31,078 research outputs found
Robust one-bit compressed sensing with partial circulant matrices
We present optimal sample complexity estimates for one-bit compressed sensing
problems in a realistic scenario: the procedure uses a structured matrix (a
randomly sub-sampled circulant matrix) and is robust to analog pre-quantization
noise as well as to adversarial bit corruptions in the quantization process.
Our results imply that quantization is not a statistically expensive procedure
in the presence of nontrivial analog noise: recovery requires the same sample
size one would have needed had the measurement matrix been Gaussian and the
noisy analog measurements been given as data
An Optimal Family of Exponentially Accurate One-Bit Sigma-Delta Quantization Schemes
Sigma-Delta modulation is a popular method for analog-to-digital conversion
of bandlimited signals that employs coarse quantization coupled with
oversampling. The standard mathematical model for the error analysis of the
method measures the performance of a given scheme by the rate at which the
associated reconstruction error decays as a function of the oversampling ratio
. It was recently shown that exponential accuracy of the form
can be achieved by appropriate one-bit Sigma-Delta
modulation schemes. By general information-entropy arguments must be less
than 1. The current best known value for is approximately 0.088. The
schemes that were designed to achieve this accuracy employ the "greedy"
quantization rule coupled with feedback filters that fall into a class we call
"minimally supported". In this paper, we study the minimization problem that
corresponds to optimizing the error decay rate for this class of feedback
filters. We solve a relaxed version of this problem exactly and provide
explicit asymptotics of the solutions. From these relaxed solutions, we find
asymptotically optimal solutions of the original problem, which improve the
best known exponential error decay rate to . Our method draws
from the theory of orthogonal polynomials; in particular, it relates the
optimal filters to the zero sets of Chebyshev polynomials of the second kind.Comment: 35 pages, 3 figure
Optimal sampling and quantization of synthetic aperture radar signals
Some theoretical and experimental results on optimal sampling and quantization of synthetic aperture radar (SAR) signals are presented. It includes a description of a derived theoretical relationship between the pixel signal to noise ratio of processed SAR images and the number of quantization bits per sampled signal, assuming homogeneous extended targets. With this relationship known, a solution may be realized for the problem of optimal allocation of a fixed data bit-volume (for specified surface area and resolution criterion) between the number of samples and the number of bits per sample. The results indicate that to achieve the best possible image quality for a fixed bit rate and a given resolution criterion, one should quantize individual samples coarsely and thereby maximize the number of multiple looks. The theoretical results are then compared with simulation results obtained by processing aircraft SAR data
On The Performance Of 1-Bit ADC In Massive MIMO Communication Systems
Massive multiple-input multiple-output (MIMO) with low-resolution analog-to-digital converters is a rational solution to deal with hardware costs and accomplish optimal energy efficiency. In particular, utilizing 1-bit ADCs is one of the best choices for massive MIMO systems. This paper investigates the performance of the 1-bit ADC in the wireless coded communication systems where the robust channel coding, protograph low-density parity-check code (LDPC), is employed. The investigation reveals that the performance of the conventional 1-bit ADC with the truncation limit of 3-sigma is severely destroyed by the quantization distortion even when the number of antennas increases to 100. The optimized 1-bit ADC, though having substantial performance gain over the conventional one, is also affected by the quantization distortion at high coding rates and low MIMO configurations. Importantly, the investigation results suggest that the protograph LDPC codes should be re-designed to combat the negative effect of the quantization distortion of the 1-bit ADC
Mean Estimation from One-Bit Measurements
We consider the problem of estimating the mean of a symmetric log-concave
distribution under the constraint that only a single bit per sample from this
distribution is available to the estimator. We study the mean squared error as
a function of the sample size (and hence the number of bits). We consider three
settings: first, a centralized setting, where an encoder may release bits
given a sample of size , and for which there is no asymptotic penalty for
quantization; second, an adaptive setting in which each bit is a function of
the current observation and previously recorded bits, where we show that the
optimal relative efficiency compared to the sample mean is precisely the
efficiency of the median; lastly, we show that in a distributed setting where
each bit is only a function of a local sample, no estimator can achieve optimal
efficiency uniformly over the parameter space. We additionally complement our
results in the adaptive setting by showing that \emph{one} round of adaptivity
is sufficient to achieve optimal mean-square error
- …