arXiv subjects

Animesh Kumar

Publications and source records attributed to Animesh Kumar.

25 records · Page 2Linked to original sources

arXiv2016

Bandlimited Spatial Field Sampling with Mobile Sensors in the Absence of Location Information

Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and proposes solutions to a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations? Unknown sampling location, sample quantization, unknown bandwidth of the field, and presence of measurement-noise present difficulties in the process of field estimation. In this work, except for quantization, the other three issues will be tackled together in a mobile-sampling framework. Spatially bandlimited fields are considered. It is assumed that measurement-noise affected field samples are collected on spatial locations obtained from an unknown renewal process. That is, the samples are obtained on locations obtained from a renewal process, but the sampling locations and the renewal process distribution are unknown. In this unknown sampling location setup, it is shown that the mean-squared error in field estimation decreases as $O(1/n)$ where $n$ is the average number of samples collected by the mobile sensor. The average number of samples collected is determined by the inter-sample spacing distribution in the renewal process. An algorithm to ascertain spatial field's bandwidth is detailed, which works with high probability as the average number of samples $n$ increases. This algorithm works in the same setup, i.e., in the presence of measurement-noise and unknown sampling locations.

cs.IT↗

arXiv2015

Optimal Quantization of TV White Space Regions for a Broadcast Based Geolocation Database

In the current paradigm, TV white space databases communicate the available channels over a reliable Internet connection to the secondary devices. For places where an Internet connection is not available, such as in developing countries, a broadcast based geolocation database can be considered. This geolocation database will broadcast the TV white space (or the primary services protection regions) on rate-constrained digital channel. In this work, the quantization or digital representation of protection regions is considered for rate-constrained broadcast geolocation database. Protection regions should not be declared as white space regions due to the quantization error. In this work, circular and basis based approximations are presented for quantizing the protection regions. In circular approximation, quantization design algorithms are presented to protect the primary from quantization error while minimizing the white space area declared as protected region. An efficient quantizer design algorithm is presented in this case. For basis based approximations, an efficient method to represent the protection regions by an `envelope' is developed. By design this envelope is a sparse approximation, i.e., it has lesser number of non-zero coefficients in the basis when compared to the original protection region. The approximation methods presented in this work are tested using three experimental data-sets.

cs.IT↗

arXiv2013

Quantitative Assessment of TV White Space in India

Licensed but unutilized television (TV) band spectrum is called as TV white space in the literature. Ultra high frequency (UHF) TV band spectrum has very good wireless radio propagation characteristics. The amount of TV white space in the UHF TV band in India is of interest. Comprehensive quantitative assessment and estimates for the TV white space in the 470-590MHz band for four zones of India (all except north) are presented in this work. This is the first effort in India to estimate TV white spaces in a comprehensive manner. The average available TV white space per unit area in these four zones is calculated using two methods: (i) the primary (licensed) user and secondary (unlicensed) user point of view; and, (ii) the regulations of Federal Communications Commission in the United States. By both methods, the average available TV white space in the UHF TV band is shown to be more than 100MHz! A TV transmitter frequency-reassignment algorithm is also described. Based on spatial-reuse ideas, a TV channel allocation scheme is presented which results in insignicant interference to the TV receivers while using the least number of TV channels for transmission across the four zones. Based on this reassignment, it is found that four TV band channels (or 32MHz) are sufficient to provide the existing UHF TV band coverage in India.

cs.IT↗

arXiv2013

Bandlimited Signal Reconstruction From the Distribution of Unknown Sampling Locations

We study the reconstruction of bandlimited fields from samples taken at unknown but statistically distributed sampling locations. The setup is motivated by distributed sampling where precise knowledge of sensor locations can be difficult. Periodic one-dimensional bandlimited fields are considered for sampling. Perfect samples of the field at independent and identically distributed locations are obtained. The statistical realization of sampling locations is not known. First, it is shown that a bandlimited field cannot be uniquely determined with samples taken at statistically distributed but unknown locations, even if the number of samples is infinite. Next, it is assumed that the order of sample locations is known. In this case, using insights from order-statistics, an estimate for the field with useful asymptotic properties is designed. Distortion (mean-squared error) and central-limit are established for this estimate.

cs.IT↗

arXiv2012

Estimation of Bandlimited Signals in Additive Gaussian Noise: a "Precision Indifference" Principle

The sampling, quantization, and estimation of a bounded dynamic-range bandlimited signal affected by additive independent Gaussian noise is studied in this work. For bandlimited signals, the distortion due to additive independent Gaussian noise can be reduced by oversampling (statistical diversity). The pointwise expected mean-squared error is used as a distortion metric for signal estimate in this work. Two extreme scenarios of quantizer precision are considered: (i) infinite precision (real scalars); and (ii) one-bit quantization (sign information). If $N$ is the oversampling ratio with respect to the Nyquist rate, then the optimal law for distortion is $O(1/N)$. We show that a distortion of $O(1/N)$ can be achieved irrespective of the quantizer precision by considering the above-mentioned two extreme scenarios of quantization. Thus, a quantization precision indifference principle is discovered, where the reconstruction distortion law, up to a proportionality constant, is unaffected by quantizer's accuracy.

cs.IT↗

arXiv2012

On the Separability of Targets Using Binary Proximity Sensors

We consider the problem where a network of sensors has to detect the presence of targets at any of $n$ possible locations in a finite region. All such locations may not be occupied by a target. The data from sensors is fused to determine the set of locations that have targets. We term this the separability problem. In this paper, we address the separability of an asymptotically large number of static target locations by using binary proximity sensors. Two models for target locations are considered: (i) when target locations lie on a uniformly spaced grid; and, (ii) when target locations are i.i.d. uniformly distributed in the area. Sensor locations are i.i.d uniformly distributed in the same finite region, independent of target locations. We derive conditions on the sensing radius and the number of sensors required to achieve separability. Order-optimal scaling laws, on the number of sensors as a function of the number of target locations, for two types of separability requirements are derived. The robustness or security aspects of the above problem is also addressed. It is shown that in the presence of adversarial sensors, which toggle their sensed reading and inject binary noise, the scaling laws for separability remain unaffected.

cs.IT↗

arXiv2008

High-resolution distributed sampling of bandlimited fields with low-precision sensors

The problem of sampling a discrete-time sequence of spatially bandlimited fields with a bounded dynamic range, in a distributed, communication-constrained, processing environment is addressed. A central unit, having access to the data gathered by a dense network of fixed-precision sensors, operating under stringent inter-node communication constraints, is required to reconstruct the field snapshots to maximum accuracy. Both deterministic and stochastic field models are considered. For stochastic fields, results are established in the almost-sure sense. The feasibility of having a flexible tradeoff between the oversampling rate (sensor density) and the analog-to-digital converter (ADC) precision, while achieving an exponential accuracy in the number of bits per Nyquist-interval per snapshot is demonstrated. This exposes an underlying ``conservation of bits'' principle: the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed along the amplitude axis (sensor-precision) and space (sensor density) in an almost arbitrary discrete-valued manner, while retaining the same (exponential) distortion-rate characteristics. Achievable information scaling laws for field reconstruction over a bounded region are also derived: With N one-bit sensors per Nyquist-interval, $Θ(\log N)$ Nyquist-intervals, and total network bitrate $R_{net} = Θ((\log N)^2)$ (per-sensor bitrate $Θ((\log N)/N)$), the maximum pointwise distortion goes to zero as $D = O((\log N)^2/N)$ or $D = O(R_{net} 2^{-β\sqrt{R_{net}}})$. This is shown to be possible with only nearest-neighbor communication, distributed coding, and appropriate interpolation algorithms. For a fixed, nonzero target distortion, the number of fixed-precision sensors and the network rate needed is always finite.

cs.IT↗