arXiv subjects

Shi Jin

Publications and source records attributed to Shi Jin.

At least 649 records · Page 36Linked to original sources

arXiv2015

The Landau-Zener transition and the surface hopping method for the 2D Dirac equation for graphene

A Lagrangian surface hopping algorithm is implemented to study the two dimensional massless Dirac equation for Graphene with an electrostatic potential, in the semiclassical regime. In this problem, the crossing of the energy levels of the system at Dirac points requires a particular treatment in the algorithm in order to describe the quantum transition-- characterized by the Landau-Zener probability-- between different energy levels. We first derive the Landau-Zener probability for the underlying problem, then incorporate it into the surface hopping algorithm. We also show that different asymptotic models for this problem derived in [O. Morandi, F. Sch{ü}rrer, J. Phys. A: Math. Theor. 44 (2011)] may give different transition probabilities. We conduct numerical experiments to compare the solutions to the Dirac equation, the surface hopping algorithm, and the asymptotic models of [O. Morandi, F. Sch{ü}rrer, J. Phys. A: Math. Theor. 44 (2011)].

math.AP↗

arXiv2015

Large System Analysis of Cognitive Radio Network via Partially-Projected Regularized Zero-Forcing Precoding

In this paper, we consider a cognitive radio (CR) network in which a secondary multiantenna base station (BS) attempts to communicate with multiple secondary users (SUs) using the radio frequency spectrum that is originally allocated to multiple primary users (PUs). Here, we employ partially-projected regularized zero-forcing (PP-RZF) precoding to control the amount of interference at the PUs and to minimize inter-SUs interference. The PP-RZF precoding partially projects the channels of the SUs into the null space of the channels from the secondary BS to the PUs. The regularization parameter and the projection control parameter are used to balance the transmissions to the PUs and the SUs. However, the search for the optimal parameters, which can maximize the ergodic sum-rate of the CR network, is a demanding process because it involves Monte-Carlo averaging. Then, we derive a deterministic expression for the ergodic sum-rate achieved by the PP-RZF precoding using recent advancements in large dimensional random matrix theory. The deterministic equivalent enables us to efficiently determine the two critical parameters in the PP-RZF precoding because no Monte-Carlo averaging is required. Several insights are also obtained through the analysis.

cs.IT↗

arXiv2015

Joint Channel-and-Data Estimation for Large-MIMO Systems with Low-Precision ADCs

The use of low precision (e.g., 1-3 bits) analog-to-digital convenors (ADCs) in very large multiple-input multiple-output (MIMO) systems is a technique to reduce cost and power consumption. In this context, nevertheless, it has been shown that the training duration is required to be {\em very large} just to obtain an acceptable channel state information (CSI) at the receiver. A possible solution to the quantized MIMO systems is joint channel-and-data (JCD) estimation. This paper first develops an analytical framework for studying the quantized MIMO system using JCD estimation. In particular, we use the Bayes-optimal inference for the JCD estimation and realize this estimator utilizing a recent technique based on approximate message passing. Large-system analysis based on the replica method is then adopted to derive the asymptotic performances of the JCD estimator. Results from simulations confirm our theoretical findings and reveal that the JCD estimator can provide a significant gain over conventional pilot-only schemes in the quantized MIMO system.

cs.IT↗

arXiv2014

Transmit Designs for the MIMO Broadcast Channel with Statistical CSI

We investigate the multiple-input multiple-output broadcast channel with statistical channel state information available at the transmitter. The so-called linear assignment operation is employed, and necessary conditions are derived for the optimal transmit design under general fading conditions. Based on this, we introduce an iterative algorithm to maximize the linear assignment weighted sum-rate by applying a gradient descent method. To reduce complexity, we derive an upper bound of the linear assignment achievable rate of each receiver, from which a simplified closed-form expression for a near-optimal linear assignment matrix is derived. This reveals an interesting construction analogous to that of dirty-paper coding. In light of this, a low complexity transmission scheme is provided. Numerical examples illustrate the significant performance of the proposed low complexity scheme.

cs.IT↗

arXiv2014

On the classical limit of a time-dependent self-consistent field system: analysis and computation

We consider a coupled system of Schrödinger equations, arising in quantum mechanics via the so-called time-dependent self-consistent field method. Using Wigner transformation techniques we study the corresponding classical limit dynamics in two cases. In the first case, the classical limit is only taken in one of the two equations, leading to a mixed quantum-classical model which is closely connected to the well-known Ehrenfest method in molecular dynamics. In the second case, the classical limit of the full system is rigorously established, resulting in a system of coupled Vlasov-type equations. In the second part of our work, we provide a numerical study of the coupled semi-classically scaled Schrödinger equations and of the mixed quantum-classical model obtained via Ehrenfest's method. A second order (in time) method is introduced for each case. We show that the proposed methods allow time steps independent of the semi-classical parameter(s) while still capturing the correct behavior of physical observables. It also becomes clear that the order of accuracy of our methods can be improved in a straightforward way.

math.AP↗

arXiv2014

Energy Efficiency of Cross-Tier Base Station Cooperation in Heterogeneous Cellular Networks

Heterogeneous cellular networks (HetNets) are to be deployed for future wireless communication to meet the ever-increasing mobile traffic demand. However, the dense and random deployment of small cells and their uncoordinated operation raise important concerns about energy efficiency. Base station (BS) cooperation is set to play a key role in managing interference in the HetNets. In this paper, we consider BS cooperation in the downlink HetNets where BSs from different tiers within the respective cooperative clusters jointly transmit the same data to a typical user, and further optimize the energy efficiency performance. First, based on the proposed clustering model, we derive the spatial average rate using tools from stochastic geometry. Furthermore, we formulate a power minimization problem with a minimum spatial average rate constraint and derive an approximate result of the optimal received signal strength (RSS) thresholds. Building upon these results, we effectively address the problem of how to design appropriate RSS thresholds, taking into account the trade-off between spatial average rate and energy efficiency. Simulations show that our proposed clustering model is more energy-saving than the geometric clustering model, and under our proposed clustering model, deploying a two-tier HetNet is significantly more energy-saving compared to a macro-only network.

cs.IT↗

arXiv2014

Power Scaling of Uplink Massive MIMO Systems with Arbitrary-Rank Channel Means

This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) antenna systems in Ricean fading channels, using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming perfect and imperfect channel state information (CSI). In contrast to previous relevant works, the fast fading MIMO channel matrix is assumed to have an arbitrary-rank deterministic component as well as a Rayleigh-distributed random component. We derive tractable expressions for the achievable uplink rate in the large-antenna limit, along with approximating results that hold for any finite number of antennas. Based on these analytical results, we obtain the scaling law that the users' transmit power should satisfy, while maintaining a desirable quality of service. In particular, it is found that regardless of the Ricean $K$-factor, in the case of perfect CSI, the approximations converge to the same constant value as the exact results, as the number of base station antennas, $M$, grows large, while the transmit power of each user can be scaled down proportionally to $1/M$. If CSI is estimated with uncertainty, the same result holds true but only when the Ricean $K$-factor is non-zero. Otherwise, if the channel experiences Rayleigh fading, we can only cut the transmit power of each user proportionally to $1/\sqrt M$. In addition, we show that with an increasing Ricean $K$-factor, the uplink rates will converge to fixed values for both MRC and ZF receivers.

cs.IT↗

arXiv2014

A multi-band semiclassical model for surface hopping quantum dynamics

In the paper we derive a semiclassical model for surface hopping allowing quantum dynamical non-adiabatic transition between different potential energy surfaces in which cases the classical Born-Oppenheimer approximation breaks down. The model is derived using the Wigner transform and Weyl quantization, and the central idea is to evolve the entire Wigner matrix rather than just the diagonal entries as was done previously in the adiabatic case. The off-diagonal entries of the Wigner matrix suitably describe the non-adiabatic transition, such as the Berry connection, for avoided crossings. We study the numerical approximation issues of the model, and then conduct numerical experiments to validate the model.

math.NA↗

arXiv2013

Max-Min Energy Efficient Beamforming for Multicell Multiuser Joint Transmission Systems

Energy efficient communication technology has attracted much attention due to the explosive growth of energy consumption in current wireless communication systems. In this letter we focus on fairness-based energy efficiency and aim to maximize the minimum user energy efficiency in the multicell multiuser joint beamforming system, taking both dynamic and static power consumptions into account. This optimization problem is a non-convex fractional programming problem and hard to tackle. In order to find its solution, the original problem is transformed into a parameterized polynomial subtractive form by exploiting the relationship between the user rate and the minimum mean square error, and using the fractional programming theorem. Furthermore, an iterative algorithm with proved convergence is developed to achieve a near-optimal performance. Numerical results validate the effectiveness of the proposed solution and show that our algorithm significantly outperforms the max-min rate optimization algorithm in terms of maximizing the minimum energy efficiency.

cs.IT↗

arXiv2013

Large System Analysis of Cooperative Multi-cell Downlink Transmission via Regularized Channel Inversion with Imperfect CSIT

In this paper, we analyze the ergodic sum-rate of a multi-cell downlink system with base station (BS) cooperation using regularized zero-forcing (RZF) precoding. Our model assumes that the channels between BSs and users have independent spatial correlations and imperfect channel state information at the transmitter (CSIT) is available. Our derivations are based on large dimensional random matrix theory (RMT) under the assumption that the numbers of antennas at the BS and users approach to infinity with some fixed ratios. In particular, a deterministic equivalent expression of the ergodic sum-rate is obtained and is instrumental in getting insight about the joint operations of BSs, which leads to an efficient method to find the asymptotic-optimal regularization parameter for the RZF. In another application, we use the deterministic channel rate to study the optimal feedback bit allocation among the BSs for maximizing the ergodic sum-rate, subject to a total number of feedback bits constraint. By inspecting the properties of the allocation, we further propose a scheme to greatly reduce the search space for optimization. Simulation results demonstrate that the ergodic sum-rates achievable by a subspace search provides comparable results to those by an exhaustive search under various typical settings.

cs.IT↗

arXiv2012

A New Protocol of Continuous-Variable Entanglement Distillation

We introduce a new protocol in continuous variable entanglement distillation that requires only linear temporal and constant physical or spatial resources.Compared with the existing protocols, our protocol uses atom-photon entanglement to substitute for atom-atom entanglement in existing protol, which will not only save the number of quantum memories, but also has the advantages in operation efficiency and temporal saving. The distillation can be realized by a fixed model of iterations, in which only three quantum memories and photon detectors are required.

quant-ph↗

arXiv2012

On Capacity of Large-Scale MIMO Multiple Access Channels with Distributed Sets of Correlated Antennas

In this paper, a deterministic equivalent of ergodic sum rate and an algorithm for evaluating the capacity-achieving input covariance matrices for the uplink large-scale multiple-input multiple-output (MIMO) antenna channels are proposed. We consider a large-scale MIMO system consisting of multiple users and one base station with several distributed antenna sets. Each link between a user and an antenna set forms a two-sided spatially correlated MIMO channel with line-of-sight (LOS) components. Our derivations are based on novel techniques from large dimensional random matrix theory (RMT) under the assumption that the numbers of antennas at the terminals approach to infinity with a fixed ratio. The deterministic equivalent results (the deterministic equivalent of ergodic sum rate and the capacity-achieving input covariance matrices) are easy to compute and shown to be accurate for realistic system dimensions. In addition, they are shown to be invariant to several types of fading distribution.

cs.IT↗

arXiv2012

Performance Analysis of Optimal Single Stream Beamforming in MIMO Dual-Hop AF Systems

This paper investigates the performance of optimal single stream beamforming schemes in multiple-input multiple-output (MIMO) dual-hop amplify-and-forward (AF) systems. Assuming channel state information is not available at the source and relay, the optimal transmit and receive beamforming vectors are computed at the destination, and the transmit beamforming vector is sent to the transmitter via a dedicated feedback link. Then, a set of new closed-form expressions for the statistical properties of the maximum eigenvalue of the resultant channel is derived, i.e., the cumulative density function (cdf), probability density function (pdf) and general moments, as well as the first order asymptotic expansion and asymptotic large dimension approximations. These analytical expressions are then applied to study three important performance metrics of the system, i.e., outage probability, average symbol error rate and ergodic capacity. In addition, more detailed treatments are provided for some important special cases, e.g., when the number of antennas at one of the nodes is one or large, simple and insightful expressions for the key parameters such as diversity order and array gain of the system are derived. With the analytical results, the joint impact of source, relay and destination antenna numbers on the system performance is addressed, and the performance of optimal beamforming schemes and orthogonal space-time block-coding (OSTBC) schemes are compared. Results reveal that the number of antennas at the relay has a great impact on how the numbers of antennas at the source and destination contribute to the system performance, and optimal beamforming not only achieves the same maximum diversity order as OSTBC, but also provides significant power gains over OSTBC.

cs.IT↗

arXiv2012

A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials

We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schrödinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by non-periodic potentials describing external electric fields. Our approach is based on the classical Bloch decomposition method which allows to diagonalize the periodic part of the Hamiltonian operator. Hence, the dominant effects from dispersion and periodic lattice potential are computed together, while the non-periodic potential acts only as a perturbation. Because the split-step communicator error between the periodic and non-periodic parts is relatively small, the step size can be chosen substantially larger than for the traditional splitting of the dispersion and potential operators. Indeed it is shown by the given examples, that our method is unconditionally stable and more efficient than the traditional split-step pseudo spectral schemes. To this end a particular focus is on the semiclassical regime, where the new algorithm naturally incorporates the adiabatic splitting of slow and fast degrees of freedom.

math.NA↗

arXiv2012

Gaussian Beam Methods for the Dirac Equation in the Semi-classical Regime

The Dirac equation is an important model in relativistic quantum mechanics. In the semi-classical regime $ε\ll1$, even a spatially spectrally accurate time splitting method \cite{HuJi:05} requires the mesh size to be $O(ε)$, which makes the direct simulation extremely expensive. In this paper, we present the Gaussian beam method for the Dirac equation. With the help of an eigenvalue decomposition, the Gaussian beams can be independently evolved along each eigenspace and summed to construct an approximate solution of the Dirac equation. Moreover, the proposed Eulerian Gaussian beam keeps the advantages of constructing the Hessian matrices by simply using level set functions' derivatives. Finally, several numerical examples show the efficiency and accuracy of the method.

math.NA↗

arXiv2012

A time-splitting spectral scheme for the Maxwell-Dirac system

We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac system conserves the Lorentz gauge condition, is unconditionally stable and highly efficient as our numerical examples show. In particular we focus in our examples on the creation of positronic modes in the semi-classical regime and on the electron-positron interaction in the non-relativistic regime. Furthermore, in the non-relativistic regime, our numerical method exhibits uniform convergence in the small parameter $\dt$, which is the ratio of the characteristic speed and the speed of light.

math.NA↗

arXiv2010

A Numerical Scheme for the Quantum Boltzmann Equation Efficient in the Fluid Regime

Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision term. A class of asymptotic preserving schemes was introduced in [6] to handle this kind of problems. The idea is to penalize the stiff collision term by a BGK type operator. This method, however, encounters its own difficulty when applied to the quantum Boltzmann equation. To define the quantum Maxwellian (Bose-Einstein or Fermi- Dirac distribution) at each time step and every mesh point, one has to invert a nonlinear equation that connects the macroscopic quantity fugacity with density and internal energy. Setting a good initial guess for the iterative method is troublesome in most cases because of the complexity of the quantum functions (Bose-Einstein or Fermi-Dirac function). In this paper, we propose to penalize the quantum collision term by a 'classical' BGK operator instead of the quantum one. This is based on the observation that the classical Maxwellian, with the temperature replaced by the internal energy, has the same first five moments as the quantum Maxwellian. The scheme so designed avoids the aforementioned difficulty, and one can show that the density distribution is still driven toward the quantum equilibrium. Numerical results are present to illustrate the efficiency of the new scheme in both the hydrodynamic and kinetic regimes. We also develop a spectral method for the quantum collision operator.

math.NA↗

arXiv2010

An Asymptotic Preserving Scheme for the ES-BGK model

In this paper, we study a time discrete scheme for the initial value problem of the ES-BGK kinetic equation. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free or relaxation time. We study an implicit-explicit (IMEX) time discretization in which the convection is explicit while the relaxation term is implicit to overcome the stiffness. We first show how the implicit relaxation can be solved explicitly, and then prove asymptotically that this time discretization drives the density distribution toward the local Maxwellian when the mean free time goes to zero while the numerical time step is held fixed. This naturally imposes an asymptotic-preserving scheme in the Euler limit. The scheme so designed does not need any nonlinear iterative solver for the implicit relaxation term. Moreover, it can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved. We also show that it is consistent to the compressible Navier-Stokes equations if the viscosity and heat conductivity are numerically resolved. Several numerical examples, in both one and two space dimensions, are used to demonstrate the desired behavior of this scheme.

math.NA↗