优化LTE-Advanced多小区资源分配：实践算法与功率控制

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本文主要关注于LTE-Advanced（Long-Term Evolution Advanced）网络中的多小区资源分配问题，针对的是蜂窝式OFDMA（Orthogonal Frequency Division Multiple Access）系统的下行链路部分。作者Nassar Ksairi、Pascal Bianchi、Philippe Ciblat和Walid Hachem，均为IEEE会员，他们在《IEEE Transactions on Signal Processing》期刊上发表了一篇论文，该论文分为两部分：第一部分探讨了优化的资源分配策略，包括功率控制和子载波分配，以最大化系统效率，同时考虑到多小区间的干扰问题（资源重用问题）[1]。在研究中，作者假设网络是一维的，便于分析，将频谱划分为两部分：一部分允许基站重用资源，即非正交使用；另一部分则保持正交性，以减少干扰。第一部分论文的主要目标是找到在满足所有用户速率需求的同时，最小化整个网络的总功率消耗，这涉及到复杂的数学优化问题[2]。资源分配算法的目的是提高频谱效率，确保信号质量，尤其是在密集城区或多个基站共存的场景中，有效的资源分配至关重要。通过考虑实际操作中的算法设计和最优的资源重用因子（reuse factor），文章提出了实用且高效的策略，以平衡系统性能和复杂度，使得在面对多小区干扰时，仍能保证用户的服务质量和网络的稳定性[3]。第二部分可能进一步讨论了这些理论的实现方法，可能包括如何处理实时计算需求、如何处理动态变化的网络条件以及如何应对用户分布和行为的变化。此外，它也可能探讨了与实际网络部署相关的挑战，如功率控制的自适应性，以及如何通过算法改进来提高资源分配的灵活性和效率。总结来说，这篇论文对无线通信领域具有重要的实践价值，特别是在多小区环境中，提供了一套理论框架和方法，有助于优化LTE-Advanced系统中的资源分配，提升网络性能并降低干扰。对于无线通信网络规划者、系统设计师以及研究人员来说，理解和应用这些研究成果对于实现高效、可靠的无线通信服务至关重要[4]。 [1] Ksairi, N., Bianchi, P., Ciblat, P., & Hachem, W. (2010). Resource Allocation for Downlink Cellular OFDMA Systems—Part I: Optimal Allocation. IEEE Transactions on Signal Processing, 58(2), 720-734. [2] 同上，Part II 文献未给出具体引用。 [3] 资源重用和正交性的权衡在多小区环境中是关键考虑因素。 [4] 理论与实际相结合，对于提升无线通信服务质量至关重要。

KSAIRI et al.: RESOURCE ALLOCATION FOR DOWNLINK CELLULAR OFDMA SYSTEMS—PART II 737

subcarriers only used by users in Cell and respectively.

The reuse factor

is deﬁned as the ratio between the number

of reused subcarriers and the total number of subcarriers:

so that contains subcarriers. If user modulates a sub-

carrier

, the additive noise contains both thermal noise

of variance

and interference. Therefore, the variance of

this noise-plus-interference process depends on

and coincides

with

, where represents

the channel between BS

and user of Cell at frequency

and OFDM block , and where is the

average power transmitted by BS

in the interference band-

width

. The remaining subcarriers are shared by the

two cells, Cell

and , in an orthogonal way. If user mod-

ulates such a subcarrier

, the additive noise

contains only thermal noise. In other words, subcarrier does

not suffer from multicell interference. Then we simply write

. The resource allocation parameters for

user

are: the power transmitted on each of the subcar-

riers of the nonprotected band

allocated to him, his share

, the power transmitted on each of the subcarriers of

the protected band

allocated to him and his share of .

In other words,

As a consequence, and

for each cell . Moreover, let (respectively, ) be the

channel gain-to-noise ratio (GNR) in band

(respectively, ),

namely

(respectively, ). “Setting a

resource allocation for Cell

” means setting a value for param-

eters

B. Joint Resource Allocation for Cells

and

Assume that each user has a rate requirement of

nats/s/Hz. In the ﬁrst Part of this work [1], our aim was to

jointly optimize the resource allocation for the two cells which

i) allows to satisfy all target rates

of all users, and ii)

minimizes the power used by the two base stations in order

to achieve these rates. For each Cell

, denote by

the adjacent cell ( and ). The ergodic capacity

associated with a user

in Cell is given by

(2)

where

is a standard exponentially distributed random vari-

able, and where coefﬁcient

is given by

(3)

where

represents the channel between BS and user

of Cell at frequency and OFDM block . Coefﬁcient

represents the signal to interference plus noise ratio

in the interference band

. We assume that users are numbered

from the nearest to the BS to the farthest. As in [1], the fol-

lowing problem will be referred to as the joint resource allo-

cation problem for Cells

and : Minimize the total power

spent by both base stations

with respect to under

the following constraint that all users’ rate requirements

are

satisﬁed i.e., for each user

in any Cell , . The solu-

tion to this problem has been determined in the ﬁrst part of this

work [1]. As a noticeable point, the results of [1] indicate the ex-

istence in each cell of a pivot-user that separates two groups of

users: The “protected” users and the “nonprotected” users. The

following proposition states this binary property of the solution.

Proposition 1 [1]: Any global solution to the joint resource

allocation problem is “binary” i.e., there exists a user

in each

Cell

such that for closest users , and

for farthest users .

In the sequel, we denote by

the position of the pivot-

user

in Cell i.e., . A resource allocation algo-

rithm is also proposed in [1]. This algorithm turns out to have a

high computational complexity and the determination of the op-

timal value of the pivot-distance

turns out to be one of the

costliest operations involved in this algorithm. This is why we

propose in the following section of the present paper a subop-

timal simpliﬁed allocation algorithm that assumes a predeﬁned

pivot-distance.

III. P

RACTICAL RESOURCE

ALLOCATION ALGORITHM

A. Motivations and Main idea

Proposition 1 provides the general form of the optimal re-

source allocation, showing in particular the existence of pivot-

users

, in both Cells , , separating the users who

modulate in band

from the users who modulate in bands

and . As a matter of fact, the determination of pivot-users

is one of the costliest operations of this optimal allo-

cation (see [1] for a detailed computational complexity anal-

ysis). Thus, it would be convenient to propose an allocation

procedure for which the pivot-position would be ﬁxed in ad-

vance to a constant rather than systematically computed/opti-

mized. We propose a simpliﬁed resource allocation algorithm

based on this idea. Furthermore, we prove that when the value

of the ﬁxed pivot-distances is relevantly chosen, the proposed

algorithm is asymptotically optimal as the number of users in-

creases. In other words, the total power spent by the network for

large

when using our suboptimal algorithm does not exceed

the minimum power that would have been spent by using the

optimal resource allocation. The proposed algorithm is based

on the following idea.

Recall the deﬁnition of

and as the respec-

tive position of the optimal pivot-users

and deﬁned by

Proposition 1. As the optimal pivot-positions

and

are difﬁcult to compute explicitly and depend on the particular

rates and users’ positions, we propose to replace

and

with predeﬁned values and ﬁxed before

the resource allocation process. In our suboptimal algorithm, all

users in Cell

whose distance to the BS is less than

modulate in the interference band . Users farther than

modulate in the protected band . Of course, we still need to

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