Self-Planning of Base Station Transmit Power for Coverage ...

Research ArticleSelf-Planning of Base Station Transmit Power forCoverage and Capacity Optimization in LTE

V. Buenestado,1 M. Toril,1 S. Luna-Ramírez,1 and J. M. Ruiz-Avilés2

1Department of Communication Engineering, University of Malaga, 29071 Malaga, Spain2Ericsson, 29590 Malaga, Spain

Correspondence should be addressed to V. Buenestado; [email protected]

Received 7 April 2017; Accepted 11 July 2017; Published 22 August 2017

Academic Editor: Antonio de la Oliva

Copyright © 2017 V. Buenestado et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

A computationally efficient self-planning algorithm for adjusting base station transmit power in a LTE system on a cell-by-cellbasis is presented. The aim of the algorithm is to improve the overall network spectral efficiency in the downlink by reducingthe transmit power of specific cells to eliminate interference problems. The main driver of the algorithm is a new indicator thatpredicts the impact of changes in the transmit power of individual cells on the overall network Signal to Interference plus NoiseRatio (SINR) for the downlink. Algorithm assessment is carried out over a static system-level simulator implementing a live LTEnetwork scenario. During assessment, the proposed algorithm is compared with a state-of-the-art self-planning algorithm based onthe modification of antenna tilt angles. Results show that the proposed algorithm can improve both network coverage and capacitysignificantly compared to other automatic planning methods.

1. Introduction

In recent years, mobile communications have experienced arapid increase in the number of users and services, whichhas led operators and manufacturers to develop systemswith greater capacity. In parallel, the complexity and size ofthese systems have increased exponentially, making networkmanagement a very challenging task. To deal with such com-plexity, operators demand automatic tools for configuringnetwork parameters, as a flexible solution to improve networkcapacity without new investments. This trend has stimulatedresearch and standardization activities in the field of Self-Organizing Networks (SON) [1].

Network Coverage and Capacity Optimization (CCO)has been identified by operators as one of the most importantuse cases of SON [2]. The aim of CCO is to provide optimal(i.e., maximum) coverage and capacity. In legacy radio accesstechnologies (e.g., Global System forMobile communication,GSM), CCO can be solved easily as coverage and capacityare decoupled by means of frequency planning. This is notthe case for Long Term Evolution (LTE) technology, whereall cells in the same layer use the same frequency band. Thistight frequency reuse scheme makes the closest cells also

the most interfering ones, so that a wider coverage usuallyleads to a higher interference, a lower spectral efficiency, and,ultimately, less capacity. As a result, network coverage andcapacity in LTE are strongly linked, so a tradeoff betweenthem is necessary [3].

Power control (PC) is a powerful strategy for dealingwith the CCO problem. The aim of PC is to reduce theamount of interference from neighbor cells while ensuringthat enough power is transmitted to (or received from) UserEquipment (UE) tomaintain an acceptable link quality [4, 5].In LTE, fractional power control is used in the UpLink (UL)to dynamically change UE transmit power [5]. Moreover,several self-planning methods have been proposed to adaptUpLink Power Control (ULPC) parameters in LTE to localnetwork conditions [6–10]. However, for the downlink (DL)of LTE, power planning is the simplest solution to solve CCOissues in the absence of a power control scheme.

Changing the base station transmit power is as costlyas changing any other radio access network parameter sinceboth actions only require modifying the network parameterfile. However, there remains the problem of finding theoptimum transmit power settings. A tradeoff exists betweenensuring a good connection quality for users served by the

HindawiMobile Information SystemsVolume 2017, Article ID 4380676, 12 pageshttps://doi.org/10.1155/2017/4380676

https://doi.org/10.1155/2017/4380676

2 Mobile Information Systems

cell changing its transmit power while reducing interferencein its neighbor cells.Thus, power planning can be formulatedas a large-scale nonseparable multiobjective optimizationproblem. To find the optimal power plan, many searchalgorithms have been proposed in the literature [11–16]. Tocheck the quality of a plan, analytical network models can beused [14]. However, analytic approaches fail to reflect relevantnetwork conditions (irregular spatial traffic distribution, basestation configuration, channel conditions, clutter type, etc.).To solve this limitation, a system-level simulator is often usedin network planning tools [11–13, 15, 16]. However, system-level simulations are time consuming. Thus, it is essentialto have an automatic search algorithm that finds the bestparameter plan in a few attempts. To the authors’ knowledge,no previous work has derived a simple rule to modify anexisting power plan ensuring that the resulting solution isindeed the best solution.

In this work, a novel self-planning algorithm for modi-fying DL transmit power in a LTE system is presented. Theproposed algorithm aims to improve the overall networkSINR by adjusting DL transmit power on a per cell basis.The algorithm is designed as a set of controllers (one percell), whose input is a new cell performance indicator. Thisnovel indicator, which is the core of the proposal, reflects if ahigher (or lower) transmit power in a particular base stationincreases (or decreases) the overall network SINR in DL.The algorithm is validated on a static system-level simulatorimplementing a real LTE dense urban scenario. During theanalysis, the proposed algorithm is compared with a state-of-the-art self-planning approach based on remote electrical tilt.

The rest of the work is organized as follows. Section 2presents the state of research in the CCO problem. Section 3presents the problem formulation from which the newindicator is derived. Section 4 outlines the proposed methodfor adjusting DL transmit power on a cell basis. Section 5shows the results of simulations carried out to validate thealgorithm. Finally, Section 6 presents the main conclusionsof the work.

2. Related Work

Depending on their purpose, SON methods can be classifiedas self-planning, self-optimization, or self-healing [17, 18].Self-planning methods are conceived for the planning stage,when the network is not deployed yet. Consequently, self-planning algorithmsmake use of network models to estimatethe quality of a network parameter plan. In the search ofthe best plan, many different parameter settings have to betested. For this purpose, classical optimization methods areused to find the best solution (e.g., brute-force enumeration[19], simulated annealing [13], Taguchi [6], and genetic [20]).To check the quality of a plan, analytical [14] or simulationmodels [5] can be used. Self-optimization (a.k.a. self-tuning)methods are designed to adapt network parameters to chang-ing network conditions during the operational stage [11–13, 15, 16]. Self-optimization algorithms usually consist of acontroller that iteratively modifies network parameters basedon certain network performance indicators. Unlike self-planning, self-optimization algorithms do not need a system

model but make use of measurements from the live networkto adjust network parameters. Finally, self-healing methodsaim to detect, diagnose, and compensate problems caused byabnormal events in the network [21–23].

SON methods can also be classified in terms of themodified network parameter. In particular, CCO is usuallyperformed by changing antenna bearings [6, 19, 20, 24–30] or power settings [11–13, 15, 16]. Strategies to modifyantenna bearings include both self-planning [6, 19, 24–26] and self-optimization methods [20, 27–30]. Althoughmost of these methods modify antenna tilt angles, a fewof them simultaneously set tilt and azimuth angles [6, 24,26]. Regarding power-based CCO methods, a power controlalgorithm is proposed in [11] for adjusting power levelsaccording to the needs of UEs. The algorithm tunes DLtransmit power based on signal quality measurements fromUEs to ensure that all UEs experience adequate transmissionquality. The algorithm also detects when UEs experience atransmission quality greater than required, so that transmitpower is decreased to minimize interference in neighborcells. In [12], the previous algorithm is extended by solv-ing convergence problems through starting planning withmaximum cell power levels for all transmitters. In [13], adecentralized algorithm for adjusting the transmit power ofbase stations in LTE is also presented. In this case, eachneighbor cell searches for the optimal setting of the transmitpower of the cell, keeping the power setting of the restof cells unaltered. The algorithm relies on the knowledgeof the interference produced by a base station in its neighborcells at different transmit power levels. In [15], a moresophisticated algorithm is proposed to jointly tune transmitpower and antenna tilt. In this algorithm, cells are classifiedin three groups depending on the ratio of covered UEsand carried traffic. Parameter changes are calculated basedon the performance of the worst cell, and changes aresimultaneously executed for all cells in the same group.Therefore, this method does not exploit the fact that networkparameters can be set on a cell-by-cell basis. In [16], adecentralized self-optimization algorithm is proposed toadjust both transmit power and tilt on a cell basis tomaximize both cell-average and cell-edge UE throughputof the whole network. The algorithm is implemented asa controller based on fuzzy reinforcement learning. Inputsare the current transmit power and tilt settings of theoptimized cell, and the average relative differences in load andspectral efficiency with neighbor cells. A central controllerenables cooperative learning by sharing the result of theadaptation process among cells. Controller parameters areadapted based on the result of random parameter changes.A major drawback is the fact that the algorithm needs manyiterations to converge and can temporarily degrade networkperformance.

Likewise, power replanning is also used in self-healingalgorithms to solve localized problems caused by networkfailures. Unlike self-optimization approaches, the aimof heal-ing is not to achieve optimal systemperformance, but to bringa faulty cell to acceptable service levels. The most commonapplication is Cell Outage Compensation (COC) [21–23].The main limitation of these methods is the assumption

Mobile Information Systems 3

that, in normal operation, base stations do not fully utilizethe available transmit power. However, in live networks,base stations are generally set to the maximum power toprovide maximum coverage. Moreover, these algorithms aremainly focused on improving coverage, with less emphasis onintercell interference or signal quality.

A major drawback of most SON algorithms is the lack ofan optimality proof. Most self-planning methods are basedon heuristic approaches that reduce the size of the solutionspace to be explored to reduce computation time. Likewise,most self-optimization algorithms rely on heuristic controlrules based on the knowledge of an experienced opera-tor. Although some advanced self-optimization algorithmsinclude unsupervised learning methods (e.g., Q-Learning[16]), simplifying assumptions often cause that there is noguarantee that optimal system performance is reached.Thus,the goodness of tuning is usually assessed based on conver-gence speed and stability issues [31]. Only in very rare cases,the optimality conditions can be reformulated as a controlproblem (e.g., [32], where the problem of traffic sharing inGSM is formulated as a balancing problem between adjacentcells).

In this work, the global CCO problem is formulated as abalancing problem by considering the tradeoff between theperformance of a cell and its neighbors when increasing thetransmit power of the cell under study. From the analysis ofoptimality conditions, a new indicator is derived that reflectsthe overall SINR gain in the vicinity of a cell increasing itstransmit power. Thus, it is ensured that changes in powersettings performed on a cell-by-cell basis always improvethe overall system performance. The main contributionsof this work are (a) a new indicator used to detect ifincreasing the transmit power of a particular base stationincreases (or decreases) the total system SINR in DL, (b) analgorithm for adjusting base station transmit power in a LTEnetwork to increase the coverage area and overall spectralefficiency based on the previous indicator, and (c) a thor-ough comparison of the proposed algorithm with classicalCCO algorithms in a realistic scenario taken from a livenetwork.

3. Problem Formulation

In the following paragraphs, variables in logarithmic unitsare written in uppercase, whereas variables in natural unitsare written in lowercase. Likewise, the term DL is omittedhereafter for brevity.

CCO should be treated as a classical multiobjectiveoptimization problem, since both coverage and capacitymustbe maximized. However, it is common practice to assigna higher priority to either coverage or capacity, since bothfeatures cannot be simultaneously optimized. In most cases,optimization is focused on network capacity, provided thata minimal network coverage is ensured [8]. In networkplanning, network capacity is often evaluated in terms ofspectral efficiency, which is given by the signal quality interms of SINR. Nonetheless, several objective functions havebeen proposed in the literature to measure the overall signal

quality of a network, depending on how the performance ofusers and cells is aggregated:

(a) Overall usermean, considering all users equally.Thus,more populated cells tend to dominate the figure formerit.

(b) Cell arithmetic mean, where all cells are treated thesame, regardless of their size and traffic. Such a figureof merit is simple to compute and easy to interpret,being the preferred option for operators. From theShannon bound, it can be inferred that the averageSINR in a cell (in dB) is a rough approximation of itsaverage spectral efficiency [34]. Thus, the arithmeticmean of the average SINR across cells approximatesthe average maximum cell capacity, provided that allcells have the same system bandwidth.

(c) Cell harmonic mean [6], where cells with small SINRvalues render the mean value small. Thus, cells withworse performance tend to dominate the figure formerit.

In this work, the arithmeticmean of the average SINR percell in dB is considered. Thus, the objective function to bemaximized is the total system SINR (in dB), computed as

Maximize Γ𝑡 = ∑𝑖

Γ (𝑖)subject to Γce (𝑖) > Γcemin

(𝑖) , (1)

where Γ(𝑖) and Γce(𝑖) are the average SINR of users in cell 𝑖and in the cell-edge of cell 𝑖, respectively. In (1), Γcemin

(𝑖) is theminimal value of Γce required in cell 𝑖. The decision variablesare cell transmit powers, 𝑃𝑇𝑋(𝑖), which determine the valueof Γ(𝑖). In this work, 𝑃𝑇𝑋(𝑖) is defined as the transmit powerlevel per Physical Resources Block (PRB). It is assumed that𝑃𝑇𝑋(𝑖) is the same for all PRBs.

In the absence of constraints, any local minimum mustsatisfy the stationary condition, that is,

𝜕Γ𝑡𝜕𝑃𝑇𝑋 (𝑖) = 0 ∀𝑖. (2)

If it is assumed that changing the transmit power of a cellonly affects a limited number of neighbor cells, the stationarycondition can be rewritten as

𝜕Γ𝑡𝜕𝑃𝑇𝑋 (𝑖) ≈𝜕 (Γ (𝑖) + ∑𝑗∈𝑁(𝑖) Γ (𝑗))𝜕𝑃𝑇𝑋 (𝑖) , (3)

where 𝑁(𝑖) is the set of neighbors of cell 𝑖. The terms in thenumerator reflect the tradeoff between the SINR of a cell andits neighbors. Specifically, increasing the transmit power of acell increases the SINR of users served by that cell, that is,

𝜕Γ (𝑖)𝜕𝑃𝑇𝑋 (𝑖) > 0, (4)


at the expense of decreasing the SINR of users in neighborcells, that is,

𝜕 (∑𝑗∈𝑁(𝑖) Γ (𝑗))𝜕𝑃𝑇𝑋 (𝑖) < 0. (5)

To find a local maximum, a simple gradient ascentmethod can be used. For this purpose, the slope of theobjective functionwith respect to each decision variablemustbe obtained. Such an indicator, 𝛽(𝑖), reflecting the gain in thetotal system SINR obtained by increasing the transmit powerof a cell 𝑖 is estimated as follows.

3.1. Novel Indicator. For convenience, the total SINR arounda cell (in dB) is first defined as

Γ𝑐 (𝑖) = Γ (𝑖) + ∑𝑗∈𝑁(𝑖)

Γ (𝑗)= 𝑆 (𝑖) − 𝐼 (𝑖) + ∑

𝑗∈𝑁(𝑖)

(𝑆 (𝑗) − 𝐼 (𝑗)) , (6)

where 𝑆(𝑖) and 𝐼(𝑖) are the average desired signal andinterference levels (in logarithmic units) received in cell 𝑖,respectively.

In (6), averages correspond to the aggregation of all usersin a cell. In most network planning tools, potential users arerepresented by locations. In a real scenario, each location hasa different probability of a user demanding service from it,which is given by the spatial traffic distribution. This canbe taken into account by multiplying the values of eachvariable in a location by a weight function representing trafficprobability in that location as

Γ𝑐 (𝑖) = ∑(𝑥,𝑦)∈𝐴(𝑖)

𝑝𝑢 (𝑥, 𝑦) (𝑆 (𝑥, 𝑦) − 𝐼 (𝑥, 𝑦))+ ∑𝑗∈𝑁(𝑖)

∑(𝑥,𝑦)∈𝐴(𝑗)

𝑝𝑢 (𝑥, 𝑦) (𝑆 (𝑥, 𝑦) − 𝐼 (𝑥, 𝑦)) , (7)

where𝐴(𝑖) is the service area of cell 𝑖 (i.e., locations served bycell 𝑖), 𝑝𝑢(𝑥, 𝑦) is the probability that a user generates trafficfrom location (𝑥, 𝑦), and 𝑆(𝑥, 𝑦) and 𝐼(𝑥, 𝑦) are the receivedsignal level from the serving cell and total interference levelfrom neighbor cells for a UE located at (𝑥, 𝑦), respectively.Obviously,

∑(𝑥,𝑦)∈𝐴(𝑖)

𝑝𝑢 (𝑥, 𝑦) = 1 ∀𝑖. (8)

From (3) and (7), it follows that the sensitivity of Γ𝑡 tochanges in 𝑃𝑇𝑋(𝑖) is the same as that of Γ𝑐, that is,

𝛽 (𝑖) = 𝜕Γ𝑡 (𝑖)𝜕𝑃𝑇𝑋 (𝑖) ≈𝜕Γ𝑐 (𝑖)𝜕𝑃𝑇𝑋 (𝑖) . (9)

For simplicity, the partial derivative in (9) is broken downin four addends as

𝛽 (𝑖) ≈ 𝐹1 − 𝐹2 + 𝐹3 − 𝐹4, (10)

where

𝐹1 = 𝜕𝑆 (𝑖)𝜕𝑃𝑇𝑋 (𝑖) ,𝐹2 = 𝜕𝐼 (𝑖)𝜕𝑃𝑇𝑋 (𝑖) ,𝐹3 = 𝜕 (∑𝑗∈𝑁(𝑖) 𝑆 (𝑗))𝜕𝑃𝑇𝑋 (𝑖) ,𝐹4 = 𝜕 (∑𝑗∈𝑁(𝑖) 𝐼 (𝑗))𝜕𝑃𝑇𝑋 (𝑖) .

(11)

𝐹1 reflects the impact of 𝑃𝑇𝑋(𝑖) on the desired signal level inthe modified cell (i.e., that received by users in cell 𝑖 fromcell 𝑖). 𝐹2 does the same for the total interference received byusers in cell 𝑖 from neighbor cells, 𝐹3 for the desired signalreceived by users in neighbor cells 𝑗, 𝑗 = 𝑖, and 𝐹4 for theinterference received by users in neighbors 𝑗. All these factorsare calculated as follows.

Source Desired Signal Term, 𝐹1. The signal level received froma cell 𝑖 in location (𝑥, 𝑦) is calculated as

𝑃𝑅𝑋 (𝑖, 𝑥, 𝑦) = 𝑃𝑇𝑋 (𝑖) − PL (𝑖, 𝑥, 𝑦) , (12)

where PL(𝑖, 𝑥, 𝑦) is the path loss (including antenna gains)between cell 𝑖 and location (𝑥, 𝑦). In particular, the desiredsignal level in a location is

𝑆 (𝑥, 𝑦) = 𝑃𝑅𝑋 (𝑖, 𝑥, 𝑦) , (𝑥, 𝑦) ∈ 𝐴 (𝑖) . (13)

Note that the spatial traffic distribution,𝑝𝑢(𝑥, 𝑦), does notdepend on power settings. Then, from (7), (12), and (13), it isdeduced that the impact of changing 𝑃𝑇𝑋(𝑖) on the desiredsignal level received by users in cell 𝑖 is𝐹1 = 𝜕 (∑(𝑥,𝑦)∈𝐴(𝑖) 𝑝𝑢 (𝑥, 𝑦) 𝑆 (𝑥, 𝑦))𝜕𝑃𝑇𝑋 (𝑖)= ∑(𝑥,𝑦)∈𝐴(𝑖)

𝑝𝑢 (𝑥, 𝑦) 𝜕𝑃𝑇𝑋 (𝑖)𝜕𝑃𝑇𝑋 (𝑖) = ∑(𝑥,𝑦)∈𝐴(𝑖)

𝑝𝑢 (𝑥, 𝑦)= 1.

(14)

Source Interference Term, 𝐹2. The interference received inlocation (𝑥, 𝑦) in cell 𝑖 from any other cell 𝑗 = 𝑖 is calculatedas

𝐼 (𝑥, 𝑦) = 10 ⋅ log10( ∑𝑗∈𝑁(𝑖)

𝑝𝑟𝑥 (𝑗, 𝑥, 𝑦) 𝑙 (𝑗) + 𝑛0) , (15)

where 𝑝𝑟𝑥(𝑗, 𝑥, 𝑦) is the power received at (𝑥, 𝑦) from inter-fering cell 𝑗 (in natural units), 𝑛0 is the thermal noise (innatural units), and 𝑙(𝑗) is the load of cell 𝑗 (dimensionless).


The average load of a cell 𝑖 is estimated by the sumof the trafficload generated by each location (𝑥, 𝑦) served by cell 𝑖 as

𝑙 (𝑖) = ∑(𝑥,𝑦)∈𝐴(𝑖)

𝑙 (𝑥, 𝑦)

= ∑(𝑥,𝑦)∈𝐴(𝑖) (𝑡 (𝑥, 𝑦) /se (𝑥, 𝑦))𝑁prb (𝑖) ,(16)

where 𝑡(𝑥, 𝑦) is the average traffic generated by location (𝑥, 𝑦)(in bps), se(𝑥, 𝑦) is the spectral efficiency obtained by users atlocation (𝑥, 𝑦) (in bps per PRB), and𝑁prb(𝑖) is the number ofPRBs in cell 𝑖, given by the system bandwidth. In this work,spectral efficiency is estimated from SINR by the truncatedShannon bound formula [34]

se (𝑥, 𝑦)

={{{{{{{{{

0 𝛾 (𝑥, 𝑦) < 𝛾min,𝛼ILlog2 (1 + 𝛾 (𝑥, 𝑦)) 𝛾min ≤ 𝛾 (𝑥, 𝑦) ≤ 𝛾max,semax 𝛾max < 𝛾 (𝑥, 𝑦) ,

(17)

where semax is the maximum spectral efficiency that can beobtained in a location, 𝛾(𝑥, 𝑦) is the SINR in a location (inlinear units), 𝛾min and 𝛾max are SINR values correspondingto 0 and semin, respectively, and 𝛼IL is an attenuation factorrepresenting implementation losses.

Thus, the impact of changing the power of a cell on thetotal interference level received by that cell is

𝐹2 = 𝜕𝐼 (𝑖)𝜕𝑃𝑇𝑋 (𝑖) = ∑(𝑥,𝑦)∈𝐴(𝑖)

𝑝𝑢 (𝑥, 𝑦) 𝜕𝐼 (𝑥, 𝑦)𝜕𝑃𝑇𝑋 (𝑖)= ∑(𝑥,𝑦)∈𝐴(𝑖)

[[10ln 10 𝑝𝑢 (𝑥, 𝑦)∑𝑗∈𝑁(𝑖) 𝑝𝑟𝑥 (𝑗, 𝑥, 𝑦) 𝑙 (𝑗) + 𝑛0

⋅ ∑𝑗∈𝑁(𝑖)

𝑝𝑟𝑥 (𝑗, 𝑥, 𝑦) 𝜕𝑙 (𝑗)𝜕𝑃𝑇𝑋 (𝑖)]] .

(18)

In (18), it is observed that changing the transmit power of acell only affects the received interference level in the same cellthrough changes in the load of neighbor cells.

As traffic demand does not depend on link quality, it isdeduced from (16) that the sensitivity of neighbor load tochanges in 𝑃𝑇𝑋(𝑖) is

𝜕𝑙 (𝑗)𝜕𝑃𝑇𝑋 (𝑖)= ∑(𝑥,𝑦)∈𝐴(𝑗) 𝑡 (𝑥, 𝑦) (𝜕 (1/se (𝑥, 𝑦)) /𝜕𝑃𝑇𝑋 (𝑖))𝑁prb (𝑗) .

(19)

From (17), it is deduced that the slope of the spectral efficiencywith respect to the transmit power is nonzero only in thoselocations where 𝛾min ≤ 𝛾(𝑥, 𝑦) ≤ 𝛾max, so that

𝜕𝑙 (𝑗)𝜕𝑃𝑇𝑋 (𝑖) = −1𝑁prb (𝑗)

⋅ ∑(𝑥,𝑦)∈𝐴(𝑗),𝛾(𝑥,𝑦)∈[𝛾min,𝛾max]

(𝑡 (𝑥, 𝑦) 1𝛼IL [log2 (1 + 𝛾 (𝑥, 𝑦))]2

⋅ 11 + 𝛾 (𝑥, 𝑦) 1ln 2𝜕 [10Γ(𝑥,𝑦)/10]𝜕𝑃𝑇𝑋 (𝑖) )

= − ∑(𝑥,𝑦)∈𝐴(𝑗),𝛾(𝑥,𝑦)∈[𝛾min,𝛾max]

𝑙 (𝑥, 𝑦)

⋅ 𝛾 (𝑥, 𝑦)(1 + 𝛾 (𝑥, 𝑦)) ln (1 + 𝛾 (𝑥, 𝑦)) ln 1010⋅ 𝜕 (−𝐼 (𝑥, 𝑦))𝜕𝑃𝑇𝑋 (𝑖) .

(20)

To compute the derivative of Γ(𝑥, 𝑦) in (20), it hasbeen considered that only the received interference, 𝐼(𝑥, 𝑦),changes with 𝑃𝑇𝑋(𝑖). For tractability, additional side effectshave not been considered. In addition, it is assumed that thesum of contributions to the change in load from all locations(𝑥, 𝑦) in a cell can be approximated by the change in loadexperienced when all the traffic in the cell is generated in asingle location with the average link performance of the cell.This consideration assumes that the change in the average cellperformance is representative of the changes in all points inthe cell. Thus, (20) can be approximated by

𝜕𝑙 (𝑗)𝜕𝑃𝑇𝑋 (𝑖)≈ 𝑙 (𝑗) 𝛾 (𝑗)(1 + 𝛾 (𝑗)) ln (1 + 𝛾 (𝑗)) ln 1010

𝜕 (𝐼 (𝑗))𝜕𝑃𝑇𝑋 (𝑖) ,

(21)

where 𝛾(𝑗) and 𝐼(𝑗) are, respectively, the traffic-weightedaverage SINR (in linear units) and interference level (inlogarithmic units) for all locations in cell 𝑗. Then,

𝜕𝐼 (𝑗)𝜕𝑃𝑇𝑋 (𝑖) = ∑(𝑥,𝑦)∈𝐴(𝑗)

𝑝𝑢 (𝑥, 𝑦) 𝜕𝐼 (𝑥, 𝑦)𝜕𝑃𝑇𝑋 (𝑖)= ∑(𝑥,𝑦)∈𝐴(𝑗)

[[10ln 10 𝑝𝑢 (𝑥, 𝑦)∑𝑚∈𝑁(𝑗) 𝑝𝑟𝑥 (𝑚, 𝑥, 𝑦) 𝑙 (𝑚) + 𝑛0

⋅ ∑𝑚∈𝑁(𝑗)

𝜕 (𝑝𝑟𝑥 (𝑚, 𝑥, 𝑦) 𝑙 (𝑚))𝜕𝑃𝑇𝑋 (𝑖) ]] .

(22)

Note that any change of transmit power in a cell affects signalquality, spectral efficiency, and, ultimately, the load of the


cell whose power is modified. Such a change in cell loadcause changes in the interference generated on neighbor cells,which also change their signal quality, spectral efficiency, andload. For tractability, it is assumed here that the only cellchanging load is the cell changing transmit power.This is trueif the change in transmit power is small enough. It has beenchecked with simulations in a typical scenario that neighbors’load changes less than 7% (in relative terms) if the change oftransmit power is less than 1 dB. If the change of cell load inneighbors is negligible,

𝜕𝑙 (𝑚)𝜕𝑃𝑇𝑋 (𝑖) ≈ 0 ∀𝑚 = 𝑖. (23)

Thus, (22) can be rewritten as

𝜕𝐼 (𝑗)𝜕𝑃𝑇𝑋 (𝑖) ≈ ∑(𝑥,𝑦)∈𝐴(𝑗)

[ 10ln 10

⋅ 𝑝𝑢 (𝑥, 𝑦)∑𝑚∈𝑁(𝑗) 𝑝𝑟𝑥 (𝑚, 𝑥, 𝑦) 𝑙 (𝑚) + 𝑛0

⋅ (𝜕𝑝𝑟𝑥 (𝑖, 𝑥, 𝑦)𝜕𝑃𝑇𝑋 (𝑖) 𝑙 (𝑖)

+ 𝑝𝑟𝑥 (𝑖, 𝑥, 𝑦) 𝜕𝑙 (𝑖)𝜕𝑃𝑇𝑋 (𝑖))] .(24)

The two partial derivatives in (24) show how the interfer-ence in neighbors changes with the change of transmit powerand load in the modified cell. These terms can be calculatedas

𝜕𝑝𝑟𝑥 (𝑖, 𝑥, 𝑦)𝜕𝑃𝑇𝑋 (𝑖) = ln 1010 𝑝𝑟𝑥 (𝑖, 𝑥, 𝑦) , and (25)

𝜕𝑙 (𝑖)𝜕𝑃𝑇𝑋 (𝑖) = −ln 1010 𝑙 (𝑖) 𝛾 (𝑖)(1 + 𝛾 (𝑖)) ln (1 + 𝛾 (𝑖)) . (26)

From (21), (24), (25), and (26), it is obtained that

𝐹2 ≈ ∑(𝑥,𝑦)∈𝐴(𝑖)

[[

𝑝𝑢 (𝑥, 𝑦)∑𝑗∈𝑁(𝑖) 𝑝𝑟𝑥 (𝑗, 𝑥, 𝑦) 𝑙 (𝑗) + 𝑛0⋅ ∑𝑗∈𝑁(𝑖)

(𝑝𝑟𝑥 (𝑗, 𝑥, 𝑦) 𝑙 (𝑗) 𝛾 (𝑗)(1 + 𝛾 (𝑗)) ln (1 + 𝛾 (𝑗)) ⋅ ∑(𝑥,𝑦)∈𝐴(𝑗)

[ 𝑝𝑢 (𝑥, 𝑦)∑𝑚∈𝑁(𝑗) 𝑝𝑟𝑥 (𝑚, 𝑥, 𝑦) 𝑙 (𝑚) + 𝑛0 ⋅ (𝑝𝑟𝑥 (𝑖, 𝑥, 𝑦) 𝑙 (𝑖) − 𝑝𝑟𝑥 (𝑖, 𝑥, 𝑦) 𝑙 (𝑖)𝛾 (𝑖)(1 + 𝛾 (𝑖)) ln (1 + 𝛾 (𝑖)))])]] .

(27)

By grouping terms, 𝐹2 can be rewritten as

𝐹2 ≈ [1 − 𝑓 (𝛾 (𝑖))] ∑𝑗∈𝑁(𝑖)

[𝑖𝑐 (𝑗, 𝑖) 𝑓 (𝛾 (𝑗)) 𝑖𝑐 (𝑖, 𝑗)] , (28)

where

𝑓 (𝛾 (𝑖)) = 𝛾 (𝑖)(1 + 𝛾 (𝑖)) ln (1 + 𝛾 (𝑖)) , (29)

and 𝑖𝑐(𝑗, 𝑖) is the average ratio of interference in cell 𝑖 due toneighbor 𝑗, defined as

𝑖𝑐 (𝑗, 𝑖) = ∑(𝑥,𝑦)∈𝐴(𝑖)

𝑝𝑢 (𝑥, 𝑦) 𝑝𝑟𝑥 (𝑗, 𝑥, 𝑦) 𝑙 (𝑗)∑𝑘∈𝑁(𝑖) 𝑝𝑟𝑥 (𝑘, 𝑥, 𝑦) 𝑙 (𝑘) + 𝑛0 , (30)

Neighbor Desired Signal Term, 𝐹3. From (7) and (11),

𝐹3 = 𝜕 (∑𝑗∈𝑁(𝑖) 𝑆 (𝑗))𝜕𝑃𝑇𝑋 (𝑖)= 𝜕 (∑𝑗∈𝑁(𝑖)∑(𝑥,𝑦)∈𝐴(𝑗) 𝑝𝑢 (𝑥, 𝑦) 𝑃𝑅𝑋 (𝑗, 𝑥, 𝑦))𝜕𝑃𝑇𝑋 (𝑖) .

(31)

As neither 𝑝𝑢(𝑥, 𝑦) nor 𝑃𝑅𝑋(𝑗, 𝑥, 𝑦) depends on 𝑃𝑇𝑋(𝑖), 𝐹3 =0.Neighbor Interference Term, 𝐹4. Similarly to 𝐹2, the change inneighbor interference can be expressed as

𝐹4 = 𝜕 (∑𝑗∈𝑁(𝑖) 𝐼 (𝑗))𝜕𝑃𝑇𝑋 (𝑖)= ∑𝑗∈𝑁(𝑖)

∑(𝑥,𝑦)∈𝐴(𝑗)

𝑝𝑢 (𝑥, 𝑦) 𝜕𝐼 (𝑥, 𝑦)𝜕𝑃𝑇𝑋 (𝑖) .(32)

Note that 𝑁(𝑗) includes cell 𝑖 as an interferer of cell 𝑗. Then,the partial derivative in (32) must be separated in two groupsof cells: the interfering cell 𝑖 and the rest of interfering cells𝑚 = 𝑖. Thus,

𝜕𝐼 (𝑥, 𝑦)𝜕𝑃𝑇𝑋 (𝑖) =10ln 10 1∑𝑚∈𝑁(𝑗) 𝑝𝑟𝑥 (𝑚, 𝑥, 𝑦) 𝑙 (𝑚) + 𝑛0

⋅ [𝜕 (∑𝑚∈𝑁(𝑗),𝑚 =𝑖 𝑝𝑟𝑥 (𝑚, 𝑥, 𝑦) 𝑙 (𝑚))𝜕𝑃𝑇𝑋 (𝑖)+ 𝜕 (𝑝𝑟𝑥 (𝑖, 𝑥, 𝑦) 𝑙 (𝑖))𝜕𝑃𝑇𝑋 (𝑖) ] .

(33)


Following the same steps as for 𝐹2, it is obtained that

𝐹4 ≈ [1 − 𝑓 (𝛾 (𝑖))] ∑𝑗∈𝑁(𝑖)

[[𝑖𝑐 (𝑖, 𝑗)

+ ∑𝑚∈𝑁(𝑗),𝑚 =𝑖

𝑖𝑐 (𝑚, 𝑗) 𝑓 (𝛾 (𝑚)) 𝑖𝑐 (𝑖, 𝑚)]] .(34)

Two terms can be identified in (34).The first term reflects thechange of interference in cell 𝑗, caused by the load variationin cell 𝑖 due to the change in spectral efficiency from thenew transmit power of cell 𝑖. The second term reflects thechange of the interference received by cell 𝑗, caused by theload variation in the rest of interferers of cell 𝑗, which alsomodify their load due to change of interference from cell 𝑖.4. Self-Planning Algorithm

In this section, a heuristic method to find the best changein DL transmit power on a cell basis is presented. Theaim of the method is to adjust the transmit power of eachcell in the system so as to improve the total system SINR,Γ𝑡. The method makes use of a classical gradient ascentalgorithm to find the best tradeoff between the SINR of a celland its neighbors, based on the above-described indicator,𝛽(𝑖), reflecting whether increasing the transmit power ofa particular base station increases (or decreases) the totalsystem SINR.

The gradient ascent algorithm is designed as a set of sim-ple proportional controllers (one per cell), which iterativelycompute changes in the DL transmit power based on thevalue of the 𝛽 indicator. Specifically, the output of one ofthese controllers is the change in DL transmit power (in dB),Δ𝑃𝑇𝑋(𝑖), computed as

Δ𝑃𝑇𝑋 (𝑖) ={{{{{{{{{

−1 𝛽 (𝑖) ≤ 𝛽min,0 𝛽min < 𝛽 (𝑖) < 𝛽max,1 𝛽 (𝑖) ≥ 𝛽max,

(35)

where 𝛽min and 𝛽max are thresholds for triggering 𝑃𝑇𝑋(𝑖)modifications, introduced to keep the number of networkchanges to a minimum. In this work, both thresholds aresymmetrical; that is, 𝛽max = −𝛽min.

The proposed algorithm works as an iterative process,starting from an initial power value, 𝑃𝑇𝑋(𝑖), which is latermodified at every iteration (referred to as optimization loop).Every loop starts with the collection of network statistics,from which 𝛽 is computed for all cells in the scenario. Thecollection period must be large enough (e.g., one day) toimprove the robustness of the algorithm. Then, (35) is usedto compute power changes, Δ𝑃(𝑙)𝑇𝑋(𝑖), where 𝑙 is the loopnumber. Finally, the new values of 𝑃𝑇𝑋(𝑖) for the next loopare calculated as

𝑃(𝑙+1)𝑇𝑋 (𝑖) = 𝑃(𝑙)𝑇𝑋 (𝑖) + Δ𝑃(𝑙)𝑇𝑋 (𝑖) . (36)

An output range [𝑃𝑇𝑋min(𝑖), 𝑃𝑇𝑋max

(𝑖)] is defined. 𝑃𝑇𝑋maxis

usually fixed by operators to the maximum value supportedby the equipment, as network coverage is thus maximized.Such a maximum value may be hardware (i.e., power ampli-fier) or software (i.e., license) limited. Note that 𝑃𝑇𝑋max

is notnecessarily the same in all cells, since the DL power amplifierand/or the licensed power may be different between cells. Incontrast, 𝑃𝑇𝑋min

is defined as a safety brake for the tuningprocess to prevent coverage issues. In this work,𝑃𝑇𝑋min

is set to10 dB less than 𝑃𝑇𝑋max

for each cell to avoid excessive transmitpower reduction.

5. Performance Assessment

The self-planning algorithm is validated with a static system-level LTE simulator implementing a live scenario adjustedwith real measurements.The assessment methodology is firstdescribed and results are presented later.

5.1. Assessment Methodology. This section describes the sim-ulation scenario and the experiments carried out to assess theproposed indicator and self-planning method.

5.1.1. Simulation Scenario. A DL static system-level LTEsimulator implementing a real macrocellular scenario hasbeen developed in MATLAB [30]. The simulator is designedto make the most of available network statistics to model alive macrocellular scenario. For this purpose, the simulatorincludes the following features:

(a) Initialization of cell load distribution across the sce-nario with PRB utilization figures obtained fromcounters in the network management system of a liveLTE network.

(b) Adjustment of spatial user distributionwithin a cell bydistance rings, so that the probability of a user being ina distance ring is derived from Timing Advance (TA)distributions [35].

(c) Tuning of propagation model parameters accordingto live RSRP measurements statistics.

Table 1 summarizes the main scenario parameters. Thesimulated area comprises 129 cells distributed in 44 siteswith an average Inter-Site Distance (ISD) of 0.8 km. Thisscenario, with a relatively low ISD, is representative of aninterference-limited scenario in a dense urban area. Thegeographical area under analysis is divided into a regulargrid of points, representing potential user locations. Receivedsignal level at each point from base stations is computed by amacrocellular propagation model including log-normal slowfading (i.e., Winner II C2 model [33]). For this purpose, userlocations are classified into Line Of Sight (LOS) or Non-Line of Sight (NLOS) conditions based on real geolocateddata of buildings and antenna positions in the scenario. Gridresolution is 40 meters. Cell service areas are computed bycombining path losses and antenna gains, so that the servingcell is that providing the maximum pilot signal level for eachpoint. Likewise, neighbor cells are defined as those providing


Table 1: Simulation scenario.

Number of sites 44Number of cells 129Avg. intersite distance [m] 815Carrier frequency [MHz] 734System bandwidth [MHz] 10Number of PRBs 50UE height [m] 1.5BS antenna height [m] [3, 54]Initial cell transmit power [dBm] [46.5, 47.4]Maximum antenna gain [dB] 15Antenna tilt angle [ ∘ ] [0, 13]Propagation model Winner II C2 [33] with𝑋 = 14 for NLOS usersGrid resolution [m] 40Spatial traffic distribution Distance based on TA measurementsPRB utilization ratio [%] [5, 70]the largest signal levels in the service area of a cell. Then,interference level at every point is computed by adding theinterference from all neighbor cells. Finally, 𝛽 is calculatedon a cell basis and the self-planning algorithm is executedto obtain new 𝑃𝑇𝑋 values for the next optimization loop.PRB utilization ratios are updated at every new loop byestimating the impact of 𝑃𝑇𝑋(𝑖) changes on the radio linkspectral efficiency at every cell. The reader is referred to [30]for a more detailed explanation of the simulation tool.

5.1.2. Validation of𝛽 Indicator. Asensitivity test is first carriedout to check the accuracy of indicator 𝛽, reflecting the impactof changing the power of a cell on the total system SINR.For this purpose, the default power plan configured by theoperator ismodified by increasing the power of a single cell by1 dB, so a new power plan is obtained.This process is repeatedfor every cell in the scenario, so 129 new power plans areconstructed. Then, the difference in the total system SINR,ΔΓ𝑡(𝑖), from each individual power change is computed bysubtracting the values with the default and the new powerplan. Such differences should coincide with the values of𝛽 forthe different cells, 𝛽(𝑖), estimated from network performancedata obtained with the default plan as in (9).

It should be pointed out that the simulation tool canaccurately model cell coupling effects. For instance, SINR inneighbor 𝑗 is modified when the power of a cell 𝑖 is modified.As a consequence, spectral efficiency in cell 𝑗 changes, and sodoes its PRB utilization ratio.This load change in cell 𝑗 causesinterference changes in both cell 𝑖 and other neighboringcells. Thus, the initial power change in cell 𝑖 is propagatedacross the network. Likewise, the simulator updates cellservice areas with the new power setting. However, theseside effects cannot be taken into account by the analyticalapproach used to derive𝛽. On the contrary, the definition of𝛽only considers first-order effects of changing power settings.For a fair comparison, and only for this experiment, PRButilization of neighbor cells 𝑗 that do not change power iskept unaltered in the simulations, that is, only the modifiedcell 𝑖 changes its PRB utilization. Likewise, cell service areas

in the simulator are not recalculated when power settings aremodified.

5.1.3. Algorithm Assessment. Three power planning methodsare compared. A first method is the DL transmit power planoriginally implemented by the operator, denoted as operatorsolution (OS). OS is the baseline against which all othermethods are compared. In OS plan, DL transmit power isset to the maximum value in all cells. This is due to thefact that DL transmit power is often configured when thesite is launched and remains unchanged when new sites aredeployed in the surroundings, which may generate uselesscell overlapping and high intercell interference.

A second method is the iterative self-planning algorithmfor DL transmit power proposed here, denoted as SINR-PWR. This method is initialized with the OS plan and 30optimization loops are simulated. It is checked a posteriorithat this number of loops is enough to reach equilibrium.

A thirdmethod is the iterative self-planning algorithm forremote electrical tilt (RET) based on trace files described in[30], denoted as TF-RET (for Trace-based Fuzzy). TF-RETadjusts antenna tilt values instead of base station transmitpower. For this purpose, three performance indicators areobtained from connection traces to detect cell overshooting,useless cell overlapping, and cell-edge coverage problems.Then, downtilting is performed in those cells generating over-shooting and/or useless overlapping, and without coverageproblems. As in [30], this method is also initialized with theOSplan and 20 optimization loops are simulated. It is checkeda posteriori that this number of loops is enough to reachequilibrium.

For brevity, the analysis of SINR-PWR and TF-RET isrestricted to the solution obtained in the last iteration.

Two figures of merit are used to assess power planningalgorithms:

(i) Overall average DL SINR, SINRavg, as a measure ofnetwork connection quality and spectral efficiency,


y = 0.93x + 0.05

R2 = 0.98

−1 −0.5 0 0.5 1 1.5−1.5 (dB) (analytical)

−1.5

−1

−0.5

0

0.5

1

1.5

ΔΓ t

(dB)

(sim

ulat

ed)

Figure 1: Analytical and simulated change of total DL SINR.

calculated as the arithmetic mean of the average DLSINR in each cell, Γ(𝑖), and

(ii) Overall cell-edge DL SINR, SINRce, as a measure ofnetwork coverage, calculated as the arithmetic meanof the 5th-percentile DL SINR in each cell, Γce(𝑖).

In practice, any change in power settings through opti-mization loops might cause that some locations in thescenario do not receive enough signal level for establishinga connection, or, conversely, some locations initially notserved by any cell could reach enough signal level to starta connection in a later optimization loop. These changes inthe coverage area would have an influence on the total trafficcarried by the network. For a fair comparison, both SINRindicators are computed in the same set of locations alongiterations (i.e., the evaluated geographical area is always thesame).

5.2. Results. Thevalidation of the𝛽 indicator is first presentedand the assessment of power planning algorithms is discussedlater.

5.2.1. Validation of 𝛽 Indicator. Figure 1 shows the accuracyof the proposed indicator by comparing estimates obtainedwith the formulas against results obtained with the simulator.Each point in the figure corresponds to one of the new129 power plans built by increasing the transmit power ofa cell by 1 dB. The 𝑥- and 𝑦-axes represent the values of 𝛽and ΔΓ𝑡, respectively. It is observed that both indicators arestrongly correlated, since the coefficient of determination,𝑅2,is 0.98, and the value of the regression slope is close to 1. Thissimilarity between simulated and analytical values proves thevalidity of the 𝛽 indicator.

Moreover, it is observed that the impact of increasing thetransmit power of a cell greatly varies from cell to cell. Insome cells (up and right points in Figure 1), the 1-dB transmitpower increase is directly translated into a 1-dB increase inthe total system SINR denoting an isolated cells scenario. Incontrast, in other cells (left and down points in the figure),

1.6 1.8 2 2.2 2.4 2.6 2.8 312.4

12.6

12.8

13

13.2

13.4

13.6

13.8

14

14.2

OSSINR−PWRTF−RET

３）．２

；ＰＡ

(dB)

３）．２＝？ (dB)

Figure 2: Performance comparison.

the same transmit power change leads to a decrease in thetotal system SINR, denoting a tightly coupled cell scenario.This result justifies the need for adjusting transmit power ona cell-by-cell basis.

5.2.2. Algorithm Assessment. Figure 2 compares the resultsof the different algorithms. The overall cell-edge and cell-average SINR metrics are shown on the 𝑥- and 𝑦-axes,respectively. Points in the upper right part of the figureshow better performance. The OS configuration methodused as a reference is represented by a single dot (dia-mond). Self-planning methods (i.e., SINR-PWR and TF-RET) are represented by a curve of multiple dots showingthe performance of intermediate network parameters set-tings reached across optimization loops. For clarity, the lastvalue in these iterative methods is highlighted with a filledmarker. Both SINR-PWR and TF-RET curves start with theOS network configuration, and their performance is thusthe same in the first iteration. Thereafter, SINR-PWR andTF-RET improve both average and cell-edge SINR alongiterations.

Table 2 compares the performance of the iterative meth-ods, SINR-PWR and TF-RET, at the end of the optimiza-tion process against the initial solution, OS. Table 2 alsopresents the overall average and cell-edge DL user through-put, UeTHavg and UeTHce, respectively, calculated as thearithmetic mean of the individual cell values (average andcell-edge DL user throughput, resp.). DL user throughputin each user location is computed from SINR values bythe bounded Shannon formula [34] with attenuation factor,𝛼imp = 0.6, assuming that the whole system bandwidth isavailable to the user (i.e., 50 PRB ⋅ 180 kHz/PRB = 9MHz). Inaddition, other important indicators are also included, suchas the average received pilot signal level from the serving cell,RSRP, average DL interference level, 𝐼, average deviation of


Table 2: Method performance at the end of the adjusting process.

OS SINR-PWR TF-RETSINRavg [dB] 12.69 13.90 13.70SINRce [dB] 1.72 2.91 2.86UeTHavg [Mbps] 23.36 25.36 25.02UeTHce [Mbps] 7.44 8.74 8.70RSRP [dBm] −88.44 −89.90 −88.17𝐼 [dBm] −101.13 −103.80 −101.88Δ𝑃𝑇𝑋 [dB] — −1.80 —Δ𝛼[ ∘ ] — — 0.50Number of modified cells — 48 65

transmit power and tilt angle from initial settings, Δ𝑃𝑇𝑋 andΔ𝛼, and the number of modified cells.In Table 2, it is observed that both methods outper-

form the current operator solution. Specifically, SINR-PWRimproves SINRavg by 1.21 dB and SINRce by 1.19 dB whencompared to OS, whereas TF-RET improves those indicatorsby only 1.01 and 1.14 dB, respectively. It is also observed thatSINR-PWR outperforms TF-RET, since a better performanceis achieved for both indicators at the end of the optimizationprocess (i.e., 13.90 against 13.70 dB for SINRavg, and 2.91against 2.86 dB for SINRce). SINR improvements are directlytranslated into a better user experience reflected in through-put indicators. Specifically, UeTHavg and UeTHce indicatorsare increased by 8.6% and 17.5% in relative terms, respectively,with SINR-PWR algorithm. In contrast, TF-RET algorithmonly achieves a 7.1% and 16.9% increase for those indicators.The reason for the better performance of SINR-PWR is thefact that SINR-PWR is based on an analytical approach thatensures a (local) maximum of system performance, whereasTF-RET is based on heuristic rules. Recall that the maingoal of SINR-PWR is to improve the overall average SINR,regardless of the overall cell-edge SINR. Then, the fact thatSINR-PWR also improves SINRce, and more than TF-RET,is a positive side effect that proves the robustness of theproposed method.

A close inspection of Table 2 shows that SINR-PWRobtains its results by decreasing both RSRP and 𝐼 values(−1.46 and −2.67 dB, resp.). Such a reduction, typical ofan interference-limited scenario, is done without deteriorat-ing the overall SINR cell-edge performance, which is alsoimproved. In contrast, TF-RETmaintains RSRP and 𝐼 values.As an additional advantage, SINR-PWR modifies fewer cellsthan TF-RET (i.e., 48 power changes versus 65 up/downtilts).

5.3. Implementation Issues. The time complexity of SINR-PWR algorithm is O(𝑁𝑐), where 𝑁𝑐 is the number of cellsin the analyzed area. The method is designed as a controlalgorithm and therefore has a low computational complexity.Specifically, the total execution time of 30 optimization loopsin the considered scenario with 129 cells, in a computerwith a clock frequency of 3.47GHz and 12GB of RAM, is1980 seconds (66 seconds per loop on average). Most of thistime is spent on simulating the scenario to obtain network

performance indicators, and only 0.085 seconds per loop isspent on the computation of the proposed indicator (i.e., lessthan 0.13% of the loop execution time).

Moreover, by computing the 𝛽 indicator analytically,instead of deriving it by perturbation analysis, the numberof parameter plans to be simulated is reduced by 𝑁𝑐 times.Note that the 𝛽 indicator can be calculated analytically bysimulating a single parameter plan, whereas a perturbationanalysis needs changing the power setting of one cell at a timeand simulating a new parameter plan per cell.

6. Conclusions

In this work, a novel self-planning algorithm has beenpresented for adjusting the transmit power of LTE basestations on a cell basis to improve both network coverage andoverall spectral efficiency. The algorithm is designed as a setof independent controllers that decide whether to increaseor decrease the transmit power of a cell based on a newindicator showing the expected impact of that change on thetotal system DL SINR.The proposed self-planning algorithmhas been tested in a static system-level simulator modelinga live dense urban interference-limited LTE scenario. Resultshave shown that the proposedmethod can improve both cell-average and cell-edge SINR values by more than 1 dB whencompared with the solution currently implemented in thenetwork.

During the tests, the proposed method has been com-pared with a state-of-the-art self-planning method based onadjusting antenna tilts. A priori, tilting is a more powerfultechnique, as it can improve both the modified cell (withhigher desired signal level) and its neighbors (with lessinterference). However, the proposed power-based methodoutperforms the tilt-based method.The reason for that supe-riority is the fact that the power-based method is designedto reach the optimal power plan, based on the analysis ofoptimality conditions. Thus, the proposed approach ensuresthat network performance is always improved after everychange of power settings. In contrast, the tilt-based methodis based on a heuristic approach, in the absence of ananalytic expression of the optimality conditions of antennatilting. Moreover, unlike antenna tilting, power adjustmentis still valid for cells with omnidirectional or multibandantennas.


Unlike other self-planning approaches, the proposedmethod is designed as a control algorithm. Due to its lowcomputational complexity, the method can be adapted to beused as a self-optimization algorithm, provided that the 𝛽indicators are computed from network performance mea-surements available in connection traces. For this purpose,periodic RSRP measurements should be activated in all sites.This data should be processed periodically in a centralizednode to obtain the new transmit power settings by thealgorithm. Alternatively, each base station might exchangeperformance measurements with its neighbors to derive theassociated 𝛽 indicator in a distributed fashion.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work has been funded by the Spanish Ministry of Econ-omy and Competitiveness (TEC2015-69982-R) and Optimi-Ericsson.

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