arXiv subjects

Sheetal Kalyani

Publications and source records attributed to Sheetal Kalyani.

90 records · Page 5Linked to original sources

arXiv2018

Signal and Noise Statistics Oblivious Orthogonal Matching Pursuit

Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of regression vector or noise statistics. Both these statistics are rarely known \textit{a priori} and are very difficult to estimate. In this paper, we present a novel technique called residual ratio thresholding (RRT) to operate OMP without any \textit{a priori} knowledge of sparsity and noise statistics and establish finite sample and large sample support recovery guarantees for the same. Both analytical results and numerical simulations in real and synthetic data sets indicate that RRT has a performance comparable to OMP with \textit{a priori} knowledge of sparsity and noise statistics.

stat.ML↗

arXiv2018

Analysis of Outage Probability of MRC with $η-μ$ co-channel interference

Approximate outage probability expressions are derived for systems employing maximum ratio combining, when both the desired signal and the interfering signals are subjected to $η-μ$ fading, with the interferers having unequal power. The approximations are in terms of the Appell Function and Gauss hypergeometric function. A close match is observed between the outage probability result obtained through the derived analytical expression and the one obtained through Monte-Carlo simulations.

cs.IT↗

arXiv2018

Residual Ratio Thresholding for Model Order Selection

Model order selection (MOS) in linear regression models is a widely studied problem in signal processing. Techniques based on information theoretic criteria (ITC) are algorithms of choice in MOS problems. This article proposes a novel technique called residual ratio thresholding for MOS in linear regression models which is fundamentally different from the ITC based MOS criteria widely discussed in literature. This article also provides a rigorous mathematical analysis of the high signal to noise ratio (SNR) and large sample size behaviour of RRT. RRT is numerically shown to deliver a highly competitive performance when compared to popular model order selection criteria like Akaike information criterion (AIC), Bayesian information criterion (BIC), penalised adaptive likelihood (PAL) etc. especially when the sample size is small.

cs.IT↗

arXiv2018

Fast, Parameter free Outlier Identification for Robust PCA

Robust PCA, the problem of PCA in the presence of outliers has been extensively investigated in the last few years. Here we focus on Robust PCA in the column sparse outlier model. The existing methods for column sparse outlier model assumes either the knowledge of the dimension of the lower dimensional subspace or the fraction of outliers in the system. However in many applications knowledge of these parameters is not available. Motivated by this we propose a parameter free outlier identification method for robust PCA which a) does not require the knowledge of outlier fraction, b) does not require the knowledge of the dimension of the underlying subspace, c) is computationally simple and fast. Further, analytical guarantees are derived for outlier identification and the performance of the algorithm is compared with the existing state of the art methods.

stat.ML↗

arXiv2017

Outage Probability and Rate for $κ$-$μ$ Shadowed Fading in Interference Limited Scenario

The $κ$-$μ$ shadowed fading model is a very general fading model as it includes both $κ$-$μ$ and $η$-$μ$ as special cases. In this work, we derive the expression for outage probability when the signal-of-interest (SoI) and interferers both experience $κ$-$μ$ shadowed fading in an interference limited scenario. The derived expression is valid for arbitrary SoI parameters, arbitrary $κ$ and $μ$ parameters for all interferers and any value of the parameter $m$ for the interferers excepting the limiting value of $m\rightarrow \infty$. The expression can be expressed in terms of Pochhammer integral where the integrands of integral only contains elementary functions. The outage probability expression is then simplified for various special cases, especially when SoI experiences $η$-$μ$ or $κ$-$μ$ fading. Further, the rate expression is derived when the SoI experiences $κ$-$μ$ shadowed fading with integer values of $μ$, and interferers experience $κ$-$μ$ shadowed fading with arbitrary parameters. The rate expression can be expressed in terms of sum of Lauricella's function of the fourth kind. The utility of our results is demonstrated by using the derived expression to study and compare FFR and SFR in the presence of $κ$-$μ$ shadowed fading. Extensive simulation results are provided and these further validate our theoretical results.

cs.IT↗

arXiv2017

An aggregating strategy for shifting experts in discrete sequence prediction

We study how we can adapt a predictor to a non-stationary environment with advises from multiple experts. We study the problem under complete feedback when the best expert changes over time from a decision theoretic point of view. Proposed algorithm is based on popular exponential weighing method with exponential discounting. We provide theoretical results bounding regret under the exponential discounting setting. Upper bound on regret is derived for finite time horizon problem. Numerical verification of different real life datasets are provided to show the utility of proposed algorithm.

cs.LG↗

arXiv2017

Reinforcement learning techniques for Outer Loop Link Adaptation in 4G/5G systems

Wireless systems perform rate adaptation to transmit at highest possible instantaneous rates. Rate adaptation has been increasingly granular over generations of wireless systems. The base-station uses SINR and packet decode feedback called acknowledgement/no acknowledgement (ACK/NACK) to perform rate adaptation. SINR is used for rate anchoring called inner look adaptation and ACK/NACK is used for fine offset adjustments called Outer Loop Link Adaptation (OLLA). We cast the OLLA as a reinforcement learning problem of the class of Multi-Armed Bandits (MAB) where the different offset values are the arms of the bandit. In OLLA, as the offset values increase, the probability of packet error also increase, and every user equipment (UE) has a desired Block Error Rate (BLER) to meet certain Quality of Service (QoS) requirements. For this MAB we propose a binary search based algorithm which achieves a Probably Approximately Correct (PAC) solution making use of bounds from large deviation theory and confidence bounds. In addition to this we also discuss how a Thompson sampling or UCB based method will not help us meet the target objectives. Finally, simulation results are provided on an LTE system simulator and thereby prove the efficacy of our proposed algorithm.

stat.ML↗

arXiv2017

Taming Non-stationary Bandits: A Bayesian Approach

We consider the multi armed bandit problem in non-stationary environments. Based on the Bayesian method, we propose a variant of Thompson Sampling which can be used in both rested and restless bandit scenarios. Applying discounting to the parameters of prior distribution, we describe a way to systematically reduce the effect of past observations. Further, we derive the exact expression for the probability of picking sub-optimal arms. By increasing the exploitative value of Bayes' samples, we also provide an optimistic version of the algorithm. Extensive empirical analysis is conducted under various scenarios to validate the utility of proposed algorithms. A comparison study with various state-of-the-arm algorithms is also included.

stat.ML↗

arXiv2017

Spectrum Access In Cognitive Radio Using A Two Stage Reinforcement Learning Approach

With the advent of the 5th generation of wireless standards and an increasing demand for higher throughput, methods to improve the spectral efficiency of wireless systems have become very important. In the context of cognitive radio, a substantial increase in throughput is possible if the secondary user can make smart decisions regarding which channel to sense and when or how often to sense. Here, we propose an algorithm to not only select a channel for data transmission but also to predict how long the channel will remain unoccupied so that the time spent on channel sensing can be minimized. Our algorithm learns in two stages - a reinforcement learning approach for channel selection and a Bayesian approach to determine the optimal duration for which sensing can be skipped. Comparisons with other learning methods are provided through extensive simulations. We show that the number of sensing is minimized with negligible increase in primary interference; this implies that lesser energy is spent by the secondary user in sensing and also higher throughput is achieved by saving on sensing.

cs.IT↗

arXiv2017

Signal and Noise Statistics Oblivious Sparse Reconstruction using OMP/OLS

Orthogonal matching pursuit (OMP) and orthogonal least squares (OLS) are widely used for sparse signal reconstruction in under-determined linear regression problems. The performance of these compressed sensing (CS) algorithms depends crucially on the \textit{a priori} knowledge of either the sparsity of the signal ($k_0$) or noise variance ($σ^2$). Both $k_0$ and $σ^2$ are unknown in general and extremely difficult to estimate in under determined models. This limits the application of OMP and OLS in many practical situations. In this article, we develop two computationally efficient frameworks namely TF-IGP and RRT-IGP for using OMP and OLS even when $k_0$ and $σ^2$ are unavailable. Both TF-IGP and RRT-IGP are analytically shown to accomplish successful sparse recovery under the same set of restricted isometry conditions on the design matrix required for OMP/OLS with \textit{a priori} knowledge of $k_0$ and $σ^2$. Numerical simulations also indicate a highly competitive performance of TF-IGP and RRT-IGP in comparison to OMP/OLS with \textit{a priori} knowledge of $k_0$ and $σ^2$.

stat.ML↗

arXiv2017

Impact of Correlation between Interferers on Coverage Probability and rate in Cellular Systems

When the user channel experiences Nakagami-m fading, the coverage probability expressions are theoretically compared for the following cases: (i). The N interferers are independent $η$-$μ$ random variables (RVs). (ii). The N interferers are correlated $η$-$μ$ RVs. It is analytically shown that the coverage probability in the presence of correlated interferers is greater than or equal to the coverage probability in the presence of independent interferers when the shape parameter of the channel between the user and its base station (BS) is not greater than one. Further, rate is compared for the following cases: (i). The user channel experiences $η$-$μ$ RV and the $N$ interferers are independent $η$-$μ$ RVs. (ii). The N interferers are correlated $η$-$μ$ RVs. It is analytically shown that the rate in the presence of correlated interferers is greater than or equal to the rate in the presence of independent interferers. Simulation results are provided and these match with the obtained theoretical results. The utility of our results are also discussed.

cs.IT↗

arXiv2017

Error Vector Magnitude Analysis in Generalized Fading with Co-Channel Interference

In this paper, we derive the data-aided Error Vector Magnitude (EVM) in an interference limited system when both the desired signal and interferers experience independent and non identically distributed $κ$-$μ$ shadowed fading. Then it is analytically shown that the EVM is equal to the square root of number of interferers when the desired signal and interferers do not experience fading. Further, EVM is derived in the presence of interference and noise, when the desired signal experiences $κ$-$μ$ shadowed fading and the interferers experience independent and identical Nakagami fading. Moreover, using the properties of the special functions, the derived EVM expressions are also simplified for various special cases.

cs.IT↗

arXiv2017

Tuning Free Orthogonal Matching Pursuit

Orthogonal matching pursuit (OMP) is a widely used compressive sensing (CS) algorithm for recovering sparse signals in noisy linear regression models. The performance of OMP depends on its stopping criteria (SC). SC for OMP discussed in literature typically assumes knowledge of either the sparsity of the signal to be estimated $k_0$ or noise variance $σ^2$, both of which are unavailable in many practical applications. In this article we develop a modified version of OMP called tuning free OMP or TF-OMP which does not require a SC. TF-OMP is proved to accomplish successful sparse recovery under the usual assumptions on restricted isometry constants (RIC) and mutual coherence of design matrix. TF-OMP is numerically shown to deliver a highly competitive performance in comparison with OMP having \textit{a priori} knowledge of $k_0$ or $σ^2$. Greedy algorithm for robust de-noising (GARD) is an OMP like algorithm proposed for efficient estimation in classical overdetermined linear regression models corrupted by sparse outliers. However, GARD requires the knowledge of inlier noise variance which is difficult to estimate. We also produce a tuning free algorithm (TF-GARD) for efficient estimation in the presence of sparse outliers by extending the operating principle of TF-OMP to GARD. TF-GARD is numerically shown to achieve a performance comparable to that of the existing implementation of GARD.

stat.ML↗

arXiv2017

High SNR Consistent Compressive Sensing

High signal to noise ratio (SNR) consistency of model selection criteria in linear regression models has attracted a lot of attention recently. However, most of the existing literature on high SNR consistency deals with model order selection. Further, the limited literature available on the high SNR consistency of subset selection procedures (SSPs) is applicable to linear regression with full rank measurement matrices only. Hence, the performance of SSPs used in underdetermined linear models (a.k.a compressive sensing (CS) algorithms) at high SNR is largely unknown. This paper fills this gap by deriving necessary and sufficient conditions for the high SNR consistency of popular CS algorithms like $l_0$-minimization, basis pursuit de-noising or LASSO, orthogonal matching pursuit and Dantzig selector. Necessary conditions analytically establish the high SNR inconsistency of CS algorithms when used with the tuning parameters discussed in literature. Novel tuning parameters with SNR adaptations are developed using the sufficient conditions and the choice of SNR adaptations are discussed analytically using convergence rate analysis. CS algorithms with the proposed tuning parameters are numerically shown to be high SNR consistent and outperform existing tuning parameters in the moderate to high SNR regime.

stat.ML↗

arXiv2014

Rate Prediction and Selection in LTE systems using Modified Source Encoding Techniques

In current wireless systems, the base-Station (eNodeB) tries to serve its user-equipment (UE) at the highest possible rate that the UE can reliably decode. The eNodeB obtains this rate information as a quantized feedback from the UE at time n and uses this, for rate selection till the next feedback is received at time n + δ. The feedback received at n can become outdated before n + δ, because of a) Doppler fading, and b) Change in the set of active interferers for a UE. Therefore rate prediction becomes essential. Since, the rates belong to a discrete set, we propose a discrete sequence prediction approach, wherein, frequency trees for the discrete sequences are built using source encoding algorithms like Prediction by Partial Match (PPM). Finding the optimal depth of the frequency tree used for prediction is cast as a model order selection problem. The rate sequence complexity is analysed to provide an upper bound on model order. Information-theoretic criteria are then used to solve the model order problem. Finally, two prediction algorithms are proposed, using the PPM with optimal model order and system level simulations demonstrate the improvement in packet loss and throughput due to these algorithms.

stat.AP↗

arXiv2014

Impact of Correlation between Nakagami-m Interferers on Coverage Probability and Rate in Cellular Systems

Coverage probability and rate expressions are theoretically compared for the following cases: $(i).$ Both the user channel and the $N$ interferers are independent and non identical Nakagami-m distributed random variables (RVs). $(ii).$ The $N$ interferers are correlated Nakagami-m RVs. It is analytically shown that the coverage probability in the presence of correlated interferers is greater than or equal to the coverage probability in the presence of non-identical independent interferers when the shape parameter of the channel between the user and its base station is not greater than one. It is further analytically shown that the average rate in the presence of correlated interferers is greater than or equal to the average rate in the presence of non-identical independent interferers. Simulation results are provided and these match with the obtained theoretical results. The utility of our results are also discussed.

cs.IT↗

arXiv2014

Spectrum Allocation for ICIC Based Picocell

In this work, we analytically study the impact of spectrum allocation scheme in picocells on the coverage probability (CP) of the Pico User (PU), when the macro base stations (MBSs) employ either fractional frequency reuse (FFR) or soft frequency reuse (SFR). Assuming a fixed size for the picocell, the CP expression is derived for a PU present in either a FFR or SFR based deployment, and when the PU uses either the centre or the edge frequency resources. Based on these expressions, we propose two possible frequency allocation schemes for the picocell when FFR is employed by the macrocell. The CP and the average rate expressions for both these schemes are derived, and it is shown that these schemes outperform the conventional scheme where no inter-cell interference coordination (ICIC) is assumed. The impact of both schemes on the macro-user performance is also analysed. When SFR is used by the MBS, it is shown that the CP is maximized when the PU uses the same frequency resources as used by the centre region.

cs.IT↗

arXiv2014

Optimal Thresholds for Coverage and Rate in FFR Schemes for Planned Cellular Networks

Fractional frequency reuse (FFR) is an inter-cell interference coordination scheme that is being actively researched for emerging wireless cellular networks. In this work, we consider hexagonal tessellation based planned FFR deployments, and derive expressions for the coverage probability and normalized average rate for the downlink. In particular, given reuse $\frac{1}{3}$ (FR$3$ ) and reuse $1$ (FR$1$) regions, and a Signal-to-Interference-plus-noise-Ratio (SINR) threshold $S_{th}$ which decides the user assignment to either the FR$1$ or FR$3$ regions, we theoretically show that: $(i)$ The optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$, where $T$ is the required target SINR (for ensuring coverage), and $(ii)$ The optimal choice of $S_{th}$ which maximizes the normalized average rate is given by the expression $S_{th}=\max(T, T')$, where $T'$ is a function of the path loss exponent and the fade parameters. For the optimal choice of $S_{th}$, we show that FFR gives a higher rate than FR$1$ and a better coverage probability than FR$3$. The impact of frequency correlation over the sub-bands allocated to the FR$1$ and FR$3$ regions is analysed, and it is shown that correlation decreases the average rate of the FFR network. Numerical results are provided, and these match with the analytical results.

cs.IT↗