arXiv subjects

Sudarshan Guruacharya

Publications and source records attributed to Sudarshan Guruacharya.

16 recordsLinked to original sources

arXiv2020

Optimal Non-Coherent Detector for Ambient Backscatter Communication System

The probability density function (pdf) of the received signal of an ambient backscatter communication system is derived, assuming that on-off keying (OOK) is performed at the tag, and that the ambient radio frequency (RF) signal is white Gaussian. The pdf of the received signal is then utilized to design two different types of non-coherent detectors. The first detector directly uses the received signal to perform a hypothesis test. The second detector first estimates the channel based on the observed signal and then performs the hypothesis test. Test statistics and optimal decision threshold of the detectors are derived. The energy detector is shown to be an approximation of the second detector. For cases where the reader is able to avoid or cancel the direct interference from the RF source (e.g., through successive interference cancellation), a third detector is given as a special case of the first detector. Numerical results show that both the first and the second detectors have the same bit error rate (BER) performance, making the second detector preferable over the first detector due to its computational simplicity.

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arXiv2018

Resource Allocation for Co-Primary Spectrum Sharing in MIMO Networks

We study co-primary spectrum sharing concept in two small cell multiuser network. Downlink transmission is explored with Rayleigh fading in interfering broadcast channel. Both base stations and all the users are equipped with multiple antennas. Resource allocation with joint precoder and decoder design is proposed for weighted sum rate (WSR) maximization problem. The problem becomes mixed-integer and non-convex. We factor the main objective problem into two subproblems. First subproblem is multiuser with subcarrier allocation where we assume that each subcarrier can be allocated to multiple users. Gale-Shapley algorithm based on stable marriage problem and transportation method are implemented for subcarrier allocation part. For the second subproblem, a joint precoder and decoder design is proposed to obtain the optimal solution for WSR maximization. Monte Carlo simulation is employed to obtain the results.

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arXiv2018

On Spectrum Sharing Among Micro-Operators in 5G

The growing demand in indoor small cell networks has given rise to the concept of micro-operators (MOs) for local service delivery. We model and analyze a spectrum sharing system involving such MOs where a buyer MO buys multiple licensed subbands provided by the regulator. Also, all small cell base stations (SBSs) owned by a buyer MO can utilize multiple licensed subbands at the same time which are also used by other MOs. A deterministic model in which the location of the SBSs are known can lead to unwieldy problem formulation, when the number of SBSs is large. Subsequently, we adopt a stochastic geometric model of the SBS deployment instead of a deterministic model. Assuming that the locations of the SBSs can be modeled as a homogeneous Poisson point process, we find the downlink signal-to-interference-plus-noise ratio (SINR) coverage probability and average data rate for a typical user (UE) served by the buyer MO in a spectrum sharing environment. In order to satisfy the QoS constraint, we provide a greedy algorithm to find how many licensed subbands and which subband for the buyer MO to purchase from the regulator. We also derive the coverage probability of the buyer MO for interference the limited system.

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arXiv2018

Inter-Operator Infrastructure Sharing: Trade-offs and Market

We model the problem of infrastructure sharing among mobile network operators (MNOs) as a multiple-seller single-buyer market where the MNOs are able to share their own base stations (BSs) with each other. First, we use techniques from stochastic geometry to find the coverage probability of the infrastructure sharing system and analyze the trade-off between increasing the transmit power of a BS and the BS intensity of a buyer MNO required to achieve a given quality-of-service (QoS) in terms of the coverage probability. We also analyze the power consumption of the network per unit area (i.e., areal power consumption) and show that it is a piecewise continuous function composed of a linear and a convex functions. We show that when the transmit power of the BSs and/or the BS intensity of a network increases, the system becomes interference limited and the coverage probability tends to saturate at a certain value. As such, when the required QoS is set above this bound, an MNO can improve its coverage by buying infrastructure from other MNOs. Subsequently, we analyze the strategy of a buyer MNO on choosing how many MNOs and which MNOs to buy the infrastructure from. The optimal strategy of the buyer is given by greedy fractional knapsack algorithm. On the sellers' side, the pricing and the fraction of infrastructure to be sold are formulated using a Cournot oligopoly game.

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arXiv2018

Edge Caching for Cache Intensity under Probabilistic Delay Constraint

In order to reduce the latency of data delivery, one of techniques is to cache the popular contents at the base stations (BSs) i.e. edge caching. However, the technique of caching at edge can only reduce the backhaul delay, other techniques such as BS densification will also need to be considered to reduce the fronthaul delay. In this work, we study the trade-offs between BS densification and cache size under delay constraint at a typical user (UE). For this, we use the downlink SINR coverage probability and throughput obtained based on stochastic geometrical analysis. The network deployment of BS and cache storage is introduced as a minimization problem of the product of the BS intensity and cache size which we refer to the product of \tit{cache intensity}' under probabilistic delay constraint. We examine the cases when (i) either BS intensity or the cache size is held fixed, and (ii) when both BS intensity and the cache size are vary. For the case when both BS intensity and the cache size are variable, the problem become nonconvex and we convert into a geometric programing which we solve it analytically.

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arXiv2018

Level-Triggered Harvest-then-Consume Protocol with Two Bits or Less Energy State Information

We propose a variation of harvest-then-consume protocol with low complexity where the harvest and consume phases change when the battery energy level reaches certain thresholds. The proposed protocol allows us to control the possible energy outage during consumption phase. Assuming that the battery is perfect and that the energy arrival is a renewal process, we analyze the duty cycle and the operating cycle speed of the protocol. The proposed protocol also allows for limited battery energy state information. The cases when the system has two-bits, one-bit, and zero-bit of battery energy state information are studied in detail. Numerical simulations verify the obtained formulas.

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arXiv2018

Approximation of Meta Distribution and Its Moments for Poisson Cellular Networks

The notion of meta distribution as the distribution of the conditional coverage probability (CCP) was introduced in \cite{Haenggi2015}. In this letter, we show how we can reconstruct the entire meta distribution only from its moments using Fourier-Jacobi expansion. As an example, we specifically consider Poisson cellular networks. We also provide a simple closed-form approximation for its moments, along with its error analysis. Lastly, we apply the approximation to obtain a power scaling law for downlink Poisson cellular networks.

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arXiv2018

Battery Recharge Time of a Stochastic Linear and Non-Linear Energy Harvesting System

Systems harvesting energy from a stochastic source have been widely studied in the literature. However, we are not aware of any work that deals with the time it takes for a battery to recharge up to a given level, when the energy source is discrete stochastic. This letter aims to examine the recharge time of a perfect battery. We examine the cases when the energy arrival is a Poisson process, and more generally, a renewal process. We obtain formulas for the distribution of the recharge time as well as the expected value of the recharge time. Using these, we find the switching time of the system, which is then applied to the design of a harvest-then-transmit protocol for green communications. Monte-Carlo simulations verify the obtained formulas.

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arXiv2018

Self-Sustainability of Energy Harvesting Systems: Concept, Analysis, and Design

Ambient energy harvesting is touted as a low cost solution to prolong the life of low-powered devices, reduce the carbon footprint, and make the system self-sustainable. Most research to date have focused either on the physical aspects of energy conversion process or on optimal consumption policy of the harvested energy at the system level. However, although intuitively understood, to the best of our knowledge, the idea of self-sustainability is yet to be made precise and studied as a performance metric. In this paper, we provide a mathematical definition of the concept of self-sustainability of an energy harvesting system, based on the complementary idea of eventual outage. In particular, we analyze the harvest-store-consume system with infinite battery capacity, stochastic energy arrivals, and fixed energy consumption rate. Using the random walk theory, we identify the necessary condition for the system to be self-sustainable. General formulas are given for the self-sustainability probability in the form of integral equations. Since these integral equations are difficult to solve analytically, an exponential upper bound for eventual outage probability is given using martingales. This bound guarantees that the eventual outage probability can be made arbitrarily small simply by increasing the initial battery energy. We also give an asymptotic formula for eventual outage. For the special case when the energy arrival follows a Poisson process, we are able to find the exact formulas for the eventual outage probability. We also show that the harvest-store-consume system is mathematically equivalent to a $GI/G/1$ queueing system, which allows us to easily find the outage probability, in case the necessary condition for self-sustainability is violated. Monte-Carlo simulations verify our analysis.

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arXiv2018

Edge Caching in Delay-Constrained Virtualized Cellular Networks: Analysis and Market

Caching of popular contents at cellular base stations, i.e., edge caching, in order to eliminate duplicate transmission through the backhaul can reduce the latency of data delivery in $5$G networks. However, since caching can only reduce the backhaul delay, techniques such as base station densification will also need to be used to reduce the fronthaul delay. In this paper, using results from stochastic geometry, we first model the effects of base station densification and cache size on the latency of the system. We then derive a tight approximation for the cache hit probability. To optimize the network cost due to the deployment of base station (BS) and cache storage, a minimization problem for the product of the BS intensity and cache size is formulated under probabilistic delay constraint, which is converted into a geometric program and solved analytically. The results are then used to analyze the economics of a cache-enabled virtualized cellular network where the network infrastructure, i.e., BSs and cache storage, owned by an infrastructure provider (InP) is shared among multiple mobile network operators (MNOs). For the pricing between the InP and the MNOs, we formulate a Stackelberg game with the InP as the leader and multiple MNOs as the followers. In this virtualized scenario, the common cost of renting the infrastructure is shared in a fair manner among the MNOs by using the Shapely value. An efficient algorithm is provided to divide the rent among MNOs.

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arXiv2017

Infrastructure Sharing for Mobile Network Operators: Analysis of Trade-offs and Market

The conflicting problems of growing mobile service demand and underutilization of dedicated spectrum has given rise to a paradigm where mobile network operators (MNOs) share their infrastructure among themselves in order to lower their operational costs, while at the same time increase the usage of their existing network resources. We model and analyze such an infrastructure sharing system considering a single buyer MNO and multiple seller MNOs. Assuming that the locations of the BSs can be modeled as a homogeneous Poisson point process, we find the downlink signal-to-interference-plus-noise ratio (SINR) coverage probability for a user served by the buyer MNO in an infrastructure sharing environment. We analyze the trade-off between increasing the transmit power of a BS and the intensity of BSs owned by the buyer MNO required to achieve a given quality-of-service (QoS) in terms of the SINR coverage probability. Also, for a seller MNO, we analyze the power consumption of the network per unit area (i.e., areal power consumption) which is shown to be a piecewise continuous function of BS intensity, composed of a linear and a convex function. Accordingly, the BS intensity of the seller MNO can be optimized to minimize the areal power consumption while achieving a minimum QoS for the buyer MNO. We then use these results to formulate a single-buyer multiple-seller BS infrastructure market. The buyer MNO is concerned with finding which seller MNO to purchase from and what fraction of BSs to purchase. On the sellers' side, the problem of pricing and determining the fraction of infrastructure to be sold is formulated as a Cournot oligopoly market. We prove that the iterative update of each seller's best response always converges to the Nash Equilibrium.

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arXiv2017

SINR Outage Evaluation in Cellular Networks: Saddle Point Approximation (SPA) Using Normal Inverse Gaussian (NIG) Distribution

Signal-to-noise-plus-interference ratio (SINR) outage probability is among one of the key performance metrics of a wireless cellular network. In this paper, we propose a semi-analytical method based on saddle point approximation (SPA) technique to calculate the SINR outage of a wireless system whose SINR can be modeled in the form $\frac{\sum_{i=1}^M X_i}{\sum_{i=1}^N Y_i +1}$ where $X_i$ denotes the useful signal power, $Y_i$ denotes the power of the interference signal, and $\sum_{i=1}^M X_i$, $\sum_{i=1}^N Y_i$ are independent random variables. Both $M$ and $N$ can also be random variables. The proposed approach is based on the saddle point approximation to cumulative distribution function (CDF) as given by \tit{Wood-Booth-Butler formula}. The approach is applicable whenever the cumulant generating function (CGF) of the received signal and interference exists, and it allows us to tackle distributions with large skewness and kurtosis with higher accuracy. In this regard, we exploit a four parameter \tit{normal-inverse Gaussian} (NIG) distribution as a base distribution. Given that the skewness and kurtosis satisfy a specific condition, NIG-based SPA works reliably. When this condition is violated, we recommend SPA based on normal or symmetric NIG distribution, both special cases of NIG distribution, at the expense of reduced accuracy. For the purpose of demonstration, we apply SPA for the SINR outage evaluation of a typical user experiencing a downlink coordinated multi-point transmission (CoMP) from the base stations (BSs) that are modeled by homogeneous Poisson point process. We characterize the outage of the typical user in scenarios such as (a)~when the number and locations of interferers are random, and (b)~when the fading channels and number of interferers are random. Numerical results are presented to illustrate the accuracy of the proposed set of approximations.

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arXiv2016

Multi-Operator Spectrum Sharing for Small Cell Networks : A Matching Game Perspective

One of the many problems faced by current cellular network technology is the under utilization of the dedicated, licensed spectrum of network operators. An emerging paradigm to solve this issue is to allow multiple operators to share some parts of each others' spectrum. Previous works on spectrum sharing have failed to integrate the theoretical insights provided by recent developments in stochastic geometrical approaches to cellular network analysis with the objectives of network resource allocation problems. In this paper, we study the non-orthogonal spectrum assignment with the goal of maximizing the social welfare of the network, defined as the expected weighted sum rate of the operators. We adopt the many-to-one stable matching game framework to tackle this problem. Moreover, using the stochastic geometrical approach, we show that its solution can be both stable as well as socially optimal. This allows for computation of the game theoretical solution using generic Markov Chain Monte Carlo method. We also investigate the role of power allocation schemes using Q-learning, and we numerically show that the effect of resource allocation scheme is much more significant than the effect of power allocation for the social welfare of the system.

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arXiv2016

Analysis of SINR Outage in Large-Scale Cellular Networks Using Campbell's Theorem and Cumulant Generating Functions

The signal-to-noise-plus-interference ratio (SINR) outage probability is one of the key performance parameters of a wireless cellular network, and its analytical as well as numerical evaluation has occupied many researchers. Recently, the introduction of stochastic geometric modeling of cellular networks has brought the outage problem to the forefront again. A popular and powerful approach is to exploit the available moment generating function (or Laplace transform) of received signal and interference, whenever it exists, by applying the Gil-Pelaez inversion formula. However, with the stochastic geometric modeling, the moment generating function may either be too complicated to exist in closed-form or at worst may not exist. Toward this end, in this paper, we study two alternate ways of evaluating the SINR outage. In the first case, we emphasize the significance of calculating cumulants over moments and exploit the fact that the cumulants of point processes are easily calculable using Campbell's theorem. The SINR outage is then analytically characterized by Charlier expansion based on Gaussian and Student's $t$-distributions and their associated Hermite and Krishnamoorthy polynomials. In the second case, we exploit the saddle point method, which gives a semi-analytical method of calculating the SINR outage, whenever the cumulant generating function of received signal and interference exists. For the purpose of demonstration, we apply these techniques on a downlink cellular network model where a typical user experiences a coordinated multi-point transmission, and the base stations are modeled by homogeneous Poisson point process. For the convenience of readers, we also provide a brief overview of moments, cumulants, their generating functions, and Campbell's theorem, without invoking measure theory. Numerical results illustrate the accuracy of the proposed mathematical approaches.

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arXiv2015

Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions

This letter proposes the use of saddle point approximation (SPA) to evaluate the outage probability of wireless cellular networks. Unlike traditional numerical integration-based approaches, the SPA approach relies on cumulant generating functions (CGFs) and eliminates the need for explicit numerical integration. The approach is generic and can be applied to a wide variety of distributions, given that their CGFs exist. We illustrate the usefulness of SPA on channel fading distributions such as Nakagami-$m$, Nakagami-$q$ (Hoyt), and Rician distributions. Numerical results validate the accuracy of the proposed SPA approach.

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arXiv2015

Integral Approximations for Coverage Probability

This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B x^{α/2}) \} \ud x$. Four different approximations are studied. For systems that are interference-limited or noise-limited, conditions are identified when the approximations are valid. For intermediate cases, we recommend the use of Laplace approximation. Numerical results validate the accuracy of the approximations.

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