Multi-tier Network Performance Analysis using a Shotgun Cellular System

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 CIR 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.Comment: 6 pages, 3 figures, accepted at IEEE Globecom 201

The E3 ubiquitin ligase c-IAP1 regulates PCSK9-mediated LDLR degradation: Linking the TNF-α pathway to cholesterol uptake

Proprotein convertase subtilisin/kexin type 9 (PCSK9), in addition to LDLR (low-density lipoprotein receptor) and APOB (apolipoprotein B), is one of three loci implicated in autosomal dominant hypercholesterolaemia (ADH)^1^. A number of PCSK9 gain-of-function mutations and loss-of-function mutations have been identified from families afflicted with ADH with hypercholesterolaemia or hypocholesterolaemia, respectively^1-4^. In humans, the main function of PCSK9 appears to be the post-transcriptional regulation of the number of cell-surface LDL receptors^5-7^. To date, only LDLR and its closest family members VLDLR and ApoER2 have been shown to bind with PCSK9^8,9^. To find new binding partners for PCSK9, we used a shotgun proteomic method to analyse the protein complex pulled down by immunoprecipitation against FLAG-tagged PCSK9 protein. Among 22 potential novel binding proteins identified, we found that the cellular inhibitor of apoptosis protein 1 (c-IAP1^10^) and the TNF receptor-associated factor 2 (TRAF2^11^) complex are regulated differently in different dominant PCSK9 mutations that occur naturally. Further immunoprecipitation analysis showed that c-IAP1 is a direct binding partner for PCSK9. One of the "gain-of-function" mutants, PCSK9-S127R, which has impaired autocatalytic activity, is defective in binding to c-IAP1. The other dominant mutation, PCSK9-D374Y^12^, which is 10-fold more potent in degrading the LDLR protein than wild-type PCSK9, can be significantly ubiquitinated by c-IAP1 in vitro. The ubiquitinated PCSK9-D374Y is unable to degrade LDLR, which is its main cause of hypercholesterolaemia in patients. These results indicate that there is a novel cholesterol uptake regulation pathway linking PCSK9/LDLR to the E3 ubiquitin ligase c-IAP1 in a TNF-[alpha] response pathway. This highlights the possibility of developing new treatments for human cardiovascular diseases through ubiquitin ligase-mediated ubiquitination of target proteins in cholesterol metabolism

Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels - A Stochastic Geometry Approach

In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.Comment: Accepted for publication in IEEE Transactions on Communications, to appea

Wireless networks appear Poissonian due to strong shadowing

Geographic locations of cellular base stations sometimes can be well fitted with spatial homogeneous Poisson point processes. In this paper we make a complementary observation: In the presence of the log-normal shadowing of sufficiently high variance, the statistics of the propagation loss of a single user with respect to different network stations are invariant with respect to their geographic positioning, whether regular or not, for a wide class of empirically homogeneous networks. Even in perfectly hexagonal case they appear as though they were realized in a Poisson network model, i.e., form an inhomogeneous Poisson point process on the positive half-line with a power-law density characterized by the path-loss exponent. At the same time, the conditional distances to the corresponding base stations, given their observed propagation losses, become independent and log-normally distributed, which can be seen as a decoupling between the real and model geometry. The result applies also to Suzuki (Rayleigh-log-normal) propagation model. We use Kolmogorov-Smirnov test to empirically study the quality of the Poisson approximation and use it to build a linear-regression method for the statistical estimation of the value of the path-loss exponent

Laplace Functional Ordering of Point Processes in Large-scale Wireless Networks

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless networks. It is shown that the ordering of point processes is preserved under independent operations such as marking, thinning, clustering, superposition, and random translation. Laplace functional ordering can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions of such metrics are unavailable. Applications in several network scenarios are also provided where tradeoffs between coverage and interference as well as fairness and peakyness are studied. Monte-Carlo simulations are used to supplement our analytical results.Comment: 30 pages, 5 figures, Submitted to Hindawi Wireless Communications and Mobile Computin