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Optimal Direct Load Control of Renewable Powered Small Cells: Performance Evaluation and Bounds

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In this paper, we propose an optimal direct load control of renewable powered small base stations based on Dynamic Programming. The optimization is represented using Graph Theory and the problem is stated as a Shortest Path problem. The proposed optimal algorithm is able to adapt to the varying conditions of renewable energy sources and traffic demands. We analyze the optimal ON/OFF policies considering different energy and traffic scenarios. Then, we evaluate network performance in terms of system drop rate and grid energy consumption. The obtained results are compared with a greedy approach. This study allows to elaborate on the behavior and performance bounds of the system and gives a guidance for approximated policy search methods.
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Optimal Direct Load Control of Renewable Powered Small Cells:
Performance Evaluation and Bounds
Nicola Piovesan, Marco Miozzo, Paolo Dini
CTTC/CERCA, Av. Carl Friedrich Gauss, 7, 08860, Castelldefels, Barcelona, Spain
{npiovesan, mmiozzo, pdini}@cttc.es
Abstract—In this paper, we propose an optimal direct load
control of renewable powered small base stations based on
Dynamic Programming. The optimization is represented using
Graph Theory and the problem is stated as a Shortest Path
problem. The proposed optimal algorithm is able to adapt to
the varying conditions of renewable energy sources and traffic
demands. We analyze the optimal ON/OFF policies considering
different energy and traffic scenarios. Then, we evaluate network
performance in terms of system drop rate and grid energy
consumption. The obtained results are compared with a greedy
approach. This study allows to elaborate on the behavior and
performance bounds of the system and gives a guidance for
approximated policy search methods.
Index Terms—Mobile Networks, Energy Sustainability, Opti-
mal Control, Demand Response, Dynamic Programming, Direct
Load Control
I. INTRODUCTION
Recently, cellular networks have witnessed an impressive
increase in mobile user demand. This is due to the introduction
of new services that require reliable and fast connectivity,
as well as the increase in the number of connected devices,
including machines. In fact, the data traffic is augmenting at
a rate of approximately 1.5 to 2 times per year, while the
emergence of machine-type communication and IoT will lead
to 29 billion connected devices in 2022 [1]. Therefore, the fifth
generation mobile network (5G) is expected to support 1000
times more data volume per unit area, 100 more user data rate,
1000 more connected devices, 10 times longer battery life and
5 times reduced end-to-end latency than 4G [2].
A new architecture and new network deployments are, thus,
necessary to meet those requirements. Massive deployment
of small base stations (SBSs) represents the most promising
architecture to meet the high capacity demand of mobile
networks. However, the deployment of such network elements
will lead to an increase in the energy consumption of the
network that will cause negative economic and environmental
impacts. Predictions confirm that, if no actions are taken, the
greenhouse gas (GHG) emissions per capita for Information
and Communication Technology (ICT) will increase from 100
kg in 2007 to 130 kg in 2020, globally [3]. Moreover, the
high energy consumption of the cellular network forces the
operators to pay high bills, which constitute half of their
operating expenditures (OPEX) [4]. Total global energy con-
sumption by all mobile networks was approximately 120 TWh
in 2010, resulting in energy costs of $13 billion [5]. Although
this is not a recent estimate, it represents a lower bound
for the actual values due to the increasing price of energy.
Therefore, there is a need for controlling and mitigating the
energy consumption in the next generation cellular networks.
The reduced energy requirements of small base stations
encourage the use of renewable energy sources (RES) as
distributed power suppliers. The adoption of renewable energy
in modern mobile networks will lead to (i) a reduction of
the grid energy consumption, (ii) a reduction of the carbon
footprint of ICT and (iii) savings on the energy bills from the
network operators [6].
The introduction of RES entails an intermittent and erratic
energy budget for the communication operations of the SBSs.
Therefore, Demand Response (DR) is fundamental to properly
manage energy inflow and spending, based on the traffic
demand. Considering the high number of SBSs in the system,
distributed self-organizing techniques represents a viable so-
lution that can enable intelligent energy management policies,
such as Direct Load Control [7]. An optimal switch ON-OFF
problem has been solved in [8] by using a two-stage DP
algorithm. In particular, the BSs’ on-off states are optimized in
the first stage, and the active BSs’ resource blocks are allocated
iteratively in the second stage. However, the problem has been
stated for a single-tier architecture.
In our previous work [9], a two-tier architecture with
hybrid power suppliers is introduced: macro base stations
(MBSs) reside in the first tier to provide baseline coverage and
capacity and are powered by the electrical grid, whereas SBSs
operate in the second tier to provide capacity enhancement
and are supplied by solar panels plus batteries. The data
traffic offloaded by the SBSs has higher spectral efficiency
and allows a reduction of the energy drained from the grid. An
optimal direct load control of renewable powered SBSs based
on dynamic programming, is proposed. The DP optimization
is represented using Graph Theory and the problem is stated as
a shortest-path search. The Label Correcting Method is used to
explore the graph and find the optimal ON/OFF policy for the
SBSs. DP has the key property of applying optimal control as
a trade-off between the present and the future costs. This is a
fundamental feature in our scenario, to prevent SBSs blackout
during periods with low renewable energy arrivals and high
traffic demands. In this paper, we extend our previous work
by analyzing the optimal policies considering different energy
harvesting and traffic conditions. The obtained policies are
also compared with a greedy approach. Finally, we evaluate
c
2018 IEEE
the network performance in terms of system drop rate and grid
energy consumption.
The remainder of the paper is organized as follows. In Sec-
tion II we present the system model, whereas the optimization
problem is formulated in Section III. In Section IV we analyze
the optimal policies for different energy harvesting and traffic
scenarios and we discuss some performance results. Finally,
in Section V we draw our conclusions.
II. SY ST EM MO DE L
The Radio Access Network (RAN) is represented as a
set of clusters. Each of them is composed of 1 macro base
station (MBS) and Csmall base stations (SBSs). Each SBS
is powered by a solar panel and it can store energy into a
battery. On the contrary, the MBS is connected to the electrical
grid. The SBSs implement an intelligent energy management
system that decides their operative state. The two feasible
operative states are: (i) ON, where the SBS serves the users
in its coverage area, and (ii) OFF, where the SBS is in an
energy saving mode and its users are handed over to the MBS.
The state of all the CSBSs at time tis described by the
vector St= [S(1)
t, S(2)
t, ..., S(C)
t]. Each element S(i)
t, with
i= 1, ..., C, is defined as follows:
S(i)
t=(0,if i-th SBS is OFF
1,if i-th SBS is ON (1)
The energy harvested by the SBSs at time tis indicated by
the vector Et= [E(1)
t, E(2)
t, ..., E(C)
t], while the amount of
energy stored in the SBSs batteries at time tis indicated by
the vector Bt= [B(1)
t, B(2)
t, ..., B(C)
t].
The energy consumption of the BS is approximated by the
linear function P=P0+βρ, where P0is the baseline power
consumption and ρ[0,1] is the normalized traffic load.
The typical values of these parameters are PMBS
0= 750W,
βMBS = 600 for MBSs and PSBS
0= 105.6W,βSBS = 39
for SBSs. This model is supported by real measurements and
closely matches the real power profile of BSs [10].
We consider a LTE RAN with a transmission bandwidth
BW divided into Rresource blocks (RBs) of 1msec per
180 kHz each [11]. The traffic level of the SBSs at time tis
indicated by the traffic load vector ρt= [ρ(1)
t, ρ(2)
t, ..., ρ(C)
t].
If the SBS iis OFF at time t, its users are managed by the
MBS and we assume that the SBS can be entirely switched
OFF (e.g., P= 0). However, the MBS may have reached its
capacity limit at that time instant (i.e. cannot allocate any RB
to users) and may drop part of the handed over users. This
situation is defined as system outage.
III. OPTIMIZATION PROB LE M
The periodicity of the traffic demand and the energy arrivals
leads to a cyclic evolution of the system. At every cycle t, a
centralized controller computes the optimal state configuration
of the SBSs in the cluster.
This sequential decision making process is modeled as a
DP optimization problem. The objective is to minimize the
grid energy consumed by the MBS and the traffic drop rate of
the system. Since there is a linear relation between the energy
consumption and the BS load, the objective is converted into
the minimization of the MBS load over a given time horizon,
by offloading the traffic to the renewable powered SBSs.
Furthermore, a threshold Bth on the battery level is introduced
to prevent damages to the storage devices [12].
The optimization problem is formulated as follows:
min
{St}t=1,...,K
K
X
t=1
f(St, t)
B(i)
t> Bth i.
(2)
where Kis defined as time horizon of the optimization and
corresponds to the number of times the control is applied.
Furthermore, the cost function f(St, t)is defined as follows:
f(St, t) = 1
2[w1·L(St, t) + w2·D(St, t)] (3)
where
L(St, t), is the normalized load of the MBS given the
SBSs states and the time instant t.
D(St, t)is the traffic drop rate of the system, given the
state of the SBSs and the time instant t. Its value ranges
from 0 (when all the traffic is served by the system) to 1
(when all the traffic is dropped by the system).
The two weights must always sum to one, i.e., w1+w2= 1.
The battery levels of the SBSs are updated at each decision
instant t, according to the following formula:
Bt+1 = min(Bt+Et((PSBS
0+βSBSρt)∆t, Bcap )) (4)
where Bcap is the maximum battery capacity. The amount of
energy exceeding the battery capacity cannot be stored and it
is wasted.
The complexity of this optimization problem increases
quasi-exponentially with the number of SBSs in the cluster
and with the time horizon. In order to solve it in an efficient
way, this problem has been graphically represented and subse-
quently transposed to a graph theory shortest-path problem in
[9]. The proposed algorithm based on the Label Correcting
Method has been used to obtain the results shown in the
following section.
IV. RES ULTS ANALYSIS
A. Simulation Scenario
We consider a square area with a side of 1 km. The MBS
is located at the center of the area and 3 SBSs are randomly
positioned. The SBSs have a transmission power of 38 dBm,
which corresponds to a coverage radius of 50 m. The coverage
areas of the SBSs do not overlap. The base stations have
a transmission bandwidth of 5 MHz. Aggregated downlink
traffic has been generated based on the traffic profiles defined
in [13]. In particular, we consider three different weekly traffic
profiles: Resident, Transport and Office. User traffic is based
0 12 24 36 48 60 72 84 96 108 120 132 144 156
Hour of the week [h]
0
1
2
3
Traffic [Mbps]
104
0
0.5
1
Energy [kWh]
January July
(a) Resident traffic profile
0 12 24 36 48 60 72 84 96 108 120 132 144 156
Hour of the week [h]
0
1
2
Traffic [Mbps]
104
0
0.5
1
Energy [kWh]
(b) Office traffic profile
0 12 24 36 48 60 72 84 96 108 120 132 144 156
Hour of the week [h]
0
1
2
Traffic [Mbps]
104
0
0.5
1
Energy [kWh]
(c) Transport traffic profile
Fig. 1. Example of temporal variation of the traffic and energy harvesting process in a week of January and July. Scenario with 90 UEs per SBS with 50%
of heavy users.
on the classification proposed in [10]. Heavy users have a
data volume of 900 MB/h, whereas ordinary users have a
data volume of 112.5 MB/h. We underline that, with the
considered approach, the traffic is described both in time
(temporal variation during the week) and in space (spacial
distribution in the area).
As for the RES system, we consider the Panasonic N235B
solar modules, which have single cell efficiencies of about
21% delivering about 186 W/m2. Each SBS is equipped with
an array of 16 ×16 solar cells (i.e. 4.48 m2). The battery
size is 2 kWh (panel and battery sizes have been chosen
so that SBS batteries can be replenished in a full winter
day). Realistic energy harvesting traces are obtained using the
SolarStat tool [14], considering the city of Los Angeles. All
the simulations have been performed considering a generic
week of January and July, in order to highlight the differences
between a generic winter (low energy arrivals) and a sum-
mer month (high energy arrivals). Moreover, the coordinator
takes actions with a time step of 1 hour, considering a time
horizon of 21 hours, as described in [9]. In the analysis here
presented, we have assigned the same importance to the energy
consumption and the system drop rate, when computing the
optimal policy. Therefore, the weights in equation (3) have
been set to w1=w2= 0.5.
The optimal approach is compared with a greedy algorithm
that operates by turning OFF the SBSs when their battery
levels go below the threshold and turning them ON when the
level is above it.
B. Optimal policies
An example of the temporal variation of the traffic and the
harvested energy arrival processes during a week is shown in
Fig. 1. The traffic requests in considered areas differ both in
terms of temporal distribution and magnitude. In particular,
the Resident area is the most demanding, with a weekly
aggregated traffic of 2.17 TB. The lowest traffic demand is
experienced in the Transport area, with a weekly aggregated
traffic of 0.41 TB. The three traffic profiles and the two energy
arrival processes are not always time correlated. In fact, in the
case of Resident traffic, the peak of the demand is at 10 pm.
In the case of Office traffic, it is at 11 am on the weekdays
and at midday on the weekends. Finally, in the Transport
case we have two peaks during the weekdays, at 8 am and
6 pm, while on the weekends there is a single peak at 5 pm.
From the energy side, the peak of energy arrivals is always
between midday and 1 pm for the two considered months.
This confirms the necessity of taking into account present and
future costs when the optimal control is applied.
The daily average switch OFF rate of the SBSs for the
optimal and the greedy policy is reported in Fig. 2 and Fig.
3, respectively. The three traffic profiles and the months of
January and July are depicted. We consider a high-traffic
intensity involving 90 UEs (50% heavy) represented by solid
lines, and a low-traffic intensity with 10 UEs (20% heavy)
indicated with dashed lines.
In Fig. 2 we observe that the number of SBSs in OFF is
generally higher during night hours. This fact is due to the
scarce availability of the energy and the low traffic demand
during the night. More in detail, we can notice that high-traffic
intensity and low energy arrivals (January) result in longer and
more intensive switch OFF periods during the night. For the
Resident profile (Fig. 2a) the switch OFF rate in a typical
week of July is intensive between 3 am and 6 am (low-traffic
low traffic - Jan high traffic - Jan low traffic - Jul high traffic - Jul Avg. traffic profile..
0 5 10 15 20
Hour [h]
0
0.2
0.4
0.6
0.8
1
Switch OFF rate
(a) Resident traffic
0 5 10 15 20
Hour [h]
0
0.2
0.4
0.6
0.8
1
Switch OFF rate
(b) Office traffic
0 5 10 15 20
Hour [h]
0
0.2
0.4
0.6
0.8
1
Switch OFF rate
(c) Transport traffic
Fig. 2. Daily average switch OFF rate for the optimal algorithm. Simulations on the Resident, Office and Transport traffic profile for a week of January and
July. The scenario with 10 UEs (20% heavy) is indicated as low traffic, whereas the scenario with 90 UEs (50% heavy) is indicated as high traffic.
low traffic - Jan high traffic - Jan low traffic - Jul high traffic - Jul Avg. traffic profile..
0 5 10 15 20
Hour [h]
0
0.2
0.4
0.6
0.8
1
Switch OFF rate
(a) Resident traffic
0 5 10 15 20
Hour [h]
0
0.2
0.4
0.6
0.8
1
Switch OFF rate
(b) Office traffic
0 5 10 15 20
Hour [h]
0
0.2
0.4
0.6
0.8
1
Switch OFF rate
(c) Transport traffic
Fig. 3. Daily average switch OFF rate for the greedy algorithm. Simulations on the Resident, Office and Transport traffic profile for a week of January and
July. The scenario with 10 UEs (20% heavy) is indicated as low traffic, whereas the scenario with 90 UEs (50% heavy) is indicated as high traffic.
case) and from 2 am to 8 am (high-traffic case). In a week of
January, the switch OFF rate is intensive from 1 am to 10 am
(low-traffic case). In the case of Office (Fig. 2b) and Transport
(Fig. 2c) profiles, these intensive night OFF periods are less
influenced by the total number of UEs served by the SBSs.
This is due to the low magnitude of the total traffic demand
experienced in these areas.
In Fig. 3 we observe that the switch OFF rate is intensive
also in periods of high traffic demand. The greedy algorithm
takes immediate decisions without considering any future evo-
lution of the traffic and energy arrival processes. In this way, a
SBS always consumes the available energy and then it remains
in an OFF state until the harvested energy is sufficient to return
operative. On the contrary, the optimal policy turns OFF a
SBS in an intelligent way, by considering future evolutions
of the traffic and energy arrivals. Therefore, it saves energy
during low traffic periods (e.g. night hours) to maintain ON
the SBS during high traffic peaks, which may correspond to
scarce energy arrivals. For instance, let’s consider the Resident
profile with high-traffic intensity in January, where the peak of
the traffic demand is at 10 pm. The greedy algorithm switch
OFF rate is 0.5at 10 pm (Fig. 3a), whereas it is zero during
the daytime (i.e., from 11 am to 7 pm). In fact, the SBSs
are immediately using the available energy during the day,
and then switching OFF in the evening due to scarce energy
availability. On the contrary, the optimal switch OFF rate
(Fig. 2a) is almost zero during the traffic peak hours and it is
not null during the daytime. This behavior indicates that some
SBSs are switched OFF during the day to save the necessary
energy to satisfy the traffic peak in the evening.
C. System outage
In this section, we analyze the system outage measured as
the percentage of the traffic dropped in the system. We present
the case of Resident profile only, since the others have similar
performance. The percentage of the traffic dropped in a week
is reported in Fig. 4 for a number of UEs ranging from 10 to
90 (50% of them are heavy users).
The optimal policy succeeds in delivering all the traffic
requested and the system does not experience any outage
in almost every studied situation. In January, however, some
traffic is dropped starting from 60 UEs per SBS, reaching the
maximum of 0.9% for 90 UEs. The greedy approach, on the
other hand, always performs worse than the optimal policy. In
particular, in January the traffic dropped is reaching 10% in
the case of 90 UEs per SBS.
This phenomenon is confirmed in Fig. 5, where the average
hourly traffic dropped is shown for a scenario with 90 UEs
per SBS with 50% of heavy users. As for the optimal policy,
the outage is concentrated in the morning (from 7 am to 10
am), afternoon (5 pm) and night, with values that reach the
10 20 30 40 50 60 70 80 90
UEs per SBS
0
2
4
6
8
10
12
Traffic drop [%]
Optimal - Jan
Optimal - Jul
Greedy - Jan
Greedy - Jul
Fig. 4. Percentage of weekly traffic request not serviced for both the greedy
and optimal algorithm in January and July. The 50% of the UEs are heavy
users.
0 5 10 15 20
Hour [h]
0
5
10
15
20
25
30
35
40
45
Avg. traffic drop [%]
Optimal - Jan
Optimal - Jul
Greedy - Jan
Greedy - Jul
Avg. traffic profile
Fig. 5. Average hourly traffic drop for the optimal and the greedy algorithms
in January and July. The traffic profile is Resident and every SBS has 90 UEs
in its coverage area; 50% of them are heavy users.
maximum value of 5% at midnight. The greedy approach,
instead, causes system outage for longer periods and with
higher values of the dropped traffic, which is reaching a
maximum of 44% at 11 pm.
D. Energy consumption
The amount of the grid energy consumed by the MBS is
shown is Fig. 6, varying the number of UEs in the coverage
area of the SBSs. We consider two cases: a scenario with 20%
and 50% of heavy users, respectively. In both scenarios, the
grid energy consumption increases linearly with the number
of UEs. The slope of the curves is higher for the scenario
Fig. 6. Grid energy consumption for the optimal and the greedy algorithms
in January and July, while increasing the number of UEs in the SBS area.
with 50% of heavy users since the traffic is increasing faster
with the number of UEs. Grid energy consumption is higher
during the winter months since the scarce availability of the
renewable energy turns out into longer SBS sleeping periods
and higher MBS operation.
The greedy approach presents higher values of the grid
energy consumption than the optimal policy. However, in the
case of January and with 50% of heavy users, we observe that
the greedy approach has lower energy consumption for more
than 70 UEs per SBS. This behavior is due to the fact that the
system is heavily in outage and loses a considerable amount
of traffic, as described in the previous subsection.
Finally, Fig. 7 reports the grid energy consumption for a
week of July of different architecture scenarios. We compare
a solution where MBS and SBSs are connected to the grid
(also referred to as grid-only) with our scenario where SBSs
are solely powered by solar panel plus battery (also referred
to as EH SBS). The grid-only scenario consumes 190.3 kWh
in a week; deploying renewable powered SBSs saves 28%
of the grid energy. Moreover, since the RES systems have
been dimensioned for winter, the harvested energy may be
abundant during summer and be discarded by the SBSs, i.e.,
it can neither be used for transmission nor stored in the battery.
This redundant energy is concentrated during the peak hours
of the energy arrival process (i.e., between midday and 2
pm). Considering that the SBSs may be connected through a
power micro-grid, the excess energy can be used for ancillary
services (e.g., light system) or shared to support the MBS
operation, thus reducing its grid energy consumption. In fact,
a grid energy saving of 38% is achieved, in case the MBS
instantly uses the energy shared by the SBSs (also referred to
as EH SBSs + energy sharing). However, the MBS might not
be able to instantly consume the whole amount of the received
energy, which would create instability in the micro-grid. For
Grid energy consumption [kWh]
Fig. 7. Grid energy consumption for different deployment architectures during
a week of July. The traffic profile is Resident and every SBS has 90 UEs in
its coverage area; 50% of them are heavy users.
this reason, we consider the option of deploying a storage
device at the MBS site (also referred to as EH SBSs + energy
sharing + MBS battery). As a result, the MBS uses the shared
energy when needed and saves 46% of the grid energy.
V. CONCLUSIONS
In this paper, we have introduced an optimal direct load
control of renewable powered SBS in a two-tier mobile
network. We have analyzed the optimal policies and their
dependence on the traffic and the energy arrival process. We
have compared the optimal approach with a greedy algorithm
and analyzed the network performance in different scenarios.
We have also introduced a new possibility of energy sharing
among the network elements to reduce the dependence on the
power grid and increase the energy savings.
From this analysis, we can draw the following conclusions.
The different temporal behavior of the traffic and energy
arrival processes highlights the necessity of deploying storage
devices along with solar panels. Moreover, it is fundamental
to properly manage the storage to maintain good network
performance. The comparison between the optimal and the
greedy approach shows that grid energy savings and traffic
drop limitations are possible only if the control algorithm is
able to forecast the evolution of the two processes. Finally, the
analysis of the redundant energy shows that sharing energy
among base stations may lead to considerable amount of grid
energy savings.
ACKNOWLEDGMENT
This work has received funding from the European Union
Horizon 2020 research and innovation programme under
the Marie Sklodowska-Curie grant agreement No 675891
(SCAVENGE) and by the Spanish Government under project
TEC2017-88373-R.
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... An offline solution of this problem is proposed in our work [32] and [33] using Dynamic Programming (DP) and with a priori knowledge of the environmental variables. In detail, the problem is represented as a graph and stated as a Shortest Path search. ...
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... Piovesan et al. [98] The search for the best DLC for the SBS powered by nonconventional sources in the mobile network of two-tier. ...
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Where this book is exceptional is that the reader will not just learn how LTE works but why it works. Adrian Scrase, ETSI Vice-President, International Partnership Projects. LTE - The UMTS Long Term Evolution: From Theory to Practice provides the reader with a comprehensive system-level understanding of LTE, built on explanations of the theories which underlie it. The book is the product of a collaborative effort of key experts representing a wide range of companies actively participating in the development of LTE, as well as academia. This gives the book a broad, balanced and reliable perspective on this important technology. Lucid yet thorough, the book devotes particular effort to explaining the theoretical concepts in an accessible way, while retaining scientific rigour. It highlights practical implications and draws comparisons with the well-known WCDMA/HSPA standards. The authors not only pay special attention to the physical layer, giving insight into the fundamental concepts of OFDMA, SC-FDMA and MIMO, but also cover the higher protocol layers and system architecture to enable the reader to gain an overall understanding of the system. Key Features: Draws on the breadth of experience of a wide range of key experts from both industry and academia, giving the book a balanced and broad perspective on LTE. Provides a detailed description and analysis of the complete LTE system, especially the ground-breaking new physical layer. Offers a solid treatment of the underlying advances in fundamental communications and information theory on which LTE is based. Addresses practical issues and implementation challenges related to the deployment of LTE as a cellular system. Includes an accompanying website containing a complete list of acronyms related to LTE, with a brief description of each (http://www.wiley.com/go/sesia_theumts). This book is an invaluable reference for all research and development engineers involved in LTE implementation, as well as graduate and PhD students in wireless communications. Network operators, service providers and R and D managers will also find this book insightful.
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