Large deviations for eigenvalues of sample covariance matrices, with applications to mobile communication systems

We study sample covariance matrices of the form $W=\frac 1n C C^T$, where $C$ is a $k\times n$ matrix with i.i.d. mean zero entries. This is a generalization of so-called Wishart matrices, where the entries of $C$ are independent and identically distributed standard normal random variables. Such matrices arise in statistics as sample covariance matrices, and the high-dimensional case, when $k$ is large, arises in the analysis of DNA experiments. We investigate the large deviation properties of the largest and smallest eigenvalues of $W$ when either $k$ is fixed and $n\to \infty$, or $k_n\to \infty$ with $k_n=o(n/\log\log{n})$, in the case where the squares of the i.i.d. entries have finite exponential moments. Previous results, proving a.s. limits of the eigenvalues, only require finite fourth moments. Our most explicit results for $k$ large are for the case where the entries of $C$ are $\pm1$ with equal probability. We relate the large deviation rate functions of the smallest and largest eigenvalue to the rate functions for independent and identically distributed standard normal entries of $C$. This case is of particular interest, since it is related to the problem of the decoding of a signal in a code division multiple access system arising in mobile communication systems. In this example, $k$ plays the role of the number of users in the system, and $n$ is the length of the coding sequence of each of the users. Each user transmits at the same time and uses the same frequency, and the codes are used to distinguish the signals of the separate users. The results imply large deviation bounds for the probability of a bit error due to the interference of the various users.Comment: corrected some typing errors, and extended Theorem 3.1 to Wishart matrices; to appear in Advances of Applied Probabilit

Linear interference cancellation in CDMA systems and large deviations of the correlation matrix eigenvalues

We analytically compute a measure of performance of various linear Parallel Interference Cancellation (PIC) decoding schemes in the infinite stage limit, for moderately loaded CDMA systems without AWGN, or with a sufficiently small amount of AWGN. This measure is the exponential rate of the BEP, which does not involve Gaussian approximations. We obtain these rates using large deviation theory for the eigenvalues of the code correlation matrix. We find that the decorrelator performs best, followed by infinitestage SD-PIC, which is found to perform better than infinite stage HD-PIC

LTE-verkon suorituskyvyn parantaminen CDMA2000:sta LTE:hen tehdyn muutoksen jälkeen

CDMA2000 technology has been widely used on 450 MHz band. Recently the equipment availability and improved performance offered by LTE has started driving the operators to migrate their networks from CDMA2000 to LTE. The migration may cause the network performance to be in suboptimal state. This thesis presents four methods to positively influence LTE network performance after CDMA2000 to LTE migration, especially on 450 MHz band. Furthermore, three of the four presented methods are evaluated in a live network. The measured three methods were cyclic prefix length, handover parameter optimization and uplink coordinated multipoint (CoMP) transmission. The objective was to determine the effectiveness of each method. The research methods included field measurements and network KPI collection. The results show that normal cyclic prefix length is enough for LTE450 although the cell radius may be up to 50km. Only special cases exist where cyclic prefix should be extended. Operators should consider solving such problems individually instead of widely implementing extended cyclic prefix. Handover parameter optimization turned out to be an important point of attention after CDMA2000 to LTE migration. It was observed that if the handover parameters are not concerned, significant amount of unnecessary handovers may happen. It was evaluated that about 50% of the handovers in the network were unnecessary in the initial situation. By adjusting the handover parameter values 47,28 % of the handovers per user were removed and no negative effects were detected. Coordinated multipoint transmission has been widely discussed to be an effective way to improve LTE network performance, especially at the cell edges. Many challenges must be overcome before it can be applied to downlink. Also, implementing it to function between cells in different eNBs involve challenges. Thus, only intra-site uplink CoMP transmission was tested. The results show that the performance improvements were significant at the cell edges as theory predicted.CDMA2000 teknologiaa on laajalti käytetty 450 MHz:n taajuusalueella. Viime aikoina LTE:n tarjoamat halvemmat laitteistot ja parempi suorituskyky ovat kannustaneet operaattoreita muuttamaan verkkoaan CDMA2000:sta LTE:hen. Kyseinen muutos saattaa johtaa epäoptimaaliseen tilaan verkon suorituskyvyn kannalta. Tämä työ esittelee neljä menetelmää, joilla voidaan positiivisesti vaikuttaa LTE-verkon suorituskykyyn CDMA2000:ste LTE:hen tehdyn muutoksen jälkeen erityisesti 450 MHz:n taajuusalueella. Kolmea näistä menetelmistä arvioidaan tuotantoverkossa. Nämä kolme menetelmää ovat suojavälin pituus, solunvaihtoparametrien optimointi ja ylälinkin koordinoitu monipistetiedonsiirto. Tavoite oli määrittää kunkin menetelmän vaikutus. Tutkimusmenetelmiin kuului kenttämittaukset ja verkon suorituskykymittareiden analyysi. Tutkimustulosten perusteella voidaan sanoa, että normaali suojaväli on riittävän pitkä LTE450:lle vaikka solujen säde on jopa 50km. Vain erikoistapauksissa tarvitaan pidennettyä suojaväliä. Operaattoreiden tulisi ratkaista tällaiset tapaukset yksilöllisesti sen sijaan, että koko verkossa käytettäisiin pidennettyä suojaväliä. Solunvaihtoparametrien optimointi osoittautui tärkeäksi huomion aiheeksi CDMA2000:sta LTE:hen tehdyn muutoksen jälkeen. Turhia solunvaihtoja saattaa tapahtua merkittäviä määriä, mikäli parametreihin ei kiinnitetä huomiota. Lähtötilanteessa noin 50 % testiverkon solunvaihdoista arvioitiin olevan turhia. Solunvaihtoparametreja muuttamalla 47,28 % solunvaihdoista per käyttäjä saatiin poistettua ilman, että mitään haittavaikutuksia olisi huomattu. Koordinoidun monipistetiedonsiirron on laajalti sanottu olevan tehokas tapa parantaa LTE-verkon suorituskykyä, etenkin solujen reunoilla. Monia haasteita pitää ratkaista, enne kuin sitä voidaan käyttää alalinkin tiedonsiirtoon. Lisäksi sen käyttöön eri tukiasemien solujen välillä liittyy haasteita. Tästä syystä monipistetiedonsiirtoa voitiin testata vain ylälinkin suuntaan ja vain yhden tukiaseman välisten solujen kesken. Tulokset osoittivat, että suorituskyky parani merkittävästi solun reunalla

A survey of self organisation in future cellular networks

This article surveys the literature over the period of the last decade on the emerging field of self organisation as applied to wireless cellular communication networks. Self organisation has been extensively studied and applied in adhoc networks, wireless sensor networks and autonomic computer networks; however in the context of wireless cellular networks, this is the first attempt to put in perspective the various efforts in form of a tutorial/survey. We provide a comprehensive survey of the existing literature, projects and standards in self organising cellular networks. Additionally, we also aim to present a clear understanding of this active research area, identifying a clear taxonomy and guidelines for design of self organising mechanisms. We compare strength and weakness of existing solutions and highlight the key research areas for further development. This paper serves as a guide and a starting point for anyone willing to delve into research on self organisation in wireless cellular communication networks

A Study about Heterogeneous Network Issues Management based on Enhanced Inter-cell Interference Coordination and Machine Learning Algorithms

Under the circumstance of fast growing demands for mobile data, Heterogeneous Networks (HetNets) has been considered as one of the key technologies to solve 1000 times mobile data challenge in the coming decade. Although the unique multi-tier topology of HetNets has achieved high spectrum efficiency and enhanced Quality of Service (QoS), it also brings a series of critical issues. In this thesis, we present an investigation on understanding the cause of HetNets challenges and provide a research on state of arts techniques to solve three major issues: interference, offloading and handover. The first issue addressed in the thesis is the cross-tier interference of HetNets. We introduce Almost Blank Subframes (ABS) to free small cell UEs from cross-tier interference, which is the key technique of enhanced Inter-Cell Interference Coordination (eICIC). Nash Bargain Solution (NBS) is applied to optimize ABS ratio and UE partition. Furthermore, we propose a power based multi-layer NBS Algorithm to obtain optimal parameters of Further enhanced Inter-cell Interference Coordination (FeICIC), which significantly improve macrocell efficiency compared to eICIC. This algorithm not only introduces dynamic power ratio but also defined opportunity cost for each layer instead of conventional zero-cost partial fairness. Simulation results show the performance of proposed algorithm may achieve up to 31.4% user throughput gain compared to eICIC and fixed power ratio FeICIC. This thesis’ second focusing issue is offloading problem of HetNets. This includes (1) UE offloading from macro cell and (2) small cell backhaul offloading. For first aspect, we have discussed the capability of machine learning algorithms tackling this challenge and propose the User-Based K-means Algorithm (UBKCA). The proposed algorithm establishes a closed loop Self-Organization system on our HetNets scenario to maintain desired offloading factor of 50%, with cell edge user factor 17.5% and CRE bias of 8dB. For second part, we further apply machine learning clustering method to establish cache system, which may achieve up to 70.27% hit-ratio and reduce request latency by 60.21% for Youtube scenario. K-Nearest Neighbouring (KNN) is then applied to predict new users’ content preference and prove our cache system’s suitability. Besides that, we have also proposed a system to predict users’ content preference even if the collected data is not complete. The third part focuses on offloading phase within HetNets. This part detailed discusses CRE’s positive effect on mitigating ping-pong handover during UE offloading, and CRE’s negative effect on increasing cross-tier interference. And then a modified Markov Chain Process is established to map the handover phases for UE to offload from macro cell to small cell and vice versa. The transition probability of MCP has considered both effects of CRE so that the optimal CRE value for HetNets can be achieved, and result for our scenario is 7dB. The combination of CRE and Handover Margin is also discussed