11,505 research outputs found
Separable Convex Optimization with Nested Lower and Upper Constraints
We study a convex resource allocation problem in which lower and upper bounds
are imposed on partial sums of allocations. This model is linked to a large
range of applications, including production planning, speed optimization,
stratified sampling, support vector machines, portfolio management, and
telecommunications. We propose an efficient gradient-free divide-and-conquer
algorithm, which uses monotonicity arguments to generate valid bounds from the
recursive calls, and eliminate linking constraints based on the information
from sub-problems. This algorithm does not need strict convexity or
differentiability. It produces an -approximate solution for the
continuous problem in time
and an integer solution in time, where is
the number of decision variables, is the number of constraints, and is
the resource bound. A complexity of is also achieved
for the linear and quadratic cases. These are the best complexities known to
date for this important problem class. Our experimental analyses confirm the
good performance of the method, which produces optimal solutions for problems
with up to 1,000,000 variables in a few seconds. Promising applications to the
support vector ordinal regression problem are also investigated
Power and Channel Allocation for Non-orthogonal Multiple Access in 5G Systems: Tractability and Computation
Network capacity calls for significant increase for 5G cellular systems. A
promising multi-user access scheme, non-orthogonal multiple access (NOMA) with
successive interference cancellation (SIC), is currently under consideration.
In NOMA, spectrum efficiency is improved by allowing more than one user to
simultaneously access the same frequency-time resource and separating
multi-user signals by SIC at the receiver. These render resource allocation and
optimization in NOMA different from orthogonal multiple access in 4G. In this
paper, we provide theoretical insights and algorithmic solutions to jointly
optimize power and channel allocation in NOMA. For utility maximization, we
mathematically formulate NOMA resource allocation problems. We characterize and
analyze the problems' tractability under a range of constraints and utility
functions. For tractable cases, we provide polynomial-time solutions for global
optimality. For intractable cases, we prove the NP-hardness and propose an
algorithmic framework combining Lagrangian duality and dynamic programming
(LDDP) to deliver near-optimal solutions. To gauge the performance of the
obtained solutions, we also provide optimality bounds on the global optimum.
Numerical results demonstrate that the proposed algorithmic solution can
significantly improve the system performance in both throughput and fairness
over orthogonal multiple access as well as over a previous NOMA resource
allocation scheme.Comment: IEEE Transactions on Wireless Communications, revisio
Traffic-Driven Spectrum Allocation in Heterogeneous Networks
Next generation cellular networks will be heterogeneous with dense deployment
of small cells in order to deliver high data rate per unit area. Traffic
variations are more pronounced in a small cell, which in turn lead to more
dynamic interference to other cells. It is crucial to adapt radio resource
management to traffic conditions in such a heterogeneous network (HetNet). This
paper studies the optimization of spectrum allocation in HetNets on a
relatively slow timescale based on average traffic and channel conditions
(typically over seconds or minutes). Specifically, in a cluster with base
transceiver stations (BTSs), the optimal partition of the spectrum into
segments is determined, corresponding to all possible spectrum reuse patterns
in the downlink. Each BTS's traffic is modeled using a queue with Poisson
arrivals, the service rate of which is a linear function of the combined
bandwidth of all assigned spectrum segments. With the system average packet
sojourn time as the objective, a convex optimization problem is first
formulated, where it is shown that the optimal allocation divides the spectrum
into at most segments. A second, refined model is then proposed to address
queue interactions due to interference, where the corresponding optimal
allocation problem admits an efficient suboptimal solution. Both allocation
schemes attain the entire throughput region of a given network. Simulation
results show the two schemes perform similarly in the heavy-traffic regime, in
which case they significantly outperform both the orthogonal allocation and the
full-frequency-reuse allocation. The refined allocation shows the best
performance under all traffic conditions.Comment: 13 pages, 11 figures, accepted for publication by JSAC-HC
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