arXiv subjects

Lin Dai

Publications and source records attributed to Lin Dai.

34 records · Page 2Linked to original sources

arXiv2019

Coherence Statistics of Structured Random Ensembles and Support Detection Bounds for OMP

A structured random matrix ensemble that maintains constant modulus entries and unit-norm columns, often called a random phase-rotated (RPR) matrix, is considered in this paper. We analyze the coherence statistics of RPR measurement matrices and apply them to acquire probabilistic performance guarantees of orthogonal matching pursuit (OMP) for support detection (SD). It is revealed via numerical simulations that the SD performance guarantee provides a tight characterization, especially when the signal is sparse.

eess.SP↗

arXiv2019

Throughput Analysis of CSMA: Technical Report

In this technical report, the throughput performance of CSMA networks with two representative receiver structures, i.e., the collision model and the capture model, is characterized and optimized. The analysis is further applied to an IEEE 802.11 network, which is a representative wireless network that adopts the CSMA mechanism, where the optimal initial backoff window sizes of nodes to achieve the maximum network throughput are derived and verified against simulation results.

cs.NI↗

arXiv2018

Maximum Sum Rate of Slotted Aloha with Successive Interference Cancellation

This is a sequel of our previous work [8] on characterization of maximum sum rate of slotted Aloha networks. By extending the analysis to incorporate the capacity-achieving receiver structure, Successive Interference Cancellation (SIC), this paper aims to identify the rate loss due to random access. Specifically, two representative SIC receivers are considered, i.e, ordered SIC where packets are decoded in a descending order of their received power, and unordered SIC where packets are decoded in a random order. The maximum sum rate and the corresponding optimal parameter setting including the transmission probability and the information encoding rate in both cases are obtained as functions of the mean received signal-to-noise ratio (SNR). The comparison to the capture model shows that the gains are significant only with the ordered SIC at moderate values of the mean received SNR $ρ$. With a large $ρ$, the rate gap diminishes, and they all have the same high-SNR slope of $e^{-1}$, which is far below that of the ergodic sum capacity of fading channels. The effect of multipacket reception (MPR) on the sum rate performance is also studied by comparing the MPR receivers including SIC and the capture model to the classical collision model.

cs.IT↗

arXiv2017

Quarkonium Polarization and the Long Distance Matrix Elements Hierarchies using Jet Substructure

We investigate the quarkonium production mechanisms in jets at the LHC, using the Fragmenting Jet Functions (FJF) approach. Specifically, we discuss the jet energy dependence of the $J/ψ$ production cross section at the LHC. By comparing the cross sections for the different NRQCD production channels ($^1S_0^{[8]}$,$^3S_1^{[8]}$,$^3P_J^{[8]}$, and $^3S_1^{[1]}$), we find that at fixed values of energy fraction $z$ carried by the $J/ψ$, if the normalized cross section is a decreasing function of the jet energy, in particular for $z > 0.5$, then the depolarizing $^1S_0^{[8]}$ must be the dominant channel. This makes the prediction made in [Baumgart et al., JHEP 1411, 003 (2014)] for the FJF's also true for the cross section. We also make comparisons between the long distance matrix elements extracted by various groups. This analysis could potentially shed light on the polarization properties of the $J/ψ$ production in high $p_T$ region.

hep-ph↗

arXiv2017

NRQCD Confronts LHCb Data on Quarkonium Production within Jets

We analyze the recent LHCb measurement of the distribution of the fraction of the transverse momentum, $z(J/ψ)$, carried by the $J/ψ$ within a jet. LHCb data is compared to analytic calculations using the fragmenting jet function (FJF) formalism for studying $J/ψ$ in jets. Logarithms in the FJFs are resummed using DGLAP evolution. We also convolve hard QCD partonic cross sections, showered with PYTHIA, with leading order Non Relativistic Quantum Chromodynamics (NRQCD) fragmentation functions and obtain consistent results. Both approaches use Madgraph to calculate the hard process that creates the jet initiating parton. These calculations give reasonable agreement with the $z(J/ψ)$ distribution that was shown to be poorly described by default PYTHIA simulations in the LHCb paper. We compare our predictions for the $J/ψ$ distribution using various extractions of nonperturbative NRQCD long-distance matrix elements (LDMEs) in the literature. NRQCD calculations agree with LHCb data better than default PYTHIA regardless of which fit to the LDMEs is used. LDMEs from fits that focus exclusively on high transverse momentum data from colliders are in good agreement with the LHCb measurement.

hep-ph↗

arXiv2017

Fragmentation to a jet in the large $z$ limit

We consider the fragmentation of a parton into a jet with small radius $R$ in the large $z$ limit, where $z$ is the ratio of the jet energy to the mother parton energy. In this region of phase space, large logarithms of both $R$ and $1-z$ can appear, requiring resummation in order to have a well defined perturbative expansion. Using soft-collinear effective theory, we study the fragmentation function to a jet (FFJ) in this endpoint region. We derive a factorization theorem for this object, separating collinear and collinear-soft modes. This allows for the resummation using renormalization group evolution of the logarithms $\ln R$ and $\ln(1-z)$ simultaneously. We show results valid to next-to-leading logarithmic order for the global Sudakov logarithms. We also discuss the possibility of non-global logarithms that should appear at two-loops and give an estimate of their size.

hep-ph↗

arXiv2016

Fragmentation of a Jet with Small Radius

In this paper we consider the fragmentation of a parton into a jet with small jet radius $R$. Perturbatively, logarithms of $R$ can appear, which for narrow jets can lead to large corrections. Using soft-collinear effective theory, we introduce the fragmentation function to a jet (FFJ), which describes the fragmentation of a parton into a jet. We discuss how these objects are related to the standard jet functions. Calculating the FFJ to next-to-leading order, we show that these objects satisfy the standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations, with a natural scale that depends upon $R$. By using the standard renormalization group evolution, we can therefore resum logarithms of $R$. We further use the soft-collinear effective theory to prove a factorization theorem where the FFJs naturally appear, for the fragmentation of a hadron within a jet with small $R$. Finally, we also show how this formalism can be used to resum the ratio of jet radii for a subjet to be emitted from within a fat jet.

hep-ph↗

arXiv2016

Analytic and Monte Carlo Studies of Jets with Heavy Mesons and Quarkonia

We study jets with identified hadrons in which a family of jet-shape variables called angularities are measured, extending the concept of fragmenting jet functions (FJFs) to these observables. FJFs determine the fraction of energy, z, carried by an identified hadron in a jet with angularity, τ_a. The FJFs are convolutions of fragmentation functions (FFs), evolved to the jet energy scale, with perturbatively calculable matching coefficients. Renormalization group equations are used to provide resummed calculations with next-to-leading logarithm prime (NLL') accuracy. We apply this formalism to two-jet events in e^+ e^- collisions with B mesons in the jets, and three-jet events in which a J/ψis produced in the gluon jet. In the case of B mesons, we use a phenomenological FF extracted from e^+ e^- collisions at the Z^0 pole evaluated at the scale μ= m_b. For events with J/ψ, the FF can be evaluated in terms of Non-Relativistic QCD (NRQCD) matrix elements at the scale μ=2 m_c. The z and τ_a distributions from our NLL' calculations are compared with predictions from monte carlo event generators. While we find consistency between the predictions for B mesons and the J/ψdistributions in τ_a, we find the z distributions for J/ψdiffer significantly. We describe an attempt to merge PYTHIA showers with NRQCD FFs that gives good agreement with NLL' calculations of the z distributions.

hep-ph↗

arXiv2015

Maximum Sum Rate of Slotted Aloha with Capture

The sum rate performance of random-access networks crucially depends on the access protocol and receiver structure. Despite extensive studies, how to characterize the maximum sum rate of the simplest version of random access, Aloha, remains an open question. In this paper, a comprehensive study of the sum rate performance of slotted Aloha networks is presented. By extending the unified analytical framework proposed in [20], [21] from the classical collision model to the capture model, the network steady-state point in saturated conditions is derived as a function of the signal-to-interference-plus-noise ratio (SINR) threshold which determines a fundamental tradeoff between the information encoding rate and the network throughput. To maximize the sum rate, both the SINR threshold and backoff parameters of nodes should be properly selected. Explicit expressions of the maximum sum rate and the optimal setting are obtained, which show that similar to the sum capacity of the multiple access channel, the maximum sum rate of slotted Aloha also logarithmically increases with the mean received signal-to-noise ratio (SNR), but the high-SNR slope is only $e^{-1}$. Effects of backoff and power control on the sum rate performance of slotted Aloha networks are further discussed, which shed important light on the practical network design.

cs.IT↗

arXiv2015

Downlink Rate Analysis for Virtual-Cell based Large-Scale Distributed Antenna Systems

Despite substantial rate gains achieved by coordinated transmission from a massive amount of geographically distributed antennas, the resulting computational cost and channel measurement overhead could be unaffordable for a large-scale distributed antenna system (DAS). A scalable signal processing framework is therefore highly desirable, which, as recently demonstrated in \cite{Dai_TWireless}, could be established based on the concept of virtual cell. In a virtual-cell based DAS, each user chooses a few closest base-station (BS) antennas to form its virtual cell, that is, its own serving BS antenna set. In this paper, we focus on a downlink DAS with a large number of users and BS antennas uniformly distributed in a certain area, and aim to study the effect of the virtual cell size on the average user rate. Specifically, by assuming that maximum ratio transmission (MRT) is adopted in each user's virtual cell, the achievable ergodic rate of each user is derived as an explicit function of the large-scale fading coefficients from all the users to their virtual cells, and an upper-bound of the average user rate is established, based on which a rule of thumb is developed for determining the optimal virtual cell size to maximize the average user rate. The analysis is further extended to consider multiple users grouped together and jointly served by their virtual cells using zero-forcing beamforming (ZFBF). In contrast to the no-grouping case where a small virtual cell size is preferred, it is shown that by grouping users with overlapped virtual cells, the average user rate can be significantly improved by increasing the virtual cell size, though at the cost of a higher signal processing complexity.

cs.IT↗

arXiv2014

A Comparative Study of Downlink MIMO Cellular Networks with Co-located and Distributed Base-Station Antennas

Despite the common belief that substantial capacity gains can be achieved by using more antennas at the base-station (BS) side in cellular networks, the effect of BS antenna topology on the capacity scaling behavior is little understood. In this paper, we present a comparative study on the ergodic capacity of a downlink single-user multiple-input-multiple-output (MIMO) system where BS antennas are either co-located at the center or grouped into uniformly distributed antenna clusters in a circular cell. By assuming that the number of BS antennas and the number of user antennas go to infinity with a fixed ratio $L\gg 1$, the asymptotic analysis reveals that the average per-antenna capacities in both cases logarithmically increase with $L$, but in the orders of $\log_2 L$ and $\tfracα{2}\log_2 L$, for the co-located and distributed BS antenna layouts, respectively, where $α>2$ denotes the path-loss factor. The analysis is further extended to the multi-user case where a 1-tier (7-cell) MIMO cellular network with $K\gg 1$ uniformly distributed users in each cell is considered. By assuming that the number of BS antennas and the number of user antennas go to infinity with a fixed ratio $L\gg K$, an asymptotic analysis is presented on the downlink rate performance with block diagonalization (BD) adopted at each BS. It is shown that the average per-antenna rates with the co-located and distributed BS antenna layouts scale in the orders of $\log_2 \tfrac{L}{K}$ and $\log_2 \frac{(L-K+1)^{α/2}}{K}$, respectively. The rate performance of MIMO cellular networks with small cells is also discussed, which highlights the importance of employing a large number of distributed BS antennas for the next-generation cellular networks.

cs.IT↗

arXiv2013

Asymptotic Rate Analysis of Downlink Multi-user Systems with Co-located and Distributed Antennas

A great deal of efforts have been made on the performance evaluation of distributed antenna systems (DASs). Most of them assume a regular base-station (BS) antenna layout where the number of BS antennas is usually small. With the growing interest in cellular systems with large antenna arrays at BSs, it becomes increasingly important for us to study how the BS antenna layout affects the rate performance when a massive number of BS antennas are employed. This paper presents a comparative study of the asymptotic rate performance of downlink multi-user systems with multiple BS antennas either co-located or uniformly distributed within a circular cell. Two representative linear precoding schemes, maximum ratio transmission (MRT) and zero-forcing beamforming (ZFBF), are considered, with which the effect of BS antenna layout on the rate performance is characterized. The analysis shows that as the number of BS antennas $L$ and the number of users $K$ grow infinitely while $L/K{\rightarrow}\upsilon$, the asymptotic average user rates with the co-located antenna (CA) layout for both MRT and ZFBF are logarithmic functions of the ratio $\upsilon$. With the distributed antenna (DA) layout, in contrast, the scaling behavior of the average user rate closely depends on the precoding schemes. With ZFBF, for instance, the average user rate grows unboundedly as $L, K{\rightarrow} \infty$ and $L/K{\rightarrow}\upsilon{>}1$, which indicates that substantial rate gains over the CA layout can be achieved when the number of BS antennas $L$ is large. The gain, nevertheless, becomes marginal when MRT is adopted.

cs.IT↗

arXiv2009

Buffered Aloha with K-Exponential Backoff -- Part I: Stability and Throughput Analysis

This two-part paper series studies the performance of buffered Aloha networks with K-Exponential Backoff collision resolution algorithms. Part I focuses on stability and throughput analysis and Part II presents the delay analysis. In Part I, the buffered Aloha network is modeled as a multi-queue single-server system. We adopt a widely used approach in packet switching systems to decompose the multi-queue system into independent first-in-first-out (FIFO) queues, which are hinged together by the probability of success of head-of-line (HOL) packets. A unified method is devised to tackle the stability and throughput problems of K-Exponential Backoff with any cutoff phase K. We demonstrate that a network with K-Exponential Backoff can be stabilized if the retransmission factor q is properly selected. The stable region of q is characterized and illustrated via examples of Geometric Retransmission (K=1) and Exponential Backoff (K=infinity). With an increasing number of nodes n, we show that the stable region of Geometric Retransmission rapidly shrinks, and vanishes as n goes to infinity. In contrast, the stable region of Exponential Backoff does not vary with the network population n, implying that a stable throughput can be achieved in networks with Exponential Backoff even with an infinite number of nodes. All the analytical results presented in this paper series are verified by simulations.

cs.NI↗

arXiv2009

Buffered Aloha with K-Exponential Backoff -- Part II: Delay Analysis

This paper presents the delay analysis for buffered Aloha networks with K-Exponential Backoff. Mean access delay and mean queueing delay are derived and demonstrated via the examples of Geometric Retransmission (K=1) and Exponential Backoff (K=infinity). The comparison shows that higher delay is incurred with Geometric Retransmission when the aggregate input rate is small, and the delay gap is enlarged as the number of nodes n increases. With a high traffic input rate, however, the delay performance with Exponential Backoff severely deteriorates. The mean queueing delay will be unbounded if the aggregate input rate exceeds 0.3. We also extend the analysis to the contention-window-based backoff model which is widely adopted in practical MAC protocols. It will be revealed that both the retransmission-probability-based and the contention-window-based models exhibit the same stable region and achieve similar queueing performance in most cases, which justifies the intuition that was taken but remained unverified in previous studies: the retransmission-probability-based backoff model can serve as a good approximation of the contention-window-based one.

cs.NI↗

arXiv2008

Throughput and Delay Analysis of Wireless Random Access Networks

This paper studies the network throughput and transport delay of a multihop wireless random access network based on a Markov renewal model of packet transportation. We show that the distribution of the source-to-destination (SD) distance plays a critical role in characterizing network performance. We establish necessary and sufficient condition on the SD distance for scalable network throughput, and address the optimal rate allocation issue with fairness and the QoS requirements taken into consideration. In respect to the end-to-end performance, the transport delay is explored in this paper along with network throughput. We characterize the transport delay by relating it to nodal queueing behavior and the SD-distance distribution; the former is a local property while the latter is a global property. In addition, we apply the large deviation theory to derive the tail distribution of transport delay. To put our theory into practical network operation, several traffic scaling laws are provided to demonstrate how network scalability can be achieved by localizing the traffic pattern, and a leaky bucket scheme at the network access is proposed for traffic shaping and flow control.

cs.NI↗

arXiv2008

Stability and Throughput of Buffered Aloha with Backoff

This paper studies the buffered Aloha with K-exponential backoff collision resolution algorithms. The buffered Aloha network is modeled as a multi-queue single-server system. We adopt a widely used approach in packet switching systems to decompose the multi-queue system into independent first-in-first-out (FIFO) queues, which are hinged together by the probability of success of head-of-line (HOL) packets. A unified method is devised to tackle the stability and throughput problems of K-exponential backoff with any cutoff phase K. For networks with a finite number of nodes, we show that the K-exponential backoff is stable if the retransmission factor is properly chosen from the stable region. The maximum stable throughput is derived and demonstrated via examples of geometric retransmission (K=1) and exponential backoff (K=infinity). For networks with an infinite number of nodes, we show that geometric retransmission is unstable, and the stable network throughput of exponential backoff can only be achieved at the cost of potential unbounded delay in each input queue. Furthermore, we address the stability issue of the systems at the undesired stable point. All analytical results presented in this paper are verified and confirmed by simulations.

cs.NI↗