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Dynamic Spectrum Refarmingwith Overlay for Legacy Devices

Xingqin Lin and Harish Viswanathan

Abstract—The explosive growth in data traffic is resulting in aspectrum crunch forcing many wireless network operators tolooktowards refarming their 2G spectrum and deploy more spectrallyefficient Long Term Evolution (LTE) technology. However, mobilenetwork operators face a challenge when it comes to spectrumrefarming because 2G technologies such as Global System forMobile (GSM) is still widely used for low bandwidth machine-to-machine (M2M) devices. M2M devices typically have long lifecycles, e.g. smart meters, and it is expensive to migrate thesedevices to newer technology since a truck roll will typically berequired to the site where a device is deployed. Furthermore,with cost of 2G modules several times less than that of LTE,even newly deployed M2M devices tend to adopt 2G technology.Nevertheless, operators are keen to either force their 2G M2Mcustomers to migrate so that they can refarm the spectrum orset aside a portion of the 2G spectrum for continuing operating2G and only refarm the rest for LTE. In this paper we proposea novel solution to provide GSM connectivity within an LTEcarrier through an efficient overlay by reserving a few physicalresource blocks for GSM. With this approach, operators canrefarm their 2G spectrum to LTE efficiently while still provi dingsome GSM connectivity to their low data rate M2M customers.Furthermore, spectrum can be dynamically shared between LTEand GSM. An approach similar to that proposed in this papercan also be applied for other narrow band technology overlaysover LTE.

I. I NTRODUCTION

The exponentially growing demand for wireless traffic isstraining cellular networks. According to Cisco’s report [1], in2011 global mobile data traffic doubled for the fourth year inarow and was eight times the traffic of the entire global Internetin 2000. Cisco further expects that global mobile data trafficwill increase 18-fold between 2011 and 2016 [1]. Obviously,mobile network operators are facing intense pressure to maketheir networks keep pace with this exponential wireless trafficgrowth.

The explosive data growth is resulting in a spectrumcrunch and thus many operators are looking to refarm their2G spectrum to deploy more spectrally efficient Long TermEvolution (LTE) technology. LTE is the key standard forwireless communications providing high speed data servicesin next-generation cellular networks [2]–[4]. Not surprisingly,evolution to LTE is critical for mobile network operators todeliver the high speed mobile broadband services that theircustomers demand. However, operators face a challenge whenit comes to spectrum refarming because of the numerous

Xingqin Lin is with the Department of Electical and ComputerEngineeringat The University of Texas at Austin, Austin, TX. Harish Viswanathan iswith Bell Labs, Alcatel-Lucent, Murray Hill, NJ. This work was performedwhen Xingqin was a summer intern at Bell Labs. Email: xlin@utexas.edu,harish.viswanathan@alcatel-lucent.com. Date revised: June 11, 2018.

legacy machine-to-machine (M2M) devices [5], [6]. M2Mdevices typically have long life cycles, e.g. smart meters,andit is expensive to migrate these devices to LTE since a truckroll is typically required to the site where a device is deployed.

Meanwhile, GSM is - and will remain attractive - for M2M.GSM is particularly suitable for M2M because most M2Mdevices require low data rate communication that is adequatelymet by GSM at module prices that are less than a fifth ofthat of third and fourth generation modules. Furthermore,because GSM is available worldwide [7] a single technologydevice based on GSM can be used for applications deployedinternationally. In fact, two thirds of all new cellular M2Mmodules shipped in 2011 are estimated to be GSM/GPRS byABI Research [8].

The above discussions imply that mobile network operatorsmay have to keep providing GSM service for legacy devices,especially M2M, although they would like to refarm theirGSM spectrum for LTE. In this paper we propose a noveldynamic spectrum refarming (DSR) approach for the co-existence of GSM and LTE. DSR allows complete refarmingof the GSM spectrum for LTE. But some LTE physicalresource blocks (PRB) will be reserved for GSM transmission,i.e., LTE Evolved Node B (eNodeB) will not schedule thosereserved PRBs for any User Equipment (UE) and accordinglysuppress the reference signals. With this approach, operatorscan migrate their GSM spectrum to LTE while still providingGSM connectivity to their low data rate M2M customers. Moreimportantly, spectrum can be dynamically shared between LTEand GSM simply through adjusting the number of reservedPRBs. This approach is advantageous compared to staticpartitioning of the legacy spectrum into a portion for GSM anda portion for LTE because of more efficient use of spectrum. Inaddition, the basic idea of reserving LTE PRBs can be appliedto other scenarios as well; for example, similar idea is usedin[9] for deploying LTE small cells sharing the same spectrumas existing GSM networks.

Despite the potential of the proposed GSM overlay onLTE for legacy devices, there are several technical issuesto be addressed. First and foremost, will LTE UEs withno modifications continue to operate as usual? This is nota priori clear since reserving PRBs for GSM modifies thechannel structure of LTE. Secondly, will GSM mobiles operateproperly? This is also nota priori clear since GSM PRBs areadjacent to LTE PRBs and the LTE interference leakage maycause problems. If so, what are the corresponding solutions?Last but not least, is the impact on the LTE spectral efficiencybecause of the GSM overlay significant? What are the methodsto recover the loss of LTE capacity because of adjacent channel

2

(a). SSR

5MHz refarmed for LTE 2.5MHz GSM spectrum

(b). DSR

10MHz refarmed for LTE

2.5MHz of embeded GSM spectrum

(c) A closer look at DSR

9 MHz = 50 PRBs = 45 200Khz Blocks

(c). A closer look at DSR

GSM

Block

Lower power LTE

transmissions in GSM

PRBs of other sectors

Block needs to be

protected for LTE

LTE

Block

Fig. 1. Static spectrum refarming versus dynamic spectrum refarming. Notethat the bottom subfigrue plots 45 200KHz blocks rather than 50 180KHz LTEPRBs. As GSM center frequency must be an integer multiple of 200KHz [10],GSM channel edges may not be always aligned with LTE PRB edges.

interference from GSM? We address these critical issues in thispaper.

The rest of this paper is organized as follows. Section IIdescribes the basic idea and the advantages of DSR by aspecific example. We then discuss how to reserve PRBs forGSM and mitigate the inter-technology interference betweenLTE and GSM in Section III. Several LTE enhancements torecover the capacity loss are presented in Section V. SectionVI presents some simulation results, and is followed by thediscussion on uplink design in Section VII and the conclusionsin Section VIII.

II. BASIC IDEA AND BENEFITS OFDSR

In this section, we use a specific example to illustrate thebasic idea and benefits of DSR. Suppose that a mobile networkoperator has 10MHz spectrum in the GSM band and that thecapacity requirement of GSM has diminished so that 2.5MHzis sufficient, as shown in Fig.1 (a) and (b).

A. DSR: A high level description

The basic idea of DSR is to exploit the flexibility of OFDMused in LTE to embed GSM transmissions within a portionof LTE transmission. In particular, with DSR an LTE eNodeBreserves certain PRBs within the 10MHz LTE carrier for GSMand does not transmit any LTE signal on those subcarriers.1

Instead, GSM signals are transmitted from the same basestation on the reserved PRBs.

Obviously, PRBs that are reserved for GSM need to becarefully picked so that the critical LTE PRBs used forsynchronization, control signaling and other signaling suchas hybrid automatic repeat request (HARQ) feedback arenot allowed for use by GSM. With this approach, LTE UEsare not significantly impacted by GSM transmissions. Theadjacent channel leakage ratio of GSM is such that the SINRof neighboring LTE PRBs will be limited to at most11dB

1Note that, with 10MHz LTE transmission bandwidth, the actual occupiedbandwidth is 9MHz while the guard band consumes 1MHz bandwidth.

because of GSM signal interference assuming that GSM powerspectral density (PSD) is13.56dB higher2 than that of LTE.(The 11dB cap on LTE SINR can be calculated using theGSM power leakage profile specified in Table I and plottedin Fig. 4.) However, this does not significantly impact overallLTE spectral efficiency because LTE UEs close to cell edgealready have SINR limited to less than1dB because ofout-of-cell interference. To mitigate interference from LTEPRBs to GSM, transmit power on the PRBs close to GSMPRBs can be reduced. Finally, GSM requires frequency reuse.Spectral efficiency can be improved by allowing low powerLTE transmissions to LTE UEs close to the base station onthe GSM PRBs of the neighboring cells/sectors. With thisfractional reuse approach between LTE and GSM, the amountof spectrum needed to support GSM can be minimized. Withthe above techniques an overlay can be supported efficiently.

The above high level description on DSR will be exploredmore in later sections. Here we show an example allocationof GSM spectrum with LTE in Fig.1(c). Each block in thefigure represents 200KHz, the width of a GSM carrier. Atotal of 12 200KHz blocks or about 2.4MHz of spectrumcan be assigned as default GSM spectrum. This representsabout 25% of the LTE spectrum. Each sector can have aGSM Broadcast Control Channel (BCCH) carrier and a trafficcarrier. A frequency reuse of 3/9 can be supported for BCCHand 1/3 for traffic channel. As an alternative to frequencyhopping, antenna selection diversity can be employed wherethe signal is transmitted on different antennas in alternate slotsto provide diversity transmission. The picture also shows thatsome of the GSM blocks meant for use in other cells canbe used in this cell for LTE with low power so that they donot cause interference to other cells. The grey blocks cannotbe assigned to GSM since they need to be protected for LTEcontrol signaling. Detailed descriptions can be found in thenext section. The spectrum sharing can be dynamic in thesense that when there is no GSM traffic in a given sector, theGSM blocks can be used for LTE transmission.

Before ending this subsection, it should be noted thatthe number of PRBs that are reserved for GSM should beappropriately determined: there would be inefficiency or lossif either excess or too few PRBs are reserved. In DSR, thenumber of reserved PRBs is based on relatively long termstatistics such as hours. In contrast, the durations of GSMsessions are at the time scale of seconds or at most minutes.Thus, on a short time scale the reserved PRBs may be underutilized or over loaded. Considering that M2M traffic suchas meter reading application is typically delay tolerant, M2Mtraffic on GSM can be time-shifted to avoid over-loading. Inthis way, the reserved PRBs utilization can be made efficientlyeven though the number of reserved PRBs are determinedbased on long term average GSM traffic trends.

B. DSR versus SSR

We compare our proposed DSR to static spectrum refarming(SSR) to highlight the key advantages of DSR. SSR com-

2GSM PSD is assumed to be13.56dB higher than LTE PSD as typically20W transmit power is used per200KHz GSM channel while40W transmitpower per9MHz LTE channel.

3

pletely separates GSM and LTE within the band, i.e., partof the GSM spectrum is kept for legacy devices while theremaining GSM spectrum is refarmed for LTE. As a specificexample, consider the scenario shown in Fig.1. Because LTEtransmission bandwidth can only be 1.4, 3, 5, 10, 14, or20 MHz wide, the operator will be restricted to refarming 5MHz of the spectrum for LTE and the remaining 2.5MHz willbe under utilized. Even if LTE can simultaneously support a5MHz channel and a 1.4MHz channel by e.g. carrier aggre-gation (see, e.g., [11]–[13]), the remaining 1.1MHz spectrumis under utilized. In contrast, DSR allows the deployment of10MHz LTE channel with 2.5MHz of GSM embedded. Thus,compared to SSR, DSR can minimize the wastage of spectrum.

The second advantage of DSR is its flexible spectrum reusecapability. In SSR, the LTE bandwidth is fixed, e.g., 5MHz inFig.1. The system cannot reassign bandwidth between GSMand LTE with changing traffic demand. In contrast, withDSR LTE in a given sector can utilize the GSM carriersof the neighboring sector with low transmit power. Lowpower LTE transmissions targeting good geometry users canprovide significant spectral efficiency. Since transmissions areof low power, GSM transmissions in the neighboring cellare (nearly) not affected. This idea can be viewed as a formof fractional frequency reuse (FFR) (see, e.g., [14]–[16])forinter-technology inter-cell interference coordination (ICIC).Besides, if immediate transmission is not strictly required forM2M such as for meter reading application, M2M traffic onGSM can be scheduled to avoid the busy hour and DSR allowsmore spectrum to be used for LTE to accommodate the needs.3

To sum up, DSR provides GSM connectivity within an LTEcarrier through an efficient, dynamic overlay by reserving afew PRBs for GSM.

III. OVERCOMING SYSTEM DESIGN ISSUES

A. How to Reserve PRBs

DSR solution reserves certain PRBs within the LTE trans-mission bandwidth for GSM signals and does not transmitany LTE signal on those subcarriers. This reservation schemechanges the channel structure of LTE. To ensure normaloperation of LTE, we need to carefully select the positionsof those reserved PRBs out of the LTE channel. We next takethe 10MHz LTE channel as an example and discuss how thesystem should reserve PRBs to avoid/minimize the potentialimpact of LTE puncturing on the broadcast and synchroniza-tion channels, reference symbols, and other control signalingchannels including Physical Control Format Indicator Channel(PCFICH), Physical Downlink Control Channel (PDCCH) andPhysical Hybrid-ARQ Indicator Channel (PHICH).

1) Avoid broadcast and synchronization channels: LTEbroadcast and synchronization channels are located withinthecentral 1.08MHz of the 10MHz LTE channel, as shown inFig.2(a). So we can avoid reserving the PRBs used by theLTE broadcast and synchronization channels.

3Wireless traffic is imbalanced over both time and space. During thedaytime, the demand is high in working areas and is low in the residentialarea. The converse is true during the night.

P-SCHPBCH S-SCHPhysical Resource Block (PRB)

first 1..3 OFDM

(a). PBCH, P-SCH, S-SCH

Reference signal

(b). PRB

f 0 1 2 3 4 5 6 0 1 2 3 4 5 6

1.08 MHz

Physical Resource Block (PRB)

f

OFDMsymbolsreservedfor L1/L2 controlsignaling(PCFICH,PDCCH

slot (0.5 ms) slot (0.5 ms)PDCCH,PHICH)

75KHz 75Khz 75KHz 75KHz2.175MHz2.175MHz2.175MHz2.175MHz

(c). PCFICH

3MHz 3MHz3MHz

(d). PHICH

2.175Mhz 2.175Mhz 2.175Mhz 2.175Mhz

Fig. 2. LTE downlink channel structure

2) No impact on reference signals: The impact of punc-turing on reference symbols is not an issue because thereserved PRBs will not be scheduled for any user and thusthe corresponding reference signals are suppressed.

3) Impact on PCFICH and PHICH: The PCFICH occupiesfour 75KHz chunks within the10MHz LTE channel, as shownin Fig.2(c). As for PHICH, multiple PHICHs are mappedto the same set of resource elements and these PHICHsconstitute a PHICH group. The number of PHICH groups canbe configured by higher layers to some extent. However, thepositions of PCFICH and PHICH are not fixed and vary withthe physical cell ID [17]. They would spread out and occupyall the PRBs if all the cell IDs were used and we would notbe able to reserve PRBs without affecting them. To overcomethis issue, we can only use a small subset of the cell IDs. ThenPCFICH and PHICH will only occupy certain part of the LTEtransmission bandwidth, which can be avoided by the reservedPRBs.

4) Impact on PDCCH: The real challenge comes fromthe PDCCH which occupies all the PRBs. This implies thata certain number of resource element groups carrying thePDCCH have to be wiped out with LTE puncturing. For-tunately, LTE multiplexes and interleaves several PDCCHswithin one LTE subframe. This helps to spread the impact ofpuncturing over all the PDCCHs and each PDCCH only needsto tolerate a certain level of the errors. Moreover, LTE allowsthe system to increase the aggregation level of the controlchannel elements, which can make PDCCHs more robustagainst errors. Note that given limited resource of the controlchannel elements, increasing its aggregation level reduces thenumber of PDCCHs that can be simultaneously used.

We further perform link level simulation to study the impactof puncturing on PDCCH. The result for LTE ExtendedPedestrian A (EPA) model is shown in Fig. 3. As expected,the PDCCH block error rate (BLER) increases due to thepuncturing. However, the loss in BLER can be recoveredby increasing one aggregation level of the control channelelements. Besides,1×2 system has better BLER performancethan1× 1 system, which is natural since the former provideshigher diversity order. Note that in Fig. 3 we assume thatGSM PSD is as high as LTE PSD in the link simulation but

4

−20 −15 −10 −5 0 5 10−4

−3

−2

−1

0

SNR (dB)

BLE

R1 by 1 EPA

Baseline: AGL = 2Punctured: AGL = 2Baseline: AGL = 4Punctured: AGL = 4Baseline: AGL = 8Punctured: AGL = 8

−20 −15 −10 −5 0 5 10−4

−3

−2

−1

0

SNR (dB)

BLE

R

1 by 2 EPA

Baseline: AGL = 2Punctured: AGL = 2Baseline: AGL = 4Punctured: AGL = 4Baseline: AGL = 8Punctured: AGL = 8

Fig. 3. Impact of puncturing on PDCCH: 10MHz LTE channel witha2.4MHz punctured portion. LTE EPA multipath fading channelmodel is used.AGL denotes the aggregation level of the control channel elements.

DSR is transparent to LTE receivers (i.e., LTE receivers donot know certain portions of the channel have been puncturedfor GSM overlay). We notice that PDCCH under DSR hasunacceptably high BLER if GSM PSD is set to be13.56dBhigher than LTE PSD and LTE receiver includes all PDCCHsymbols in the decoder. In constrast, if LTE receivers take intoaccount certain portions of the channel have been puncturedfor GSM overlay when decoding PDCCH, then PDCCH underDSR has better BLER performance than the performance of itscounterpart presented in Fig. 3. We do not present the specificnumerical results here due to space constraints.

The awareness of GSM signals at LTE UEs can be achievedby explicitly signaling to the LTE UEs. The informationabout spectrum puncturing can be conveyed together withother system information in the Physical Broadcast Channel(PBCH), which is not affected by the proposed puncturing.Explicit signaling may be avoided at the cost of additionalcomplexity in the receiver design of LTE UEs. For example,the LTE receivers can detect the presence of GSM throughenergy detection. This is possible because those symbolscorresponding to the GSM PRBs will be received with muchhigher power relative to the other LTE symbols.

5) Impact on channel estimation quality: With the aware-ness of the presence of GSM overlay (required to achieve ac-ceptable PDCCH performance), LTE UEs’ channel estimationquality will be slightly degraded from the limited interpolationdue to LTE puncturing. However, UEs are generally designedto deal with frequency selective channels and thus will notobtain an average channel estimate over the whole band. Evenif some LTE UEs exploit the pilots located in the entire band,the performance degradation can be tolerated within the designmargin.

To sum up, though DSR inevitably affects the channelstructure of LTE, it appears feasible with a careful design.

B. How to Mitigate the Inter-technology Interference betweenLTE and GSM

Since LTE signal and GSM signal are transmitted in thesame band, there is GSM adjacent channel interference leakageon LTE UE and vice versa. To mitigate interference fromLTE PRBs to GSM, transmit power on the PRBs close toGSM PRBs can be reduced. This also helps mitigate theimpact of GSM on LTE since other non-adjacent PRBs can beallocated more power and partially recover the LTE capacityloss because of GSM overlay.

In the next section, we formally formulate the above poweradjustment problem and study how to adjust the LTE transmitpower accordingly. Before that we note that adjacent channelleakage only captures how much power is transmitted byGSM base station on LTE subcarriers. It is also necessaryto consider the LTE receiver in-channel selectivity (ICS):LTEreceiver FFT will grab some in-band GSM power becauseof the rectangular windowing effect. The grabbed in-bandGSM power will essentially appear as noise and degrade theSNR of LTE signal, which matters because the GSM PSDis much higher compared to that of LTE. To formalize theabove arguments, let us use the continuous time FFT in thereceiver for ease of exposition and letxg(t) be the receivedGSM signal. Then after FFT,

Xg(f∗) =

∫ Ts/2

−Ts/2

xg(t) exp(j2πf∗t)dt

=

∫ ∞

−∞

xg(t) exp(j2πf∗t)rect(

t

Ts)dt

=

∫ ∞

−∞

Xg(f)Tssinc(Ts(f − f∗))df,

whereTs is the OFDM symbol time, rect(t) is the rectanglefunction, i.e., rect(t) = 1 if t ∈ [− 1

2 ,12 ] and zero otherwise,

sinc(t) = sin(πt)πt , and the last equality is due to the generalized

Parseval’s theorem. It follows that the “virtual” GSM PSD seenby the LTE receiver can be written as

Sg(f∗) =

∫ ∞

−∞

Sg(f)Tssinc2(Ts(f − f∗))df, (1)

whereSg(f) is the real received GSM PSD. To gain someinsight, let us consider two examples. First,Sg(f) = N0/2

5

which is the PSD of background white noise. Then

Sg(f∗) = N0/2

∫ ∞

−∞

Tssinc2(Ts(f − f∗))df

= N0/2

∫ ∞

−∞

(

1√Ts

rect(t

Ts)

)2

dt

= N0/2,

which agrees with intuition: white noise still appears “white”.Now consider another example with arbitrary PSDSg(f) butTs → ∞. Then

Sg(f∗) =

∫ ∞

−∞

Sg(f) limTs→∞

(

Tssinc2(Ts(f − f∗)))

df

=

∫ ∞

−∞

Sg(f)sinc(Ts(f − f∗))δ(f − f∗)df

= limTs→∞

Sg(f)sinc(Ts(f − f∗))|f=f∗

= Sg(f∗).

where we use the factlima→01asinc( fa ) = δ(f) in the second

equality. This implies that if the continuous FFT operationwas of infinite duration the “virtual” GSM PSDSg(f) seenby the LTE receiver would be the same as the real GSM PSDSg(f). Hence the grabbed in-band GSM powers at those LTEOFDM subcarriers are zero in this ideal case. In general, thisis not true due to the finite windowing effect and the grabbedin-band GSM power at thek-th subcarrier is given by

N(g)k =

∫ (k+ 1

2)b

(k− 1

2)b

Sg(f)df, (2)

whereb denotes the subcarrier bandwidth.Note that we do not have to worry about the ICS so much

from LTE to GSM. In particular, since LTE PSD is much lowerthan that of GSM, GSM receiver’s adjacent channel selectivitywill handle that fairly well.

IV. T RANSMIT POWER ALLOCATION IN LTE

We first model the GSM leakage, which is specified inTable I and plotted in Fig. 4 [10]. As for LTE transmit powerallocation, the problem formulation involves the PSD of theLTE signal as well as that of the GSM signal. To this end, wefirst introduce the following notations:

• Let Q be the total number of LTE subcarriers, which isassumed to be even.

• Let 1/T be the subcarrier spacing.• Ω = ±1,±2, ...,±Q/2 denotes the indices of all the

subcarrier frequencies.• S ⊂ Ω denotes the set of indices of the subcarrier

frequencies that get punctured for GSM overlay.• Φ = Ω\S denotes the indices of OFDM subcarrier fre-

quencies used for LTE transmissions. Denote byN = |Φ|the cardinality ofΦ.

• Let 1, 2, ..., N be the enumeration ofΦ. Define themappingvi : 1, 2, ..., N 7→ Φ, which maps eachi tothe corresponding subcarrier frequency indexvi.

• d(n) denotes the sequence of data symbols and areassumed to be white withE[d(n)] = 0, E[|d(n)|2] = 1.

−1000 −800 −600 −400 −200 0 200 400 600 800 1000−70

−60

−50

−40

−30

−20

−10

0

Frequency (KHz)

GP

RS

Pow

er L

eaka

ge (

dB)

Fig. 4. Linear interpolation of GPRS adjacent channel interference leakageusing data (cf. Table I) from [10]

Then the LTE baseband signalx(t) can be written as

x(t) =N∑

i=1

√

piTs

∑

k

d(kN + i)qi(t− kTs),

wherepi is the transmit power on subcarriervi, andqi(t) isdefined as

qi(t) = w(t) exp(j2πviTt),

wherew(t) is the windowing function for spectrum shaping.Then the corresponding PSD is given by

S(f) =

N∑

i=1

pi|W (f − viT)|2,

whereW (f) is the Fourier transform ofw(t).

For practical implementation, the transmitter generates thesamples ofx(t) at a sufficiently high rate1/Tc. These samplesare passed through digital-to-analog converter, resulting in x(t)given by

x(t) =∑

n

x(nTc)g(t− nTc),

whereg(t) is the interpolation function with Nyquist autocor-relation. Then the corresponding PSD is given by

S(f) =1

T 2c

|G(f)|2∑

m

S(f − m

Tc)

=

N∑

i=1

pi ·1

T 2c

|G(f)|2∑

m

|W (f − m

Tc− vi

T)|2

=

N∑

i=1

pi|W (f − viT)|2,

where G(f) is the Fourier transform ofg(t), W (f) =1T 2c

|G(f)|2 ∑m |W (f − mTc

)|2.

We would like to control the LTE interference leakage tothe GSM signal. In particular, the LTE PSD at frequencyf∗

occupied by the GSM signal should be below some threshold

6

∆f (KHz) 100 200 250 400 600 700 800 900 1000ACLR (dB) -1 30 33 60 67 67 67 67 67

TABLE IGSM ADJACENT CHANNEL INTERFERENCE LEAKAGE SPECIFICATIONS[10]

level C, i.e.,

S(f∗) =N∑

i=1

Wi(f∗)pi ≤ C.

whereWi(f

∗) = |W (f∗ − viT)|2.

For discrete-time approximation, one can simply substituteS(f∗) for S(f∗) in the above inequality. As for the LTE signal,its SINR of subcarrieri is

SINRi =piNi

,

whereNi is the background noise power (possibly includingin-band GSM leakage and the grabbed in-band GSM powerN

(g)i ) of the LTE signal in subcarrieri.

We are interested in maximizing the LTE spectral efficiencywhile limiting LTE leakage to GSM signal and meeting thepower budget constraint:

maximizep≥0 R(p) =

N∑

i=1

log(1 +piNi

)

subject to S(fj) =

N∑

i=1

Wi(fj)pi ≤ Cj , j = 1, ...,M,

N∑

i=1

pi ≤ Pmax, (3)

wherefj is thej-th constrained sample frequency point;Cj isthe corresponding threshold value; andM is the total numberof sample frequency points. For example, we may takefj tobe the center frequency of each GSM subcarrier. In this ex-ample,M equals the number of subcarriers reserved for GSMtransmissions. More general constraints are also possible. Withconvex objective function and convex feasible set, this isa convex programming problem that has a strictly feasiblesolution and thus can be decoupled across subcarriers. Wepropose a waterfilling-based search algorithm which exploitsthe special structure of the above optimization problem. Thealgorithm can be found in the Appendix.

Next we provide a numerical result to show the structureof the optimal LTE power allocation. 4 portions, each ofbandwidth 600KHz, of the10MHz LTE channel are punctured.We assume that the GSM PSD is flat in the punctured portionsbut 13.56dB above that of LTE. Fig. 5 shows the virtualPSD of GSM signal “seen” by LTE receiver due to ICS. Asexpected, LTE subcarriers adjacent to the punctured portionsgrab more in-band GSM power and thus suffer more fromICS.

The optimal power allocation solution to the problem in (3)is plotted in Fig. 6, while the PSD of the punctured LTE signal

−5 −4 −3 −2 −1 0 1 2 3 4 5−75

−70

−65

−60

−55

−50

−45

−40

−35

Frequency (MHz)

PS

D (

dB)

Virtual PSD of GSM Signal

Fig. 5. Virtual PSD of GSM signal due to the LTE receiver’s in-channelselectivity.

0 100 200 300 400 500 600

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Subcarrier index

Pow

er a

lloca

tion

(W)

Fig. 6. Optimal LTE power allocation:Ts/T = 1200/1024 with T =1

1200×10−3, total transmit powerPmax = 40W , noise power per subcarrier

is 1/(10 ∗ Ts ∗ 192000)W . (Thus, the ratio of total transmit power to totalnoise power is10dB.)

is shown in Fig.7. The optimal power allocation shown inFig. 6 isalmost uniform power allocation across the spectrumexcept zero power in the punctured spectrum and nearly zeropower in the nearest two subcarriers on each side of the 4punctured portions of the spectrum. It can be seen from Fig.7 that LTE leakage to GSM is limited below−15dB and thusthe GSM channels are well protected. The design insight hereis thus to reserve 2 subcarriers as the guard band betweenGSM and LTE at each side of every punctured portion of thespectrum. This would protect GSM signals from LTE leakage.Note that in our optimization formulation we only protectGSM signals from LTE leakage. Of course, this is only oneaspect of the design; more subcarriers may need to be reservedin real systems for other concerns.

7

−8 −6 −4 −2 0 2 4 6 8−95

−90

−85

−80

−75

−70

−65

−60

−55

−50

Frequency (MHz)

PS

D (

dB)

PSD of LTE Signal

Fig. 7. PSD of the LTE signal: LTE leakage to the 4 punctured spectrumportions reserved for GSM is limited below−15dB.

−10 −5 0 5 10 15 20 25 300

10

20

30

40

50

60

70

SNR (dB)

Rat

e (M

bps)

NoiseNoise+LeakageNoise+ICSNoise+Leakage+ICS

Fig. 8. Impact of GSM power leakage and LTE receiver’s ICS: SNR isdefined as the ratio of total LTE received power to total noisepower in 9MHzLTE channel.

Fig. 8 shows the impact of GSM power leakage and LTEreceiver’s ICS. It can be seen that GSM power leakage sig-nificantly reduces the LTE rate. Besides GSM power leakage,LTE receiver’s ICS further reduces the rate, particularly in thehigh SNR regime, i.e., SNR>15dB. In real LTE networks,SNR is typically much lower than15dB, which implies thatfrom a system wide perspective GSM power leakage is a moredominant issue compared to LTE receiver’s ICS. Note thatthe Noise+Leakage and Noise+ICS curves cross at high SNR,which arises from the following facts: In the low SNR regimethe limiting factor is the bad SINR of adjacent PRBs dueto GSM power leakage, while in the high SNR regime ICSdominates because a−72 − (−39) = −33dB floor (cf. Fig.5) exists throughout the LTE channel, which eventually limitsthe achievable rate.

Before ending this section, we stress that the above poweroptimization is formulated from the link-level perspective.Compared to a system-wide perspective, the link-level powercontrol problem is relatively simple; better performance can be

Cell A Cell A

Cell C Cell C

C ll B C ll B

LTE UE

Cell B Cell B

GSM t i i i GSM PRB f ll AGSM transmission in GSM PRBs of cell ALow power LTE transmission in GSM PRBs of Cell A

Fig. 9. Fractional frequency reuse of GSM PRBs in neighboring cells

obtained with system-level power optimization. Indeed, semi-static power allocation over different PRBs is supported byLTE for the purpose of inter-cell interference coordination(ICIC). The proposal in this paper can be combined with suchheterogeneous network concepts. In addition, the focus here ison a commonly used rate metric to demonstrate the benefits onspectrum sharing on throughput. Other metrics like delay maybecome relevant in system-level study, where multiple queuesexist and scheduling plays an important role in determiningthe delay performance. Though desired delay performanceis normally achieved by designing appropriate schedulingalgorithms (see e.g. [18]–[20]), delay can be incorporatedinto the power optimization by following e.g. [21]. Roughlyspeaking, one can come up with an (possibly approximate)expression for the mean delay of each queue as a functionof the power allocation. Then for each link one can seta maximum delay constraint. The difficulty of the delay-incorporated power optimization will be largely determinedby the delay constraints (which determine the feasible set ofpower allocation) and deserves future study.

V. LTE ENHANCEMENTS TORECOVERCAPACITY LOSS

Due to GSM overlay, there is a capacity loss in the LTEsystem. This loss stems from the reduced number of PRBs thatcan be used for LTE UEs as well as from the GSM interferencedue to leakage and LTE receiver’s ICS. In this section, weinvestigate ways for LTE to recover the capacity loss.

A. Fractional Frequency Reuse

Since adjacent GSM cells/sectors use orthogonal carriers,FFR can be applied between LTE and GSM to mitigate thecapacity loss of LTE. In particular, LTE in a given cell canutilize GSM carriers in the neighboring cells with low transmitpower. Low power LTE transmissions targeting good geometryUEs can provide significant spectral efficiency. Nevertheless,we need to determine how low the power should be so as notto affect GSM transmissions in the neighboring cells.

We next roughly calculate this low power. Consider theworst scenario as shown in the left plot in Fig. 9. LetPg andPs denote the GSM transmit power and the LTE low power (in

8

a 200KHz GSM channel), respectively. To guarantee reliableGSM transmission, we require

PgH

2PsH +N0≥ γ ⇒ Ps ≤

Pg

2γ− N0

2H(4)

where γ is the required SINR threshold for reliable GSMtransmission, e.g. 10dB,Pg is the GSM transmit power,His the mean channel gain (i.e., only path loss is considered)which is the same for all the3 links in the left plot in Fig. 9,N0 is the noise power per 200KHz GSM channel. Based on(4), we can at least get a rough estimate about the low powerlevel that could be used in FFR.

The right hand side plot in Fig. 9 shows that the lowpower LTE transmission in cell C suffers from intercellinterference caused by cochannel GSM transmission in cellA and low power LTE transmission in cell B (since cell Balso reuses the GSM PRBs of cell A). However, comparedto the interference caused by the neighboring cochannel GSMtransmission, interference generated by the neighboring lowpower LTE transmission is negligible since it uses a muchlower transmit power.

B. Intelligent Scheduling

There are two types of “special” PRBs in LTE that areoverlaid by GSM and enhanced with FFR. The first typeincludes those PRBs adjacent to GSM PRBs. Due to the GSMinterference leakage, the maximum average SINR of LTE UEin these PRBs is limited to11dB, as pointed out before. In LTEnetwork, the SINR of50% of UEs is less than 1dB because ofout-of-cell interference. As a result, from system point ofview,scheduling cell edge UEs (bottom 50%) in PRBs adjacent toGSM PRBs will result in nearly no loss of spectral efficiencyin LTE PRBs.

The second type refers to those fractional reused PRBswith low transmit power. Since these PRBs are allocated withlow power and suffer from strong GSM interference from theneighboring cell, we ought to schedule UEs of good geometry4

in these reused PRBs to maximize the spectral efficiency.The above discussion seems to imply that we need to

revise the existing scheduling algorithms. However, the currentproportional fair (PF) scheduling (see, e.g., [22]–[24]) exploitsthe multiuser diversity and we find that a frequency-selectivePF scheduler performs pretty well in LTE with GSM overlay,as demonstrated by simulation results in Section VI.

Specifically, the generalized frequency-time PF schedulingworks as follows. In time slotn, the LTE eNodeB computesthe achievable instantaneous ratesRm

k (n) for UE k at timenin PRBm. Then the scheduler allocates the PRBm to the UEk⋆m with the largest

Pmk (n) =

Rmk (n)

Tk(n)

among all the associated UEs. HereTk(n) denotes the averagethroughput of UEk up to timen and is updated according to

4Though referred to as goodgeometry UE, a better quantification may bebased on SINR, e.g., UEs with topx% (x ∈ [5, 15]) SINR in a network.Typically, the interference experienced by these UEs is small and may beignored for discussion purpose.

the following weighted low-pass filer:

Tk(n+ 1) = (1− 1

NT)Tk(n) +

1

NT

∑

m

δ(k − k⋆m)Rmk (n),

whereδ(x) = 1 if x = 0 and zero otherwise, andNT denotesthe response time of the low-pass filer.

As a high level understanding on the good performanceof the frequency-selective PF scheduler, let us compare goodgeometry UEs and other UEs in the reused PRBs. Note that theintercell interference does not matter much for good geometryUEs and thus is ignored in the following high level discussion.Thus, the instantaneous achievable rate of good geometry UEsin the reused PRBs would roughly be given by

log(1 +1

Γ

PsH

N0)

where Γ is the Shannon gap andN0 is the noise powerper PRB (180KHz) channel. In contrast, the instantaneousachievable rate of other UEs in the reused PRBs would begiven by

log(1 +1

Γ

PsH

Ig + Il +N0)

whereH ≫ H. Thus, it appears that PF scheduler wouldschedule good geometry UEs in the reused PRBs more oftenthan other UEs. This is also demonstrated through simulationin Section VI.

To sum up, though one may consider designing novelscheduling algorithms to achieve better performance, PFscheduling is sufficient for initial evaluation of the proposedDSR.

C. Partial PRB Usage

Recall that GSM center frequency must be an integer mul-tiple of 200KHz while the bandwidth of each PRB, the basicLTE scheduling unit, is 180KHz. Hence, GSM channel edgesmay not be always aligned with LTE PRB edges. For example,suppose we puncture the LTE spectrum for a 600KHz GSMband. Then 4 PRBs would have to be reserved, leading to120KHz unutilized spectrum as it is only a fraction of one PRBand thus can not be scheduled. This simple numerical exampleis illustrated in Fig. 10, which further takes guard band intoaccount. Fig. 10 shows that better spectrum utilization canbeachieved if the system regains access to the fractional PRBsresulted from GSM overlay.

Motivated by the above observation, we propose the conceptof partial PRB usage. One possible implementation of partialPRB usage may work as follows: In the MAC layer LTE sched-uler treats a fractional PRB as a normal PRB and allocates thewhole PRB to some UE based on any implemented schedulingalgorithm; in the PHY layer, LTE eNodeB allocates zero poweron the subcarriers used by GSM channels as well as the guardband. Using this implementation, the impact of partial PRBusage is equivalent to puncturing the codewords of those UEsusing partial PRBs. So we might need to slightly decreasethe coding rate of those UEs in the rate matching step duringdownlink transport channel processing to maintain similarbiterror rate (BER) performance.

9

Guard band:

2 subcarriers

LTE transmission:

1 fractional

PRB=8PRB=8

subcarriers

600KHz GSM

h l b 4channels but use 4

PRBs=720 KHz

LTE transmission:LTE transmission:

1 fractional1 PRB=12

subcarriers

1 fractional

PRB=8

subcarriers

Fig. 10. Partial PRB usage: On the left plot, only one PRB is available forLTE transmission. On the right plot, two fractional PRBs (orequivalently, 4/3PRBs) can be used for LTE transmission.

To sum up, partial PRB usage essentially enables overlayingGSM channels on LTE channel on subcarrier basis rather thanon PRB basis. Regaining access to the fractional PRBs resultedfrom GSM overlay can provide better spectrum utilization.In addition, subcarrier-based overlay enjoys higher flexibilityin selecting the positions of the punctured spectrum in LTEchannel.

VI. SIMULATION RESULTS

In this section we provide simulation results to evaluatethe impact of GSM overlay on LTE spectral efficiency. Thenetwork layout used in simulation consists of regular hexago-nal cells, each of which is composed of 3 sectors. The centersector is treated as the typical one, while the remaining sectorsact as interfering sources. The radiation pattern used for thedirectional antennas is as follows:

G(φ) =1

2(1 + cosφ) · sin(0.72π sinφ)

0.72π sinφ. (5)

The GSM transmit power is measured by its PSD offset to thePSD of LTE signal; it is set to be13.56dB in the simulations.

The system simulation conducted is running at the granular-ity of transmission time interval (TTI) of 1ms, based on whichscheduling decisions are made. The statistics are collectedfrom 3 drops of the UEs. The main simulation parametersused are summarized in Table II unless otherwise specified.

The specific LTE puncturing and GSM frequency planningused in the simulation are shown in Fig.11. In particular, thereis one BCCH carrier and one traffic carrier in each sector forGSM transmission. The reuse factor is 3/9 for BCCH carriersand is 1/3 for traffic carrier. Note that with this particularfrequency planning, a sector, say the one with carrier A3 andD3 in Fig.11 can reuse all the carriers denoted by Bi,Ci,i =1, 2, 3. Partial PRB usage is not needed with this particularGSM frequency planning. For example, the sector labeled by(C2, D2) in Fig.11 can fully reuse the originally unused2 ×720KHz spectrum reserved for GSM carriersAi andBi.

We first would like to show that the LTE capacity loss isless than2.4/9 ≈ 26%, since a portion of 2.4MHz in the9MHz occupied LTE bandwidth is reserved for GSM. To this

# of hexagonal cells 6× 6Length of cell edge 500m# of sectors per cell 3# of UEs per sector 24

Max TX power 40WNoise PSD −174dBmWavelengthλ 0.375mPath loss exponentα 3Shadowing deviationσ2 36

LTE transmission bandwidth 10MHzSubcarrier bandwidthB 15KHz# of PRBs 50

GSM power offset 13.56dBGSM carrier bandwidth 200KHzGSM SINR thresholdγ 10dB

GapΓ 3dB

TABLE IISIMULATION PARAMETERS

A1

A2

200KHz

A1, D1

A2 D2

A2

A3

A2, D2

A3, D3C1 D1

B1

B2A3, D3C1, D1

C2, D2

B2

B3

B1 D1

C2, D2

C3, D3C1

C2B1, D1

B2, D2

C2

C3

B3, D3

Ai Bi Ci: BCCH carrier (3/9 reuse)

D1

D2Ai, Bi, Ci: BCCH carrier (3/9 reuse)Di: Traffic carrier (1/3 reuse) D3

Fig. 11. LTE puncturing and GSM frequency planning: 10MHz LTE channelwith a 2.4MHz punctured portion reserved for GSM with 3/9 reuse for BCCHcarriers and 1/3 reuse for traffic carrier.

end, the following 4 scenarios are studied and compared inthe simulation:

• Baseline: This corresponds to the normal 10MHz LTEdeployment without puncturing.

• PF w/o GSM: This corresponds to the 10MHz LTEdeployment with 2.4MHz puncturing but without GSMoverlay. This scenario is considered purely for compari-son.

• PF: This corresponds to the 10MHz LTE deployment with2.4MHz puncturing and GSM overlay.

• PF+FFR: This corresponds to the 10MHz LTE deploy-ment with 2.4MHz puncturing and GSM overlay and FFRenhancement.

The LTE rate statistics are summarized in Table III and theassociated empirical CDFs of UE throughput are shown in Fig.12. We make the following remarks:

• Compared to PF w/o GSM, we can see only very minor

10

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

UE Throughput (Mbps)

Empirical CDF of UE ThroughputF

(x)

PF w/o GSMPFPF+FFRBaseline

Fig. 12. Empirical CDF of UE throughput.

performance degradation exists in PF for mean rate ofall the UEs and no performance degradation for meanrates of both top and bottom 5% of UEs, as shown inTable III. In addition, they have very similar CDFs ofUE throughput.

• When PF is jointly applied with FFR, the loss of themean rate of all the UEs is less than20%. This showsthat the loss of LTE capacity caused by GSM overlay canbe significantly reduced with the proposed enhancements.

• Compared to PF, there is a rate loss for bottom-5% UEs inPF+FFR. This shows that while FFR improves the meanrate of all the UEs by reusing the spectrum more, it doeslead to poorer SINR and thus degraded throughput to celledge users.

• The CDFs of UE throughput for PF w/o GSM, PF, andPF+FFR have very minor difference for the bottom 50%UEs, i.e., the range withF (x) ≤ 0.5 in Fig. 12.

We next show the scheduling statistics of normal PRBs,PRBs adjacent to GSM PRBs, and FFR PRBs in Fig.13,where users are ranked according to their rates. We can seethat the allocation probability of a normal PRB is almostuniform among the UEs. This is consistent with the factthat PF scheduling maintains fairness in the long run. Incontrast, the allocation probability of a PRB adjacent to GSMPRBs is not uniform among the UEs. When it comes to FFRPRBs, as expected, good geometry UEs have relatively higherprobabilities to be allocated with FFR PRBs.

VII. D ISCUSSION ONUPLINK DESIGN

Though in this paper we focus on describing and evaluatingthe proposed DSR approach in the downlink, we discuss in thissection on the various issues involved in the uplink design.

A. Reserving PRBs

Compared to the downlink, the LTE uplink channel structureis simpler [17]. This makes the selection of the reserved PRBs

10 20 30 40 50 60 700

0.02

0.04

Normal PRBs

10 20 30 40 50 60 700

0.02

0.04

0.06

PRBs adjacent to GSM PRBs

10 20 30 40 50 60 700

0.05

0.1

FFR PRBs

Fig. 13. PRB scheduling statistics.

(c) PRACH

(a) Uplink Reference Signals (b) PUSCH and PUCCH

UE 1

UE 2

UE 3

0.5ms 0.5ms

DM-RS UE 1

DM-RS UE 2

DM-RS UE 3

SRS

resource 1

resource 0

0.5ms slot

resource 0

resource 1

0.5ms slot

System

BW

resource 2 resource 3

resource 2resource 3

PUCCHPUSCH

PRACH

opportunities

1 ms 10 ms

f

6 PRBs = 1.08

MHz

Fig. 14. LTE uplink channel structure

out of the LTE uplink channel easier.1) Impact on reference signals: Two types of reference

signals exist in the uplink: Demodulation Reference Sig-nals (DM-RS) and Sounding Reference Signals (SRS). LTEeNodeB relies on DM-RS for coherent demodulation. Asshown in Fig. 14(a), each UE’s DM-RS is time multiplexedwith the corresponding uplink data and occupies the samebandwidth as the data. In LTE, UE transmissions are localizedby Single-carrier Frequency-Division Multiple Access (SC-FDMA); thus, DM-RS would not be affected by LTE punc-turing as the reserved PRBs will not be scheduled for any UEand thus the corresponding DM-RS is suppressed.

The SRS is used by LTE eNodeB to estimate the uplinkchannel quality, based on which the UEs are scheduled acrossthe frequency domain. Unlike DM-RS occupying the samebandwidth as each UE’s data, SRS of each UE stretches outthe allocated bandwidth for wider channel quality estimation.The SRS transmission mode can be either wideband or nar-rowband. As a single SRS transmission is used in wideband

11

Mean rate PF w/o GSM PF PF+FFR Baseline

All the UEsMbps 0.44999 0.44189 0.54237 0.66991% 67.17 65.96 80.96 100

Top-5% UEsMbps 1.2381 1.2471 1.5041 1.8588% 66.61 67.09 80.92 100

Bottom-5% UEsMbps 0.06477 0.06620 0.05295 0.09763% 66.35 67.79 54.24 100

TABLE IIILTE ENHANCEMENTS TO RECOVER CAPACITY LOSS.

mode, LTE puncturing may restrict the frequency range ofchannel estimation. From this perspective, we suggest usingthe narrowband option, in which SRS transmission is split intoa series of narrowband transmissions. Thus, the narrowbandoption is flexible enough to cover the frequency range ofinterest for channel estimation.

2) Impact on uplink physical channels: Three types ofphysical channels exist in the uplink: Physical UplinkShared Channel (PUSCH), Physical Uplink Control Channel(PUCCH) and Physical Random Access Channel (PRACH).PUSCH carries UE data as well as certain associated controlinformation. For similar reason as in the DM-RS case, PUSCHwould not be affected by LTE puncturing.

PUCCH carries control signaling such as ACK/NAK, chan-nel quality indicators (CQI) and scheduling requests. Unlikeits downlink counterpart PDCCH stretching over the wholetransmission bandwidth, Fig. 14(b) shows that PUCCH issent on the band edges of the system bandwidth unless theover-provisioned Physical Uplink Control Channel (PUCCH)(i.e., moving PUCCH away from the LTE channel edges) issupported. So we can avoid affecting PUCCH by not reservingthe PRBs used by PUCCH.

PRACH carries the random access preamble sent by a UEfor asynchronous network access. As shown in Fig. 14(c), itoccupies 1.08 MHz contiguous bandwidth (i.e. 6 contiguousPRBs). The specific PRACH resources are assigned by LTEeNodeB within PUSCH region. Thus, we can reserve thePRBs for GSM without overlapping with the resources usedby PRACH.

B. Mitigating Mutual Interference between LTE and GSM

As in the downlink, there exists mutual interference betweenLTE and GSM.

1) GSM uplink transmission on LTE reception: Due toadjacent channel leakage and ICS, GSM terminals will causeinterference to LTE UEs. The interference can be especiallystrong from those GSM terminals close to LTE eNodeB, whichcan limit the LTE eNodeB’s ability to detect weak LTE uplinksignals. This leads a near-far problem between GSM and LTE,analogous to that in a CDMA system. This problem can bepartially solved by GSM power control: GSM terminals closeto LTE eNodeB reduce their transmit power.

Ideally, it is expected that all the GSM received signalstrengths are roughly at the same level. This may be hardto achieve due to the crude GSM power control. Thus,LTE closed loop power control is also crucial to overcome

GSM interference. Specifically, the LTE eNodeB measuresthe received SINR, and compares it to the target value. ThenUE-specific power offsets can be sent to UEs via RadioResource Control (RRC) signaling. These transmit powercontrol commands can be used by LTE UEs to correct open-loop errors or to allow proprietary methods to create a powerprofile. Further aperiodic fast power control is also possible byadditionally allowing a dynamic adjustment of the UE transmitPSD with 1 or 2 bit power control commands.

Note that the UEs scheduled on those PRBs adjacent tothe GSM PRBs are the main victims suffering from GSMinterference; thus with power control they use higher transmitpower. In order to mitigate the out-of-cell interference fromthese higher power transmissions, it will be helpful to scheduleLTE UEs close to the eNodeB in PRBs adjacent to GSM PRBs.

2) LTE uplink transmission on GSM reception: Adjacentchannel interference impact of LTE uplink on GSM receptionwill be similar to that in downlink. Considering the facts thatGSM terminal close to the BS may blast significant amountof power (since the power control in GSM is crude), andthat the PSD of LTE UEs are generally lower (since LTE UEuplink transmissions are wideband while GSM transmissionsare narrowband), LTE interference will be less of an issue toGSM reception.

VIII. C ONCLUSIONS

In this paper we propose a novel solution to provideGSM connectivity within an LTE carrier through an efficient,dynamic overlay by reserving a few physical resource blocksfor GSM. With this approach, operators can migrate their2G spectrum to LTE while still providing reduced capacityGSM connectivity to their low data rate M2M customers.Furthermore, spectrum can be dynamically shared betweenLTE and GSM. The system design and feasibility of DSRare carefully detailed. Several enhancements including inter-technology ICIC, intelligent scheduling and partial PRB usageare proposed to recover LTE capacity loss due to the GSMoverlay. Our study shows that the loss of LTE capacitycaused by GSM overlay can be significantly reduced with theproposed enhancements. Though the focus of this paper isabout GSM networks, the same ideas can be applied for othernarrow band technology overlays over LTE.

APPENDIX

OPTIMIZING LTE TRANSMIT POWER ALLOCATION

The general optimal power allocation problem is convexwith linear constraints. The feasible set is anN -dimensional

12

polytope and the optimal point lies on the face definedby either hyperplane

∑Ni=1 Wi(fj)pi = Cj or hyperplane

∑Ni=1 pi = P . This suggests a simple algorithm to compute

the optimal power allocation as follows.

1) Initialize Ψ = 0, 1, ...,M.2) Let

p0i =

(

1

µ−Ni

)+

, i = 1, ..., N,

whereµ is chosen such that

N∑

i=1

(

1

µ−Ni

)+

= Pmax.

Compute the associated spectral efficiency as

R0 =

N∑

i=1

log(1 +p0iNi

).

3) For j = 1, ...,M ,

• Check if∑N

i=1 Wi(fj)p0i ≤ C.

• If yes, Ψ = Ψ\j.• Otherwise,

pji =

(

1

Wi(fj)λj−Ni

)+

, i = 1, ..., N,

whereλj is chosen such that

N∑

i=1

(

1

Wi(fj)λj−Ni

)+

= Cj .

Compute the associated spectral efficiency as

Rj =

N∑

i=1

log(1 +pjiNi

).

4) Find j⋆ = argmaxj∈Ψ Rj . Output the optimal solution:p⋆ = pj

⋆

Remark: The main computation burden associated is tocalculate waterfilling solutions, which can be computed effi-ciently using, e.g., the framework proposed in [25]. The num-ber of times to invoke waterfilling algorithm lies in[1,M+1].The above algorithm is viable whenM is not large since thewaterfilling solution can be obtained very efficiently. For theproblem of GSM overlay on LTE, we puncture 9MHz LTEchannel to have 12 GSM channels with bandwidth 200KHzeach. Every three of the GSM channels are in the same group.If we could protect the GSM transmission of the leftmost andrightmost GSM channels in one group, the GSM signal of themiddle carrier in this group would automatically get protected.So we only haveM = 8 GSM SINR constraints. This enablesthe above search algorithm suitable in this paper.

REFERENCES

[1] Cisco, “Cisco visual networking index: Global mobile data trafficforecast update, 2011-2016,”white paper, February 2012.

[2] 3GPP, “LTE official website,” 2012. [Online]. Available:http://www.3gpp.org/LTE

[3] D. Astely, E. Dahlman, A. Furuskar, Y. Jading, M. Lindstrom, andS. Parkvall, “LTE: the evolution of mobile broadband,”IEEE Commu-nications Magazine, vol. 47, no. 4, pp. 44–51, April 2009.

[4] A. Ghosh, J. Zhang, R. Muhamed, and J. G. Andrews,Fundamentals ofLTE. Prentice Hall, 2010.

[5] Vodafone, “Global machine to machine communication,”white paper,2010. Available at goo.gl/4V8az.

[6] Ericsson, “Device connectivity unlocks value,”white paper, January2011. Available at goo.gl/alou6.

[7] A. Mehrotra, GSM System Engineering. Artech House Inc., 1997.[8] ABI Research, “Cellular M2M connectivity services,” Tech. Rep., 2012.[9] X. Lin and H. Viswanathan, “Dynamic spectrum refarming of GSM

spectrum for LTE small cells,”arXiv preprint arXiv:1305.2999, 2013.[10] ETSI, “Digital cellular telecommunications system (Phase 2+); Radio

transmission and reception (GSM 05.05 version 5.12.0 Release 1996),”ETSI TS 100 910 V5.12.0, February 2001.

[11] M. Iwamura, K. Etemad, M.-H. Fong, R. Nory, and R. Love, “Carrieraggregation framework in 3GPP LTE-Advanced [WiMAX/LTE update],”IEEE Communications Magazine, vol. 48, no. 8, pp. 60–67, August2010.

[12] Z. Shen, A. Papasakellariou, J. Montojo, D. Gerstenberger, and F. Xu,“Overview of 3GPP LTE-Advanced carrier aggregation for 4G wirelesscommunications,”IEEE Communications Magazine, vol. 50, no. 2, pp.122–130, February 2012.

[13] X. Lin, J. G. Andrews, and A. Ghosh, “Modeling, analysisand design forcarrier aggregation in heterogeneous cellular networks,”arXiv preprintarXiv:1211.4041, 2012.

[14] G. Boudreau, J. Panicker, N. Guo, R. Chang, N. Wang, and S. Vrzic,“Interference coordination and cancellation for 4G networks,” IEEECommunications Magazine, vol. 47, no. 4, pp. 74–81, April 2009.

[15] A. L. Stolyar and H. Viswanathan, “Self-organizing dynamic fractionalfrequency reuse in OFDMA systems,” inProceedings of IEEE Infocom,April 2008, pp. 691–699.

[16] S. Ali and V. Leung, “Dynamic frequency allocation in fractionalfrequency reused OFDMA networks,”IEEE Transactions on WirelessCommunications, vol. 8, no. 8, pp. 4286–4295, August 2009.

[17] 3GPP, “Evolved universal terrestrial radio access (E-UTRA); physicalchannels and modulation,”3GPP TS 36.211 V10.5.0, June 2012.

[18] A. K. Parekh and R. G. Gallager, “A generalized processor sharingapproach to flow control in integrated services networks: The single-node case,”IEEE/ACM Transactions on Networking, vol. 1, no. 3, pp.344–357, June 1993.

[19] H. Fattah and C. Leung, “An overview of scheduling algorithms inwireless multimedia networks,”IEEE Wireless Communications, vol. 9,no. 5, pp. 76–83, October 2002.

[20] Q. Liu, X. Wang, and G. B. Giannakis, “A cross-layer schedulingalgorithm with qos support in wireless networks,”IEEE Transactionson Vehicular Technology, vol. 55, no. 3, pp. 839–847, May 2006.

[21] Y. Li, M. Chiang, A. R. Calderbank, and S. N. Diggavi, “Optimalrate-reliability-delay tradeoff in networks with composite links,” IEEETransactions on Communications, vol. 57, no. 5, pp. 1390–1401, May2009.

[22] D. Tse and P. Viswanath,Fundamentals of Wireless Communcation.Cambridge University Press, 2005.

[23] H. J. Kushner and P. A. Whiting, “Convergence of proportional-fairsharing algorithms under general conditions,”IEEE Transactions onWireless Communications, vol. 3, no. 4, pp. 1250–1259, July 2004.

[24] A. L. Stolyar, “On the asymptotic optimality of the gradient schedulingalgorithm for multiuser throughput allocation,”Operations Research,vol. 53, no. 1, pp. 12–25, January 2005.

[25] D. P. Palomar and J. R. Fonollosa, “Practical algorithms for a family ofwaterfilling solutions,”IEEE Transactions on Signal Processing, vol. 53,no. 2, pp. 686–695, February 2005.