Research Article An Enhanced OFDM Resource Allocation ...denoted by Y Z × =()×,where is the number of RBs allocated to PSU by RRH .Particularly, =0 means PSU is not served by RRH

Research ArticleAn Enhanced OFDM Resource Allocation Algorithm inC-RAN Based 5G Public Safety Network

Lei Feng, Wenjing Li, Peng Yu, and Xuesong Qiu

State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications,Beijing 100876, China

Correspondence should be addressed to Wenjing Li; [email protected]

Received 27 April 2016; Accepted 20 July 2016

Academic Editor: Bo Rong

Copyright © 2016 Lei Feng et al.This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Public Safety Network (PSN) is the network for critical communication when disaster occurs. As a key technology in 5G, Cloud-Radio Access Network (C-RAN) can play an important role in PSN instead of LTE-based RAN. This paper firstly introduces C-RAN based PSN architecture and models the OFDM resource allocation problem in C-RAN based PSN as an integer quadraticprogramming, which allows the trade-off between expected bitrates and allocating fairness of PSN Service User (PSU). However,C-RANbased PSNneeds to improve the efficiency of allocating algorithmbecause of amass of PSU-RRHassociationswhen disasteroccurs. To deal with it, the resources allocating problem with integer variables is relaxed into one with continuous variables in thefirst step and an algorithm based on Generalized Bender’s Decomposition (GBD) is proposed to solve it. Then we use FeasiblePump (FP) method to get a feasible integer solution on the original OFDM resources allocation problem. The final experimentsshow the total throughput achieved by C-RAN based PSN is at most higher by 19.17% than the LTE-based one. And the averagecomputational time of the proposed GBD and FP algorithm is at most lower than Barrier by 51.5% and GBD with no relaxation by30.1%, respectively.

1. Introduction

With the rapid upgrading of emergency application, PublicSafety Network (PSN) is getting increasingly popular. It isbeing recognized that wireless-based PSN is a key to a suc-cessful response to emergency situations. Article [1] providesa good introduction to the field by surveying public safetyuse cases, current status of the related standards activitieswithin the 3rd Generation Partnership Project (3GPP), andchallenges ahead. Several works [2–4] have pointed out asafety network is a basic guarantee in different industries.Article [5] analyzes the infrastructure of LTE-based PSN andexamines the capacity of LTE to meet the requirements ofcritical communications.The researchers and standards orga-nizations both firmly believe PSN can be further enhanced by5G emerging technologies, such asD2D,massive-MIMO, andC-RAN [1, 6, 7].

There are many PSN issues that needs to be settledby new B4G or 5G technologies. Article [8] uses D2Dcommunication to extend the coverage for PSN communi-cations. Although D2D improves the efficiency of wireless

communication, the key or the basic guarantee in PSN is theutilization on the bandwidth spectrum. Article [9] proposesa spectrum allocation scheme to avoid the interference withcommercial network. And the American FirstNet is assignedBand 14 on 700MHz to run the PSN service. Actually, asthe increasing demand for rich-content-based emergencyapplications, PSN needs not only a clean sharing spectrum,but also a flexible centralized bandwidth allocation schemethat can maximally satisfy the data-rate required by allPSN users. Cloud-Radio Access Network (C-RAN), as animportant access architecture in 5G, provides a centralizedmanner of bandwidthmanagement [10]. InC-RAN structure,the spectrum resource of a user associated with a certainRRH is processed by a centralized resource allocator. Thisintegrated resource allocation mechanism enables the usersto utilize the service resources more efficiently and makesthe system allocate the user’s demanded bandwidth flexibly[11]. In addition, RRHs are always placed high above theground, which means they are more difficult to be destroyedin disaster than the conventional BBU placed on the ground.In a consequence of that C-RAN lets BBU together to form

Hindawi Publishing CorporationMobile Information SystemsVolume 2016, Article ID 9586287, 14 pageshttp://dx.doi.org/10.1155/2016/9586287

2 Mobile Information Systems

a BBU pool in a position which is far away from RRHs; C-RAN is safer than LTE base-station infrastructure. It can beseen that these features of C-RAN are more suitable for therequirement of PSN service than LTE E-UTRAN.

However, the PSN Service Users (PSUs) will produce alarge amount of traffic in times of disaster. Hence, the abilityof bandwidth allocation algorithm is a key to assure the crit-ical communication. Article [12] compares the performanceof different scheme disciplines for PSN service. But the workis only designed to LTE-based PSN which is in a distributedmanagement scheme [13]. Therefore it is necessary to pro-pose a more high-effective centralized bandwidth allocationalgorithm if we introduce a C-RAN based PSN.The previousworks concerning the resource allocation in C-RAN net-workmainly involve the flexible RRH configuration [14, 15]and the application of the spatialmultiplexing technologies inC-RAN [16, 17]. Although spectrum allocation in C-RAN isalso discussed in some of them, it is merely treated as a simpleconstraint. In addition, compared with the normal C-RAN,C-RAN based PSN maybe serve more users when disasteroccurs. That means more efficient algorithm to solve theresource allocation problem is required. On the basis of theaforesaid works, in particular for their demerits, this paperproposes a Generalized Benders Decomposition- (GBD-)based OFDM resource allocation algorithm in C-RAN basedPSN to find out the solution on the system performance.This algorithm perfects the optimization through primalrelaxation and the GBD algorithm that sufficiently enhancesthe efficiency of resource allocation.

The contributions of this paper include two key aspects.The first is we introduce C-RAN based PSN architectureand propose the OFDM resources allocation model in thisnetwork. To the best of our knowledge, C-RAN basedPSN has not been investigated in the previous works. Weformulate OFDM resources allocation problem in C-RANbased PSN as a quadratic programming (QP) with integervariables of OFDM resource block that aims to maximize theemergency system performance. In the formulated problem,the objective system performance is affected by the expectedbit-rates revenue and the allocation fairness among differentPSUs. By analyzing the wireless channel model, we proposean objective function of the C-RAN based PSN system per-formance that allows trade-off between the expected bit-ratesrevenue and the PSU’s fairness when allocating resources.

Second, we present an efficient solution for the problemfacing the centralized resource allocation in C-RAN basedPSN. We firstly relax the integer variable in this QP probleminto the continuous one. And a GBD-based algorithm isproposed to address this relaxed problem. The traditionalBender’s Decomposition (BD) algorithm is used to solvetheMixed-IntegerNonlinear Programming (MINP) problemby decomposing the original problem into a master and asubproblem [18–21]. GBD extends the BD approach to amore general class of problems by adopting nonlinear dualitytheory, and some nonlinear problems are thereby broughtinto range, including QP we want to solve in this paper.Because of its high computational efficiency for solving therelaxed QP, the proposed algorithm is suitable in C-RANbased PSN which has many PSU associations. Proved by

theory, the proposed algorithm is guaranteed to obtain theoptimal solution on the relaxed problem. Then we use theFeasible Pump (FP) [22] method to guarantee we can findout a feasible integer solution on the original QP from theoptimal solution on the relaxed problem with continuousvariables.We also analyze the error tolerance as the algorithmterminated condition to allow the balance trade-off betweenthe nice convergence properties and the system performance.

The rest of the paper is organized as follows: In Sec-tion 2, we describe the C-RAN based PSN architectureand formulate the OFDM resource allocation problem. InSection 3, we solve the formulated QP of integer variablesby problem relaxation, Generalized Bender’s Decomposition,and Feasible Pump. The specific algorithm is also proposedand analyzed in this section. In Section 4, we firstly inves-tigate the performance of C-RAN based PSN. And then theconvergence and computing time of the proposed algorithmare analyzed. Finally, we drew some concluding remarks.

2. System Model

2.1. C-RAN Based PSN Architecture. Figure 1 shows aschematic diagram of our introduced C-RAN based PSNarchitecture for public safety applications. Each PSU runsdifferent PSN service covered by a RRH. C-RAN basedPSN adopts a centralized processing manner, namely, theBBU processing pool. The spectrum resource of a PSUassociated with a certain RRH is processed by a centralizedresource allocator in C-RAN. This integrated resource allo-cation mechanism enables the PSU to utilize the dedicatedPSN service bandwidth resources more effectively and on-demand.

Our C-RAN based PSN architecture allocates PSN spec-trum resources centrally to improve the whole network per-formance. But to meet the critical communication require-ment, this raises one important issue that needs to beconsidered: the assignment algorithm efficiency, especiallyfor that there are a lot of PSU-RRH associations whendisaster occurs. This is the key problem we want to solvein this paper. Since the OFDM is the dominant resource-multiplexing technology currently, in this paper, we focus onthe OFDM resource allocation in C-RAN based PSN witha view to maximizing the system performance by optimallyscheduling the centralized OFDM bandwidth resources.

2.2. PSU-RRHAssociationModel. Firstly, it needs to establishan association model between PSU and RRH. Assume that ina C-RAN based PSN system, 𝑈 = {𝑢

𝑛| 1, 2, . . . , 𝑁} expresses

the PSUs set and 𝐵 = {𝑏𝑚| 𝑚 = 1, 2, . . . ,𝑀} the RRHs set.

We consider the network is an OFDM systemwhose resourceelement is called Resource Block (RB). Let 𝐵RB denote thebandwidth of each RB and𝐵𝑊 the total bandwidth.Hence thetotal number of RBs is 𝐵𝑊/𝐵RB. The RB scheduling matrix isdenoted by Y ∈ Z𝑁×𝑀 = (𝑦

𝑖𝑗)𝑁×𝑀

, where 𝑦𝑖𝑗is the number

of RBs allocated to PSU 𝑢𝑗by RRH 𝑏

𝑖. Particularly, 𝑦

𝑖𝑗= 0

means PSU 𝑢𝑗is not served by RRH 𝑏

𝑖, which also stands for

no association between PSU 𝑢𝑗and RRH 𝑏

𝑖.

To facilitate analysis, we leave the reusable resourcecase to our further study, and temporarily in this section,

Mobile Information Systems 3

BBU pool

RRH in C-RAN

PSU equipment

BBU in C-RAN

Figure 1: C-RAN based PSN architecture.

the resource cannot be reused in the same C-RAN basedPSN system. Then we get one of the constraints of 𝑦

𝑖𝑗that

∑𝑁,𝑀

𝑖=1,𝑗=1𝑦

𝑖𝑗𝐵RB= 𝐵

𝑊. To make the model more convenient tosolve, the RB allocation matrix Y should be transformed intoa vector, the definition of which is given below.

Definition 1 (RB allocation vector). Let X ∈ 𝑅𝑀𝑁 = (𝑥𝑖𝑗)𝑀𝑁

,where 𝑖 = (𝑚 − 1) ⋅ 𝑁 + 𝑛, if

𝑥(𝑚−1)⋅𝑁+𝑛

= 𝑦𝑛𝑚. (1)

Then X is called RB allocation vector for RB allocationmatrix Y, where 𝑥

(𝑚−1)𝑁+𝑛stands for the amount of RBs

allocated to PSU 𝑢𝑛from RRH 𝑏

𝑚. Particularly, 𝑥

(𝑚−1)𝑁+𝑛= 0

means PSU 𝑢𝑛is not served by RRH 𝑏

𝑚. A simple illustration

of the transformation from a RB scheduling matrix to acorresponding RB allocation vector is shown in Figure 2.

In Figure 2, 2 RRHs and 3 PSUs make up the network,and the total number of RBs amounting to 100 is allocatedby a C-RAN allocator uniformly. It can be seen from theRB allocation matrix in the above example that PSU 1 andPSU 3 are served by RRH 1 with 23 RBs and RRH 2with 24 RBs bandwidth, respectively. As multiple RRHs canperform joint transmission such as CoMP [23], PSU 2 isserved by RRH1 and RRH2 simultaneously, and the spectrum

RB allocation vectorRB allocation matrix

RRH1 RRH1

RRH2

RRH2

Y = (ymn)3×2 X = (xi)6

PSU1

PSU2

PSU3

(23 031 220 24

) Numberof RBs

Number of RBs

PSU1

PSU2

PSU3

PSU4

PSU5

PSU6

(((((((

23

31

0

0

22

24

)))))))

Figure 2

resources allocated to PSU 2 totals at 53 RBs. The matrixY is transformed into a column vector X with the same6 elements, following the rules illustrated in (1) that thecolumns in X are rearranged into one column. The columnvector is the corresponding RB allocation vector.

2.3. SystemBit-Rate Revenue. Bit-rate capacity is a key featureto the performance of future wideband PSN rich-contentservices. The typical aim of the resource allocation schemeis to maximize the total bit-rate capacity in the traditionalcellular. Hence, in this paper we use the achievable bit-ratecapacity of all PSUs as the C-RAN based PSN system’s


revenue. This section analyzes the characteristics of thewireless fading channel to derive the outage probability ofthe system, based on which the achievable bit-rate capacityof a PSU in unit bandwidth can be resolved. Finally, theachievable PSU bit-rate per unit bandwidth is defined torepresent the system revenue.

Let 𝑃𝑡𝑚denote the transmit power of RRH 𝑏

𝑚, 𝐺𝑎

𝑚the

antenna gain, and 𝑃𝑟𝑛𝑚

the signal power received by 𝑢𝑛from

RRH 𝑏𝑚.The fading channel is characterized by amatrix𝐻

𝑛𝑚,

which is composed of 3 parts: path loss𝐻𝑑𝑛𝑚, slow fading𝐻𝑠,

and fast fading𝐻𝑓𝑛.𝐻

𝑛𝑚can be expressed by

𝐻𝑛𝑚= 𝐻

𝑑

𝑛𝑚⋅ 𝐻

𝑠

⋅ 𝐻𝑓

𝑛, (2)

where 𝐻𝑑𝑛𝑚

= 𝑑−𝛼

𝑛𝑚, 𝑑

𝑛𝑚is the physical distance between

PSU 𝑢𝑛and RRH 𝑏

𝑚, and 𝛼 is the path loss exponent. Slow

fading 𝐻𝑠 = 𝑒𝑠, where 𝑆 ∼𝑁(𝜇𝑠, (𝜎2)2); that is, 𝐻𝑠 followslognormal distribution, and the Probability DistributionFunction (PDF) is given in

𝑓𝐻𝑠 (𝑠) =

{

{

{

1

𝑠𝜎√2𝜋𝑒−(ln 𝑠−𝜇𝑠)2/2(𝜎𝑠)2

, 𝑠 > 0,

0, 𝑠 ≤ 0.

(3)

Assume that the PSU uses Maximal Ratio Combining(MRC) scheme to achieve full diversity gain, and the fastfading𝐻𝑓

𝑛can be calculated by

𝐻𝑓

𝑛=

𝐿𝑛

∑

𝑙=1

ℎ𝑛𝑙

2

, (4)

where ℎ𝑛𝑙is the fast fading diversity gain from the 𝑙th antenna

of PSU and ℎ𝑛𝑙can bemodeled as a randomvariable following

standard normal distribution, that is, ℎ𝑛𝑙∼ 𝑁(0, 1). 𝐿

𝑛is the

number of antennas in the PSU 𝑢𝑛. If 𝑙 ≥ 2, 𝐻𝑓

𝑛∼ Γ(𝐿

𝑛, 1),

and the PDF is given by

𝑓𝐻𝑓

𝑛

(V) ={{

{{

{

V𝐿𝑛−1𝑒−V

(𝐿𝑛− 1)!

, V > 0,

0, V ≤ 0(5)

then the received power of UE 𝑢𝑛from RRH 𝑏

𝑚, 𝑃𝑟

𝑛𝑚is given

in

𝑃𝑟

𝑛𝑚= 𝑃

𝑡

𝑚𝐺

𝑎

𝑚𝐻

𝑛𝑚= 𝑃

𝑡

𝑚𝐺

𝑎

𝑚𝐻

𝑠

𝐻𝑓

𝑛𝑑

−𝛼

𝑛𝑚. (6)

Supposing the threshold of the received power guaran-teeing the basic communication service is 𝑇𝑟, the outageprobability of PSU 𝑢

𝑛to access RRH 𝑏

𝑚at a distance 𝑑 can

be written as

Pr (𝑃𝑟𝑛𝑚< 𝑇

𝑟

) = Pr(𝐻𝑠𝐻𝑓𝑛<𝑇

𝑟

𝑑𝛼

𝑛𝑚

𝑃𝑡𝑚𝐺𝑎

𝑚

) . (7)

In this paper, we take the impacts of two different scalesof fading into consideration, which results in an outageprobability resolving problem in elaborately modeled fading

channel. Let 𝛽𝑛𝑚

= 𝑑𝛼

𝑛𝑚/𝑃

𝑡

𝑚𝐺

𝑎

𝑚, because 𝐻𝑠 and 𝐻𝑓

𝑛are

independently and identically distributed; then

Pr (𝐻𝑠𝐻𝑓𝑛< 𝑇

𝑟

𝛾𝑛𝑚)

= ∫

+∞

0

∫

𝑇𝑟

𝛽𝑛𝑚

/𝑠

0

𝑓𝐻𝑠 (𝑠) 𝑓

𝐻𝑓

𝑛

(V) 𝑑V 𝑑𝑠

= 1 − ∫

+∞

0

𝑓𝐻𝑠 (𝑠) ∫

+∞

𝑇𝑟𝛽𝑛𝑚

/𝑠

𝑓𝐻𝑓

𝑛

(V) 𝑑V 𝑑𝑠.

(8)

The cumulative distribution function of a gamma dis-tributed variable with scale parameter being 1 can be writtenas 𝛾(𝑎, 𝑏) = ∫+∞

𝑏

𝑧𝑎−1

𝑒−𝑧

𝑑𝑧, so the integral term of the slowfading can be written as

∫

+∞


/𝑠

𝑓𝐻𝑓

𝑛

(V) 𝑑V = ∫+∞


/𝑠

V𝐿𝑛−1𝑒−V

(𝐿𝑛− 1)!

𝑑V

=𝛾 (𝐿

𝑛, 𝑇

𝑟

𝛽𝑛𝑚/𝑠)

Γ (𝐿𝑛)

.

(9)

Substituting (9) into (7), the outage probability of PSU 𝑢𝑛

to access RRH 𝑏𝑚at a distance 𝑑 can be rewritten as

Pr (𝑃𝑟𝑛𝑚< 𝑇

𝑟

)

= 1

− ∫

+∞

0

1

𝑠𝜎√2𝜋

𝛾 (𝐿𝑛, 𝑇

𝑟

𝛽𝑛𝑚/𝑠)

Γ (𝐿𝑛)

𝑒−(ln 𝑠−𝜇𝑠)2/2(𝜎𝑠)2

𝑑𝑠.

(10)

Then we can use the Gauss-Hermite quadrature to solvethe numerical result of (10). Next, we are to derive theachievable bandwidth efficiency 𝑐

𝑛𝑚of PSU 𝑢

𝑛served byRRH

𝑏𝑚. Firstly, according to (10), the PDF of SNR is

𝑓SNR (𝑇𝑟

) =𝜕Pr (𝑇𝑟 > 𝑃𝑟

𝑛𝑚)

𝜕𝑇𝑟

=

𝑘𝐻

∑

𝑘=1

𝐴𝐻

𝑘

√𝜋Γ (𝐿𝑛)

𝜕𝛾 (𝐿𝑛, 𝑇

𝑟

𝛽𝑛𝑚𝑒−(√2𝜎

𝑠

𝜔𝐻

𝑘+𝜇𝑠

)

)

𝜕𝑇𝑟.

(11)

As 𝛾(𝑎, 𝑏) is used to define CDF and its infinity integral isconvergent, according to the derivation rule of the uncertainlimit integral, we have

𝜕𝛾 (𝐿𝑛, 𝑇

𝑟

𝛽𝑛𝑚𝑒−(√2𝜎

𝑠

𝜔𝐻

𝑘+𝜇𝑠

)

)

𝜕𝑇𝑟

= (𝛽𝑛𝑚𝑒−(√2𝜎

𝑠

𝜔𝐻

𝑘+𝜇𝑠

)

)

𝐿𝑛

⋅ 𝑇𝑟𝐿𝑛−1

𝑒−𝑇𝑟

𝛽𝑛𝑚

𝑒−(√2𝜎𝑠𝜔𝐻

𝑘+𝜇𝑠)

.

(12)

The PDF of SNR in (12) can be rewritten as

𝑓SNR (𝑇𝑟

) =

𝑘𝐻

∑

𝑘=1

(

𝐴𝐻

𝑘(𝛽

𝑛𝑚𝑒−(√2𝜎

𝑠

𝜔𝐻

𝑘+𝜇)

)

𝐿𝑛


)

⋅ 𝑇𝑟𝐿𝑛−1

𝑒−𝑇𝑟

𝛽𝑛𝑚


𝑘+𝜇𝑠)

.

(13)


Let random variable 𝑐𝑛𝑚= log

2(1+𝑇

𝑟

/𝑁0

) denote the bit-rate capacity per unit bandwidth of PSU𝑢

𝑛served byRRH 𝑏

𝑚,

in which 𝑁0 is the average power of Gauss white noise. Theexpectation of 𝑐

𝑛𝑚, 𝜇𝑐

𝑛𝑚can be written as

𝜇𝑐

𝑛𝑚= 𝐸 (𝑐

𝑛𝑚) = ∫

+∞

0

𝑓SNR (𝑇𝑟

) log2(1 +

𝑇𝑟

𝑁0)𝑑𝑇

𝑟

. (14)

Then (14) can be rewritten as

𝜇𝑐

𝑛𝑚=

𝑘𝐻

∑

𝑘=1

𝐴𝐻

𝑘𝑒−𝐿𝑛(√2𝜎𝑠

𝜔𝐻

𝑘+𝜇𝑠

)

(𝛽𝑛𝑚)𝐿𝑛


⋅ ∫

+∞

0

𝑒−𝑇𝑟

𝛽𝑛𝑚


𝑘+𝜇𝑠)

(𝑇𝑟

)𝐿𝑛−1

⋅ log2(1 +

𝑇𝑟

𝑁0)𝑑𝑇

𝑟

.

(15)

Then we can adopt the Gauss-Laguerre quadrature tosolve the numerical result of (15). Based on (15), we give thedefinition of the expected revenue vector in C-RAN basedPSN.

Definition 2 (expected revenue vector). Let R ∈ R𝑀𝑁 =(𝑟

𝑖)𝑀𝑁

. If (16) holds

𝑟(𝑚−1)⋅𝑁+𝑛

= 𝜇𝑐

𝑛𝑚, (16)

where 𝑖 = (𝑚−1)⋅𝑁+𝑛, then 𝑟(𝑚−1)⋅𝑁+𝑛

is the average bit-ratecapacity of PSU 𝑢

𝑛in unit bandwidth served by RRH 𝑏

𝑚, and

R is called the expected revenue vector of the system.

In addition, the variance of 𝑐𝑛𝑚

denoted as (𝜎𝑐𝑛𝑚)2 is

𝜎𝑐

𝑛𝑚

2

= 𝐷 (𝑐𝑛𝑚) = 𝐸 (𝑐

𝑛𝑚

2

) − (𝜇𝑐

𝑛𝑚)2

= ∫

+∞

0

𝑓SNR (𝑇𝑟

) (log2(1 +

𝑇𝑟

𝑁0))

2

𝑑𝑇𝑟

− (𝜇𝑐

𝑛𝑚)2

.

(17)

The correlation coefficients of 𝑐𝑛𝑚

and 𝑐𝑛𝑚 , 𝜌𝑐

𝑛𝑚,𝑛𝑚 , is

𝜌𝑐

𝑛𝑚,𝑛𝑚 =

𝐸 (𝑐𝑛𝑚⋅ 𝑐

𝑛𝑚) − 𝜇

𝑐

𝑛𝑚𝜇

𝑐

𝑛𝑚

𝜎𝑐𝑛𝑚𝜎

𝑐

𝑛𝑚

. (18)

As complete joint transmission technology is adoptedin C-RAN and a PSU can be served by multiple RRHssimultaneously, in the case of𝑚 = 𝑚 and 𝑛 = 𝑛, 𝜌𝑐

𝑛𝑚,𝑛𝑚 = 1

and in other cases, 𝜌𝑐𝑛𝑚,𝑛𝑚 = 0.

2.4. Resource Allocation Problem Formulation. This papertakes into account both expected revenue of the system andPSU’s fairness when allocating the RBs in C-RAN based PSN.

Hence, for the sake of maximizing the system performance,the following quadratic programming (QP) is derived:

maxX

𝑧 = 𝐵RBX𝑇R − 𝜅 (𝐵RB)

2

X𝑇QX

s.t.𝑀𝑁

∑

𝑖=1

𝑥𝑖=𝐵

𝑊

𝐵RB

X = (𝑥𝑖)𝑀𝑁, 𝑥

𝑖∈ {0, 1, . . . ,

𝐵𝑊

𝐵RB} ,

(19)

where Q = (𝑞𝑖𝑗)𝑀𝑁×𝑁𝑀

is a matrix relative to the covarianceof the system revenue. The element 𝑞

𝑖𝑗= 𝜌

𝑐

𝑛𝑚,𝑛𝑚𝜎

𝑐

𝑚𝑛𝜎

𝑐

𝑚𝑛 ,

where 𝑖 = (𝑚−1) ⋅𝑁+𝑟 and 𝑗 = (𝑚 −1) ⋅𝑁+𝑛. It is noticedthat the optimization problem aims atmaximizing the systemperformance, where 𝐵RBX𝑇R stands for the expectation ofthe bit-rate capacity, that is, the average revenue of the radioaccess system with a RB allocation scheme X. Based on thedefinition of Q, the second term (𝐵RB)2X𝑇QX stands for thevariance of the system performance. If the parameter 𝜅 →0, the model is inclined to allocate more resources to PSUscontributing more revenue to the system, which means poorfairness of PSUs. If𝜅 increases, themodelwill caremore aboutthe allocation fairness of PSUs.

Because of the integer decision variables of PSU, whenhaving a large amount of PSU-RRH associations whendisaster occurs, the time complexity of solving this NPproblem will increase distinctly. Hence, this paper proposes acorresponding Generalized Bender’s Decompositionmethodon the basis of integer variable continuation, which satisfiesthe demand on efficiency of algorithm in PSN service.

3. GBD Based Resource Allocation Algorithm

3.1. Relaxation and Generalized Bender’s Decomposition.Firstly, relax problem (19) into

maxX

𝑧 = 𝐵RBX𝑇R − 𝜅 (𝐵RB)

2

X𝑇QX

s.t.𝑀𝑁

∑

𝑖=1

𝑥𝑖=𝐵

𝑊

𝐵RB


𝑖∈ [0,

𝐵𝑊

𝐵RB] .

(20)

It can be seen that (20) is a typical QP problem withcontinuous variablesX after relaxing. Based on the definitionofQ, it is easy to knowQ is positive definitematrix.Therefore,the relaxed problem is a convex quadratic programmingproblem. However, this kind of problem is also hard to solvedirectly where there are a large number of quadratic variables.So in this paper, an algorithm based on Generalized Bender’sDecomposition is adopted to resolve the complex quadraticvariables, resulting in a much simplified two-stage solvingprocess.

Let X in R − 𝜅𝐵RBQX be defined as X ≜ X𝑏. Thenthe other X can be taken as the main variable. As X𝑏 is


taken as an auxiliary variable, it can be regarded as a constantparameter in resolving main variable X. And (20) can berewritten as

maxX

𝐵RB(R − 𝜅𝐵RBQX𝑏)

𝑇

X

s.t. 𝐵RBe𝑇X = 𝐵𝑊


𝑖∈ [0,

𝐵𝑊

𝐵RB] .

(21)

Problem in (21) is called the slave-problem of GBD, andthe dual of (21) can be written as

min𝜔

𝐵𝑊

𝜔

s.t. 𝜔e ≥ R − 𝜅𝐵RBQX𝑏.(22)

From (22), it can be seen that due to the limit of thetotal bandwidth resources in theC-RANbased PSN, themainvariable X conforms an equality constraint. Therefore thedual problem turned out to be a simple variable 𝜔 ∈ 𝑅,though (22) the optimal solution 𝜔∗ of the dual problemcan be computed by simply finding the maximum element invectorR−𝜅𝐵RBQX𝑏. Because there are only a limited numberof optimal solutions on the dual problem, according to thestrong duality theorem [24], there are also a limited numberof optimal solutions on (20) and we have

𝐵RB(R − 𝜅𝐵RBQX𝑏)

𝑇

X∗ = 𝐵𝑊𝜔∗. (23)

Let 𝜃 ≥ 1 denote the current number of Bender’sDecomposition iteration steps. Equation (20) can be writtenas a two-stage optimization problem, composed of a BendersDecomposition slave-problem as (24) and a relaxed BendersDecomposition master-problem as (25):

min𝜔

𝐵𝑊

𝜔𝜃

s.t. 𝜔𝜃e ≥ R − 𝜅𝐵RBQX𝑏

𝜃

(24)

maxX𝜃,𝜂𝜃

𝜂𝜃𝐵

𝑊

(𝐵RB)−1

(R − 𝜅𝐵RBQX𝜃)𝑇

((R − 𝜅𝐵RBQX𝑏𝜃)𝑇

)

−1

s.t. e𝑇X𝜃= 𝐵

𝑊

(𝐵RB)−1

X𝜃≥ 0

𝜂𝜃≤ 𝜔

∗

ℓ∀ℓ = 0, 1, 2, . . . , 𝜃 − 1,

(25)

where X𝑏𝜃= X∗

𝜃−1(X∗

𝜃−1is the optimal solution in (𝜃 − 1)th

iteration).Lemma 3 will prove the convergence of the above algo-

rithm by demonstrating that the gap between the upperbound 𝐵𝑈and lower bound 𝐵𝐿 of the optimal objectivefunction value 𝑧∗ in (20) can be tightened, where 𝐵𝑈 is thevalue of objective function in (25); 𝐵𝐿 is the maximum valueof problem in (24) in all the iterations, that is, the maximumelement in {𝐵𝑊𝜔

ℓ| ℓ = 1, 2, . . . , 𝜃}.

Lemma 3. Each iteration in Generalized Bender’s Decomposi-tion will narrow the gap between the upper bound 𝐵𝑈 and thelower bound 𝐵𝐿 of the value of objective function 𝑧∗, where at𝜃th iteration, 𝐵𝑈 is 𝑧𝑈

𝜃= 𝜂

∗

𝜃𝐵

𝑊

(𝐵RB)−1

(R − 𝜅𝐵RBQX∗𝜃)𝑇 and

𝐵𝐿 is 𝑧𝐿

𝜃= max

1≤ℓ≤𝜃{𝐵

𝑊

𝜔∗

ℓ}.

Proof. Firstly, we prove the upper bound of 𝑧∗ being 𝑧𝑈𝜃.

Based on the strong duality theorem, we know problem in(21) is equivalent to the problem in (26) according to (22):

maxX,X𝑏

𝜔∗

𝐵𝑊

(𝐵RB)−1

(R − 𝜅𝐵RBQX)𝑇

((R − 𝜅𝐵RBQX𝑏)𝑇

)

−1

s.t. e𝑇X = 𝐵𝑊 (𝐵RB)−1

e𝑇X𝑏 = 𝐵𝑊 (𝐵RB)−1

X ≥ 0, X𝑏 ≥ 0.

(26)

So with the optimal solution of problem in (20) beingX∗, the value of the objective function is 𝐵RBX∗𝑇R −

𝜅(𝐵RB)2X∗𝑇QX∗. As (25) is the relaxation of (26), there

should be


(1) Initialization: 𝜃 = 1, X𝑏0= X∗

0= 0, 𝜔∗

0= 𝛿, where 𝛿 is big enough.

(2) Repeat:(3) Work out (25) to obtain optimal solution (X∗

𝜃, 𝜂

∗

𝜃), and compute the upper bound

𝜂∗

𝜃𝐵

𝑊

(𝐵RB)−1

(R − 𝜅𝐵RBQX∗𝜃)𝑇

((R − 𝜅𝐵RBQX∗𝜃−1)𝑇

)−1

(4) X𝑏𝜃= X∗

𝜃

(5) Work out (24) to obtain 𝜔∗𝜃, and compute the lower bound 𝐵𝐿 = max

1≤ℓ≤𝜃{𝐵

𝑊

𝜔∗

ℓ}

(6) 𝜃 = 𝜃 + 1(7) Until 𝐵𝑈 − 𝐵𝐿 = 0(8) Return X∗ = X∗

𝜃−1as the optimal solution to problem (20), and compute the value

of the objective function 𝑧∗ by (24).

Algorithm 1: Generalized bender’s decomposition-based resource allocation algorithm to solve relaxed problem (20).

𝑧∗

= 𝐵RBX∗𝑇R − 𝜅 (𝐵RB)

2

X∗𝑇QX∗ ≤ 𝑧𝑈𝜃

= 𝜂∗

𝜃𝐵

𝑊

(𝐵RB)−1


⋅ ((R − 𝜅𝐵RBQX∗𝜃−1)𝑇

)

−1

,

(27)

where (𝜂∗𝜃,X∗

𝜃) is the optimal solution to question in (25).

Therefore, the upper bound of the optimal solution 𝐵𝑈 is 𝑧𝑈𝜃.

Then, we prove the lower bound of 𝑧∗is 𝑧𝐿𝜃. Because

of the asymmetry in constraints of two dual problems, 𝜔∗𝑡

can be bounded or unbounded. If 𝜔∗𝑡= −∞, ∀ℓ ∈

[1, 𝜃], ∃𝑧𝐿𝜃= max

1≤ℓ≤𝜃{𝐵

𝑊

𝜔∗

ℓ} = −∞. In this case, the

proposition that the bound of 𝑧∗is 𝑧𝐿𝜃holds. If 𝜔∗

𝑡> −∞, let

𝐵𝑊

𝜔∗

ℓ= max

1≤ℓ≤𝜃{𝐵

𝑊

𝜔∗

ℓ}. Suppose 𝑧𝐿

𝜃> 𝑧

∗, and accordingto the above assumptions and strong duality properties, thereshould be an X that conforms the following constraint:

𝐵𝑊

𝜔∗

̃ℓ= 𝐵

RB(R − 𝜅𝐵RBQX)

𝑇

X > 𝑧∗

= 𝐵RBX∗𝑇R − 𝜅 (𝐵RB)

2

X∗𝑇QX∗.(28)

Equation (28) indicates that X makes the objective functionget a larger value to the objective function, which conflictswith the precondition that X∗ is the optimal solution of (20).Therefore, 𝑧𝐿

𝜃= max

1≤ℓ≤𝜃{𝐵

𝑊

𝜔∗

ℓ} is the lower bound of the

value to the problem in (19).

According to Lemma 3, the system can find the optimalsolution of problem (20), as 𝐵𝑈 − 𝐵𝐿 = 0. Hence, therelaxation problem can be solved by Algorithm 1, and the

specific solution is as follows: firstly, in the first iteration,that is, 𝜃 = 1, the total system performance is greaterthan 0. According to the duality property, let X𝑏

0= 0 and

𝜔∗

0= 𝛿, where 𝛿 indicates a great enough value. These

preconditions will ensure (25) can be feasibly constrainedand the solution (X∗

1, 𝜂

∗

1) on the master-problem in (25) can

be resolved. Then let X𝑏1= X∗

1and solve the slave-problem

in (24). As slave-problem in (24) is a Linear Programming(LP), the result 𝐵𝑊𝜔∗

1should be an extreme point in the

feasible domain of the problem. Afterwards, let iterationsplus 1, and go on with the iterations to obtain an X∗

𝜃, until

𝐵𝑈

− 𝐵𝐿

= 0, which means the gap between the upperbound and lower bound is narrowed to 0. The extremepoint corresponds to the optimal solution to the problem.TheGeneralized Bender’s Decomposition algorithm needs toobtain the channel information from all PSUs to construct asystem revenuematrix, so it is a centralized algorithm and it issuitable to perform the system like C-RAN based PSN, whichpools all resources in a computing center.

The proposed GBD algorithm takes the differencebetween 𝐵𝐿 and 𝐵𝑈 as the criteria to judge the terminationof the iteration. When the difference between 𝐵𝐿 and 𝐵𝑈becomes 0, the whole algorithm terminates and the optimalsolution to the problem in (19) is retrieved. The convergenceof the algorithm will be proved byTheorem 4.

Theorem 4. The Generalized Bender’s Decomposition-basedAlgorithm 1 converges to an optimal solution after finiteiterations.

Proof. As an optimization problemwith continuous variablesand linear constraints [24], there exists a polyhedral convexconeΩ to make problems in (24) and (25) equivalent to

maxX𝜃,𝜂𝜃

𝜂𝜃𝐵

𝑊

(𝐵RB)−1

(R − 𝜅𝐵RBQX𝜃)𝑇

((R − 𝜅𝐵RBQX𝑏𝜃)𝑇

)

−1

s.t. e𝑇X𝜃= 𝐵

𝑊

(𝐵RB)−1

X𝜃≥ 0

(X𝜃, 𝜂

𝜃) ∈ Ω,

(29)


where the convex cone Ω is composed of finite radials alongwith extreme directions. In each iteration, the set of (X, 𝜂)in (25) will be tighten eventually, because a new radial willbe added as a new extreme directions to refine the solutionregion; namely, 𝜂

𝜃≤ 𝜔

∗

ℓ. In addition, it is considered that

Ω is a convex hull composed of finite radials in extremedirections, and the newly introduced radial is different fromthe existing ones, so theΩ, which is determined by a completeset of constraints, can be obtained after finite iterations.This suggests that the optimal resource allocation vector X∗and the value of the objective function in (24), that is, theupper bound 𝐵𝑈, can be obtained after finite iterations. Sothe optimal objective function value 𝑧∗ of relaxed problem(20) can also be obtained after finite iterations. Because thesequence {𝑧𝑈

ℓ, ℓ = 1, 2, 3, . . . , 𝜃} is not increasing, 𝑧∗ =

𝐵𝑈

= 𝑧𝑈

𝜃can be obtained after Ω is completely determined

by the constraints 𝜂𝜃≤ 𝜔

∗

ℓ, ∀ℓ = 0, 1, 2, . . . , 𝜃. Additionally,

due to 𝑧𝐿𝜃= max

1≤ℓ≤𝜃{𝐵

𝑊

𝜔∗

ℓ}, the sequence {𝑧𝐿

ℓ, ℓ =

1, 2, 3, . . . , 𝜃} is nondecreasing. After retrieving X∗ for theproblem in (25), we have 𝑧∗ = 𝐵𝑈 = 𝑧𝐿

𝜃. According to

the properties of the two sequences, terminated condition𝐵

𝑈

− 𝐵𝐿

= 0 can be satisfied and the global optimalsolution to the problem (20) can be obtained after finiteiterations.

3.2. Feasible Pump (FP). GBD algorithm can solve the solu-tion of relaxation problem (20). Nevertheless, the vectorX∗

𝜃solved by each iteration is not the integer vector, and

it is not a feasible solution for problem (19). Therefore, itneeds to find the actual feasible integer vector solution.There is a kind of simple method to find the integer vectorsolution; that is, the general vector solution X∗

𝜃is taken

as the starting point to look for its nearest integer vectorsolution in the solution space. Article [22] proposes a kindof FP way which was taken as the standard to look for theinteger vector solution. Specifically, the calculation �̃�

𝑖=

[𝑥∗

𝑖] is carried on each element 𝑥∗

𝑖in the optimal solution

of 𝜃th iteration in the relaxation problem (20), where [⋅]signifies that the nearest integer is taken for the scalar. So thenew integer vector X̃

𝜃= (�̃�

𝑖)𝑀𝑁

is obtained. The functionΔ(⋅) is defined as the sum of 𝐿1 norm distance of variouselements between a general vector and an integer vector;then

Δ (X∗𝜃, X̃

𝜃) =

𝑀𝑁

∑

𝑖=1

𝑥∗

𝑖− �̃�

𝑖

. (30)

The principle of FP adopts a heuristic way to find thefeasible integer solution X̃

𝜃. The determination standard of

FP is that there exists a certain point X∗𝜃in the general feasi-

ble region after relaxation and this point meets Δ(X∗𝜃, X̃

𝜃) =

0. In this case, X∗𝜃

is the integer vector and meets X∗𝜃=

X̃𝜃. Aiming at the relaxed problem (20), the FP stan-

dard is equivalent to the following minimum optimizationproblem:

minX𝜃

Δ (X𝜃, X̃

𝜃) =

𝑀𝑁

∑

𝑖=1

𝑥𝑖 − �̃�𝑖

𝑀𝑁

∑

𝑖=1

𝑥𝑖=𝐵

𝑊

𝐵RB

X𝜃= (𝑥

𝑖)𝑀𝑁, 𝑥

𝑖∈ [0,

𝐵𝑊

𝐵RB] .

(31)

It is clearly observed that if X𝜃= X̃

𝜃exists in the

feasible region, then Δ(X𝜃, X̃

𝜃) = 0. This is equivalent to

a fact that X̃𝜃= [X∗

𝜃] is a feasible solution. The entire

execution flow of FP is as follows. Initially, optimal solutionX∗

𝜃, which was obtained by the relaxed problem (20), carried

on [⋅] operator to obtain the initial integer solutions X̃𝜃, and

X̃𝜃may not be the feasible integer vector solution. If X̃

𝜃is

not the feasible solution, X̃𝜃is fixed, and then the general

vector solution closest to the 𝐿1 norm distance of X̃𝜃is

looked for in the feasible region of relaxation. This processis called as a Pumping Cycling. Afterwards, FP standard(i.e., whether the norm distance is 0) was used to verify thissolution. If the norm distance is equal to 0, the solution isX∗

𝜃. Otherwise, operator [⋅] is carried on the newly obtained

general vector solution to update X̃𝜃and the Pumping

Cycling iteration is continually carried on until X∗𝜃is finally

found.

3.3. OFDM RBs Allocation Algorithm Based on GBD and FP.Thus, this paper proposes the allocation algorithm on thebasis of taking the OFDM RB as basic allocated unit, whichis shown in Algorithm 2. The characteristic of this algorithmis that, firstly, the original allocation problem with integer RBis simplified by relaxing into one with continuous variable.And GBD method is used to solve this relaxed problemin each iteration. Then, the FP-based distance criterionis used to find the feasible integer solution. Afterwards,terminated condition 0 ≤ 𝐵𝑈 − 𝐵𝐿 ≤ 𝜏 is used to judgewhether this solution is the acceptable approximate optimalsolution.

3.4. Trade-Off between Performance and Convergence Time.It can be seen that 0 ≤ 𝐵𝑈 − 𝐵𝐿 ≤ 𝜏 is used as theterminated condition of Algorithm 2. Therefore the valueof 𝜏 will determine the accuracy of approximately-optimalsolution. And it is not surprising that when 𝜏 is small theaccuracy of the solution is higher, however with a greatercomputing time. Hence we use Theorem 5 to illustratethe proper value of 𝜏 as a reference to the implementedsystem.

Theorem 5. As for problem (19) and Algorithm 2, the systemperformance is at most 𝜏 < 1/𝜛 less than the maximum systemperformance when 𝜏 = 0 (the operator ⌊⋅⌋ signifies that thenearest integer is taken downward.), and as 𝜏 < 1/𝜛 thedifference between the system performance of Algorithm 2 andthemaximum one is 0where𝜛 is a constant that is greater than0 and can be expressed as


(1) Relax problem (19) into problem (20)(2) Initialization: 𝜃 = 1, X𝑏

0= X∗

0= 0, 𝜔∗

0= 𝛿, where 𝛿 is big enough.

(3) Repeat:(4) By Algorithm 1, decompose the problem (20) into master problem (25) and slave problem (24).(5) Work out (25) to obtain optimal solution (X∗

𝜃, 𝜂

∗

𝜃), and compute the upper bound

𝜂∗

𝜃𝐵

𝑊

(𝐵RB)−1


((R − 𝜅𝐵RBQX∗𝜃−1)𝑇

)−1

(6) Let X̃𝜃= [X∗

𝜃], by FP standard expressed by (31) to find the feasible integer solution X∗

𝜃, and then X𝑏

𝜃= X∗

𝜃

(7) Work out (24) to obtain 𝜔∗𝜃, and compute the lower bound 𝐵𝐿 = max

1≤ℓ≤𝜃{𝐵

𝑊

𝜔∗

ℓ}

(8) 𝜃 = 𝜃 + 1(9) Until 𝐵𝑈 − 𝐵𝐿 = 0(10) Return X∗ = X∗

𝜃−1as the approximate optimum solution to problem (19), and compute the value

of the objective function 𝑧∗ by (24).

Algorithm 2: Generalized bender’s decomposition and FP-based RB allocation algorithm to solve problem (23).

𝜛 =𝑟

𝑖

𝑟𝑖𝐵𝑅𝐵

=

𝑞

𝑖𝑗

𝑞𝑖𝑗(𝐵𝑅𝐵)

2,

∀𝑖 = 1, 2 . . . ,𝑀𝑁, ∀𝑗 = 1, 2 . . . ,𝑀𝑁,

(32)

where 𝑟𝑖, ∀𝑖 = 1, 2 . . . ,𝑀𝑁 and 𝑞

𝑖𝑗, ∀𝑖, 𝑗 = 1, 2 . . . ,𝑀𝑁 are all

integers

Proof. For problem (19), there exist 𝐵𝐿 = 𝑍(X) and𝑧∗

≤ 𝐵𝑈; hence, the difference between the maximum

system performance and the actual system performance ofAlgorithm 2 is

𝑧∗

− 𝑍 (X) ≤ 𝐵𝑈 − 𝐵𝐿 ≤ 𝜏. (33)

Because 𝜛 is an integer that is greater than 0, then

𝜛 (𝑧∗

− 𝑍 (X)) = 𝜛𝐵RB(𝑀𝑁

∑

𝑖=1

𝑥∗

𝑖𝑟𝑖

−

𝑀𝑁

∑

𝑗=1

𝑀𝑁

∑

𝑖=1

𝐵RB𝑥

∗

𝑖𝑞𝑖𝑗𝑥

∗

𝑗

− (

𝑀𝑁

∑

𝑖=1

𝑥

𝑖𝑟𝑖−

𝑀𝑁

∑

𝑗=1

𝑀𝑁

∑

𝑖=1

𝐵RB𝑥

𝑖𝑞𝑖𝑗𝑥

𝑗))

=

𝑀𝑁

∑

𝑖=1

(𝑥∗

𝑖− 𝑥

𝑖) 𝑟

𝑖−

𝑀𝑁

∑

𝑗=1

𝑀𝑁

∑

𝑖=1

(𝑥∗

𝑖𝑥

∗

𝑗− 𝑥

𝑖𝑥

𝑗) 𝑞

𝑖𝑗

≤ 𝜛𝜏.

(34)

Since 𝑟𝑖, 𝑞

𝑖𝑗, and 𝑥

𝑖are all the integers, there exists

𝑧∗

− 𝑍 (X) ≤ 1𝜛⌊𝜛𝜏⌋ . (35)

Because the operator ⌊⋅⌋ signifies that the nearest integeris taken downward, when ⌊𝜛𝜏⌋ = 0, namely, 𝜏 < 1/𝜛, then𝑧∗

= 𝑍(X). In this case, the result obtained fromAlgorithm 2is the original approximately-optimal solution on the integerprogramming (19).

Table 1: Simulation parameters.

Parameter Value (unites)Transmitting power of each RRH 𝑃𝑡 20WAntenna gain 𝐺𝑎 15 dBiSlow fading mean 𝜇𝑠 3 dBSlow fading standard deviation 𝜎𝑠 1.5 dBNumber of UE’s antenna 𝐿 2Gauss-Laguerre phase 𝑘𝐿 5Gauss Hermite phase 𝑘𝑁 5Path loss exponent 𝛼 4.5Bandwidth of each resource block 𝐵RB 0.2MHzFairness factor 𝜅 0.3 and 0.6

4. Simulation Results

This paper evaluates the performance from both C-RANbased PSN architecture and proposed GBD algorithm. Thethroughput and PSU’s allocation fairness in C-RAN basedPSN are investigated in Section 4.1. The convergence proper-ties and computational time of the proposed GBD algorithmare investigated in Sections 4.2 and 4.3, respectively. InSection 4.4, the trade-off between the performance andthe terminated parameter 𝜏 is discussed. We select CPLEXas the experimental solver and write the problem modeland GBD and FP algorithm script into the CPLEX solver.The computational time evaluation is based on a Lenovodesktopwith 3.7GHz dual-core processors and 4Gb of RAM.All corresponding results are averaged over 500 differentsimulation runs. The basic channel and radio parameters areshown in Table 1.

4.1. Performance Evaluation on C-RAN Based PSN. Ourexperiment assumes a C-RAN based PSN architecture of10 RRHs of 20W transmitting power with a fixed positionplaced in a 2000mby 2000m area. EachRRH serves 20 PSUs.These PSUs are randomly placed in each run and satisfiesthat 50% of them have average SNRs lower than 3 dB.In the simulation a variable bandwidth value per RRH isassumed (5, 10, 15, 20)MHz in both downlink and uplink.These bandwidths per RRH are equivalent to 25, 50, 75,


PF-LTE based PSNPS-LTE based PSNGBD 𝜅 = 0.3-C-RAN based PSNGBD 𝜅 = 0.6-C-RAN based PSN

5M

Hz∗

10

RRH

s

10

RRH

s

10

RRH

s

10

RRH

s

10

MH

z∗

15

MH

z∗

20

MH

z∗

0

200

400

600

Syste

m to

tal t

hrou

ghpu

t (M

bps)

Total resources (bandwidth per RRH ∗ num. of RRHs)

Figure 3: System total throughput versus total resources with C-RAN based and LTE-based PSN.

and 100 OFDM RBs, respectively. The fairness factor ofAlgorithm 2 𝜅 = 0.3 and 𝜅 = 0.6 is selected. On thebase of the previous analysis, when 𝜅 is small, the allocatorpursues to a high network performance revenue ratherthan PSU’s fairness of allocation. It is opposite when 𝜅 islarge. This paper assumes all the RBs (Num. of RRHs ∗Num. of RBs per RRH) can be allocated centrally withoutinterference in the C-RAN based architecture because all thechannel information can be collected by the allocator; theinterference pair of RBs can be arranged to the users whoare far away enough to avoid the signal interference. Wechoose LTE-based PSN architecture as comparison with atypical allocation algorithm Proportional Fair (PF) [25] andan improved one called PS which is dedicatedly proposedfor the PSN service [12]. The interference between PSUsin LTE-based PSN can also be ignored by the interferencenotice signaling message that communicated on the LTE X2interfaces. We compare C-RAN based PSN and LTE-basedPSN from two perspectives: system total throughput andJain’s Fairness Index (


UB: bender onlyLB: bender onlyUB: bender with relaxation and FPLB: bender with relaxation and FP

−1000

0

1000

2000

3000

4000

Upp

er an

d lo

wer

bou

nd v

alue

50 15 2010

Iteration step

Figure 5: Upper and lower bound value versus iteration step withdifferent algorithms.

𝜅 = 0.3 is lower than LTE-based with PS although thethroughput is much better. This implies a suitable 𝜅 valuecan allow a well-balanced trade-off between the maximalthroughput and the allocation fairness among each PSU.

4.2. Convergence of GBD and FP-Based RB Allocation Algo-rithm. In Section 4.1, the performance of C-RAN based PSNwith GBD scheduler has been investigated.Then we move onto the algorithm’s convergence and efficiency. Figure 5 showsthe convergence of proposed Generalized Bender’s Decom-position and FP-based algorithm compared with one onlyon the basis of Bender’s Decomposition with no relaxation.We assume a C-RAN based PSN consisting of 10 RRHs and60 PSUs. Firstly, this figure implies that difference betweenthe upper bound and lower bound is tightened by Bender’sDecomposition so that an approximately-optimal solutionof problem (19) can be obtained after finite iterations. Thischange is consistent with Lemma 3 and Theorem 4 inSection 3. And secondly, it can also be seen that the proposedalgorithm needs 14 iterations to obtain the approximately-optimal solution of the system, which is less than the otherone of only Bender’s Decomposition. The acceleration isbrought by the relaxation to the original problem (19). Weuse continuation to deal with the integer variable and thenfind the feasible integer solution by FP whose convergedspeed is faster than the method that directly search for theinteger solution in the regional feasible set constrained bymax

1≤ℓ≤𝜃{𝐵

𝑊

𝜔∗

ℓ} in each iteration.

Figure 6 illustrates the convergence of proposed Gen-eralized Bender’s Decomposition algorithm with different-sized network consisting of 10 RRHs × 50 PSUs, 10 RRHs ×60 PSUs, and 10 RRHs × 70 PSUs. It can be seen that the algo-rithms in any assumptions converge to the approximately-optimal solution quickly. The figure also implies that theiterations in large-sized network are less than a small-sized one. The reason is that when the RRH’s position and

UB: 10 RRHs, 50 PSUs

UB: 10 RRHs, 60 PSUs

LB: 10 RRHs, 60 PSUsUB: 10 RRHs, 70 PSUsLB: 10 RRHs, 70 PSUs

LB: 10 RRHs, 50 PSUs

−1000

0

1000

2000

3000

4000

Upp

er an

d lo

wer

bou

nd v

alue

50 15 2010

Iteration step

Figure 6: Upper and lower bound value versus iteration step withdifferent-sized networks.

simulation area are assumed and PSUs are in large quantity,it is more likely to place more center users who are nearbythe RRHs. Hence, the system performance in large-sizednetwork is generally higher than it in small-sized one. Judgingfrom the same upper bound the algorithm started fromand analysis in Section 3, it can be concluded that theiterations to a great value of approximately-optimal solutionin a large-sized network are less than to a small one ina small-sized network. One can conclude that the iteration ofthe proposed GBD and FP based-algorithm is more relevantto the achievable optimal solution rather than the size of thenetwork.This result on convergence features the applicabilityof the proposed algorithm in the centralized schedulingsystem like C-RAN based PSN in this paper.

4.3. Computational Time of GBD and FP-Based RB AllocationAlgorithm. The average computational time of proposedGBD algorithm is expressed against the different-sized net-work in Figure 7. We select Simplex, Barrier and Bender’sDecompositionwith no relaxation for comparison. Simplex isa general method to search for the (approximately-) optimalsolution of programming problem. Barrier is a commonlyused way to solve QP problem. It is not surprising that thecomputational time needed in proposed GBD and FP-basedalgorithm is much less than that in Simplex and Barrier. Andthe time of Barrier and Simplex algorithms tends to increasein a nearly linear and exponential fashion, respectively, alongwith the network size while that of GBD algorithm has amore flatted one. Since the analysis on Figure 3, iterations ofthe proposed algorithm are less than that of one based onBender’s Decomposition with no relaxation for an assumednetwork size. So the average computational of the proposedalgorithm is least. It is reasonable that the average com-putational time of Simplex tends to increase in a nearlyexponential fashion along with the network size. Howeverthe computational time of the proposed GBD algorithm


SimplexBender onlyBender with relaxation and FPBarrier

10 ∗ 50 10 ∗ 60 10 ∗ 7010 ∗ 40

Size of network (num. of RRHs ∗ num. of PSUs)

0

100

200

300

400

500

Com

puta

tiona

l tim

e (se

c.)

Figure 7: Computational time versus size of C-RAN based PSN.

increases in a more smooth fashion. The reason is that thecomputational time of Bender’s Decomposition depends ontwo factors: total iterations and the computing time in eachiteration by the experimental desktop.The iterations decreaseas the size of network increases as shown in Figure 6. But theexperimental observation shows that the computing time ineach iteration increases almost in a linear way along with theincreased network size. Associated with the iteration steps,the average computational time of the proposedGBD and FP-based algorithm has a smoothly increasing fashion along thenetwork size.

The similar results are obtained from the perspectiveof the jitter of the computational time which is shown inFigure 8. GBD converts the relaxed master QP problem intoa dual problem as analyzed in Section 3.1 so that the jittermainly depends on the experimental desktop performancerather than the solution-searching method in each iterationon which the Simplex and Barrier depends.

4.4. Trade-Off between Objective Function Value and Com-putational Time. Algorithm 2 is also run with differentterminated parameter 𝜏. We assume a C-RAN based PSNnetwork consisting of 10 RRHs and 60 PSUs. In Figure 9,the objective function value of the proposed algorithm isplotted against 𝜏. It is not surprising to see that the objectivefunction value degrades as the terminated parameterde-creases. Moreover, the objective function value obtained isnot sensitive to the value of 𝜏 when it is small enough,namely, smaller than 100 in our instance, which is consistentwith Theorem 5 in Section 3. And the degradations of theobjective function value with each 𝜏 are also not greaterthan the value proposed by Theorem 5. It is easy to knowthe greater 𝜏 is, the less computation is time-consuming.Therefore we can select on-demand value of error tolerance 𝜏that considers the trade-off between the computational timeand the objective function value in the C-RAN based PSNsystem.

SimplexBender onlyBender with relaxation and FPBarrier

10 ∗ 50 10 ∗ 60 10 ∗ 7010 ∗ 40

100

200

300

400

500

Posit

ive j

itter

of c

ompu

tatio

nal t

ime (

sec.)

Size of network (num. of RRHs ∗ num. of PSUs)

Figure 8: Positive jitter of computational time versus size of C-RANbased PSN.

600

800

1000

1200

1400

1600

1800

2000

Obj

ectiv

e fun

ctio

n va

lue

800400 1600100 2000

𝜏

Figure 9: Objective function value versus terminated parameter 𝜏.

5. Conclusion

This paper researches on the C-RAN based PSN architectureand OFDM resources allocation problem in it. Firstly, wedesign the C-RAN based PSN and then by formulating theOFDM RB resources allocation problem into a QP withinteger variable, we work out a solution considering both theexpected system revenue and the PSU’s allocation fairness. Tosolve this complicated QP with integer variable, the continu-ation of integer variable is used to relax the original probleminto a general QP problem. The relaxed problem is optimallysolved by a proposed Generalized Bender’s Decompositionalgorithm after finite iterations. Then FP standard is adoptedto obtain the actual integer solution on the original problem.The trade-off between the system degradation and the errortolerance of the proposed algorithm is given theoretically.The numerical results finally show the C-RAN based PSN


obtains a good throughput performance without a cost ofPSU’s allocation fairness and the proposedGBDandFPbasedalgorithm has the fine convergence and low computationaltime.

One achievement of this paper is to propose a PSN archi-tecture based on C-RAN and model the resource allocationproblem in this centralized allocation system. In addition,OFDM resource allocation problem in C-RAN based PSNis complicated because of the integer variables and a largeamount of PSU-RRH associations when disaster occurs.However, the allocating efficiency is more important in PSNthan commercial network. Hence, another achievement isthat we use a corresponding GBD and FP method to solveresources allocating problem efficiently in the proposed C-RAN based PSN, which is referential to the future works onthe similar problem.

Competing Interests

The authors declare that they have no competing interests.

Acknowledgments

This paper is supported by the 863 Program (2015AA01A705)and NSFC (61271187).

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Research Article An Enhanced OFDM Resource Allocation ...denoted by Y Z × =()×,where is the number of RBs allocated to PSU by RRH .Particularly, =0 means PSU is not served by RRH