled-state) source, when all other system parameters are equal for the two
systems. With high efficiency photon-number resolving detectors, a
low-brightness, high-flux entangled-state source may achieve a higher SNR than
that obtained with a high-brightness thermal-state source.Comment: 12 pages, 4 figures. This version incorporates additional references
and a new analysis of the nonclassical case that, for the first time,
includes the complete transition to the classical signal-to-noise ratio
asymptote at high source brightnes
Signal-to-Noise Ratio in Squeezed-Light Laser Radar
The formalism for computing the signal-to-noise ratio (SNR) for laser radar
is reviewed and applied to the tasks of target detection, direction-finding,
and phase change estimation with squeezed light. The SNR for heterodyne
detection of coherent light using a squeezed local oscillator is lower than
that obtained using a coherent local oscillator. This is true for target
detection, for phase estimation, and for direction-finding with a split
detector. Squeezing the local oscillator also lowers SNR in balanced homodyne
and heterodyne detection of coherent light. Loss places an upper bound on the
improvement that squeezing can bring to direct-detection SNR.Comment: Typos correcte
Bounds on Portfolio Quality
The signal-noise ratio of a portfolio of p assets, its expected return
divided by its risk, is couched as an estimation problem on the sphere. When
the portfolio is built using noisy data, the expected value of the signal-noise
ratio is bounded from above via a Cramer-Rao bound, for the case of Gaussian
returns. The bound holds for `biased' estimators, thus there appears to be no
bias-variance tradeoff for the problem of maximizing the signal-noise ratio. An
approximate distribution of the signal-noise ratio for the Markowitz portfolio
is given, and shown to be fairly accurate via Monte Carlo simulations, for
Gaussian returns as well as more exotic returns distributions. These findings
imply that if the maximal population signal-noise ratio grows slower than the
universe size to the 1/4 power, there may be no diversification benefit, rather
expected signal-noise ratio can decrease with additional assets. As a practical
matter, this may explain why the Markowitz portfolio is typically applied to
small asset universes. Finally, the theorem is expanded to cover more general
models of returns and trading schemes, including the conditional expectation
case where mean returns are linear in some observable features, subspace
constraints (i.e., dimensionality reduction), and hedging constraints
Optimization of a Third-Order Gradiometer for Operation in Unshielded Environments
The optimum geometry of a third-order gradiometer for operation in unshielded environments is discussed. The optimization result depends on the specific signal and noise conditions. The fetal heart is considered as an example of the signal source. We optimized the gradiometer such that the signal-to-noise ratio is maximized in an averaged sense for all relevant environmental noise conditions and distances to the signal source. The resulting design consists of two second-order gradiometers that can be combined to form a third-order gradiometer in noisy environments, whereas a single second-order gradiometer can be used in low-noise environments. The gradiometer can provide the signal-to-noise ratio that allows detection of fetal heart signals in all relevant environmental noise conditions
- …