25,326 research outputs found
Numerical Solution of Quantum-Mechanical Pair Equations
We discuss and illustrate the numerical solution of the differential equation satisfied by the firstāorder pair functions of SinanoÄlu. An expansion of the pair function in spherical harmonics and the use of finite difference methods convert the differential equation into a set of simultaneous equations. Large systems of such equations can be solved economically. The method is simple and straightforward, and we have applied it to the firstāorder pair function for helium with 1ā/ār_(12) as the perturbation. The results are accurate and encouraging, and since the method is numerical they are indicative of its potential for obtaining atomicāpair functions in general
Decentralized Delay Optimal Control for Interference Networks with Limited Renewable Energy Storage
In this paper, we consider delay minimization for interference networks with
renewable energy source, where the transmission power of a node comes from both
the conventional utility power (AC power) and the renewable energy source. We
assume the transmission power of each node is a function of the local channel
state, local data queue state and local energy queue state only. In turn, we
consider two delay optimization formulations, namely the decentralized
partially observable Markov decision process (DEC-POMDP) and Non-cooperative
partially observable stochastic game (POSG). In DEC-POMDP formulation, we
derive a decentralized online learning algorithm to determine the control
actions and Lagrangian multipliers (LMs) simultaneously, based on the policy
gradient approach. Under some mild technical conditions, the proposed
decentralized policy gradient algorithm converges almost surely to a local
optimal solution. On the other hand, in the non-cooperative POSG formulation,
the transmitter nodes are non-cooperative. We extend the decentralized policy
gradient solution and establish the technical proof for almost-sure convergence
of the learning algorithms. In both cases, the solutions are very robust to
model variations. Finally, the delay performance of the proposed solutions are
compared with conventional baseline schemes for interference networks and it is
illustrated that substantial delay performance gain and energy savings can be
achieved
Delay-Optimal User Scheduling and Inter-Cell Interference Management in Cellular Network via Distributive Stochastic Learning
In this paper, we propose a distributive queueaware intra-cell user
scheduling and inter-cell interference (ICI) management control design for a
delay-optimal celluar downlink system with M base stations (BSs), and K users
in each cell. Each BS has K downlink queues for K users respectively with
heterogeneous arrivals and delay requirements. The ICI management control is
adaptive to joint queue state information (QSI) over a slow time scale, while
the user scheduling control is adaptive to both the joint QSI and the joint
channel state information (CSI) over a faster time scale. We show that the
problem can be modeled as an infinite horizon average cost Partially Observed
Markov Decision Problem (POMDP), which is NP-hard in general. By exploiting the
special structure of the problem, we shall derive an equivalent Bellman
equation to solve the POMDP problem. To address the distributive requirement
and the issue of dimensionality and computation complexity, we derive a
distributive online stochastic learning algorithm, which only requires local
QSI and local CSI at each of the M BSs. We show that the proposed learning
algorithm converges almost surely (with probability 1) and has significant gain
compared with various baselines. The proposed solution only has linear
complexity order O(MK)
Dynamic Interference Mitigation for Generalized Partially Connected Quasi-static MIMO Interference Channel
Recent works on MIMO interference channels have shown that interference
alignment can significantly increase the achievable degrees of freedom (DoF) of
the network. However, most of these works have assumed a fully connected
interference graph. In this paper, we investigate how the partial connectivity
can be exploited to enhance system performance in MIMO interference networks.
We propose a novel interference mitigation scheme which introduces constraints
for the signal subspaces of the precoders and decorrelators to mitigate "many"
interference nulling constraints at a cost of "little" freedoms in precoder and
decorrelator design so as to extend the feasibility region of the interference
alignment scheme. Our analysis shows that the proposed algorithm can
significantly increase system DoF in symmetric partially connected MIMO
interference networks. We also compare the performance of the proposed scheme
with various baselines and show via simulations that the proposed algorithms
could achieve significant gain in the system performance of randomly connected
interference networks.Comment: 30 pages, 10 figures, accepted by IEEE Transaction on Signal
Processin
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