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

10 1 2 11 1 1 1

mn

n zmn m

m z z z z z zz

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:

10

2 2

1 1

1

1 1 1

1 1 ....

n

n zn

zz z

ze

e z

e e z

From expansion the general term is calculated as:

1

1

1

1 1!

1 11 !

n kn

n k k

n

k

n kn

n k k

kk n

ke

n k

ke

n k

Finally average expected delay is calculated as:

Fig. 1. Mean expected buffering delay (ms)

1

1 1

1

1 1

1 1!

1 11 !

n

n

n kn

n k k

n k

n kn

n k

n k

k n

k

W n

kn e

n k

kn 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 / MmacMover 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 macMac

AP RB

overIs s

T

M MW m n

M MT 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 mL dB

d m d m

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/0K and the absolute temperature in Kelvin T = 290 0K 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 LI 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/0K and absolute temperature in

Kelvin T = 290 0K , 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

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

UEreceived

t et RBUE RB

t etRB RB

UE

RBpath RB RB t et

P

L nP

noise erference N I

Pceiling 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 ) macMbp 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 , 11

macMb 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 22 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.

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:

42.22607 2 160

39288

s

I macMac

AP RB

overIs s

T

M MW m n

ms ms ms

M MT 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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