This document proposes a methodology for incorporating uplink delay constraints into LTE cell planning for smart grid applications. It presents the following: 1) A semi-analytical approach is proposed to evaluate uplink transmission delays considering buffering delays before scheduling, packet transmission/retransmission delays over the air interface, and constraints from smart grid standards. 2) Analytical models are used to estimate buffering delays before scheduling based on queue length and service rate. Packet transmission delays are estimated considering packet segmentation, link adaptation, resource block allocation and retransmissions. 3) A cell planning algorithm is described that incorporates these delay metrics to validate compliance with smart grid delay constraints and determine the maximum cell range based on

1. LTE Uplink Delay Constraints for Smart Grid
Applications
Spiros Louvros, member IEEE, Michalis Paraskevas, Vassilis Triantafyllou, Agamemnon Baltagiannis
Abstract—LTE cell planning requires special constraints in
case of smart grid applications. Cell planners decide about the
cell coverage mostly based on worst radio conditions (cell edge)
acceptable level of minimum throughput, but not on delay
constraints which are of extreme importance for smart grid
solutions. In this paper a semi-analytical approach for uplink
cell planning with delay constraints for smart grid applications
is proposed, using theoretical outputs from analytical
mathematical models combined with real measurements from
drive test.
Keywords-LTE; smart grid; uplink delay
I. INTRODUCTION
Long Term Evolution [LTE] is the evolution of High
Speed Packet Access [HSPA] cellular networks towards 4G
[1]. Lately, on international literature, there are research
papers and technical reports for LTE applications over smart
grid networks [2-4]. However effective EUTRAN radio
delay and latency constraints are never considered so far on
international literature regarding cell planning algorithms;
nevertheless it is extremely important to include delay
constraints into cell planning analysis since LTE 3GPP
standards and smart grid IEC 61850-5 standards [5] define
strict restrictions on radio delays. In this paper we propose a
methodology of correcting initial cell coverage planning
using delay constraints, based on a semi-analytically
evaluated relation among packet transmission delays, cell
edge path losses, MAC retransmissions and real drive test
measurements. MAC scheduler provides uplink decisions
mainly based on γRB measurements per resource block (RB),
required Quality of Service received from core network
(Quality Class Identifier – QCI) [6] and cell load conditions
including interference and availability on RB together with
fast scheduling [7]. Rest of the paper is organized in the
following way: in section II we present service buffering
delay estimation before MAC scheduler functionality. In
section III packet transmission/retransmission delays over air
interface are considered. In section IV the proposed cell
planning algorithm with emphasis on smart grid delay
constraints is analyzed in concrete steps, where all
calculations are detailed and analytically explained. Finally
on section V conclusions are summarized.
II. BUFFERING BEFORE SCHEDULING DELAY ESTIMATION
A generalized queue system is considered, with one
single server (MAC scheduler), m channels (RB resources)
in parallel, finite queue length, Poisson λ packets per second
(although lately has been found that other distributions fit the
packet arrival, Poisson is still a very good approximation)
and service time μ0. Moreover transit time effects are
neglected on this analysis. In order to have queue system in
equilibrium we do suppose that per 1 ms TTI always m > λ.
Define πn the probability of existing n packets in queue at a
given time τ and pn the probability that zero packets exist in
the queue as long as n packets exist in the server at given
time τ, overall probability analytical solution πn will be [8]:
      
      
1 2
1
0 1 2 11 1 1 1
mn
n zm
n m
m z z z z z z
z
z z z z e





 
    

      
  
To analytically calculate πn it is needed to expand the
right part of (1) into the Laurent series around z = 0, where
πn for n = 0, 1, 2,…,n will be the coefficients of zn
after the
expansion is performed. Consider the case of m = 1 (MAC
scheduler considers each packet as a unique SDU service
input) the numerator is degenerated into a simple polynomial
of order one with one single real root

 
1 1
0 0 1
0 1 0 1 0
0
0 1, 0
n
n m
n n n
z z
z z z z
 
    
  
 
   
 
      
   
The polynomial expansion coefficients, after expanding
the polynomial into Laurent series around z = 0 and
substituting λ/μ = ρ as the utilization factor, are becoming:

 
  
 
    
    
1
0
2 2
1 1
1
1 1 1
1 1 ....
n
n z
n
z
z z
ze
e z
e e z


 


 
 



 
   

     
    

 
From expansion the general term is calculated as:

   
 
 
   
 
 
1
1
1
1 1
!
1 1
1 !
n k
n
n k k
n
k
n k
n
n k k
k
k n
k
e
n k
k
e
n k



 





 



   
     
    
   
     
     


 
Finally average expected delay is calculated as:

2. Fig. 1. Mean expected buffering delay (ms)

   
 
 
   
 
 
1
1 1
1
1 1
1 1
!
1 1
1 !
n
n
n k
n
n k k
n k
n k
n
n k
n k
k n
k
W n
k
n e
n k
k
n e
n k












 
 


 

 
  

 
 
   
    
   
          

 
 
 
In Fig. 1 the average expected delay is plotted
against offered load ρ = λ/μ considered the arrival rate of
packets λ at the buffer and the service rate of μ packets going
from buffer inside the scheduler system.
III. SCHEDULING TRANSMISSION DELAY ESTIMATION
IP packets will be segmented into many RLC/MAC
Signaling Data Units (SDUs) to be mapped into OFDM RB
and transmitted over air interface. Between user equipment
(UE) and eNodeb each MAC packet is supposed to be
transmitted completely over the air interface before starting
transmission of next MAC packet in a time transmission
interval duration of Ts = 1ms due to Hybrid ARQ (HARQ)
MAC functionality . Moreover multiple consecutive resource
blocks nRB might be selected from MAC scheduler for uplink
transmission, minimizing the transmission latency and
improving the UE throughput. Our analysis will be based on
transmissions of IP packets over RLC/MAC blocks based on
channel conditions [9]. Suppose that an IP packet of average
length MI be fragmented in such a way that the resulting
MAC packets of variable length (due to link adaptation
modulation & coding decisions) Mmac contain a fixed
number of Mover header bits per packet [10]. In such a model
MI packet will be segmented into MI / Mmac total number of
RLC/MAC packets with MI  MI / MmacMover total number
of transmitted bits. Considering non-ideal radio channel
conditions, in such a scenario, the transmission time needed
to completely transmit the IP packet will be increased due to
eventual retransmissions and non-scheduling periods of time.
It is important to remember that scheduler link adaptation
(LA) function will decide about non-scheduling periods and
MAC packet sizes based on Quality Class Identifier (QCI)
priorities and γ uplink measurements. The expected average
whole IP packet transmission time would be:
  
s
I mac
Mac
AP RB
overI
s s
T
M M
W m n
M M
T T
n n n
   

 
 

 
where nTs is the number of transmitted bits per RB
depending on Link Adaptation Modulation Scheme. nRB is
the average allocated number of 180 kHz RB blocks per Ts
transmission interval. nAP is the spatial multiplexing rank and
finally n and m are two integers indicating the average
number of Ts units of time one MAC packet is not scheduled
by scheduler and the average number of retransmissions one
packet should undergo due to channel conditions
respectively.
IV. CELL PLANNING ALGORITHM
In order to include the delay smart grid constraints into
the nominal cell planning procedure, design steps should be
considered introducing metrics to conclude average delay.
Substituting all these metrics into (6) the average scheduler
delay is estimated. Adding also the expected average
buffering delay the planners have an estimation of the
maximum expected radio delay for a service at cell edge.
Based on IEC 61850-5 [5] standards for Advanced Meter
Infrastructures smart grid applications planners could check
whether they are compliant with RDelay restriction, where
RDelay is the expected cell range due to delay constraints,
(Fig. 2). Following the analysis on nominal cell planning
with strict throughput constraints RThroughput [13] LTE cell
coverage range prediction for outdoor Urban coverage of
95% was roughly estimated to be d = 125 m. We should
follow explicitly the proposed steps for d = 125 m cell range
to validate our analysis on delay constraints. Cell Planning
analysis follows:
A. Path loss evaluation
Cell planners, during nominal cell planning, should
evaluate a cell range RThroughput that fulfills certain throughput
constraints. Following this assumption we could calculate
expected worst scenario pathloss Ltarget. Our analysis should
be based on certain defined pathloss models for LTE in
international literature. A well defined formula for 2.5 GHz
LTE microcell outdoor to outdoor coverage is [9]:

 
 
10
10
39 20log [ ] , 10 45
[ ]
39 67log [ ] , 45
d m m d m
L dB
d m d m
    
 
    
 

3. Fig. 2. IEC 61850-5 standards
Fig. 3. Absolute Inter-cell Interference
At worst radio conditions (cell edge user at d = 125 m)
[8] pathloss is calculated to be (7) -101.5 dB.
B. Noise floor per RB
Noise NRB per resource block is considered to be the
background wideband noise mostly created by Thermal
Noise Power Density in dB/Hz, calculated from Boltzmann’s
constant kB = 1.38 x 10-23
J/0
K and the absolute temperature
in Kelvin T = 290 0
K to be -174 dB/Hz and for 180 kHz
resource block bandwidth it is calculated as -111.44 dB, [13].
C. Uplink Interference per RB
Interference is considered to be inter-cell interference
from a neighbour cell UE transmitting on the same resource
block on same TTI. It could be calculated either from
mathematical assumptions [15], or simulation results or real
network measurements. From our perspective we do
consider that it is more accurate to have an average
estimation of inter cell interference per resource block at a
given path loss from real drive test measurements. During
drive test for 20 MHz band cell configurations, different
uplink received power levels Pr per RB have been reported
and the appropriate plots of Absolute Interference per RB vs.
cell edge Path Loss Ltarget have been created, Fig. 3. The
analytical mathematical functions after curve fitting are
expressed from up to bottom as:

2 3
2 3
2 3
2 3
480.631 9.850 0.08 0.0002
292.047 4.683 0.0372 0.000087
[ ]
264.84 3.832 0.03 0.000073
142.8 0.2315 0.002 0.00002
p p p
p p p
p p p
p p p
L L L
L L L
I dBm
L L L
L L L

   

   

    

    
 
At worst cell conditions we do suppose maximum UE
uplink power of PUE = 31.76 dBm = 1.5 W, an assumption
that is validated from most LTE handsets on market.
Considering typical cell bandwidth configuration of 20 MHz,
meaning 100 available number of physical resource blocks,
the available power per resource block is 1.5 W / 100 =
0,015 W = 11.76 dBm . Hence the expected received uplink
power per RB on the eNodeB antenna, considering a typical
Kathrein directional antenna gain of 18 dBi, will be Pr [dBm]
= PUE + GR – Ltarget = 11.76 dBm + 18 dBi – 101.5 = - 71.74
dBm. From (8) and figure 3 for Pr =< -100 dBm estimated
interference is considered to be IRB = -119.6 dBm.
D. Uplink γ estimation at cell edge
An adequate cell planning restriction is to select specific
SINR target γ0,target higher than expected eNB receiver
sensitivity. The eNB receiver sensitivity, SeNodeB, is defined
as the minimum uplink received power on base station
required to correctly decode uplink RB with 10-10
bit error
rate [13]:
 0, arg[ ] eNodeB
eNodeB TPDF figure BW t etS dB N N RB      
where TPDFN is the thermal noise power density,
calculated analytically from Statistical Physics Boltzmann’s
constant kB = 1.38 x 10-23
J/0
K and absolute temperature in
Kelvin T = 290 0
K , to be - 174 dB/Hz.
eNodeB
figureN is the
eNodeB noise figure which defines a degradation of SNR
due to RF components in an RF signal chain (2 dB for
uplink) [13,14] and RBBW is the resource block bandwidth of
180kHz .Substituting into (9) we get SeNodeB = -119.44 +
γ0,target dB. Considering a pre-selected link budget at cell edge
from (7), then a specific required SINR target could be
calculated as [13] and [15]:

,
arg ,
0, arg arg
[ ]
144.45
UE RB
t et T s eNodeB LNF BL
t et t et LNF BL
L dB P S M L
L M L
    
   
 
where MLNF is the log-normal fading margin, given by
Jakes formula, for 95% coverage calculated to be 6 dB for
Dense outdoor, 8.4 dB for Urban indoor or 10 dB for Dense
Urban Indoor [8]. LBL is body loss which could be considered
either as 2 dB for handset palm-top or 0 dB for lap-top [8].
Target γ0,target is considered extremely important since it will

4. Fig. 4. BER measurments, TU3 model
affect the decision upon selection of the number of resource
elements on uplink scheduling and MAC link adaptation
software module. Expected uplink γtarget at cell edge distance
(10) is estimated to be γtarget = 34.95 dB
E. Average number of uplink RB
Based on the target γ0,target on cell edge, the number of
allocated resource blocks nRB is calculated considering
uniform power distribution of nominal UE power PUE over
all transmitted resource blocks. This is an assumption which
is validated for most LTE handsets on the market [11].
Following basic link budget reasoning:

 
 
 
arg,
0, arg
0, arg
int
UE
received
t et RBUE RB
t et
RB RB
UE
RB
path RB RB t et
P
L nP
noise erference N I
P
ceiling n
L N I



  
 
      
 
The average number of uplink allocated RBs is estimated
to be ceiling[nRB] = 19, where ceiling[x] is the function
selecting the maximum integer number x from an analytical
calculation.
F. Transmitted bits per RB
Number of transmitted bits per RB nTs could be easily
calculated considering the worst case of cell edge UEs. In
such a case MAC scheduler [10], [14] will allocate QPSK
modulation (2 bits per symbol) with TX diversity, thus nAP =
1 in (6). One sub-frame contains 14 X 12 = 168 resource
elements (RE) and two OFMD symbols (24 RE) of the
subframe are allocated for sounding reference signals.
Available user plane bits per RB in (6) is considered to be
nTs = (168-24) x 2 = 288 bits/ ms.
G. MAC scheduling subframe intervals
During drive test on cell edge for 20 MHz bandwidth, an
FTP file of 3Mbyte = 24 Mbits was downloaded from an
intranet Teledrom AB server. Considering UE to be ideally
scheduled every subframe by MAC scheduler without
retransmissions, then according to the estimated number of
transmitted bits per RB on cell edge, nTs = 288 bits/ ms, the
expected max rate for cell edge user should be RB
n  288
kbps. Then minimum downloading time should be
24Mbits/( RB
n  288 kbps). From drive test the reported
average total downloading session service time, considering
non ideal conditions with initial transmissions,
retransmissions and non-scheduled periods, was estimated to
be 4.425 s. This means that the non-ideal contribution on
latency of retransmissions m and non-scheduled time periods
n is (m + n)Ts = (4.425 – 24Mbits/( RB
n  288 kbps)) s =
(4.425 – 24Mbits/(19 • 288 kbps)) s = 0,039 s.
H. Average number of HARQ MAC retransmissions m
The average number of retransmissions m is a function of
the physical packet error rate. Let p be the packet non
successful probability (error probability). Non successful
probability is related to the MAC packet length Mmac and the
bit error probability pb as [9]:
 1 (1 ) macM
bp p    
During nominal cell planning, γtarget and consequently bit
error probability pb have very low values, hence the average
number of retransmissions is approximated as [9]:
    
1
1 1 , 1
1
macM
b mac b bm p M p p
p
     

=  
From (13) it is obvious that retransmissions depend
explicitly on the bit error probability pb and on the average
size of the MAC packet Mmac. To calculate pb most
researchers rely on simulations. In our paper instead we did
initiated drive test measurements in an urban environment
which is highly dispersive using a test e-NB of Teledrom AB
with a rooftop car antenna to remove car penetration losses.
Real data have been collected using TEMS investigation
Data Collection software and statistical counters have been
reported using Operation & Maintenance GUI Ericsson
tools. An LTE UE category 4 with typical characteristics of
max uplink bit rate = 50 Mbps, uplink higher supported
modulation 16 QAM with spatial multiplexing 22 or QPSK
with TX diversity has been used [11]. In Fig.4 BER vs.
blocking probability has been plotted. Test drive was
compliant with the Typical Urban channel model (TU3
model, 3Km/h) requirements [12]. Throughout the drive test
the average Eb/N0 has been reported to be equal to 30 dB,
indicating thus a relative good quality. From Fig. 4
Eb/N0  30dB corresponds to an approximate pb of 0.06.

5. Ericsson statistical counter pmUeThpVolUl in units of
[kbits] measures uplink MAC SDU volume and finally
Ericsson counter pmUeThpTimeUl in units [ms] provides
the period of MAC volume measurements in ms. From
TEMS investigation, during drive test, MAC reported
measurements have been calculated to be pmUeThpVolUl =
345282 kbits and pmUeThpTimeUl = 900000 ms = 900 sec
= 15 min. Hence pmUeThpVolUl/ pmUeThpTimeUl =
383.6 bits/1ms which provides average Mmac = 384 bits per
TTI interval of Ts = 1 ms. Substituting into (13) pb = 0,06
and Mmac = 384 bits results into average m = 24. Following
previous analysis (m + n)Ts = 0,039 s  (24 + n) = 39  n
= 15.
I. Average MI and Mover estimation
Average MI and Mmac bits on (6) could be estimated from
drive test, following network statistics on Operation &
Maintenance SubSystem OSS for Ericsson test eNB on
Teledrom AB test equipment. Ericsson counter
PmPdcpVolUlDrb in units [kbits] measures total uplink
volume (PDCP Signaling Data Units SDU) in an established
Data Radio Bearer per measurement period, providing a
good estimate of MI. RLC/MAC overhead on LTE is
considered to be Mover = 20 bytes [15]. Following drive test
reported statistics PmPdcpVolUlDrb = 545627 kbits per
measurement period of 15 minutes = 900000 ms.
Consequently MI = PmPdcpVolUlDrb/900000ms= 607
bits/ms. Consequently MI / Mmac = 2. Overall delay in the
uplink transmission will be the contribution of MAC layer
delays (6) and PDCP buffer input delays (5). Substituting
previous analysis into (6) the final MAC delay will be:

 
42.22
607 2 160
39
288
s
I mac
Mac
AP RB
overI
s s
T
M M
W m n
ms ms ms
M M
T T
n n n
bits bits
    


 
 

 

 
Adding also (5) the worst case of a loaded handset service
of ρ = 0.8 then average buffer delay will be W = 6 ms,
contributing to total average delay of 42.22 ms + 6 ms =
48.22 ms. Following Fig. 2 it is obvious that, for all types of
smart grid signaling messages, outdoor LTE cell coverage
range of d = 125 m [8] fulfills delay constraints.
V. CONCLUSIONS
In general case planners should always reconsider the
cell range to minimize delay. To minimize delay, Wmac
should be minimized and from (14) it is obvious that the
highest contribution to MAC delay is produced by MAC
scheduler delay which is a function of Signal to Noise and
Interference ratio γ.
ACKNOWLEDGMENT
Authors would like to express their gratitude to P.
Kostopoulos, C.E.O. of Teledrom AB, Sweden, for its
prompt support on setting up LTE eNB for the Drive Test.
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