Research Article  Open Access
Channel Estimation and PeaktoAverage Power Ratio Analysis of Narrowband Internet of Things Uplink Systems
Abstract
Narrowband Internet of Things (NBIoT) is a cellular based promising lowpower widearea network (LPWN) technology standardized by the 3rd Generation Partnership Project (3GPP) in release13 as a part of the future 5th Generation (5G) wireless communication systems. The main design target of NBIoT was to enhance radio coverage by repeating signal over an additional period of time for the ultralowend IoT devices that would be operated in extreme coverage environments. But the power efficiency of the lowcost NBIoT user equipment (NBIoT UE) in the uplink is the major concern. Coverage improvement from signal repetitions depends on the channel estimation quality at extremely bad radio conditions. The typical operating signaltonoise ratio (SNR) for NBIoT is expected to be much lower than the zero. In this paper, we have proposed two efficient narrowband demodulation reference signal (NDMRS)assisted channel estimation algorithms based on the conventional least squares (LS) and minimum mean square error (MMSE) estimation methods. The theoretical analysis and the linklevel performance of our proposed estimation methods are presented. Simulation results exhibit that the proposed methods provide better estimation precision compared to the traditional LS and MMSE methods at the low SNR situations. Furthermore, we have analyzed the raisedcosine (RC) and squarerootraised cosine (RRC) pulse shaping to reduce peaktoaverage power ratio (PAPR) as an uplink transmit filter. The PAPR values are evaluated through extensive computer simulations for both singletone and multitone transmissions. Our evaluation results vindicate that the RRC pulse shaping with lower PAPR values is feasible to design of practical NBIoT uplink transmitter and increases power efficiency.
1. Introduction
The Internet of Things (IoT) is a novel prototype which offers massive connectivity to physical objects, radiofrequency identification (RFID) tags, vehicles, sensors, actuators, and other things embedded with electronics to the Internet. IoT allows things to be connected across existing network infrastructure, interacting with each other through unique addressing schemes, thus reducing extra deployment cost and improving accuracy and efficiency. According to [1], there will be more than 30 billion devices connected wirelessly to the IoT by 2020. Nokia [2], based on Machina research 2015, predicted that about 30 billion connected IoT devices will be deployed by 2025, of which cellular IoT (CIoT) and lowpower widearea (LPWA) modules are about 23 percent. Traditionally, mobile broadband networks need high throughput and low latency, whereas LPWA applications require lowthroughput, extended coverage, lowcost, low complexity, scalability, low delay sensitivity, and high power efficiency [3–6].
There are many shortrange wireless communication technologies [7, 8] like Bluetooth low energy (BLE), WiFi, LiFi, ZigBee, and Zwave, to enable the IoT. Some of the IoT enabling technologies [9, 10] such as SigFox and LoRa that are operating in licenseexempted band (i.e., industrial, scientific, and medical (ISM) band). On the other hand, Global System for Mobile Communications (GSM) and the 3rd Generation Partnership Project (3GPP) standard LongTerm Evolution (LTE) are operating in licensed spectrum to enable the IoT. A new cellular based IoT enabling technology named narrowband IoT (NBIoT) was specifically designed for ultralowend IoT applications. The 3GPP finalized the specifications of NBIoT in LTE release13 [11]. It is secure and reliable for data transmission because of the deployment in licensed spectrum of GSM or LTE [12]. NBIoT enables IoT whose applications are very diverse including smart metering, smart cities, smart water, smart environment, smart agriculture, smart animal firming, retail, logistics, security and emergencies, industrial control, and domestic and home automation. Therefore, the channel condition of NBIoT is very complicated due to its diverse application scenarios.
Since NBIoT is still in its infancy, the proper guidelines for efficient channel estimation and equalization are still missing in the current literature. Channel estimation based on the pilot signal has been studied well for traditional orthogonal frequency division multiplexing (OFDM) and singlecarrier frequency division multiple access (SCFDMA) systems, e.g., [13, 14]. In the literature, most of the NBIoT research focused on frame structure design [15], scheduling and link adaptation [16], random access procedure [17], and system acquisition [18]. Positioning performance of NBIoT has been studied in [19, 20]. Y. D. Beyene et al. in [21] have investigated the performance of three traditional channel estimators only for 15 kHz subcarrier spacing. L. Zhang et al. in [22] have analyzed the channel equalization and coexistence problem of NBIoT and LTE signals using only traditional LTE supported subcarrier spacing. To the best of our knowledge, the channel estimation of NBIoT uplink with 3.75 kHz subcarrier spacing has not been studied yet. Thus, efficient channel estimation is the prerequisite of coverage improvement, equalization, and signal decoding at the receiver.
In NBIoT uplink, low peaktoaverage power ratio (PAPR) enhances the efficiency of the lowcost power amplifier. Low outofband radiation is desired for the uplink transmitter due to its very narrow bandwidth. The PAPR problem is more of a concern in the NBIoT uplink (i.e., lowcost transmitter). The efficiency of the power amplifier is crucial for the lowcost NBIoT user equipment (NBIoT UE) with limited battery power. Thus, low PAPR in the NBIoT uplink is ultimate desire owing to lowcost power amplifier. PAPR reduction techniques such as scrambling, discrete Fourier transform (DFT) spreading, and cyclic prefix (CP) insertion can be applied at the uplink transmitter. NBIoT supports modulation schemes like BPSK (binary phase shift keying) and QPSK (quadrature phase shift keying), which are also robust against PAPR by applying constellation rotation to make smooth transition between constellation points. However, these techniques are not fully preserved. Further reduction of PAPR would be great demand at the uplink because transmitter is the lowcost and lowpower IoT device. In [23], the authors have been evaluated the PAPR values employing rootraised cosine (RRC) pulse shaping (PS) filter only for the singletone transmission. This is the first time that the partial analysis of PAPR was taken into account in the NBIoT uplink transmitter.
In this paper, we have developed an uplink NBIoT system model according to the 3GPP specifications in release13 [24–26]. The motivation was that the uplink transmission of NBIoT systems is more complicated compared to the downlink transmission. We have considered both types of transmission schemes and subcarrier spacing for channel estimation and PAPR analysis. The major contributions of this paper can be summarized as follows:(1)We have provided a brief overview of NBIoT technology including deployment options, physical channels and signals, uplink frame structure, and resource unit (RU) definition. An analytic NBIoT uplink received signal model is derived as a function of transmitted signal and channel impairments. Narrowband demodulation reference signal (NDMRS) generation and mapping to timefrequency grid is also presented.(2)We have proposed two NDMRSaided channel estimation algorithms based on the traditional least squares (LS) and minimum mean square error (MMSE) estimators that can be coped with the complicated channel conditions of NBIoT systems. Through simulations, we have investigated and verified the effectiveness of our proposed algorithms compared with the conventional LS and MMSE algorithms in terms of bit error rate (BER) related to signaltonoise ratio (SNR). Simulation results show that our proposed channel estimation algorithms outperform the others.(3)In addition, we have provided theoretical analysis of PAPR for the NBIoT uplink employing raisedcosine (RC) and squarerootraised cosine (RRC) pulse shaping filters. We have also showed the comparison of PAPR values that are obtained with and without PS through computer simulations for both singletone and multitone transmissions. Numerical results elucidate that RRC PAPR reduction technique is feasible for the implementation of NBIoT uplink transmitter.
The rest of the paper is organized as follows: in Section 2, a brief overview of the NBIoT technology is provided. NBIoT uplink signal model and NDMRS generation and mapping are presented in Section 3. Theoretical analysis of channel estimation and its performance analysis by simulations are given in Section 4. In Section 5, PAPR reduction techniques and its numerical results are presented. Finally, we conclude the paper in Section 6.
Notations. Bold face lowercase letters are used to represent timedomain vectors (or matrices), while frequencydomain vectors/matrices are denoted by uppercase bold characters. Superscripts and denote the transpose and Hermitian of a vector, a scalar, or a matrix, respectively, and denotes matrix inversion. The circular convolution operation is denoted by and the operators , , and represent the expectation, absolute value, and Euclidean norm, respectively. denotes the identity matrix.
2. Overview of NBIoT Technology
NBIoT was designed by 3GPP as a key technology to meet the demands of massive lowpower IoT connectivity for the evolution of future 5G wireless communication systems. It can be implemented in three different operation modes specified by 3GPP in release13 [27, 28]: standalone, inband, and guardband. The illustrations of three deployment options are given in Figure 1. NBIoT can be deployed by replacing one or more efficiently reframed 200 kHz GSM carriers, a socalled standalone mode of operation. Radio coverage for NBIoT can be enhanced significantly by using all the transmit power at the evolved node B (eNB) also known as base station. In inband operation, it can be implemented inside the LTE carrier using one or more physical resource blocks (PRBs); a PRB corresponds to 180 kHz bandwidth. LTE and NBIoT share the total transmit power at the eNB. Widearea coverage can also be achieved by boosting power on the NBIoT PRB. The spectrum efficiency can also be increased by the sharing of PRB between LTE and NBIoT. The third option can be deployed within the LTE carrier’s unused guardband. This is allowed only for 5 MHz or higher LTE system bandwidth. Inband and guardband deployments of NBIoT reuse the existing LTE base station’s radiofrequency (RF) frontend and the baseband numerologies with some modifications to fit into the narrow bandwidth [29]. The coexistence of LTE and NBIoT has been investigated through rigorous simulations in [27]. Thus, it will not incur extra deployment cost and time to come in operation. The modes of operation should be known to the NBIoT UE when it is turned on and searches for an NBIoT carrier. NBIoT supports 100 kHz channel raster for all types of operation modes.
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NBIoT channels and signals are designed based on the existing LTE channels and signals with required modifications and simplifications to fit the 3GPP specified 180 kHz narrow bandwidth. The NBIoT downlink and uplink channels and signals with their functions according to release13 are given in Table 1. The 3GPP is specified as narrow as system bandwidth of 180 kHz for both downlink and uplink transmissions. NBIoT supports only frequency division duplexing (FDD) with half duplex transmission. In the downlink, NBIoT inherits the downlink numerology from existing LTE although with further restricted support. It uses OFDM with 15 kHz subcarrier spacing as in LTE. The basic time unit for NBIoT is specified by a factor of seconds. The slot duration ms. A pair of consecutive slots constitute a subframe with duration 1 ms. The NBIoT radio frame for downlink consists of 10 subframes with duration ms. Thus, a radio frame contains 20 slots; the slot number within a radio frame is denoted here as , where . In NBIoT uplink, two schemes are supported for the baseband modulation: singletone transmission based on frequency division multiple access (FDMA) and multitone (i.e., 3, 6, or 12 subcarriers) transmission according to SCFDMA. Two different subcarrier spacing types are allowed for singletone transmission: 15 kHz and 3.75 kHz [25]. NBIoT with 3.75 kHz subcarrier spacing is designed to provide more capacity in power limited scenarios [27]. The first one is the same as in LTE with 0.5 ms slot, 1 ms subframe, and 10 ms frame in timedomain, whereas there are 12 subcarriers within 180 kHz system bandwidth in frequencydomain. A timefrequency grid structure for 15 kHz subcarrier spacing within a frame is illustrated in Figure 2. On the other hand, the second one is different from LTE with slot duration ms. Thus, five consecutive slots constitute a radio frame with the duration of ms, where the slot number within a radio frame can be selected from the set . In the frequencydomain, 180 kHz system bandwidth consists of 48 subcarriers. Figure 3 shows the NBIoT uplink resource grid structure within a frame for 3.75 kHz subcarrier spacing. For singletone transmission both subcarrier spacing types can be used, whereas only 15 kHz subcarrier spacing is specified for multitone transmission.

The 3GPP in [24] defined a new feature for NBIoT uplink called resource unit (RU), which is the basic unit for narrowband physical uplink shared channel (NPUSCH) allocation. In the timedomain, one transport block size (TBS) can be mapped to multiple RUs from the set . In 3GPP [25], TBSs are defined as a function of the number of RUs and modulation and coding scheme (MCS) level. The maximum TBS is 1000 bits for the uplink. The characterization of a RU is given in Table 2. In NBIoT systems, repetition of user data and associated control signal transmission has been taken in the 3GPP as a key technique to achieve widearea coverage. Repetitions of same signal can be increased transmission reliability but reduced spectral efficiency. Maximum 2048 and 128 repetitions are allowed for downlink and uplink transmissions, respectively, suggesting that the received data would be decoded even when the noise power is far greater than the signal power. In other words, the eNB and NBIoT UE transmits the same TBS repeatedly as many times as indicated in the downlink and uplink, respectively. The NBIoT UE and eNB at the receiver combines the repetitions before decoding the transmitted data. The number of repetitions is determined by the eNB and NBIoT UE to achieve the desired SNR at the NBIoT UE and eNB receiver, respectively.

3. NBIoT Uplink System Model
The system model of uplink NBIoT systems with NDMRS sequence, channels, and the associated estimation and equalization blocks is shown in Figure 4. The uplink transmitter comprises transport channel also known as uplink shared channel (ULSCH) and data channel (NPUSCH) processing. Binary input data arrives to the channel coding unit in the form of one transport block over a number of RUs per uplink cell. The number of RUs is scheduled according to [25]. In 3GPP [30], ULSCH processing consists of transport block cyclic redundancy check (CRC) attachment (e.g., 24 bits with generator polynomial (D)), 1/3rate based turbo coding, and rate matching to yield a codeword input to the NPUSCH.
3.1. NDMRS Sequence Generation and Mapping
A NDMRS sequence can be generated for the case when the number of subcarriers in a RU is as
where is the binary sequence defined by a length31 Gold sequence, denotes the repetition number of same signal transmissions, represents number of slots in a RU, and is the number of RUs. The initialization value of the first sequence is specified with a unit impulse function of length31. The second sequence is initialized with the seed at the start of the NPUSCH transmission [24]. The variable is defined in [24], where the base sequence index is for NPUSCH format1 without enabling group hopping. Thus, the NDMRS sequence for NPUSCH format1 can then be represented as
The NDMRS sequence for the number of subcarriers greater than one in a RU is defined by a cyclic shift of a base sequence as
where is defined in [24] for the scheduled number of subcarriers in a RU. Without loss of generality, we assume that there is no higher layer signaling; then the base sequence index can be obtained as
The cyclic shift for and 6 is defined in [24], whereas for .
The NDMRS sequence is also known as pilot symbol, which is transmitted together with the user data symbols to estimate channel response in uplink NBIoT systems. In each NBIoT uplink slot, NDMRS symbols are mapped to the allocated number of subcarriers in a RU of the fourth SCFDMA symbol for 15 kHz subcarrier spacing, whereas the fifth symbol is for 3.75 kHz subcarrier spacing. An inverse discrete Fourier transform (IDFT) operation is performed on the contents of resource grid that contains the NDMRS symbols to convert timedomain reference sequence followed by CP addition.
3.2. Analytical Uplink Signal Model
Let us consider that an NBIoT UE transmits a block of bits , where is the number of transmitted bits in a codeword on the NPUSCH in one subframe. The codeword bits are scrambled using NBIoT UE specific scrambling sequence in neighboring cells to ensure that the interference is randomized and the transmission from different cells is separated prior to decoding at the eNB receiver. Thus, we obtain a block of scrambled bits as
where and is the scrambling sequence defined by a length31 Gold sequence [24]. The initialization value of the first sequence is specified with a unit impulse function of length31. The second scrambling sequence will be initialized with the seed according to
where denotes the index of the radio network temporary identifier (RNTI), is the first slot of the transmission of the codeword, and the narrowband cell identity number can be selected from the set . The scrambling sequence will be reinitialized for the repetitions of NPUSCH according to (6) after every transmission with and set to the first slot and the frame, respectively. In constellation mapping of NPUSCH transmission, the block of bits is modulated by employing low PAPR modulation schemes (e.g., BPSK and QPSK), which are specified for NBIoT systems to improve the power efficiency at the transmitter (i.e., NBIoT UE). Thus, we have a block of complexvalued modulation symbols , where denotes the number of modulated symbols.
The block of modulation symbols is divided into sets, each corresponding to one SCFDMA symbol. The parameter indicates the number of subcarriers allocated for NPUSCH transmission, where (e.g., for NBIoT) corresponding to the bandwidth of NPUSCH in terms of PRB and is the number of subcarriers in a PRB. The frequencydomain symbols after performing DFT operation can be represented as
The physical resource element mapping is accomplished by placing frequencydomain user data symbols and known NDMRS symbols within the uplink timefrequency grid. NPUSCH can be mapped to one or more than one RU according to [25], each of which can be transmitted times. The block of frequencydomain symbols is mapped in a sequential manner (i.e., localized mapping) to subcarriers assigned for transmission [24, 26, 31, 32]. The mapping to resource elements corresponding to subcarriers allocated for transmission within a RU will be in increasing order of the first subcarrier index , then the symbol index , and finally the slot number. After mapping to slots, repeats additional times, before continuing the mapping of to the following slot, where the quantities and can be defined as follows:andwhere denotes the subcarrier spacing. The mapping of is then repeated until slots have been transmitted. Figure 5 shows the mapping pattern of user data (NPUSCH) symbols and NDMRS symbols within a resource grid for NPUSCH format1; for example, a RU contains 12 subcarriers for multitone transmission and only one subcarrier for singletone transmission.
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The physical resource element mapping is followed by an inverse DFT (IDFT) operation to convert the data into timedomain signal. For singletone transmission, the timedomain baseband signal after the CP insertion with length and PS operation for the th subcarrier in SCFDMA symbol in an uplink slot can be expressed as
for , where parameters for and are specified in Table 3, is the frequencydomain modulation value of symbol , and the phase rotation is defined as [24]

where is the symbol counter that is reset at the start of a transmission and incremented for each symbol during the time of transmission.
The timedomain signal in SCFDMA symbol in an uplink slot for multitone transmission can be modelled as
for , where , , , and is the content of resource element . Note that only normal CP length of existing LTE is supported in release13 of the NBIoT specification.
The timedomain baseband signal is upconverted by a RF frontend and then transmits through a multipath fading channel whose delay speared is assumed to be smaller than the CP length. The received signal is composed of the signals from different channel paths and additive noise; then resultant signal for both singletone and multitone transmissions can be represented as the circular convolution of transmitted signal and channel impulse response (CIR). Thus, we havewhere is the additive white Gaussian noise (AWGN) with zero mean and variance , , and are the received signal for singletone and multitone transmissions, respectively, and denotes the CIR of the multipath fading channel with distinct complextaps, which can be expressed aswhere and represent the attenuation and the delay of the th path, respectively. Therefore, the noisy and delayed version of the signals at the receiver can be written asAfter removing CP, the receiver performs inverse operations of the NPUSCH and ULSCH processing. In addition, NDMRSassisted frequencydomain channel estimation and equalization are performed.
4. Channel Estimation in NBIoT Uplink
4.1. Theoretical Analysis
We first compute the channel estimates for all the allocated subcarriers in a RU of the symbols (i.e., , 10 or 4, 11, depending on the subcarrier spacing) within a subframe that contain NDMRS sequences. Then, we obtain the channel estimates for the rest of the symbols employing one dimensional (1D) timedomain interpolation of the channel estimates within one subframe of a RU. NPUSCH and NDMRS hopping are not considered in this work to make out derivations generally applicable to any multicarrier communication systems. The NDMRSaided channel estimation can be done by using widely used estimation algorithms like LS [33] estimator and MMSE [34] estimator. We assume that all the scheduled number of subcarriers in a RU are occupied by NDMRS symbols (i.e., pilots) generated in Section 3.1 within the specified symbol locations. Then, the group of received pilot symbols in the frequencydomain can be represented as
For the pilot symbol , is the true channel frequency response (CFR) at the pilot locations and represents Gaussian white noise vector and its noise variance . Then, CFR estimates can be written as
where is the channel coefficient matrix in frequencydomain, denotes the maximum channel delay speared, which is assumed to be shorter than the NBIoT supported CP length , and represents matrix. Therefore, the channel estimates based on the conventional LS method of the whole channel response can be obtained as
where is the matrix which has the lines where NDMRS symbols are located and the previous column of DFT matrix.
The LS algorithm is computationally less complex but the problem is that the quantity in (20), which turns out to be an illconditioned matrix. Thus, the conventional LS estimator cannot be a practical estimator to NBIoT uplink systems due to the presence of some subcarriers without SCFDMA modulation. The problem of conventional LS estimator can be mitigated to fit in the low complexity NBIoT systems by adding a normalization matrix , where is a regularization parameter and its value has to be chosen from the range 0~1 such that the resulting eigenvalues are all defined and the inverse matrix is least perturbed and denotes the identity matrix. Therefore, the channel estimates of the proposed LS estimator in frequencydomain can be estimated as
The mean square error (MSE) of the proposed LS estimator can be computed as
Consequently, after simplification of (22), we have
The MMSE is an optimal estimation technique that exploits the knowledge of the channel statistics and channel covariance matrix. For the conventional MMSE estimator, we have
where represents the autocovariance matrix of . MMSE is a modified form of conventional LS estimator in (20), but it is very intricate to obtain the precise knowledge of the channel covariance matrix in very low SNR regime. For the application of MMSE in NBIoT uplink systems, we assume that the delay spectrum of the channel power is evenly distributed, then the channel covariance matrix turns out to be an identity matrix , resulting in the elimination of real time matrix inversion. Furthermore, the noise power is also normalized by dividing the average power of the NDMRS symbols. Thus, channel estimates for the proposed MMSE estimator can be estimated as
The MSE of the proposed method can be computed as
Subsequently, the simplified form of (26) can be represented as the following form:
where represents the average SNR, which is defined as
and
where is the modulation scheme dependent constant, for example, for QPSK modulation.
4.2. Simulation Results and Analysis
We have considered LTEbased NBIoT uplink systems whose parameters are selected based on the specifications of 3GPP NBIoT in release13. We have investigated and compared the performance of our proposed NDMRSassisted channel estimation algorithms with conventional LS and MMSE algorithms in terms of BER in contrast to SNR. In this paper, we have considered a simple singleinput singleoutput (SISO) system for both singletone transmission with 15 kHz and 3.75 kHz subcarrier spacing and multitone transmission with 15 kHz subcarrier spacing. We have set the repetition number to guarantee the transmission reliability (i.e., BER<10^{−1}) at low SNR. Transmission time and resource utilization are also our concern because low transmission time and high rate of resource utilization can improve the data rate of NBIoT systems. Low complexity zero forcing (ZF) equalizer is employed. In this simulation, we have considered identical transmission time and resource utilization. The fundamental parameters are used to carry out simulations as listed in Table 4 and referred to figure captions for better readability.

Simulation results of the performance of singletone transmission for different channel estimators using –BPSK modulation are shown in Figure 6. It is observed that the channel estimation accuracy cannot be improved when SNR is extremely low, but estimation precision rises as the receive SNR increases (i.e., better channel condition). For 15 kHz subcarrier spacing as shown in Figure 6(a), our proposed LS and MMSE estimators perform better than the traditional LS and MMSE estimators. As shown in Figure 6(b), the system performance of 3.75 kHz subcarrier spacing employing –BPSK for all estimation methods is slightly lower compared to 15 kHz subcarrier spacing.
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The BER performance curves of different channel estimators employing QPSK constellation for singletone transmission are shown in Figure 7. The simulation results elucidate that the system performance with QPSK modulation is little bit lower than –BPSK modulation due to extremely low SNR values. However, the system performance improves with our proposed algorithms compared to the conventional LS and MMSE algorithms regardless of the modulation scheme and subcarrier spacing.
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The BER performance curves of NPUSCH format1 for multitone (e.g., 12tone) transmission for different channel estimation techniques are shown in Figure 8. It is also seen that the system performs better with our proposed algorithms than the traditional LS and MMSE algorithms. Since NBIoT supports only phaseshiftkeying (PSK) modulation, the receiver’s performance of such two algorithms has linear change and no significant variation when SNR is extremely lower. Finally, we conclude that our proposed MMSE algorithm can be coped with the practical implementation of NBIoT uplink systems to ensure successful transmission of user data for both singletone and multitone transmissions.
5. PAPR Analysis of NBIoT Uplink
5.1. Theoretical Analysis
The baseband timedomain transmit signals and are derived in (10) and (12) for singletone and multitone transmissions, respectively. To make our derivations generally applicable to any multicarrier communication systems, we assume that is the continuous time baseband SCFDMA signal for both types of transmission. The PAPR of the timedomain baseband SCFDMA signal can be defined as the ratio of the maximum instantaneous power (i.e., peak power) to the average power of the signal. Thus, we have
where
and
where is the symbol duration. In NBIoT uplink transmitter (i.e., NBIoT UE), the PAPR can be reduced by exploiting linear filtering operation referred to as pulse shaping to limit the outofband radiation, which decreases the spectral efficiency. In this paper, RC and RRC filters are employed to pulse shape the SCFDMA signals. The RC filter can be characterized by the rolloff factor and the symbol duration . Then, the impulse response of the RC filter in timedomain can be expressed as
Equation (33) can also be expressed in frequencydomain as
The squareroot of the RC filter output characterizes the impulse response of the RRC filter. Therefore, the impulse response of the RRC filter in frequencydomain can be written as
Consequently, the channel impulse response of RRC filter in timedomain can be represented as
Finally, the distribution of PAPR of the baseband SCFDMA signal is the most practical performance indicator. D. Wulich et al. in [35] have investigated the amplitude of a singlecarrier modulated signal that does not have a Gaussian distribution and it is also hard to deduce analytically the precise form of the distribution. In this paper, we perform numerical analysis to investigate the PAPR properties of SCFDMA signals. For a given threshold value of PAPR , the cumulative distribution function (CDF) can be defined as
where . The complementary CDF (CCDF) of PAPR is the probability that the PAPR of the SCFDMA signal exceeds a given threshold , which can then be expressed as
5.2. Simulation Results and Analysis
The CCDF is taken to represent the statistical probability that the PAPR value of a TBS exceeds a predefined threshold PAPR_{0}. We have considered an NBIoT uplink transmission system for both singletone and multitone transmissions with 180 kHz system bandwidth. Low PAPR modulation schemes like BPSK and QPSK for singletone and only QPSK for multitone transmissions are employed. Total repetitions are employed to calculate the CCDF of PAPR. In addition, the RC and RRC pulse shaping filters with rolloff factor and oversampling factor of 4 are used as transmit filter to limit the outofband radiation. We have compared the PAPR value that is exceeded with the probability less than 0.1 percent (i.e., ) PAPR.
Figure 9 shows the comparison of CCDF of PAPR among no pulse shaping, RC, and RRC pulse shaping for singletone transmission with BPSK modulation. In this case, both 15 kHz and 3.75 kHz subcarrier spacing types are considered. As shown in Figure 9(a), it is observed that the 0.1 percent or 99.9 percentile PAPR of 15 kHz subcarrier spacing using RRC filter are approximately 1.3 and 0.4 dB less compared to the no pulse shaping and the RC filter, respectively. On the other hand, 3.75 kHz subcarrier spacing with RRC filter as depicted in Figure 9(b) shows about 1.3 and 0.21 dB less PAPR value at 0.1 percent of CCDF than without pulse shaping and RC filter, respectively. Figure 10 shows the comparison of CCDF of PAPR with and without pulse shaping for singletone transmission employing QPSK modulation. It can be seen that the PAPR values for QPSK modulation are higher than the PAPR values evaluated with BPSK modulation in Figure 9 regardless of the subcarrier spacing. The PAPR evaluation results for singletone transmission can be summarized in Table 5.

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The CCDF of PAPR curves with and without pulse shaping for multitone (e.g., 3, 6 and 12tone) transmission employing QPSK modulation are shown in Figure 11. As shown in Figure 11, the PAPR value is increasing as the number of tones increases at the 99.9 percentile of CCDF. Table 6 shows the summery of our evaluations for multitone transmission. Finally, we conclude that the lower values of PAPR by using RRC filter is feasible for NBIoT uplink transmitter, thus requiring very little power backoff to maintain the linearity of the power amplifier.

6. Conclusion
In this paper, we have provided a brief survey of NBIoT technology including deployment options, physical channels and signals, uplink resource grid structure, and resource unit configuration. We have developed a system model for uplink NBIoT based on the 3GPP specifications in release13. An analytical signal model and NDMRS generation and mapping are presented. To guarantee the successful detection of user data (i.e., BER<10^{−1}) in extremely low SNR regime, we have proposed two channel estimation algorithms as a modified form of traditional LS and MMSE estimators. We have investigated the effectiveness of our proposed NDMRSassisted channel estimators compared with others through extensive linklevel computer simulations. The simulation results vindicate that our proposed estimation techniques perform better at the SNR<0 dB compared to the conventional LS and MMSE algorithms and suggesting that the proposed algorithms can be adopted to NBIoT uplink receiver. The improved channel estimation techniques can be applied to not only NBIoT systems, but also in any multicarrier communication systems. Furthermore, we have analyzed and evaluated the PAPR by employing RC and RRC pulse shaping at the transmitter. Through numerical simulations, the PAPR values are evaluated for both singletone and multitone transmissions. Our evaluation results show that the RRC pulse shaping with lower PAPR values is feasible to the actual hardware design of lowcost NBIoT UE. In the future, we will consider carrier frequency offset (CFO) and receiver diversity to improve the system performance in uplink NBIoT systems.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
The authors would like to acknowledge the CASTWAS President’s Fellowship Program. They would also like to thank the Information Science Laboratory Center of University of Science and Technology of China (USTC) for hardware and software services.
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Copyright © 2018 Md Sadek Ali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.