82,573 research outputs found
Matched Filtering from Limited Frequency Samples
In this paper, we study a simple correlation-based strategy for estimating
the unknown delay and amplitude of a signal based on a small number of noisy,
randomly chosen frequency-domain samples. We model the output of this
"compressive matched filter" as a random process whose mean equals the scaled,
shifted autocorrelation function of the template signal. Using tools from the
theory of empirical processes, we prove that the expected maximum deviation of
this process from its mean decreases sharply as the number of measurements
increases, and we also derive a probabilistic tail bound on the maximum
deviation. Putting all of this together, we bound the minimum number of
measurements required to guarantee that the empirical maximum of this random
process occurs sufficiently close to the true peak of its mean function. We
conclude that for broad classes of signals, this compressive matched filter
will successfully estimate the unknown delay (with high probability, and within
a prescribed tolerance) using a number of random frequency-domain samples that
scales inversely with the signal-to-noise ratio and only logarithmically in the
in the observation bandwidth and the possible range of delays.Comment: Submitted to the IEEE Transactions on Information Theory on January
13, 201
Channel Sounding for the Masses: Low Complexity GNU 802.11b Channel Impulse Response Estimation
New techniques in cross-layer wireless networks are building demand for
ubiquitous channel sounding, that is, the capability to measure channel impulse
response (CIR) with any standard wireless network and node. Towards that goal,
we present a software-defined IEEE 802.11b receiver and CIR estimation system
with little additional computational complexity compared to 802.11b reception
alone. The system implementation, using the universal software radio peripheral
(USRP) and GNU Radio, is described and compared to previous work. By overcoming
computational limitations and performing direct-sequence spread-spectrum
(DS-SS) matched filtering on the USRP, we enable high-quality yet inexpensive
CIR estimation. We validate the channel sounder and present a drive test
campaign which measures hundreds of channels between WiFi access points and an
in-vehicle receiver in urban and suburban areas
Matching matched filtering with deep networks in gravitational-wave astronomy
We report on the construction of a deep convolutional neural network that can
reproduce the sensitivity of a matched-filtering search for binary black hole
gravitational-wave signals. The standard method for the detection of well
modeled transient gravitational-wave signals is matched filtering. However, the
computational cost of such searches in low latency will grow dramatically as
the low frequency sensitivity of gravitational-wave detectors improves.
Convolutional neural networks provide a highly computationally efficient method
for signal identification in which the majority of calculations are performed
prior to data taking during a training process. We use only whitened time
series of measured gravitational-wave strain as an input, and we train and test
on simulated binary black hole signals in synthetic Gaussian noise
representative of Advanced LIGO sensitivity. We show that our network can
classify signal from noise with a performance that emulates that of match
filtering applied to the same datasets when considering the sensitivity defined
by Reciever-Operator characteristics.Comment: 5 pages, 3 figures, submitted to PR
Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels
We analyze the capacity of a continuous-time, time-selective, Rayleigh
block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading
process is assumed stationary within each block and to change independently
from block to block; furthermore, its realizations are not known a priori to
the transmitter and the receiver (noncoherent setting). A common approach to
analyzing the capacity of this channel is to assume that the receiver performs
matched filtering followed by sampling at symbol rate (symbol matched
filtering). This yields a discrete-time channel in which each transmitted
symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that
the capacity of this discrete-time channel grows logarithmically with the SNR,
with a capacity pre-log equal to . Here, is the number of
symbols transmitted within one fading block, and is the rank of the
covariance matrix of the discrete-time channel gains within each fading block.
In this paper, we show that symbol matched filtering is not a
capacity-achieving strategy for the underlying continuous-time channel.
Specifically, we analyze the capacity pre-log of the discrete-time channel
obtained by oversampling the continuous-time channel output, i.e., by sampling
it faster than at symbol rate. We prove that by oversampling by a factor two
one gets a capacity pre-log that is at least as large as . Since the
capacity pre-log corresponding to symbol-rate sampling is , our result
implies indeed that symbol matched filtering is not capacity achieving at high
SNR.Comment: To appear in the IEEE Transactions on Information Theor
Recommended from our members
Super-Efficient Cross-Correlation (SEC-C): A Fast Matched Filtering Code Suitable for Desktop Computers
Extraction of black hole coalescence waveforms from noisy data
We describe an independent analysis of LIGO data for black hole coalescence
events. Gravitational wave strain waveforms are extracted directly from the
data using a filtering method that exploits the observed or expected
time-dependent frequency content. Statistical analysis of residual noise, after
filtering out spectral peaks (and considering finite bandwidth), shows no
evidence of non-Gaussian behaviour. There is also no evidence of anomalous
causal correlation between noise signals at the Hanford and Livingston sites.
The extracted waveforms are consistent with black hole coalescence template
waveforms provided by LIGO. Simulated events, with known signals injected into
real noise, are used to determine uncertainties due to residual noise and
demonstrate that our results are unbiased. Conceptual and numerical differences
between our RMS signal-to-noise ratios (SNRs) and the published matched-filter
detection SNRs are discussed.Comment: 15 pages, 11 figures. Version accepted for publicatio
Noise in a Calorimeter Readout System Using Periodic Sampling
Fourier transform analysis of the calorimeter noise problem gives
quantitative results on a) the time-height correlation, b) the effect of
background on optimal shaping and on the ENC, c) sampling frequency
requirements, and d) the relation between sampling frequency and the required
quantization error
An excess power statistic for detection of burst sources of gravitational radiation
We examine the properties of an excess power method to detect gravitational
waves in interferometric detector data. This method is designed to detect
short-duration (< 0.5 s) burst signals of unknown waveform, such as those from
supernovae or black hole mergers. If only the bursts' duration and frequency
band are known, the method is an optimal detection strategy in both Bayesian
and frequentist senses. It consists of summing the data power over the known
time interval and frequency band of the burst. If the detector noise is
stationary and Gaussian, this sum is distributed as a chi-squared (non-central
chi-squared) deviate in the absence (presence) of a signal. One can use these
distributions to compute frequentist detection thresholds for the measured
power. We derive the method from Bayesian analyses and show how to compute
Bayesian thresholds. More generically, when only upper and/or lower bounds on
the bursts duration and frequency band are known, one must search for excess
power in all concordant durations and bands. Two search schemes are presented
and their computational efficiencies are compared. We find that given
reasonable constraints on the effective duration and bandwidth of signals, the
excess power search can be performed on a single workstation. Furthermore, the
method can be almost as efficient as matched filtering when a large template
bank is required. Finally, we derive generalizations of the method to a network
of several interferometers under the assumption of Gaussian noise.Comment: 22 pages, 6 figure
- …