arXiv subjects

Jian Song

Publications and source records attributed to Jian Song.

At least 199 records · Page 11Linked to original sources

arXiv2017

Spectral-Efficient Analog Precoding for Generalized Spatial Modulation Aided MmWave MIMO

Generalized spatial modulation (GenSM) aided millimeter wave (mmWave) multiple-input multiple-output (MIMO) has recently received substantial academic attention. However, due to the insufficient exploitation of the transmitter's knowledge of the channel state information (CSI), the achievable rates of state-of-the-art GenSM-aided mmWave MIMO systems are far from being optimal. Against this background, a novel analog precoding scheme is proposed in this paper to improve the spectral efficiency (SE) of conventional GenSM-aided mmWave MIMOs. More specifically, we firstly manage to lower-bound the achievable SE of GenSM-aided mmWave MIMO with a closed-form expression. Secondly, by exploiting this lower bound as a cost function, a low-complexity iterative algorithm is proposed to design the analog precoder for SE maximization. Finally, numerical simulations are conducted to substantiate the superior performance of the proposed design with respect to state-of-the-art GenSM-aided mmWave MIMO schemes.

cs.IT↗

arXiv2017

Generalized Spatial Modulation Aided MmWave MIMO with Sub-Connected Hybrid Precoding Scheme

Due to the high cost and low energy efficiency of the dedicated radio frequency (RF) chains, the number of RF chains in a millimeter wave (mmWave) multiple-input multiple-output (MIMO) system is usually limited from a practical point of view. In this case, the maximum number of independent data streams is also restricted by the number of RF chains, which consequently leads to limiting the potentially attainable spatial multiplexing gain. In order to address this issue, in this paper, a novel generalized spatial modulation (GenSM) aided mmWave MIMO system is proposed, which enables the transmission of an extra data stream via the index of the active antennas group and requires no extra RF chain. Moreover, a two-step algorithm is also proposed to optimize the hybrid precoder design with respect to spectral efficiency (SE) maximization. Finally, numerical simulation results demonstrate the superior SE performance achieved by the proposed scheme.

cs.IT↗

arXiv2017

Second order Lyapunov exponents for parabolic and hyperbolic Anderson models

In this article, we consider the hyperbolic and parabolic Anderson models in arbitrary space dimension $d$, with constant initial condition, driven by a Gaussian noise which is white in time. We consider two spatial covariance structures: (i) the Fourier transform of the spectral measure of the noise is a non-negative locally-integrable function; (ii) $d=1$ and the noise is a fractional Brownian motion in space with index $1/4<H<1/2$. In both cases, we show that there is striking similarity between the Laplace transforms of the second moment of the solutions to these two models. Building on this connection and the recent powerful results of Huang, Le and Nualart (2015) for the parabolic model, we compute the second order (upper) Lyapunov exponent for the hyperbolic model. In case (i), when the spatial covariance of the noise is given by the Riesz kernel, we present a unified method for calculating the second order Lyapunov exponents for the two models.

math.PR↗

arXiv2017

Spectral Efficiency Analysis for Spatial Modulation in Massive MIMO Uplink over Dispersive Channels

Flat-fading channel models are usually invoked for analyzing the performance of massive spatial modulation multiple-input multiple-output (SM-MIMO) systems. However, in the context of broadband SM transmission, the severe inter-symbol-interference (ISI) caused by the frequency-selective fading channels can not be ignored, which leads to very detrimental effects on the achievable system performance, especially for single-carrier SM (SC-SM) transmission schemes. To the best of the author's knowledge, none of the previous researchers have been able to provide a thorough analysis on the achievable spectral efficiency (SE) of the massive SC-SM MIMO uplink transmission. In this context, the uplink SE of single-cell massive SC-SM MIMO system is analyzed, and a tight closed-form lower bound is proposed to quantify the SE when the base station (BS) uses maximum ratio (MR) combining for multi-user detection. The impacts of imperfect channel estimation and transmit correlation are all considered. Monte Carlo simulations are performed to verify the tightness of our proposed SE lower bound. Both the theoretical analysis and simulation results show that the SE of uplink single-cell massive SC-SM MIMO system has the potential to outperform the uplink SE achieved by single-antenna UEs.

cs.IT↗

arXiv2016

On the Multi-User, Multi-Cell Massive Spatial Modulation Uplink: How Many Antennas for Each User?

Massive spatial modulation aided multiple-input multiple-output (SM-MIMO) systems have recently been proposed as a novel combination of spatial modulation (SM) and of conventional massive MIMO, where the base station (BS) is equipped with a large number of antennas and simultaneously serves multiple user equipment (UE) that employ SM for their uplink transmission. Since the massive SM-MIMO concept combines the benefits of both the SM and massive MIMO techniques, it has recently attracted substantial research interest. In this paper, we study the achievable uplink spectral efficiency (SE) of a multi-cell massive SM-MIMO system, and derive closed-form expressions to asymptotically lower-bound the SE yielded by two linear BS combining schemes, including maximum ratio (MR) combining and zero forcing (ZF) combining, when a sufficiently large number of BS antennas are equipped. The derivation takes into account the impact of transmitter spatial correlations, of imperfect channel estimations, of user-specific power controls and of different pilot reuse factors. The proposed asymptotic bounds are shown to be tight, even when the scale of BS antennas is limited. The new SE results facilitate a system-level investigation of the optimal number of uplink transmit antennas (TAs) $N$ with respect to SE maximization. Explicitly, we provide theoretical insights on the SE of massive SM-MIMO systems. Furthermore, we demonstrate that massive SM-MIMO systems are capable of outperforming the SE of conventional massive MIMOs relying on single-TA UEs.

cs.IT↗

arXiv2016

Schauder estimates for equations with cone metrics, I

This is the first paper in a series to develop a linear and nonlinear theory for elliptic and parabolic equations on Kähler varieties with mild singularities. Donaldson has established a Schauder estimate for linear and complex Monge-Ampère equations when the background Kähler metrics on $\mathbb{C}^n$ have cone singularities along a smooth complex hypersurface. We prove a sharp pointwise Schauder estimate for linear elliptic and parabolic equations on $\mathbb{C}^n$ with background metric $g_β= \sqrt{-1} ( dz_1 \wedge d\bar{z_1} + \ldots + β^2|z_n|^{-2(1-β)} dz_n \wedge d\bar{z_n}) $ for $β\in (0,1)$. Our results give an effective elliptic Schauder estimate of Donaldson and a direct proof for the short time existence of the conical Kähler-Ricci flow.

math.DG↗

arXiv2016

Multiuser Diversity Gain from Superposition of Infinite Users over Block-Fading MAC

In uplink block-fading multiple access channel (BF-MAC), the advantage of multiuser diversity (MUD) can be taken to achieve higher system throughput. In this letter, with rate constraints for all users and only channel state information available at the receiver assumed, we demonstrate that non-orthogonal multiple access (NOMA) outperforms the counterpart of orthogonal multiple access (OMA) via exploiting the MUD from the superposition of multiple users. The MUD gain achieved by NOMA compared with OMA is quantitatively analyzed for finite users, and the closed-form upper bound of MUD gain from the superposition of infinite users is also derived. Numerical results show that the potential MUD gain from superposition of infinite users can be well approached with limited superposed users, which indicates that multiple access schemes with limited superposed users can provide a good tradeoff between system performance and decoding complexity.

cs.IT↗

arXiv2016

Geometric convergence of the Kähler-Ricci flow on complex surfaces of general type

We show that on smooth minimal surfaces of general type, the Kähler-Ricci flow starting at any initial Kähler metric converges in the Gromov-Hausdorff sense to a Kähler-Einstein orbifold surface. In particular, the diameter of the evolving metrics is uniformly bounded for all time and the Kähler-Ricci flow contracts all the holomorphic spheres with $(-2)$ self-intersection number to isolated orbifold points. Our estimates do not require a priori the existence of an orbifold Kähler-Einstein metric on the canonical model.

math.DG↗

arXiv2016

Temporal asymptotics for fractional parabolic Anderson model

In this paper, we consider fractional parabolic equation of the form $ \frac{\partial u}{\partial t}=-(-Δ)^{\fracα{2}}u+u\dot W(t,x)$, where $-(-Δ)^{\fracα{2}}$ with $α\in(0,2]$ is a fractional Laplacian and $\dot W$ is a Gaussian noise colored in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result for space-time Hamiltonians driven by $α$-stable process. As a byproduct, we obtain the critical values for $θ$ and $η$ such that $\mathbb{E}\exp\left(θ\left(\int_0^1 \int_0^1 |r-s|^{-β_0}γ(X_r-X_s)drds\right)^η\right)$ is finite, where $X$ is $d$-dimensional symmetric $α$-stable process and $γ(x)$ is $|x|^{-β}$ or $\prod_{j=1}^d|x_j|^{-β_j}$.

math.PR↗

arXiv2016

A Survey on the Computational Complexity of Colouring Graphs with Forbidden Subgraphs

For a positive integer $k$, a $k$-colouring of a graph $G=(V,E)$ is a mapping $c: V\rightarrow\{1,2,...,k\}$ such that $c(u)\neq c(v)$ whenever $uv\in E$. The Colouring problem is to decide, for a given $G$ and $k$, whether a $k$-colouring of $G$ exists. If $k$ is fixed (that is, it is not part of the input), we have the decision problem $k$-Colouring instead. We survey known results on the computational complexity of Colouring and $k$-Colouring for graph classes that are characterized by one or two forbidden induced subgraphs. We also consider a number of variants: for example, where the problem is to extend a partial colouring, or where lists of permissible colours are given for each vertex.

cs.CC↗

arXiv2016

On a class of stochastic partial differential equations

In this paper, we study the stochastic partial differential equation with multiplicative noise $\frac{\partial u}{\partial t} =\mathcal L u+u\dot W$, where $\mathcal L$ is the generator of a symmetric Lévy process $X$ and $\dot W$ is a Gaussian noise. For the equation in the Stratonovich sense, we show that the solution given by a Feynman-Kac type of representation is a mild solution, and we establish its Hölder continuity and the Feynman-Kac formula for the moments of the solution. For the equation in the Skorohod sense, we obtain a sufficient condition for the existence and uniqueness of the mild solution under which we get Feymnan-Kac formula for the moments of the solution, and we also investigate the Hölder continuity of the solution. As a byproduct, when $γ(x)$ is a nonnegative and nonngetive-definite function, a sufficient and necessary condition for $\int_0^t\int_0^t |r-s|^{-β_0}γ(X_r-X_s)drds$ to be exponentially integrable is obtained.

math.PR↗

arXiv2015

Feynman-Kac Formulas for Solutions to Degenerate Elliptic and Parabolic Boundary-Value and Obstacle Problems with Dirichlet Boundary Conditions

We prove Feynman-Kac formulas for solutions to elliptic and parabolic boundary value and obstacle problems associated with a general Markov diffusion process. Our diffusion model covers several popular stochastic volatility models, such as the Heston model, the CEV model and the SABR model, which are widely used as asset pricing models in mathematical finance. The generator of this Markov process with killing is a second-order, degenerate, elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the $2α$-power of the distance to the boundary of the half-plane, with $α\in(0,1]$. Our stochastic representation formulas provide the unique solutions to the elliptic boundary value and obstacle problems, when we seek solutions which are suitably smooth up to the boundary portion $Γ_{0}$ contained in the boundary of the upper half-plane. In the case when the full Dirichlet condition is given, our stochastic representation formulas provide the unique solutions which are not guaranteed to be any more than continuous up to the boundary portion $Γ_{0}$.

math.PR↗

arXiv2015

On Feldman-Ilmanen-Knopf conjecture for the blow-up behavior of the Kahler Ricci flow

We consider the Ricci flow on $\mathbb{CP}^n$ blown-up at one point starting with any $U(n)$-invariant Kähler metric. It is known that the Kähler-Ricci flow must develop Type I singularities. We show that if the total volume does not go to zero at the singular time, then any Type I parabolic blow-up limit of the Ricci flow along the exceptional divisor is the unique $U(n)$-complete shrinking Kähler-Ricci soliton on $\mathbb C^n$ blown-up at one point. This establishes the conjecture of Feldman-Ilmanen-Knopf.

math.DG↗

arXiv2015

On drift parameter estimation for reflected fractional Ornstein-Uhlenbeck processes

We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our goal is to estimate an unknown drift parameter $α\in (-\infty,\infty)$ on the basis of continuous observation of the state process. We establish Girsanov theorem for the process $X$, derive the standard maximum likelihood estimator of the drift parameter $α$, and prove its strong consistency and asymptotic normality. As an improved estimator, we obtain the explicit formulas for the sequential maximum likelihood estimator and its mean squared error by assuming the process is observed until a certain information reaches a specified precision level. The estimator is shown to be unbiased, uniformly normally distributed, and efficient in the mean square error sense.

math.ST↗

arXiv2015

Convergence of the conical Ricci flow on S2 to a soliton

In our previous work [PSSW], we showed that the Ricci flow on S^2 whose initial metric has conical singularities \sum_{j=1}^k β_j[p_j] converges to a constant curvature metric with conic singularities (in the stable and semi-stable cases) or to a gradient shrinking soliton with conical singularities (in the unstable case). The purpose of this note is to show that in the unstable case, that is, the case where β_k>β_k'=\s_{j<k}β_j, that the limiting metric is the unique shrinking soliton with cone singularity β_k[p_\infty]+β_k'[q_\infty]. This verifies the prediction made in [PSSW].

math.DG↗

arXiv2014

Feynman-Kac formula for fractional heat equation driven by fractional white noise

In this paper we obtain a Feynman-Kac formula for the solution of a fractional stochastic heat equation driven by fractional noise. One of the main difficulties is to show the exponential integrability of some singular nonlinear functionals of symmetric stable Lévy motion. This difficulty will be overcome by a technique developed in the framework of large deviation. This Feynman-Kac formula is applied to obtain the Hölder continuity and moment formula of the solution.

math.PR↗

arXiv2014

Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem

It is proved by Kawamata that the canonical bundle of a projective manifold is semi-ample if it is big and nef. We give an analytic proof using the Ricci flow, degeneration of Riemannian manifolds and $L^2$-theory. Combined with our earlier results, we construct unique singular Kahler-Einstein metrics with a global Riemannian structure on canonical models. Our approach can be viewed as the Kodaira embedding theorem on singular metric spaces with canonical Kahler metrics.

math.DG↗

arXiv2014

The Ricci flow on the sphere with marked points

The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is given. The semi-stable and unstable cases are new, and it is shown that the flow converges in the Gromov-Hausdorff topology to a limiting metric space which is also a 2-sphere, but with different marked points and hence a different complex structure. The limiting metric space carries a unique conical constant curvature metric in the semi-stable case, and a unique conical shrinking gradient Ricci soliton in the unstable case.

math.DG↗