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Low SNR Uplink CFO Estimation for EnergyEfficient IoT using LTE

Naveen Mysore Balasubramanya, Student Member, IEEE, Lutz Lampe, Senior Member, IEEE, Gustav Vos andSteve Bennett

Abstract—Machine Type Communications (MTC) is one of theprominent solutions to enable the Internet of Things (IoT). Witha large number of IoT applications envisioned over the cellularnetwork, the Third Generation Partnership Project (3GPP) hasinitiated the support for MTC in the Long Term Evolution (LTE)/ LTE-Advanced (LTE-A) standards. A significant portion of theMTC devices is expected to be low-complexity and low-poweruser equipment (UE), requiring an energy efficient mode ofoperation. Also, many such UEs can be located in regions oflow network coverage. In this paper, we show that an accurateestimation and compensation of the residual carrier frequencyoffset (CFO) at the base-station (eNB) results in a reductionin energy consumption for MTC devices in low coverage. Forrobust and accurate CFO estimation in low coverage, we proposea Maximum Likelihood (ML) based CFO estimation techniquethat works for data and/or pilot repetitions in LTE/LTE-A uplink.Through simulations, we illustrate that our technique showssignificant performance improvement over the conventional CFOestimation technique using the phase angle of the correlationbetween the repeated data. We determine that residual CFOestimation and compensation at the eNB results in 22.5%-55.2% reduction in energy consumption of MTC devices, whencompared to the case without CFO compensation.

I. INTRODUCTION

THE Internet is evolving from connecting computers anddedicated terminals to a quintessential medium that can

engulf a plethora of “smart” devices like mobile phones,electronic meters, location sensors, etc. The reducing size ofsilicon on chip and continuously declining price of compo-nents have increased the ease of integration of “smart” sensingand decision-making devices into everyday objects, leadingto the emergence of the Internet of Things (IoT). Diverseapplications within the IoT umbrella are not only promising tothe consumer, but also appealing to researchers across variousfields. The IoT relies on advancements in different fields suchas communication technologies, microelectronics, data mining,big data handling, etc. In this work, we focus on the physicallayer communication mechanisms for IoT devices.

One of the prominent solutions for IoT is the Machine-to-Machine Communications (M2M) or Machine Type Commu-nications (MTC), which involves the definition, design anddevelopment of communication and service mechanisms thatassist in the connectivity of different IoT devices. The MTCmechanisms face a variety of challenges depending on theapplication for which the MTC device is being used. These

This work is supported by MITACS, Canada and Natural Sciences andEngineering Research Council of Canada (NSERC). Naveen Mysore Balasub-ramanya and Lutz Lampe are with the Department of Electrical and ComputerEngineering, University of British Columbia, Vancouver, Canada. Gustav Vosand Steve Bennett are with Sierra Wireless Inc., Richmond, BC, Canada.

challenges can be completely in contrast with those faced byconventional human-to-human (H2H) communication mecha-nisms. While the current communication networks are adeptat managing the demands of H2H devices, the IoT scenariorequires the network to handle a huge number of MTC deviceswith contrasting demands. For example, a network that is ableprovide a good quality of service to a high data rate, lowlatency, videoconferencing application over few devices usingH2H communication, may not be able to optimally serve alarge number of low data rate, delay tolerant MTC devicesdeployed for smart meter data reporting. Moreover, these low-complexity MTC devices do not require to be constantly“connected” or “active”, since their data transmission is notcontinuous and the amount of data to be sent per transmissionis small. Furthermore, low-cost and low data rate devicesoperating with extended battery life (lasting 10 or more years),form a substantial part of the IoT equipment. Therefore, it isimportant to tune the MTC transmission mechanisms so thatthe energy consumption of the MTC devices is reduced [1].

MTC devices may be located in areas where the networkcoverage is very low, such as basements of buildings, un-derground parking facilities at malls, interiors of hospitals,etc. Due to the restrictions on the total available power andthe maximum power allowed for transmission in the channel(arising from the spectral mask constraints), the MTC devicecannot arbitrarily increase its transmission power to reach thebase-station. This results in a very low operating Signal-to-Noise ratio (SNR) at the base-station. Therefore, it is necessaryto design and develop MTC mechanisms that can enhance theperformance of devices in low network coverage areas.

The need to design energy efficient MTC transmissionmechanisms for low data rate, low-complexity devices isbeing addressed by different standardization committees, suchas, the IEEE 802.11 Low Power Wireless Local Area Net-work (WLAN) [2], [3], IEEE 802.15.4 Bluetooth [4], [5]and the Third generation Partnership Project (3GPP) LongTerm Evolution (LTE)/ LTE-Advanced (LTE-A) [6]. The firsttwo technologies support MTC over short-range, while theLTE/LTE-A uses the cellular network for enabling long-rangeoperation for MTC. A large number of IoT based services suchas automated security systems with monitoring and reportingfeatures, pet trackers, agriculture-based applications, etc. arevisualized over the cellular network and considered a majordriver for its growth. In this paper, we explore the MTCmechanisms for energy efficient uplink transmission usingLTE/LTE-A.

The network architecture adopting the current LTE/LTE-A standards is designed for H2H applications and needs to

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be upgraded to handle MTC applications [7]–[9]. The 3GPPhas recognized the potential of IoT services and instituted thestandardization of MTC from Release 11 of the LTE/LTE-Astandards. Moreover, it has classified the low-complexity, low-power, low data rate MTC User Equipment (UE) as “Category0” (CAT-0) UEs [10], [11] and is in the process of definingthe transmission/reception mechanisms for optimal operationof such UEs. Current standardization activities indicate that theCAT-0 UEs operate on narrower bandwidths and use differentsignaling mechanisms than that of the legacy LTE/LTE-A UEs.

Several prior works in LTE/LTE-A separately address thefacets of energy efficiency and coverage enhancement in MTCUEs. From the UE receiver design perspective, the analysis ofenergy consumption of the UEs adopting the DiscontinuousReception (DRX) mechanism [12], [13] in LTE/LTE-A hasbeen analyzed in [14]–[17]. Energy efficient MTC UE trans-mission mechanisms are demonstrated in [18] and [19]. Butthe methods discussed in these works have only been evaluatedfor UEs under normal coverage. For UEs in low coverage, [20]provides different procedures for downlink broadcast channeldecoding and uplink data transmission used for LTE/LTE-AMTC. More uplink transmission mechanisms that enhancethe capability of the UEs to decode data in low coverageare discussed in [21] and [22]. However, these works do notaddress the UE energy efficiency perspective.

Some recent works jointly address the energy efficiency andcoverage enhancement aspects of MTC UEs. For example,in [23], the authors describe a modified DRX mechanism,where the UE radio is switched on only for data transmissionand switched off otherwise, thereby eliminating the need tocheck for periodic paging message from the base-station andsaving power. Our previous work also illustrated a new DRXmechanism with quick sleeping, where the UE quickly goesback to the idle mode or sleep mode when there is no validpage from the base-station [24]. These solutions are effectiveand address the energy efficiency and coverage enhancementaspects in the downlink.

In this paper, we analyze the energy efficiency of an MTCUE in the uplink under low network coverage and show thatit is enhanced by accurate frequency offset estimation at theLTE/LTE-A base-station (called the eNB). Our contributionsin this work are as follows.

• We show the effect of carrier frequency offset (CFO) onthe time taken by the UE to reliably transmit differentsized data blocks and analyze the energy consumption.

• We propose a Maximum Likelihood (ML) algorithm,which exploits the transport block repetitions and/or thepilot signals for robust CFO estimation in low coverage.

• We show that our CFO estimation algorithms resultin a reduction in energy consumption of 22.5%-55.2%,when compared to the MTC transmission without CFOestimation.

• We propose a variation of the LTE/LTE-A frame structureincorporating additional pilot signals during the initialMTC transmissions, which assists in faster CFO estima-tion at the eNB with minimal overhead.

The rest of the paper is organized as follows. In Section II,we briefly describe the narrow-band transmission mechanism

being adopted in LTE/LTE-A and analyze the effect of CFOon the energy efficiency of the MTC UEs. In Section III, wedescribe the conventional techniques used for CFO estimationand in Section IV, we introduce our ML based CFO estima-tion technique for LTE/LTE-A MTC. Using simulations, wecompare the performance of our CFO estimation techniquewith the conventional techniques in Section V, followed bya detailed analysis of the energy efficiency of MTC UEsusing CFO estimation and compensation. In Section VI, wepropose a new MTC transmission technique with increasedpilot density, which uses our ML based CFO estimationtechnique for faster CFO estimation in low coverage. Theconclusions are drawn in Section VII.

II. NARROW-BAND INTERNET OF THINGS (NB-IOT) INLTE/LTE-A

With a large number of MTC devices requiring the cellularnetwork for operation and a substantial portion of these devicesbeing deployed in areas with bad network coverage, the 3GPPis in the process of standardizing the procedures for optimaloperation of such UEs. The research activities in this domainhave been categorized as Narrow-Band Internet of Things(NB-IoT) and various mechanisms in downlink and uplink arebeing analyzed to address the requirements of MTC UEs [25]–[27]. In this section, we describe the narrow-band transmissionmechanism being standardized in the 3GPP LTE/LTE-A uplinkand analyze the energy efficiency of the MTC UEs using thismechanism.

The basic unit of resource allocation in LTE/LTE-A is aPhysical Resource Block (PRB). Considering a system withnormal cyclic prefix (CP), one PRB consists of 12 subcarriers× 7 symbols (see Fig. 1). Therefore, a PRB pair spans 12subcarriers × 14 symbols = 12 subcarriers × 1 subframe [28]–[31]. Since the subcarrier spacing in LTE/LTE-A is 15 kHz, aPRB pair occupies a bandwidth of 15 × 12 = 180 kHz. Thecurrent LTE/LTE-A standards support UE transmission overmultiple PRBs. However, considering that the MTC UEs arelow data rate and low power devices, the 3GPP has proposedthe use of a single PRB pair transmission scheme for CAT-0MTC UEs. Also, the modulation supported by these devicesis restricted to Quadrature Phase Shift Keying (QPSK).

The major advantage of using a single PRB pair (hencesmaller number of subcarriers) is that the Peak to AveragePower Ratio (PAPR) of the UE transmission is reduced, whichhelps in energy efficient operation of the power amplifiersused in the MTC devices. Moreover, LTE/LTE-A has allowedthe use of sub-PRB transmission, where the UE uses lessthan 12 subcarriers for its transmission. For example, the UEcan adopt a single-tone transmission scheme, where the UEuses 1 subcarrier × 1 subframe transmission and occupies abandwidth of only 15 kHz [25]–[27]. Although using a singlesubcarrier reduces the data rate, it can still be effective forMTC UEs that are delay tolerant and only require occasionalsmall bursts of data to be transmitted. Furthermore, when MTCUEs are in low coverage, the operating SNR at the eNB isvery low (around -15 dB). Consequently, in the uplink, theUE has to transmit multiple repetitions of the data block to

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Subframe =1ms

Slot 0 Slot 1

0.5ms 0.5ms

Sub

-ca

rrie

rs

1 Slot = 7 symbols

PRB = 12 Sub-carriers x 7 Symbols (Normal CP)

Sub

-car

rier

sData Symbols DMRS Symbols

Fig. 1. Uplink subframe and PRB in LTE/LTE-A

be successfully decoded by the eNB, thereby increasing theON time and the energy consumption of the UE. Therefore,identifying signal processing techniques that can reduce thenumber of repetitions is necessary.

In LTE/LTE-A, a data block at the physical layer is calledthe transport block. The transport block is encoded using aConvolution Turbo Code (CTC) before transmission and 4Redundancy Versions (RVs) are generated [28], [32]. One RVof the transport block is transmitted in one subframe. EachRV includes a 24-bit header from the upper layers [28], [32].Therefore, the effective data rate is given by

Reff =(TBS− 24)

(NSF × tSF)(1)

where TBS is transport block size, NSF is the number ofsubframes required by the eNB to successfully decode thedata and tSF = 1 ms, is the duration of a subframe inLTE/LTE-A. In the case of low data rate MTC UEs, thetransmission consists of a burst of data packets followed by along idle duration. When the effective data rate increases, theUE can complete its data transmission quickly and switch tothe idle mode sooner, thereby saving power. For a given TBS,the effective data rate increases if the number of subframesrequired for successful decoding decreases. This depends onthe SNR, the underlying channel and the offset in UE’stiming/frequency estimation at the eNB.

The UE timing/frequency offset is derived from the detec-tion of the random access signal transmitted by the UE when itfirst requests network access and/or the periodic DemodulationReference Signals (DMRS) transmitted by the UE in everysubframe [28]. Both the random access and DMRS signalsare Zadoff-Chu sequences, which possess good detectionproperties (good autocorrelation, low cross-correlation) [28],[32]. However these estimates are not perfect and there willbe some residual timing and frequency offset in the system.The effective data rate and hence the energy efficiency of theUE can be improved if these residual offsets are reduced to anegligible level.

The residual timing offset can be estimated with a sufficientdegree of accuracy using the CP [33], [34]. The eNB ensuresthat all UE transmissions are time synchronized using thetiming advance indication mechanism after the initial randomaccess request procedure in LTE/LTE-A and minor deviations

in the received frame timing are tracked using CP autocorre-lation [28] However, the residual CFO of each UE might bedifferent and tracking each UE’s CFO using CP autocorrelationis complex (explained later in Section III-A). Therefore, theeNB needs a separate mechanism to compensate for this CFOand improve the energy efficiency of the UE. In the following,we demonstrate our model for energy consumption analysisand determine the effect of residual CFO on the energyconsumption using numerical calculations.

A. Energy consumption model

In order to calculate the energy consumption, we adopt asimple model,

E = PONtON + POFFtOFF (2)

where PON and POFF denote the power consumed by theUE when during its active (ON) period and sleep (OFF)period respectively. The durations ON and OFF periods arerepresented by tON and tOFF respectively. The total timelength tTotal = (tON + tOFF) and we define v = POFF

PON, where

v � 1 since the sleep time power consumption is much lowerthan the active time power consumption. Then, the energyconsumption is calculated as

E = PON(tON + v(tTotal − tON)). (3)

B. Numerical Results

To illustrate the impact of CFO on the UE energy con-sumption, we consider a scenario with no residual timingoffset, since it can be estimated with a sufficient degree ofaccuracy using the CP and determine the number of repetitionsrequired for an MTC UE for different values of the residualCFO. Specifically, we first analyze the performance for CFO= 100 Hz, which is the value used for MTC performanceevaluation by the 3GPP [10] and then for lower values of CFO,corresponding to 50 Hz, 25 Hz and 10 Hz. Among the differentCFO values, we use CFO = 10 Hz to model the scenario wherethe frequency offset is negligible, based on simulations whichindicated that the number of repetitions required by the UEdid not change significantly for 0 ≤ CFO ≤ 10 Hz.

The simulations are performed using the LTE toolbox inMATLAB. In order to analyze the low coverage scenario, the3GPP recommends the evaluation of performance for 18 dBadditional coverage [10], which corresponds our operatingSNR of -15.5 dB. For the channel model, we use the ExtendedPedestrian A (EPA) model with a Doppler spread of 1 Hz,which is advocated by the 3GPP for MTC UEs with limitedmobility [10]. We use a single PRB pair transmission scheme(12 subcarriers× 1 subframe) with the Modulation and CodingScheme (MCS) index chosen to be 5 (corresponding to QPSKmodulation and a code rate of 0.4385 [31]), consistent withthe 3GPP recommendation for NB-IoT. We use TBS = 72 bits,which is the maximum transport block size for MCS = 5 [31].Other simulation parameters are summarized in Table I.

Table II gives the number of subframes required by theeNB to decode the transport block and the effective data ratefor different values of the residual CFO. It is evident that a

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TABLE ISIMULATION PARAMETERS

Parameter ValueNo. data symbols 12 subcarriers ×per subframe 12 symbolsNo. of DMRS symbols 12 subcarriers ×per subframe 2 symbolsNo. UE antennas 1No. eNB antennas 2eNB bandwidth 10 MHzeNB Sampling Rate 15.36 MHzChannel Model EPA 1 HzSNR -15.5 dBBlock Error Rate (BLER) 0.1

TABLE IIENERGY EFFICIENCY V/S CFO FOR TBS = 72 BITS

CFO NSF Reff (kbps) Energy Efficiency GainD = 10% D = 1% D = 0.1%

100 110 0.44 - - -50 100 0.48 8.6% 8.5% 7.5%25 92 0.52 15.5% 15.3% 13.5%10 80 0.60 25.9% 25.5% 22.5%

transport block with lower CFO requires fewer repetitions thanthe one with higher CFO, thereby increasing the effective datarate. This suggests that a lower residual CFO at the eNB helpsthe MTC UE to complete its transmission quickly, turn off itsradio and save power.

We obtain the energy consumed by the UE for the differentCFO values using equation (3) with tON = 1

Reffs per bit,

where Reff is the effective data rate given by equation 1.We consider the energy consumed by the UE for CFO =100 Hz, denoted by Eorig, as our reference and compute tothe energy efficiency gain as

(1− Enew

Eorig

), where Enew is the

energy consumption of the UE corresponding to the lowerCFO values.

Table II summarizes the energy efficiency results whentTotal is an integer multiple of torig, which is the time takenfor successful decoding with CFO = 100 Hz. That is, tTotal =qtorig and q = 10, 100, 1000, which correspond to duty-cycles(D) of 10%, 1% and 0.1% respectively, PON = 100 mW(corresponding to the 20 dBm transmission power of MTCUEs [10], [27]) and POFF = 0.015 mW (based on the sleeptime power consumption indicated in [35], [36]). The reasonto choose these duty-cycles is that for each case, the inactiveduration of the UE is much greater than the active duration,which suitably models the infrequent data transmission andlow-data rate mode of operation of MTC UEs.

A common trend that we note in these results is that theenergy efficiency gain decreases with decrease in D. Thisis intuitive because the reduction in energy consumption isobtained by reducing the ON time of the UE and smallervalues of D results in lower ON time. We observe that theenergy efficiency gain increases with a decrease in residualCFO. The reduction of residual CFO from 100 Hz to 10 Hzresults in 22.5% reduction in energy consumption even fora low duty cycle of 0.1%, which is significant. Therefore, arobust CFO estimation mechanism at the eNB, which works

accurately at low operating SNRs and helps in reducing theenergy consumption of the MTC UE is desirable.

III. CONVENTIONAL CFO ESTIMATION TECHNIQUES

Having established the need for accurate CFO estimationto enable high energy efficiency of IoT communication, wenow discuss the CFO estimation techniques that are currentlyused in the uplink. In particular, we consider two techniques- a) CP autocorrelation [33], [34] and b) symbol repetitiondemonstrated in [37], [38] and the references within, whichare widely used for fractional frequency offset estimation inthe uplink. We illustrate why these techniques cannot be usedby MTC UEs using LTE/LTE-A in low coverage.

In literature, fractional frequency offset is often representedand estimated in terms of the normalized CFO, i.e., theactual CFO value divided by the subcarrier spacing (∆F ).The subcarrier spacing is related to the sampling rate (Ns)and the Fast Fourier Transform (FFT) size (NFFT) suchthat Ns = NFFT∆F . However, we choose to represent thefrequency offset using actual CFO instead of normalized CFObecause our work considers the estimation of residual CFO,which is typically represented in terms of the actual value.Also, the residual CFO values are very small and normalizingthem will make them even smaller and more difficult to retainthe desired accuracy in numerical computations.

A. CP Autocorrelation

In Orthogonal Frequency Division Multiplexing (OFDM)based systems, the CFO is estimated from the phase of theautocorrelation of the CP as

ε =Ns

2πNFFT

(angle

(NCP−1∑n=0

y(n+NFFT)y∗(n)

))(4)

where y(n) is the nth sample of the received time-domainsignal at the eNB, Ns is the sampling rate, NFFT is the FFTsize used at the eNB and NCP is the CP length [33], [34].From (4), we see that ε is the product of the normalized CFOwith the subcarrier spacing (indicated by the Ns

NFFTscaling

factor), which denotes the actual CFO in the system.In multiple access systems like OFDMA and Single Carrier

- Frequency Division Multiple Access (SC-FDMA), whenmultiple UEs occupy the spectrum, the time-domain symboland the CP contains components from all the UEs . Assumingthat UEs have perfect timing synchronization, the CP portionof the received signal at the eNB will consist of the sum ofthe CPs of all the UEs. Each UE might have a different CFO.Therefore, detection of each UE’s CFO requires the separationof its time-domain symbol and its CP from the multiplexedreceived signal.

In order to get the per-UE time-domain symbol, the eNBfirst takes an FFT of the multiplexed time-domain signal,retains the subcarriers of the UE of interest, sets the remainingsubcarriers to zero and takes an Inverse FFT (IFFT). Thisprocedure is illustrated in Fig. 2. Moreover, in the case ofMTC UEs in low coverage, multiple repetitions of the timedomain symbol and CP are required successful detection,which further increases the complexity. For example, an eNB

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Fig. 2. Illustration of CFO estimation using CP autocorrelation

with a bandwidth of 10 MHz has 50 PRBs available for userdata and uses a 1024-point FFT. For MTC UEs using singlePRB transmission and a large number of MTC devices presentin the network, we can potentially have 50 UEs served ateach instant. To separate the time-domain symbol and CP ofeach UE, the eNB requires 1 FFT and 50 IFFTs. Since theFFT/IFFT is O(N log2(N)) complex operations, this requires51 × 1024 × 10 ≈ 5.2 × 105 complex operations, which iscomputationally intensive. Furthermore, if the UEs are in lowcoverage and assuming that 14 symbols (1 sub-frame) arerequired for successful frequency offset detection, the numberof complex operations increases to 7.3 × 106. Therefore, CPautocorrelation is not an ideal candidate for CFO estimationin the case of MTC UEs.

B. Symbol Repetition

Besides the CP autocorrelation method, CFO estimation canbe done by correlating repetitions of data or pilot signals andmeasuring the correlation phase angle (see Fig. 3) [37], [38].However, the repetitions should be close enough in time, sothat the phase angle does not roll-over. If a UE has to measurea CFO ranging from -f0 Hz to f0 Hz, the maximum amountof time between two repetitions is given by Trep = 1

2f0. For

example, we require Trep = 1 ms, if the UE has to measurea CFO ranging from -500 Hz to 500 Hz. In other words,the detectable CFO range decreases as Trep increases. Theestimation method is formulated as

ε =Ns

2πNg

(angle

(N−1∑n=1

Yn · Y ∗n−1

))(5)

where Y is the frequency-domain received symbol spanningover Nsc subcarriers, “·” denotes element-wise multiplication,n indicates the repetition index, N is the number of repetitionsrequired to successfully detect the CFO, Ns is the samplingrate and Ng is the number of samples between the consec-utive symbol repetitions in terms of the FFT size, NFFT.For example, when the repetitions occur every 2 symbols,Ng = 2NFFT. Again, ε in (5) also denotes the actual CFOin the system.

Unlike the method of CP autocorrelation, this technique canbe scaled to accommodate multiple UEs. This is because themethod uses frequency-domain symbols and the signals ofdifferent UEs can be easily separated and the CFO of eachUE can be separately calculated in the frequency domain.However, in LTE/LTE-A, the DMRS symbols repeat every

Reference SymbolRepetition

period

Combine consecutive repetitions

Sub-carriers

Fig. 3. Illustration of CFO estimation using symbol repetition

10 ms and the range of the CFO that could be detectedwith this is only from -50 Hz to 50 Hz, which is smallerthan the residual CFO range (-100 Hz to 100 Hz) in thesystem. Therefore, the DMRS symbols cannot be directlyused for correlation phase angle based CFO estimation. In thefollowing, we propose our mechanisms for CFO estimationfor MTC UEs using LTE/LTE-A in low coverage.

IV. ML BASED CFO ESTIMATION

In this section, we describe the design of our ML basedCFO estimation algorithm for two cases - 1) using repeatedRV transmission and 2) using the DMRS. Our ML based CFOestimation method is an extension of the method discussed in[38], which was designed for consecutive symbol repetition.We modify the algorithm in [38] so as to fit the LTE/LTE-Aframe structure and operate on subframe repetitions (in case1) and reference signal repetition (in case 2).

Let d denote the transmitted signal of length K samples.The CFO of the UE is denoted by ε. Since the CFO is aphase-ramp in time-domain, the signal with CFO is given by

s(k) = d(k)e( j2πεkNs) = d(k)ejkθ (6)

where Ns is the sampling rate, k = 0, 1, 2, · · · ,K − 1 and

θ =2πε

Ns. (7)

Using equation (6), the LTE/LTE-A transport block transmis-sion in time-domain can be expressed as

sn(k) = dn(k)ej(k+nK)θ (8)

where k = 0, 1, 2, · · · ,K − 1, n = 0, 1, 2, · · ·NSF − 1 andNSF is the number of sub-frames required for the successfuldecoding of the transport block.

The current LTE/LTE-A standards support 4 RVs of the UEdata block to be transmitted. The UE transmits one RV per

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subframe and the RV index is cycled in the order [0, 2, 3, 1],i.e., d0 = d4 = d8 = · · · = r0, d1 = d5 = d9 = · · · = r2 andso on. where rq denotes the RV being transmitted with the RVindex q = 0, 2, 3, 1. This means that the RV is repeated every4 subframes and considering that each subframe is 1 ms, therange of CFO detection is -125 Hz to 125 Hz.

In the ongoing LTE MTC standardization, RV repetition isbeing proposed for MTC UEs. When the UE uses RV repeti-tion, it respects the standard RV cycling order, but can transmitN repetitions of the same RV index before switching to thenext index, i.e, d0 = d1 = d2 = · · · = dN−1 = r0, dN =dN+1 = dN+2 = · · · = d2N−1 = r2 and so on. For example,if N = 3, the UE transmits [0,0,0,2,2,2,3,3,3,1,1,1,0,0,0,. . . ].Therefore, for the MTC UEs, the CFO detection range is -500 Hz to 500 Hz.

A. ML based CFO estimation using repeated data

In the following, we derive an ML based technique, whichuses the RV repetitions to estimate the CFO. We define a newsignal x, which consists of N repetitions of the same RV(denoted by r). Then, we have

xn(k) = r(k)ej(k+nLK)θ (9)

where k = 0, 1, 2, · · · ,K − 1, n = 0, 1, · · ·N − 1, L = 4for legacy UEs (since the same RV is repeated every 4subframes) and L = 1 for MTC UEs (since the repetitionsare consecutive).

Let R denote the Discrete Fourier Transform (DFT) ofr(k)ejkθ. Then, in frequency domain, each RV reception atthe eNB can be expressed as

Yn = Hn ·RejnLKθ +Wn (10)

where Hn is the channel vector (n = 0, 1, · · · , N − 1), Wn

is the noise vector and Hn · R denotes the element-wisemultiplication between Hn and R.

We assume that the channel remains the same for Nsub-frames, which holds in the case of pedestrian channels.Therefore, Hn = H,∀n. In order to estimate the CFO, we haveto estimate θ from equation (10). Since we have no informationabout the data and the channel, the unbiased estimate for thevector H ·R is given by

C =1

N

N−1∑n=0

Yne−jnLKθ. (11)

Substituting equation (11) to equation (10), the ML estimatorfor the phase angle θ, denoted by θ and the correspondingCFO estimate (ε) are given by

θ = minθ

N−1∑n=0

‖Yn − CejnLKθ‖2, (12)

ε =θNs

2πLK. (13)

1) Cramer-Rao Lower Bound: The performance of anestimator is typically analyzed using the Mean Squared Error(MSE), which is lower bounded by the Cramer-Rao bound. For

our ML based CFO estimator using repeated data, Cramer-Raobound is given by

CRB(ε) =3N2

sΨ−1

4π2L2K2MN(N − 1)(4N − 3)(14)

where Ψ is the SNR and M is the number of DFT samplesused for estimating the CFO. The procedure to derive CRB(ε)is illustrated in the Appendix.

B. ML based CFO estimation using the DMRS

The generic structure of our ML based CFO estimationtechnique enables us to extend its applicability to the periodicrepetitions of DMRS signals in LTE/LTE-A. A DMRS symbolis transmitted every half subframe. For DMRS transmission,equation (10) changes to

Ynm = Gnm · Pnmej(2n+m)Kθ

2 + Wnm (15)

where Pnm are the known DMRS sequences, Gnm andWnm are the channel and the noise vectors with n =0, 1, · · · , N − 1, denoting the subframe index and m = 0, 1indicates whether the DMRS is transmitted on the first half(m = 0) or the second half of the subframe (m = 1).Therefore, L is set to 1

2 for DMRS transmission and there is nodifference between the legacy and MTC UEs. This is becausethe DMRS is transmitted in the same manner for legacy as wellas MTC UEs with a periodicity of half subframe (0.5 ms).

Now, we derive the ML based CFO estimator using theDMRS. Similar to the ML estimator for repeated data, weassume that the channel does not vary over the N subframes ofinterest. Hence, Gnm = G,∀n,m. Then, the channel estimateis given by

G =1

2N

N−1∑n=0

1∑m=0

Ynm · P ∗nme

−j(2n+m)Kθ2 , (16)

and the ML estimator for θ is given by

θ = minθ

N−1∑m=0

1∑n=0

‖Ynm − G · Pnmej(2n+m)Kθ

2 ‖2, (17)

and the corresponding CFO estimate can be calculated usingequation (13). The range of CFO values that can be detectedusing this mechanism is between -1 kHz to 1 kHz, since theDMRS periodicity is 0.5 ms. The Cramer-Rao bound for thiscase can also be obtained from (14), using L = 1

2 , M equal tothe length of the DMRS sequence and 2N repetitions insteadof N .

C. Modified conventional CFO estimation scheme for DMRS

Although DMRS symbols are transmitted every 0.5 msin LTE/LTE-A, the duration of repetition between identicalDMRS symbols is 10 ms. If the conventional correlation phaseangle method is used on these DMRS repetitions, it results ina reduced CFO detection range of -50 Hz to 50 Hz (referto Section III-B). Here, we suggest a modification to theconventional method so that it can make use of all the DMRStransmissions to estimate the CFO within the desired range.

7

We multiply each received DMRS symbol (Ynm in equa-tion (15) by the conjugate of the reference DMRS symbol(Pnm) and obtain the CFO estimate by using the phase angleof the correlation of consecutive DMRS symbols. To illustratethis mechanism, we denote Z2n+m = Ynm·P ∗

nm,∀n,m, wheren = 0, 1, · · ·N − 1 and m = 0, 1. Then, the CFO estimate isgiven by

εconv =Ns

πK

(angle

(2N−1∑l=1

Zl · Z∗l−1

)). (18)

The range of CFO detection using such a modified mechanismis between -1 kHz and 1 kHz, similar to the ML based CFOestimation technique using DMRS.

D. ML based CFO estimation using repeated data with DMRScompensation

Our ML based CFO estimation using repeated data proposedin Section IV-A uses only the data symbols for estimatingthe CFO. The DMRS symbols are not used because they arenot the same between consecutive subframes. Here, we extendthis method such that it also incorporates the DMRS symbols.This is done by multiplying each received DMRS symbol bythe conjugate of the reference DMRS symbol (similar to themethod in Section IV-C). Then, all the DMRS symbols willbe a vector of ones, multiplied by the channel co-efficientand the CFO in that symbol plus the noise at the receiver.This will give us two additional symbols per subframe forML estimation of CFO.

V. SIMULATION RESULTS

In this section, we first present the simulation results forour ML based CFO estimation algorithms and compare theirperformance with the conventional CFO estimation techniques.Then, we introduce the large transport block transmissionmechanism for MTC, where the UE transmits transport blockswhose size is larger than that supported in the currentLTE/LTE-A standards. We illustrate that this mechanism im-proves the effective data rate of the UE and reduces the energyconsumption. We also show that the energy efficiency of theMTC UE is further enhanced when this mechanism is used inconjunction with our ML based CFO estimation technique.

A. Performance of CFO estimation techniques

In order to analyze the performance of our ML based CFOestimation and the conventional CFO estimation techniques,we consider three cases - a) using data symbols only, b)using the entire subframe with DMRS compensation and c)using DMRS symbols only. In the first case, we have 12symbols available per subframe for CFO estimation and in thesecond case, the DMRS symbols of the received subframe aremultiplied with their conjugates, so that the entire subframecan be used for CFO estimation. In the third case, we useonly the 2 DMRS symbols in each subframe to estimate theCFO. The residual CFO in the system is 100 Hz and theCFO estimation error is measured as the absolute value ofthe difference between the actual CFO and the estimated CFO

values. We evaluate the performance based on the numberof subframes required to estimate the CFO within 10 Hzaccuracy, denoted by NCFO.

B. MSE and Cramer-Rao bound for the Gaussian channel

First, we determine the MSE of our ML based CFO estima-tor for the three cases in an Additive White Gaussian Noise(AWGN) channel and compare the MSE with the Cramer-Rao bound given in (14). The eNB bandwidth is chosento be 10 MHz and the corresponding sampling rate Ns =15.36 MHz. Therefore, each subframe (1 ms) contains K =1 ms × 15.36 MHz = 15360 samples. In the first two cases,the data is repeated every subframe (MTC RV transmissioncase), which corresponds to L = 1. For the first case, thenumber of DFT samples used for CFO estimation, we haveM = 12 symbols × 12 subcarriers = 144 and for the secondcase, M = 14 symbols × 12 subcarriers = 168. The MSEand Cramer-Rao bound for these two cases are shown inFig. 4a and Fig. 4b respectively. In the third case, we haveDMRS symbols spanning 12 subcarriers transmitted everyhalf-subframe, corresponding to L = 1

2 , M = 12 and a total of2N DMRS transmissions. The results for this case are shownin Fig. 4c.

The SNR considered for this analysis is between -20 dB and-10 dB, corresponding to the operating scenarios for MTCUEs in low network coverage. It can be observed that withincreasing SNR, the MSE of our ML based CFO estimatorgets closer to the Cramer-Rao bound for all the three cases.Also, the performance of the first two cases is better thanthat of the third case due to larger value of M in thesecases. Moreover, the MSE is measured for actual CFO values,which means that an estimation error of 10 Hz corresponds toMSE = 100. Therefore, for an AWGN channel with SNR of-15.5 dB (corresponding to 18 dB coverage enhancement) andthe desired CFO estimation accuracy of 10 Hz, the NCFO = 16for the first two cases and NCFO = 32 for the third case.

C. Results for the fading channel

Now, we analyze the performance of our ML based CFOestimation techniques for the EPA channel. Since the operatingSNR is very low and convergence (100% correct estimation)may take a very large number of repetitions for fading chan-nels, we provide a probabilistic measure of the accuracy interms of the 95-th percentile of the CDF of the estimationerror. A similar approach is adopted by different companiesin the 3GPP when they provide the performance results fordownlink synchronization, where the 90-th percentile of theCDF of the synchronization signal detection is used as theperformance metric.

For the first two cases, we compare the results obtainedby our method with the CFO estimation scheme using theconventional angle-based scheme (see equation (5)). For theDMRS only case, we compare the results from the ML basedestimation scheme with that obtained from the modified angle-based scheme (see equation (18)). The simulation settings aresummarized in Table I.

8

SNR in dB

-20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10

MS

E

10-3

10-2

10-1

100

101

102

103

104

CRB

Simulation

N = 16

N = 32

N = 64

N = 128

(a) Using data symbols only

SNR in dB

-20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10

MS

E

10-3

10-2

10-1

100

101

102

103

104

CRB

Simulation

N = 16

N = 32

N = 64

N = 128

(b) Using the entire subframe

SNR in dB

-20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10

MS

E

10-3

10-2

10-1

100

101

102

103

104

CRB

Simulation

N = 16

N = 32

N = 64

N = 128

(c) Using DMRS symbols only

Fig. 4. MSE v/s SNR and Cramer-Rao bound for ML based CFO estimation in AWGN

x = |Actual CFO - Estimated CFO| in Hz

0 5 10 15 20 25 30

F(x

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

16 SF (DMRS compensated)32 SF (DMRS compensated)64 SF (DMRS compensated)128 SF (DMRS compensated)16 SF32 SF64 SF128 SF

(a) Using ML estimation

x = |Actual CFO - Estimated CFO| in Hz

0 5 10 15 20 25 30

F(x

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

16 SF (DMRS compensated)32 SF (DMRS compensated)64 SF (DMRS compensated)128 SF (DMRS compensated)16 SF32 SF64 SF128 SF

(b) Using angle-based estimation

Fig. 5. CDF of the estimated CFO error using RV repetitions for LegacyLTE/LTE-A uplink

Fig. 5a and Fig. 5b indicate the performance of our MLbased CFO estimation algorithm and the conventional angle-based CFO estimation algorithm respectively, for the legacyRV transmission scheme (RV pattern: 0, 2, 3, 1, 0, 2, 3, 1, · · · )in LTE/LTE-A uplink. We observe that our ML estimation

based method requires at least NCFO = 64 for ≥ 95% prob-ability of successful CFO estimation, while for NCFO = 16,this probability reduces to 68%. Therefore, for the desiredCFO performance (95% success rate with 10 Hz accuracy),the eNB has to buffer 64 subframes. The conventional angle-based method has only 80% success rate in CFO estimationeven when NCFO = 128. In both the cases, using the en-tire subframe with DMRS compensation performs marginallybetter than using only the data symbols because we have 14symbols instead of 12 available for CFO estimation.

Fig. 6a and Fig. 6b depict the performance the two CFOestimation algorithms for the MTC RV transmission scheme(RV pattern with N RV-0s, followed by N RV-2s and so on)in LTE/LTE-A uplink. Since the CFO is estimated using Nsubframes, NCFO = N . In this case, we observe that ourML estimation based method with NCFO = 16 has around82% probability of successful CFO estimation, which is asignificant improvement when compared to the legacy case,while for NCFO = 32, we see that the probability of successfulestimation increases to 95%. This means that the eNB hasto buffer 32 subframes for CFO estimation and correction,which is half the size required for the legacy RV transmissionscheme. The conventional angle-based method has similarperformance to that of the legacy case. Therefore, for both thelegacy and MTC RV repetition schemes, the correlation phaseangle method fails to achieve the same estimation accuracy asthat of the ML based CFO estimator.

Fig. 7a and Fig. 7b show the CDF of the CFO estimationerror using our ML estimation based method and the conven-tional angle-based method using only the DMRS signals. Also,there is no need to differentiate the legacy and MTC scenariossince the DMRS transmission mechanism remains the samefor both the scenarios. We observe that the conventionalmethod fails to provide an accurate CFO estimation evenwith averaging over 128 subframes because there are only 2symbols available per subframe for CFO estimation. Also, ourML based CFO estimation technique using 2 DMRS symbolsperforms as well as the same technique for legacy RV scheme,requiring N = 64 subframes for estimating the CFO within10 Hz with 95% probability. Using 2 DMRS symbols persubframe is as good as using 12 data symbols because thenoise on the DMRS symbols is averaged 2N times, whilethat on data symbols is averaged N times, resulting in betterperformance. Although this means that we use only one-

9

x = |Actual CFO - Estimated CFO| in Hz

0 5 10 15 20 25 30

F(x

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

16 SF (DMRS compensated)32 SF (DMRS compensated)64 SF (DMRS compensated)128 SF (DMRS compensated)16 SF32 SF64 SF128 SF

(a) Using ML estimation

x = |Actual CFO - Estimated CFO| in Hz

0 5 10 15 20 25 30

F(x

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

16 SF (DMRS compensated)32 SF (DMRS compensated)64 SF (DMRS compensated)128 SF (DMRS compensated)16 SF32 SF64 SF128 SF

(b) Using angle-based estimation

Fig. 6. CDF of the estimated CFO error using RV repetitions for MTCLTE/LTE-A uplink

seventh of the symbols for CFO estimation (2 DMRS symbolsinstead of 14 symbols in the legacy RV scheme), the eNBstill needs to buffer the entire 64 subframes, since the CFOcorrection has to be applied on all the data symbols.

To this end, we have shown that the reduction in residualCFO results in an increase in the energy efficiency of theMTC UE (see Table II) and that our proposed ML basedCFO estimation techniques provide a robust and an accuratemechanism to reduce the residual CFO in low coverage.Also, the number of subframes required by our technique forCFO detection is smaller than the total number of subframesrequired for successful data decoding (see Table II), i.e.,NCFO < NSF, ensuring the feasibility of implementationof our technique at the eNB. In the following, we go onestep further and apply our improved methods to the so-calledlarge transport block transmission mechanism for MTC UEsin LTE/LTE-A, to further enhance their energy efficiency.

x = |Actual CFO - Estimated CFO| in Hz

0 5 10 15 20 25 30

F(x

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

16 SF

32 SF

64 SF

128 SF

(a) Using ML estimation

x = |Actual CFO - Estimated CFO| in Hz

0 5 10 15 20 25 30

F(x

)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

16 SF

32 SF

64 SF

128 SF

(b) Using modified angle-based estimation

Fig. 7. CDF of the estimated CFO error using DMRS only for both Legacyand MTC LTE/LTE-A uplink

D. Large Transport Block Transmission

In the current LTE/LTE-A standards, the maximum TBS isfixed based on the MCS and the number of PRBs allocatedto the UE. With QPSK chosen as be the highest orderof modulation for NB-IoT, the maximum TBS that can betransmitted corresponds to MCS = 9, which is 136 bits [28],[31]. The 3GPP standardization activities are considering alarge transport block transmission mechanism, where the UEtransits transport blocks whose size is larger than the currentmaximum size of 136 bits. Now, we briefly review the largetransport block transmission mechanism and demonstrate theenergy efficiency gains when our CFO estimation technique isapplied to such a mechanism.

The large transport block transmission mechanism relies onthe precedent that the effective data rate of the UE increaseswhen larger sized blocks are transmitted, which means thatthe UE can finish complete its transmission quickly, go backto idle state and save power. The effective data rate of theUE equation (1). If we increase the TBS by a factor α in

10

equation (1), then NSF need not increase by the same amount.This is because the performance of the turbo decoder usedfor decoding the transport block does not vary linearly withrespect to the code rate. In most of the cases, NSF will scaleby a factor less than α, thereby increasing the effective datarate. However, the TBS cannot be increased arbitrarily and islimited by the code rate.

The transport block is appended with a 24-bit Cyclic Redun-dancy Checksum (CRC) [28], [32]. The code rate per subframeis calculated as

corig =(TBS + 24)

(Tsc × nb)(19)

where Tsc denotes the total number subcarriers available fortransmitting the transport block and nb is the number of bitsper subcarrier. Since, MTC transmission is restricted to QPSK,nb = 2. Considering that the uplink transmission for a singleantenna UE requires 2 symbols for DMRS transmission (seeFig. 1), there are 12 symbols available for control and datatransmission. Assuming that the UE uses a single PRB pairtransmission (12 subcarriers per symbol) and does not transmitany control information when it is sending data, Tsc = 12 ×12 = 144.

Legacy LTE/LTE-A standards indicate that the transportblock transmission should obey the condition of each RV beingindependently decodable [28]. Hence, the code rate must bechosen per RV. However, this condition is relaxed for low-complexity MTC UEs, since they are low data-rate devicesand require multiple retransmissions of data in most of thecases. Therefore, we have a new metric called the effectivecode rate, which is a measure of the code rate over 4 RVs,given by ceff =

corig4 and the data block can be decoded when

all 4 RVs are received.To illustrate this aspect, let us choose TBS = 324 bits.

Noting that Tsc = 144 and nb = 2, we get corig = 1.21(> 1),which suggests that each RV transmission will not be inde-pendently decodable for this TBS and it cannot be used in thelegacy scheme. However, for the MTC scheme, the effectivecode rate ceff = 0.3(< 1), which suggests that the TBS is canbe readily used.

E. Energy Efficiency Analysis

Now, we illustrate the reduction in energy consumption ofMTC UEs obtained by the use of large transport block trans-mission and our ML based CFO estimation. We use the energyconsumption model described in Section II-A to calculate theenergy efficiency of the MTC UEs. The simulation parametersare listed in Table I and the power consumption values usedare the same as in Section II-B.

Table III gives the number of subframes required by theeNB to decode the transport block (N100Hz and N10Hz) andthe effective data rate for large transport block transmission(R100Hz and R10Hz) with CFO = 100 Hz and CFO = 10 Hz,respectively. The former CFO value is the one currentlyused by the 3GPP for MTC performance evaluation and thelatter models the negligible frequency offset scenario (referSection II-B). Similar to the performance of the regular sizedtransport block (TBS = 72 bits) in Section II-B, we observe

TABLE IIINUMBER OF REPETITIONS V/S CFO

TBS N100Hz N10Hz R100Hz R10Hz

(kbps) in (kbps)72 110 80 0.44 0.60144 200 144 0.60 0.83224 304 216 0.66 0.93328 376 256 0.81 1.19424 448 304 0.89 1.32

TABLE IVENERGY EFFICIENCY GAINS V/S TBS FOR CFO = 100 HZ AND CFO =

10 HZ

TBS η1 η2 with p = 0.95

D = D = D = D = D = D =10% 1% 0.1% 10% 1% 0.1%

72 - - - 25.8% 25.6% 22.5%144 27.2% 26.9% 23.7% 45.2% 44.6% 39.3%224 33.6% 33.2% 29.3% 50.2% 49.5% 43.7%328 46.0% 45.3% 40.0% 60.0% 59.2% 52.3%424 51.1% 50.4% 44.5% 63.4% 62.5% 55.2%

that the effective data of the UE increases with a decrease inthe residual CFO value even for large transport blocks.

1) Large transport block transmission only: First, we cal-culate the energy efficiency obtained solely by the use of largetransport block transmission, where the residual CFO is notcompensated and remains at 100 Hz. Let Eltb denote theenergy consumed in this scenario. Eltb is obtained by usingtON = tltb = 1

R100Hzs per bit in equation (3). The energy

efficiency gain is calculated as

η1 =Eorig − Eltb

Eorig=

tltb + v(tTotal − tltb)

torig + v(tTotal − torig)(20)

2) Large transport block transmission with CFO estima-tion: When our ML based CFO estimation techniques areused, the corresponding energy consumption, Ecfo is obtainedby using tON = tcfo = 1

R10Hzs per bit in equation (3).

However, the CFO estimation is successful with probabilityp owing to the low operating SNR and limited symbol buffersize available at the eNB. Therefore, the energy consumptionof the UE with CFO estimation is given by

Efinal = pEcfo + (1− p)Eorig (21)

Then, the energy efficiency gain of the UE using CFO esti-mation is calculated as

η2 =Eorig − Efinal

Eorig= p

(1− Ecfo

Eorig

)= p

(tcfo + v(tTotal − tcfo)

torig + v(tTotal − torig)

)(22)

We use the energy consumed by the UE for TBS = 72 bitsand CFO = 100 Hz, Eorig, as our reference and evaluate theenergy efficiency of different sized transport blocks transportblocks with CFO = 100Hz and CFO = 10 Hz. Table IVsummarizes the energy efficiency results for three differentduty-cycles (D), corresponding to 10%, 1% and 0.1% (referSection II-B).

11

We observe that solely the large transport block (withoutCFO estimation) results in 23.7% to 44.5% more energyefficiency than the current mode of operation with TBS =72 bits even for a very low duty cycle of 0.1%. When our MLbased CFO estimation techniques are used, the residual CFOis within 10 Hz with 95% probability (p = 0.95). With this,we obtain a further improved energy efficiency of 39.3% to55.2% for larger TBS, indicating that robust CFO estimationat the eNB significantly reduces the energy consumption ofthe MTC UEs in low coverage.

VI. FURTHER ENHANCEMENTS FOR MTC UES

The ML based CFO estimation scheme using RV repetitionfor MTC UEs (see Fig 6a), which demonstrated the bestperformance, suggests that the eNB requires 32 consecutiverepetitions of the same RV for the desired CFO estimationperformance. It would be beneficial to have an MTC trans-mission scheme, which not only assists in CFO estimation,but also removes the constraints on RV block transmissionand repetition. In this section, we propose a new uplinktransmission scheme with increased DMRS density, whichachieves this objective. Also, we briefly discuss how our MLestimation based CFO estimation mechanisms can be used innon-LTE scenarios.

A. Increased DMRS density scheme in LTE/LTE-A uplink

In the following, we propose a new transmission scheme forLTE/LTE-A uplink, where the DMRS density is doubled forN initial subframes and evaluate the performance of our MLbased CFO estimation technique using the DMRS technique.In the current LTE/LTE-A uplink, the DMRS sequences aretransmitted on the fourth and the eleventh symbols of asubframe with normal CP (see Fig. 1). For our proposedtransmitted scheme, the MTC UEs double the DMRS densityby transmitting new DMRS sequences on the third and thetenth symbols along with the legacy DMRS sequences forthe initial N subframes and then reverts back to the legacyscheme.

Fig. 8 gives the performance our ML based CFO estimationscheme when the DMRS density is doubled. We observe thatwe can estimate the CFO within 10 Hz of the actual valuewith 95% probability when the accumulation time is 32 msor more. The performance results are close to that of the MLbased CFO estimation scheme using RV repetition for MTCUEs (see Fig 6a) and the doubled DMRS density scheme doesnot impose any restriction on the RV block being transmittedand the number of repetitions, as desired.

The only disadvantage of this scheme is that there isan overhead of 2 symbols for first N subframes for eachtransmission. For example, with N = 32, we have an overheadof 64 symbols. With 14 symbols per subframe (1 subframe= 1 ms), the overhead time is less than 5 ms. Since, thetransmission takes more than 100 subframes for any TBS, theoverhead is less than 5% for all the cases. Moreover, the eNBcan utilize the increased DMRS density for better channelestimation, which improves the overall performance of datadecoding and further reduces the overhead.

x = |Actual CFO - Estimated CFO| in Hz

0 5 10 15 20 25 30

F(x

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

16 SF

32 SF

64 SF

128 SF

Fig. 8. CDF of the estimated CFO error using ML estimation using 2x DMRS

B. Application of ML based CFO estimation to non-LTEscenarios

Hitherto, we designed and developed CFO estimation mech-anisms specific to the LTE/LTE-A frame structure consider-ing RV repetitions and DMRS transmissions. However, thistechnique can be readily extended to any communicationmechanism incorporating periodic data and/or pilot repetitions.The ML based CFO estimation for such scenarios can bederived by choosing the appropriate values of K and L basedon the length and the periodicity of the repeated data/pilotsignals in (15) (similar to how we derived the DMRS basedestimation as a special case).

VII. CONCLUSION

In this paper, we address the problem of improving theenergy efficiency of MTC devices, which form an integral partof the IoT. We considered MTC using LTE/LTE-A for low-power, low-complexity devices located in low coverage areas.We showed that the energy efficiency of the MTC UE increasesif the eNB adopts CFO estimation mechanisms that reduce inthe residual CFO to negligible limits. We proposed an MLbased CFO estimation mechanism that uses the data and pilotrepetitions in LTE/LTE-A and illustrated that it significantlyoutperforms the legacy CFO estimation technique using thephase of the correlation between consecutive data repetitions.We demonstrated that incorporating our ML based CFO esti-mation technique at the eNB results 22.5%-55.2% reductionin energy consumption of the MTC UEs, when compared tothe case where the residual CFO is not compensated. Wealso proposed a variation of the LTE/LTE-A frame structureincorporating additional pilot signals during the initial MTCtransmissions, which assists in faster CFO estimation at theeNB with minimal overhead. We conclude that our ML basedCFO estimation technique provides a robust mechanism toestimate the CFO in low coverage and improves the energyefficiency of MTC UEs used for IoT applications.

APPENDIX

In this Appendix, we derive the Cramer Rao bound for ourML based CFO estimator for repeated data. We begin with

12

re-writing (10) for a given sub carrier m and the Gaussianchannel as follows

Y (m) = R(m)u(m) + W (m), (23)

where Y (m) = [Y0(m), Y1(m), · · ·YN−1(m)]T is the re-ceived signal vector on the m-th subcarrier, R(m) de-notes the data transmitted on the m-th subcarrier, u(m) =

[1, e( j2πεLKNs), e( j2πε2LKNs

), · · · e(j2πε(N−1)LK

Ns

)]T is the CFO

vector and W (m) = [W0(m),W1(m), · · ·WN−1(m)]T isthe Gaussian noise with zero mean and covariance matrixσ2(m)IN (IN is the identity matrix of order N). The SNR iscalculated as

Ψ =1

M

M−1∑m=0

|R(m)|2

σ2(m)(24)

This is similar to the eqn. (4) in [38], for which the Cramer-Rao bound is derived using the Fischer information matrix F(eqn. (42) in [38]). In our case, we obtain

F =

[D v

vT βRHP−1R

](25)

where

P = diag{σ2(0), σ2(1), · · · , σ2(M − 1)}, (26)

D = N · diag{2P−1, 2P−1,P−2}, (27)

v =2πLKN(N − 1)

Ns· [−RT

I P−1 RT

RP−1 0TM ], (28)

with RR and RI denoting the real and imaginary parts of Rand

β =4π2L2K2N(N − 1)(2N − 1)

3N2s

(29)

The Cramer-Rao bound is given by

CRB(ε) = [F−1]3M+1,3M+1 (30)

where F−1 is the inverse of F . Similar to eqn. (47) in [38],for our case, we obtain

b = α

[RTI −RT

R 0TM3Ns

πLK

](31)

as the last column of F−1, where

α =Ns

2πLKN(N − 1)(4N − 3)RHP−1R(32)

Substituting (31) to (30) and simplifying, we get

CRB(ε) =3N2

s

2π2L2K2N(N − 1)(4N − 3)RHP−1R(33)

Given that

RHP−1R =

M−1∑m=0

|R(m)|2

σ2(m)= MΨ, (34)

substituting (34) to (33), we obtain the final expression for theCramer-Rao bound given in (14).

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