Prasanna Madhusudhanan

Downlink Performance Analysis for a Generalized Shotgun Cellular System

In this paper, we analyze the signal-to-interference-plus-noise ratio (SINR) performance at a mobile station (MS) in a random cellular network. The cellular network is formed by base-stations (BSs) placed in a one, two or three dimensional space according to a possibly non-homogeneous Poisson point process, which is a generalization of the so-called shotgun cellular system. We develop a sequence of equivalence relations for the SCSs and use them to derive semi-analytical expressions for the coverage probability at the MS when the transmissions from each BS may be affected by random fading with arbitrary distributions as well as attenuation following arbitrary path-loss models. For homogeneous Poisson point processes in the interference-limited case with power-law path-loss model, we show that the SINR distribution is the same for all fading distributions and is not a function of the base station density. In addition, the influence of random transmission powers, power control, multiple channel reuse groups on the downlink performance are also discussed. The techniques developed for the analysis of SINR have applications beyond cellular networks and can be used in similar studies for cognitive radio networks, femtocell networks and other heterogeneous and multi-tier networks.

Downlink coverage analysis in a heterogeneous cellular network

In this paper, we consider the downlink signal-to-interference-plus-noise ratio (SINR) analysis in a heterogeneous cellular network with K tiers. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain BS density, transmission power, random shadow fading factors with arbitrary distribution, arbitrary path-loss exponent and a certain bias towards admitting the mobile-station (MS). The MS associates with the BS that has the maximum instantaneous biased received power under the open access cell association scheme. For such a general setting, we provide an analytical characterization of the coverage probability at the MS.

Carrier to Interference Ratio Analysis for the Shotgun Cellular System

This paper analyzes the carrier-to-interference ratio of the so-called shotgun cellular system (SCS). In the SCS, base-stations are placed randomly according to a two-dimensional Poisson point process. Such a system can model a dense cellular or wireless data network deployment, where the base station locations end up being close to random due to constraints other than optimal coverage. The SCS is a simple cellular system where we can introduce several variations and design scenarios such as shadow fading, power control features, and multiple channel reuse groups, and assess their impact on the performance. We first derive an analytical expression for the characteristic function of the inverse of the carrier-to-interference ratio. Using this result, we show that the carrier-to-interference ratio is independent of the base station density and further, we derive a semi-analytical expression for the tail-probability. These results enable a complete characterization of the cellular performance of the SCS. Next, we incorporate shadow fading into the SCS and demonstrate that it merely scales the base station density by a constant. Hence, the cellular performance of the SCS is independent of shadow fading. These results are further used to analyze dense cellular scenarios.

Multi-Tier Network Performance Analysis Using a Shotgun Cellular System

Abstract--- This paper studies the carrier-to-interference ratio (CIR) and carrier-to-interference-plus-noise ratio (CINR) performance at the mobile station (MS) within a multi-tier network composed of M tiers of wireless networks, with each tier modeled as the homogeneous n-dimensional (n-D, n=1,2, and 3) shotgun cellular system, where the base station (BS) distribution is given by the homogeneous Poisson point process in n-D. The CIR and CINR at the MS in a single tier network are thoroughly analyzed to simplify the analysis of the multi-tier network. For the multi-tier network with given system parameters, the following are the main results of this paper: (1) semi-analytical expressions for the tail probabilities of CIR and CINR; (2) a closed form expression for the tail probability of CIR in the range [1,infinity); (3) a closed form expression for the tail probability of an approximation to CINR in the entire range [0,infinity); (4) a lookup table based approach for obtaining the tail probability of CINR, and (5) the study of the effect of shadow fading and BSs with ideal sectorized antennas on the CIR and CINR. Based on these results, it is shown that, in a practical cellular system, the installation of additional wireless networks (microcells, picocells and femtocells) with low power BSs over the already existing macrocell network will always improve the CINR performance at the MS.

Stochastic Ordering Based Carrier-to-Interference Ratio Analysis for the Shotgun Cellular Systems

An analytical tool based on usual stochastic ordering is developed to compare the distributions of carrier-to-interference ratio at the mobile station of cellular systems where the base stations are distributed randomly according to certain non-homogeneous Poisson point processes. The comparison is done by studying the base station densities without having to solve for the distributions of the carrier-to-interference ratio, which are often hard to obtain.

Modeling of Interference from Cooperative Cognitive Radios for Low Power Primary Users

Cognitive radios (CR) must ensure that their transmissions do not cause harmful interference to the primary users that operate in the same band. Primary users with short communication range transmitters, such as wireless microphone systems, are considered. The CR network is distributed according to a Poisson process. The CRs detect the primary user either through primary transmitter signals or through beacons collocated with the primary receiver. Three levels of cooperative sensing by CRs are analyzed, namely, no cooperation, full cooperation and partial cooperation. The characteristic function of the interference at the primary receiver for all combinations of primary user detection and cooperative sensing schemes are derived for the system modeled along a line (1-D) and about a plane (2-D). The analysis in 1-D corresponds to a highway scenario and 2-D corresponds to a planar system. The carrier-to-interference ratio (C/I) at the primary receiver is evaluated using the characteristic function. The analysis clearly shows the need for cooperative spectrum sensing when the density of the CRs is high. It is shown that the effect of shadowing, small scale fading, and power control at the CRs can be captured into the density of the CR network. The results hold for the CRs that are wide-band devices as well as narrow-band devices.

Analysis of Downlink Connectivity Models in a Heterogeneous Cellular Network via Stochastic Geometry

In this paper, a comprehensive study of the downlink performance in a heterogeneous cellular network (or HetNet) is conducted via stochastic geometry. A general HetNet model is considered consisting of an arbitrary number of open-access and closed-access tiers of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs within each tier have a constant transmission power, random fading factors with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability are derived for the max-SINR connectivity and nearest-BS connectivity models. Using stochastic ordering, interesting properties and simplifications for the HetNet downlink performance are derived by relating these two connectivity models to the maximum instantaneous received power (MIRP) connectivity model and the maximum biased received power (MBRP) connectivity models, providing good insights about HetNets and their downlink performance in these complex networks. Furthermore, the results also demonstrate the effectiveness and analytical tractability of the stochastic geometric approach to study the HetNet performance.

Heterogeneous cellular network performance analysis under open and closed access

We study the downlink signal-to-interference ratio (SIR) in a multi-tier heterogeneous cellular network under the open and closed access schemes. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain density, constant transmission power and random shadow fading factors with arbitrary distribution. The mobile-station (MS) communicates with the BS that has the maximum instantaneous received power among those to which it is allowed access. The chosen BS provides coverage to the MS if the SIR is above a certain threshold determined by the BSs tier. The coverage probability and average rate expressions are derived for the open access scheme for any arbitrary SIR threshold assigned for each tier, and for the closed access scheme when the SIR thresholds are greater than one.

On Primary User Coverage Probabilities and Faulty Cognitive Radios

In a cognitive radio (CR) network, the CR devices opportunistically communicate in the frequency bands occupied by the primary users in order to improve the spectral efficiency in these bands. By sensing the primary users, e.g., the television transmitter-receiver pairs and the wireless microphone systems, each CR device determines whether or not to operate in the band. The CR devices, due to erroneous sensing, either fail to detect the primary user, causing excessive interference at the primary users, or have a false-alarm, causing it to remain silent in a white-space band leading to poor spectrum utility. The impact of these imperfections on the primary user operations in terms of the coverage probability is characterized where the primary users and the CR devices are distributed according to independent homogeneous Poisson point processes on the plane.

On the interference due to cooperative cognitive radios in the presence of multiple low-power primary users

We analyze a cognitive radio network where the low-power primary users and cognitive radio (CR) devices are distributed according to two independent homogeneous Poisson processes over the k-dimensional space, where k = 1, 2, 3. The CRs cooperate among themselves in detecting the beacons transmitted by the primary users, to ensure that they cause reduced interference at the primary users. A range of cooperative sensing schemes including the no (NC), partial (PC) and full cooperation (FC) scenarios are analyzed. Using the concepts of stochastic geometry, we assess the impact of the presence of the multiple primary users on the distribution of the signal-to-interference-plus-noise ratio (SINR) at a given primary user, for each cooperation scheme. Further, we characterize the improvement in the spectrum usage due to the CR operation in the licensed frequency band in terms of the probability, denoted by rho, that a CR is able to operate within the k-dimensional space. Using our calculations of the SINR at the primary user and rho, it is shown that the PC scheme achieves enhanced spectrum usage vis-a-vis the FC scheme and an improved SINR as compared to the NC scheme. Moreover, the PC scheme can be tuned in such a way that any desired value for spectrum usage and SINR is achievable.