53,756 research outputs found
Robust Sum MSE Optimization for Downlink Multiuser MIMO Systems with Arbitrary Power Constraint: Generalized Duality Approach
This paper considers linear minimum meansquare- error (MMSE) transceiver
design problems for downlink multiuser multiple-input multiple-output (MIMO)
systems where imperfect channel state information is available at the base
station (BS) and mobile stations (MSs). We examine robust sum mean-square-error
(MSE) minimization problems. The problems are examined for the generalized
scenario where the power constraint is per BS, per BS antenna, per user or per
symbol, and the noise vector of each MS is a zero-mean circularly symmetric
complex Gaussian random variable with arbitrary covariance matrix. For each of
these problems, we propose a novel duality based iterative solution. Each of
these problems is solved as follows. First, we establish a novel sum average
meansquare- error (AMSE) duality. Second, we formulate the power allocation
part of the problem in the downlink channel as a Geometric Program (GP). Third,
using the duality result and the solution of GP, we utilize alternating
optimization technique to solve the original downlink problem. To solve robust
sum MSE minimization constrained with per BS antenna and per BS power problems,
we have established novel downlink-uplink duality. On the other hand, to solve
robust sum MSE minimization constrained with per user and per symbol power
problems, we have established novel downlink-interference duality. For the
total BS power constrained robust sum MSE minimization problem, the current
duality is established by modifying the constraint function of the dual uplink
channel problem. And, for the robust sum MSE minimization with per BS antenna
and per user (symbol) power constraint problems, our duality are established by
formulating the noise covariance matrices of the uplink and interference
channels as fixed point functions, respectively.Comment: IEEE TSP Journa
Linear Transceiver design for Downlink Multiuser MIMO Systems: Downlink-Interference Duality Approach
This paper considers linear transceiver design for downlink multiuser
multiple-input multiple-output (MIMO) systems. We examine different transceiver
design problems. We focus on two groups of design problems. The first group is
the weighted sum mean-square-error (WSMSE) (i.e., symbol-wise or user-wise
WSMSE) minimization problems and the second group is the minimization of the
maximum weighted mean-squareerror (WMSE) (symbol-wise or user-wise WMSE)
problems. The problems are examined for the practically relevant scenario where
the power constraint is a combination of per base station (BS) antenna and per
symbol (user), and the noise vector of each mobile station is a zero-mean
circularly symmetric complex Gaussian random variable with arbitrary covariance
matrix. For each of these problems, we propose a novel downlink-interference
duality based iterative solution. Each of these problems is solved as follows.
First, we establish a new mean-square-error (MSE) downlink-interference
duality. Second, we formulate the power allocation part of the problem in the
downlink channel as a Geometric Program (GP). Third, using the duality result
and the solution of GP, we utilize alternating optimization technique to solve
the original downlink problem. For the first group of problems, we have
established symbol-wise and user-wise WSMSE downlink-interference duality.Comment: IEEE TSP Journa
Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems
We present the mixed Galerkin discretization of distributed parameter
port-Hamiltonian systems. On the prototypical example of hyperbolic systems of
two conservation laws in arbitrary spatial dimension, we derive the main
contributions: (i) A weak formulation of the underlying geometric
(Stokes-Dirac) structure with a segmented boundary according to the causality
of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac
structure by a finite-dimensional Dirac structure is realized using a mixed
Galerkin approach and power-preserving linear maps, which define minimal
discrete power variables. (iii) With a consistent approximation of the
Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models.
By the degrees of freedom in the power-preserving maps, the resulting family of
structure-preserving schemes allows for trade-offs between centered
approximations and upwinding. We illustrate the method on the example of
Whitney finite elements on a 2D simplicial triangulation and compare the
eigenvalue approximation in 1D with a related approach.Comment: Copyright 2018. This manuscript version is made available under the
CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0
The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
We give a detailed Operator Product Expansion interpretation of the results
for conformal 4-point functions computed from supergravity through the AdS/CFT
duality. We show that for an arbitrary scalar exchange in AdS(d+1) all the
power-singular terms in the direct channel limit (and only these terms) exactly
match the corresponding contributions to the OPE of the operator dual to the
exchanged bulk field and of its conformal descendents. The leading logarithmic
singularities in the 4-point functions of protected N=4 super-Yang Mills
operators (computed from IIB supergravity on AdS(5) X S(5) are interpreted as
O(1/N^2) renormalization effects of the double-trace products appearing in the
OPE. Applied to the 4-point functions of the operators Ophi ~ tr F^2 + ... and
Oc ~ tr FF~ + ..., this analysis leads to the prediction that the double-trace
composites [Ophi Oc] and [Ophi Ophi - Oc Oc] have anomalous dimension -16/N^2
in the large N, large g_{YM}^2 N limit. We describe a geometric picture of the
OPE in the dual gravitational theory, for both the power-singular terms and the
leading logarithms. We comment on several possible extensions of our results.Comment: 42 page
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