Mobility Enhancement for IEEE 802.15.4 SUN-OFDM Using Channel Estimation and Viterbi Decoder With Likelihood Ratio Adjustment Methods

Wireless smart utility network (Wi-SUN) is one of the wireless communication technologies that realize the Internet of things (IoT). The existing Wi-SUN adopts frequency shift keying compliant with IEEE 802.15.4 for smart utility networks, also known as SUN-FSK, as its physical layer. However, owing to the increased demand for Wi-SUN applications, higher-performance communication methods even in severe fading environments with mobility are required. Orthogonal frequency-division multiplexing compliant with IEEE 802.15.4 is expected to be the most promising candidate for this. Studies on receiving methods have been conducted to accommodate high environment mobility. However, the maximum moving speed of the device is 200 km/h if diversity reception is adopted. In this study, we proposed two channel estimation methods to obtain accurate channel state information (CSI), particularly in a frequency selective fading environment with high mobility using the coherent and linear method. Further, we also proposed a Viterbi decoder with a likelihood ratio adjusted for CSI. Using the proposed channel estimation method and decoder, the required packet error rate of 10% is achieved at a maximum moving speed of 216 km/h by computer simulation. If a two-branch maximum ratio combining antenna diversity is used, the PER is achieved at 720 km/h.


I. INTRODUCTION
Recently, the Internet of things (IoT) technology has been spreading worldwide.There exist different wireless communication methods for realizing the IoT technologies, such as cellular networks, wireless local area network (WLAN), wireless personal area network (WPAN), and low power wide area network (LPWA) [1].These wireless technologies are utilized appropriately depending on the application requirements because each technology has different characteristics.Cellular networks can achieve high throughput.However, they require a core network and cannot build a wireless network autonomously with only the base stations and terminals.WLAN can achieve broadband communication but cannot transmit widely over several kilometers.LPWA can realize a long transmission distance of several kilometers.However, the achievable data rate ranges from several bps to several tens of kbps, and it is not suitable for IoT applications that need to transmit images and video.Moreover, performing firmware update over the air (FOTA) of the IoT devices is difficult.Wireless smart ubiquitous network (Wi-SUN) solves the problems of the aforementioned three systems and enables transmission at several tens of kbps to several Mbps.
Wi-SUN is based on the IEEE 802.15.4g/4x standards [2], [3], which are incorporated into the IEEE 802.15.4-2020 [4].It realizes low power consumption and middle-range transmission rate with several tens of kbps to several Mbps [5], [6], [7].Further, Wi-SUN supports bi-directional multi-hop transmission [5], [8].Particularly in Japan and the United States, the Wi-SUN system is adopted for smart utility systems, and has already been installed in more than tens of millions of devices [9].In 2021, the Wi-SUN for field area network profile (Wi-SUN FAN), which is a mesh wireless standard for applications such as next-generation smart metering and distributed automation, was released [8].It is known as Wi-SUN FAN 1.0, and only the IEEE 802.15.4-compliant smart utility network-FSK (SUN-FSK) modulation is adopted for the physical layer (PHY) because the FSK modulation has a constant amplitude property that permits the use of power efficient amplifiers such as class C amplifiers [5], [10].
Target use cases utilizing IoT technologies have grown rapidly.In [5], assuming a maximum transmission power of 20 mW, Wi-SUN based communications for IoT applications were categorized into the following: 1) wide-area open space communication, 2) wide-area urban area communication, and 3) wide-area mobile communication.Wide-area open-space communication is based on a point-to-multipoint, line-ofsight (LOS), and fixed communication with a coverage area of 1-5 km, whereas wide-area urban area communication is based on a fixed communication with a coverage area of 100 m-2 km in the non-line-of-sight (NLOS) and line-of-sight regions.Wide-area mobile communication is an application that collects sensing data from vehicles and is used for controlling and managing vehicles.It is based on point-to-multipoint, NLOS, and mobile communication with a typical speed of 40-80 km/h and with a coverage area of 100 m-2 km [5], [6].
These applications require high-performance communication abilities such as higher transmission rates, real-time communication, reliability, and mobility under the GSM typical urban (TU) channel model [5], [11].Wi-SUN FAN 1.1 was developed to meet the application requirements [12].To enhance the PHY for high-performance communication, the IEEE 802.15.4g/4x-compliantSUN-orthogonal division multiplexing (SUN-OFDM) is one of the most promising candidates in next-generation Wi-SUN [6], [7], [12].The SUN-OFDM PHY can improve spectrum efficiency and realize high-data-rate communication [6], [7].Furthermore, SUN-OFDM PHY is robust against multipath fading when using training and/or pilot signals, thereby causing its maximum transmission rate to increase to 2.4 Mbps [3], [6], [7].
There have been some reports on SUN-OFDM PHY evaluation [6], [7], [13], [14], [15].The packet delivery ratio (PDR) evaluation was performed using modulation diversity in [13].Based on [13], reliability could be improved by introducing modulation diversity.However, the PDR results of the SUN-OFDM depend on the situation.Evaluation results based on the packet error rate (PER) are presented in [6], [14].Based on [6], [14], when only the long training field (LTF) of the SUN-OFDM PHY option 3 with 400 kHz channel bandwidth is used to estimate the multipath radio channels, the required PER of 10% is not achieved.To improve the PER performance, a receiving method is proposed that uses not only the LTF but also the pilot signals inserted into the transmitter to estimate the radio propagation characteristics [6].Consequently, the maximum moving speed that realizes the PER of 10% is 40 km/h when the SUN-OFDM (option 3, modulation and coding scheme (MCS) 2) is utilized under the GSM TU channel model.However, the proposed method did not support the vehicle speeds of the device considered in [5].To improve the performance, [7] proposed a receiving method that obtains the channel estimates in a similar manner as in [6] along the time axis.However, on the frequency axis, the proposed method obtains the channel estimates by copying the estimates of the neighboring subcarriers based on the coherence bandwidth of the multipath fading channel to update the channel estimates.Consequently, using the proposed receiving method and maximum ratio combining (MRC) antenna diversity, the maximum moving speed of the device that realizes the PER of 10% was 200 km/h under the GSM TU channel model.However, the improvement in the PER characteristics was largely owing to the MRC antenna diversity.Generally, the sizes of the IoT devices are limited.Hence, implementing antenna diversity may be difficult.Further, the improvement was also owing to frequency spreading.However, frequency spreading reduces transmission rate.Thus, other receiving methods have to be formulated to improve the PER performance in a single-input single-output (SISO) environment without reducing the transmission efficiency, even when the moving speed is high.Another study on the SUN-OFDM and mobility was conducted in [15].However, [15] proposed only the carrier frequency offset estimation method, and communication quality evaluations, such as the PER performance, were not reported.
In this study, we propose a receiving scheme that improves the PER performance at low and high speeds exceeding 200 km/h in a SISO environment under the GSM TU channel model.To improve the PER performance, the proposed method comprises two stages: The first stage is channel estimation and the second stage is decoding.
There are many channel-estimation methods for OFDM [6], [7], [16].However, we propose two channel estimation methods to obtain accurate channel state information (CSI), particularly in a frequency-selective fading environment with high mobility.The first method is based on the method proposed in [7], and is known as the coherent and linear method, which linearly interpolates channel estimates for data tones using a coherent method in the time domain.The second method is also based on the coherent method.However, the interpolation of the channel estimates is performed to estimate the channel in the data tone using prior and previous channel estimates in the time domain.
Furthermore, we propose a new decoding method.Coding can improve the communication performance.Convolutional coding-based forward error correction (FEC) is mandatory for IEEE 802.15.4 SUN-OFDM [4].The coded sequences can be decoded using maximum likelihood decoding and Viterbi algorithm [7], [17], [18].Particularly, in coded OFDM (COFDM), a high-performance Viterbi decoder can be constructed using CSI in a frequency-selective fading environment [19], [20], [21], [22].Additionally, we also propose a likelihood ratio (LLR) method adjusted for the CSI to improve the PER performance, particularly when the moving speed is low.The proposed method reduces the effects of the channel-estimation errors by investigating the error patterns of the proposed channel-estimation methods.To the best of our knowledge, no study has examined the improvement of the transmission characteristics of the IEEE 802.15.4 SUN OFDM by proposing new channel estimation methods and LLR methods and integrating them.The main contributions of this study are as follows: r We comprehensively investigated the PER performance using existing channel estimation schemes and a Viterbi decoder with its estimated CSI.
r We proposed two new channel-estimation methods that obtained CSI even in a frequency-selective fading environment with high mobility.These methods are less complex and require less memory than conventional methods.Further, the proposed channel estimation methods are suitable for SISO and single input and multiple output (SIMO) environments.
r A new LLR adjustment method to improve the PER performance is proposed.This adjustment was effective when the time variation in the propagation channel was small.
r We evaluated the PER performance using antenna di- versity, the different proposed channel estimation methods, and decoders using the proposed LLR adjustment method if antenna diversity could be utilized.
r Using the proposed method, it is possible to support the terminal movement of 200 km/h in a GSM TU environment without changing the current standard system and without using receiver diversity.When receiver diversity is used, the proposed method can support the terminal movement of up to 720 km/h.The scheme proposed in this article can finally achieve the goal that could not be achieved in previous studies.The remaining part of this study is organized as follows: Section II describes an overview of the IEEE 802.15.4compliantSUN-OFDM and provides the configuration of the transmitter and receiver, including the decoding schemes.Section III describes the conventional and proposed channel estimation methods.Section IV describes the proposed LLR adjustment method for the Viterbi decoder with CSI.Section V shows the PER evaluation performance when the propagation channels have time-varying and frequencyselective characteristics.Section VI concludes the study.

II. SUN-OFDM COMPLIANT WITH IEEE 802.15.4
In this section, we provide an overview of IEEE 802.15.4gcompliantSUN-OFDM [4].

A. GENERAL TRANSMITTER CONFIGURATION
The IEEE 802.15.4-compliantSUN-OFDM (hereinafter referred to as SUN-OFDM) has attracted considerable attention as a physical layer scheme candidate for next-generation Wi-SUN because it tolerates fading (caused by high-speed terminal movement) and has a higher transmission rate than SUN-FSK [5], [6].The SUN-OFDM supports four options.The channel spacing of the SUN-OFDM Option 3 is similar to the SUN-FSK Mode 2, a mode globally utilized in the current Wi-SUN system [5].In this study, evaluations and technical proposals were made based on the SUN-OFDM Option 3 for comparison with the SUN-FSK Mode 2. Tables 1 and 2 present the main parameters of the SUN-OFDM Option 3 and SUN-FSK Mode 2, respectively [4].The subcarrier spacing of the SUN-OFDM is constant at 10416-2/3 Hz for all the options.Each option has seven patterns of modulations and coding schemes (MCS).The cyclic prefix (CP) length is constant at 24 μs in any option.Contrary to the SUN-FSK, the FEC is mandatory for the SUN-OFDM.The applied FEC is a convolutional encoder with generator polynomials expressed in an octal representation [133,171] with a constraint length of 7 [4].Fig. 1 shows the pilot allocation for the SUN-OFDM Option 3. Here, a scattered pilot allocation is adopted.In Option 3, the pilot pattern is repeated for every seven OFDM symbols.Channel estimation is performed using the pilot signals and a long training field (LTF) comprising two OFDM symbols.Fig. 2 shows the configuration of the transmitter of the SUN-OFDM.In Fig. 2, the short training field (STF) generator and physical layer packet header (PHR) generator are omitted because we assume that synchronization has been performed perfectly.

B. GENERAL RECEIVER CONFIGURATION AND DECODING SCHEMES 1) GENERAL RECEIVER CONFIGURATION
Fig. 3 shows the general configuration of the SUN-OFDM receiver.We assume that the synchronization is performed perfectly in this study; hence, the synchronization procedure is   omitted from Fig. 3.After applying the FFT, channel estimation and equalization are necessary to demodulate and decode the signals.The channel estimation shown in Fig. 3 comprises two steps.First, the propagation channels at the LTF and pilot signals are estimated.Further, using these estimated propagation channels, the channel interpolation or extrapolation is performed to obtain the estimated channel at the data tones.The communication performance is considerably influenced by channel interpolation.Channel equalization is performed using the estimated channel, followed by subcarrier demapping and deinterleaving.Finally, the interleaved data are inputted into the decoder.

2) DECODING SCHEMES
Here, we describe the decoding method for the convolutional codes in detail.There are several methods for decoding the convolutional code.The maximum a posteriori probability (MAP) decoder using the BCJR algorithm can minimize the bit error rate [23].MAP decoder requires forward and backward recursion, branch transition probability, and loglikelihood ratio (log-LLR) calculations to decode the received bits [24].However, this algorithm requires considerable amounts of storage and calculation.The soft output Viterbi algorithm (SOVA) can considerably reduce the computational complexity of the MAP decoder [24], [25] by omitting the backward recursion calculation in the MAP decoder.
Another method for decoding the convolutional codes is the Viterbi decoder using the Viterbi algorithm (VA).The difference between the SOVA and VA lies in the calculation of the metric [25].A Viterbi decoder is known as a maximum likelihood decoder because it is intended to find a sequence that maximizes the likelihood [17], [18], [19], [20], [21], [22], [23].When binary source symbols exist with equal probabilities, the Viterbi decoder can minimize the bit error probability [17], [23].Conversely, if the likelihoods of the binary source symbols are not equal, the performance of the Viterbi decoder is worse than that of the MAP decoder.However, because the performance degradation is not considerable [23] and the Viterbi decoder can easily realize the maximum likelihood decoder, it is often utilized.A Viterbi decoder was used in this study.

3) NORMAL VITERBI DECODER
The goal of the Viterbi decoder is to find the sequence that is transmitted with the highest likelihood when sequence r is received as follows: where ŝ and s μ represent the estimated and candidate transmission sequences, respectively.In the maximum likelihood decoder, the size relationship must be maintained because the decoding result is the sequence with the largest likelihood.Thus, to simplify the calculation, log-likelihood is used in the metric calculation.When i represents the branch index, the log-likelihood is calculated as follows: Here, N denotes the number of the code symbols.The log-likelihood changes the branch metric calculation from a product operation to a summation operation.
In the additive white Gaussian noise (AWGN) channel, the distribution density function of the reception data for transmitted data s i and received data r i are expressed as follows: where N 0 is the spectral density of the Gaussian noise.The log-likelihood metric, L(r|s μ ), can be calculated using (3) as follows: (4) Here, we need to find a sequence that maximizes L(r|s μ ).However, as mentioned previously, it is sufficient for the metric calculations if the size relationship is maintained.Hence, the terms log(1/ √ π N 0 ) and r 2 i /N 0 can be ignored because they do not depend on the candidate transmission sequences.Additionally, the term s 2 iμ /N 0 can be ignored because s 2 iμ is a constant.( 4) can be rewritten as follows: ( The negative sign is omitted in (5) because it is sufficient to find the sequence that maximizes (−r i s iμ ).The convolutional code is decoded by computing the metric as expressed in (5).

4) VITERBI DECODER WITH CSI
The metric calculation in (5) can be used to decode the convolutional codes.In (5), the metric for each branch is calculated with equal reliability.However, if the received signal is considerably attenuated by fading, the signal-to-noise power ratio (SNR) decreases.However, if the received signal power increases owing to fading, the SNR increases.In other words, it is very important to introduce CSI into the metric calculation.
[19], [20], [21], [22] showed that the Viterbi decoder can be rewritten to utilize the CSI as follows: where |h i | 2 denotes the channel gain of the ith path branch.This Viterbi decoder is referred to as the Viterbi decoder with CSI.
When the MRC antenna diversity is applied, the metric calculation of the Viterbi decoder with CSI is expressed as follows: where denotes the channel gain of the ith path branch of the jth antenna and J the total number of branches in the antenna.Further, the output SNR of MRC is expressed as ).

III. PROPOSED CHANNEL ESTIMATION METHOD
As discussed in Section II, improving the accuracy of the channel estimation is important for improving the quality of the SUN-OFDM demodulation and decoding, particularly in frequency-selective fading environments with high mobility.
In this section, we describe conventional general channel estimation methods.Further, we propose a channel estimation method applicable to the SUN-OFDM, particularly for highspeed terminal mobility.Hereafter, the estimated channels at the mth subcarrier of the lth OFDM symbol are defined as h(m, l ).

A. CONVENTIONAL METHOD 1
The conventional method 1 (CM1) [6] estimates the channel at the data symbols by interpolation using sequential processing without the memory.First, the average of the channels estimated in both LTF symbols is copied to the first PSDU symbol, excluding the pilot symbol, as follows: where h LTF (m , 1) and h LTF (m , 2) are the estimated channels for the first and second LTF symbols, respectively.The channel at the data symbols of the odd subcarriers is later expressed as follows: Here, channel copying is referred to as the zeroth-order interpolation.Channel estimation at the even subcarriers of the data symbols is further expressed as follows:

B. COHERENT METHOD (CONVENTIONAL METHOD 2)
The coherent method (conventional method 2, CM2) [7] also estimates the channel at the data symbols by interpolation using sequential processing without the memory.In a multipath environment, the relationship between the delay spread and coherent bandwidth is expressed as follows: where BW 90 and τ rms refer to the coherent bandwidth with channel correlation exceeding 90% and delay spread, respectively.For example, in the GSM TU channel model shown in Table 3, the delay spread is 1.06 μs.Hence, the BW 90 is calculated as 18.8 kHz.CM2 uses this coherent characteristic in the frequency domain for channel estimation.When the m th subcarrier of the l th OFDM symbol is a pilot symbol, the estimated channel at this pilot symbol is used as the estimated channel of the data symbols from the (m − C)th subcarrier to the (m + C)th subcarrier as expressed below: where C is the copy width.If the copy width value is too large compared to the coherent bandwidth, the accuracy of the channel estimation on the subcarriers far from the pilot symbol deteriorates.In this study, the copy width was set to two, assuming a GSM TU [14].The estimated channel for the other data symbols is calculated by copying the estimated channel for the previous data symbol in the time domain (zeroth-order interpolation), as shown in (9).Here, the average of the channel estimated in both LTF symbols is copied to the first PSDU symbol, excluding the pilot symbol, similar to the CM1.

C. LINEAR METHOD (CONVENTIONAL METHOD 3)
In the linear method (conventional method 3, CM3), the channel at the data symbols is calculated by linearly interpolating the estimated channel at the pilot symbols.Because SUN-OFDM adopts a scattered pilot allocation, as shown in Fig. 1, linear interpolation is performed only in the time domain.The channel for the odd subcarriers is expressed as follows: where the m th subcarrier of the l th OFDM symbol is the pilot symbol.The channel estimation at even subcarriers and data tone is calculated using (10).Here, the average of the channel estimated in both LTF symbols is copied to the first PSDU symbol, excluding the pilot symbol, similar to the CM1.

D. PROPOSED METHOD 1
The proposed method 1 (PM1) is a combination of the coherent (CM2) and linear methods (CM3).Fig. 4 shows the channel estimation process for the PM1.First, the average of the channel estimated in both LTF symbols is copied to the first PSDU symbol, excluding the pilot symbol, as shown in (8).Further, each channel at the pilot symbol is estimated using the pilot symbol.Furthermore, the estimated channel at the pilot symbol is copied to the adjacent subcarriers using coherent characteristics (the red channel shown in Fig. 4).Finally, a linear interpolation is performed in the time domain (blue arrow in Fig. 4).

E. PROPOSED METHOD 2
The proposed method 2 (PM2) introduces the zeroth-order interpolation in the time domain to CM2 to account for the time coherence.Fig. 5 shows the channel estimation process for PM2.Three consecutive OFDM symbols are defined as the search range.For example, in the search range shown in Fig. 5, the central symbol is the 4th OFDM symbol.The procedure for measuring PM2 is as follows:

1) STEP 1: CHANNEL ESTIMATION WITH PILOT AND LTF
Assume that the central symbol of the search range is the l th OFDM symbol, and m l is the subcarrier number of the pilot symbol of the l th OFDM symbol.If the center OFDM symbol in the search range is the first OFDM symbol (l = 1), the channel at the LTF and pilot symbols at the first and second OFDM symbols are calculated.If the center OFDM symbol in the search range is not the first OFDM symbol (l = 1), the channel at subcarrier number of m l +1 (the channel at the pilot signal) is calculated (green channel shown in Fig. 5).
2) STEP 2: CHANNEL COPYING If the center OFDM symbol of the search range is the first OFDM symbol (l = 1), the copying process according to ( 12) is performed on the first and second OFDM symbols (red channel in Fig. 5).If the center OFDM symbol of the search range is not the first OFDM symbol (l = 1), the copy procedure using (12) in the l + 1)th OFDM symbol is performed (red-colored channel shown in Fig. 5).

3) STEP 3: CHANNEL INTERPOLATING
The channel of the l th OFDM symbol is interpolated using the zero-order interpolation.The closest pilot symbol is used for the interpolation.If the center OFDM symbol in the search range is the first OFDM symbol (l = 1), the channel of the data symbol that has not been calculated by channel copying is interpolated using the channel calculated by the LTF (zeroth-order interpolation).If the center OFDM symbol in the search range is not the first OFDM symbol (l = 1), the channel of the data symbol that has not been calculated by channel copying is interpolated from the adjacent symbols using the copied channel.Let m l denote the mth subcarrier in the (l th OFDM symbol (m l ∈ {1, 2, 3, . . ., 13, −1, −2, −3, . . ., −13}, / ∈ {m l − 2, m l − 1, m l , m l + 1, m l + 2}).At this time, the channel interpolation is performed based on the following three rules: r Rule 1: If the channels of two adjacent OFDM symbols in the m l th subcarrier are not copies, the channel in the m l th subcarrier is interpolated by copying the channel of the previous symbol (purple arrows in Fig. 5).
r Rule 2: If only one of the channels of the adjacent OFDM symbols is a copy, the channel of the m l th subcarrier is interpolated by copying the channel of the previous symbol (blue arrows in Fig. 5).
r Rule 3: If both channels of both adjacent OFDM symbols in the m l th subcarrier are copies, the channel in the m l th subcarrier is interpolated using the channel in the most adjacent pilot symbol.In the case of |m l − m (l−1) | = |m l − m (l+1) |, the channel of the m l th subcarrier is interpolated by averaging the adjacent channel data as (m l −1 + m l +1 )/2(green arrows in Fig. 5).

IV. PROPOSED ADJUSTMENT FOR VITERBI DECODER USING CSI
To improve the accuracy of the channel estimation and quality of the SUN-OFDM demodulation and decoding, several channel estimation schemes were proposed in the previous section.In this section, to further improve the quality of the SUN-OFDM demodulation and decoding, we propose the LLR adjustment method provided to the Viterbi decoder using CSI.

A. RECONSIDERATION OF VITERBI DECODER USING CSI
To propose the LLR adjustment method for the Viterbi decoder using CSI, we study the Viterbi decoder with CSI in more detail than in [19], [20], [21], [22] using mathematical formulas and simulations, with the aim of using it for the SUN-OFDM decoding.By rechecking ( 5), the symbols received in COFDM are equalized.Hence, we rewrite (5) using the estimated channel h i , actual transmitted data s i , and AWGN as follows: Because the estimated channel is calculated by interpolation, it has a channel-estimation error e i .Hence, we rewrite (14) as follows: where h i /(h i + e i ) and n i /(h i + e i ) are the channel estimation error function (CEF), E c (h i ), noise error function (NEF), E n (h i ), respectively.If the SNR is sufficiently large and the channel is perfectly estimated, NEF can be ignored, and the CEF can be calculated as h i /(h i + e i ) = 1.Channel-estimation errors can be classified into two types.One is a pattern wherein the absolute value of the channel estimation error function is smaller than 1 This pattern is known as under-equalization (UDE).In the other pattern, the absolute value of the CEF is larger than 1 (|h i + e i || < |h i |).This pattern is known as over-equalization (OVE).Fig. 6 shows examples of the UDE and OVE when QPSK is employed.In the case of UDE, the value of the metric is very small.A very small metric is equivalent to a data puncture on the receiver side.However, the metric value in the case of OVE is very large, thereby making the metric calculation inaccurate.Fig. 7(a) shows the absolute value of the CEF |E c | as a function of the absolute value of the channel |h i | when the parameters presented in Table 4 are used.Note that, since the packet length of 250 octets is defined in IEEE 802.15.4-2020 as the packet length for testing receiver sensitivity, this article also uses the packet length of 250 octets.The GSM-TU [27],

TABLE 4. Parameters Utilized for Channel Estimation Error Function
shown in Tables 1 and 3, and the PM2 proposed in Section II-I-E, were applied as the channel model and channel estimation method, respectively.When |h i | is large, |E c | is approximately one.However, when |h i | is small, we observe very large and very small |E c |.The OVE and UDE occur when |E c | is large and small, respectively.The possibility of inaccurate metric calculation results is high when |E c | is large owing to the occurrence of OVEs.Fig. 7(b) shows the absolute value of the CEF multiplied by the channel gain |E c ||h i | 2 as a function of |h i |.By multiplying the channel gain (i.e., CSI), the effect of the OVE can be suppressed when the absolute value of the channel is small.However, when |h i | was large, |E c ||h i | 2 was also large.Generally, if the channel gain |h i | 2 is large, the SNR will also be high, and the channel estimation error will be smaller.In other words, multiplying by the channel gain is similar as weighting the metric based on the reliability of the Viterbi decoder using the CSI.

B. PROPOSED LIKELIHOOD ADJUSTMENT FOR VITERBI DECODER WITH CSI
The Viterbi decoder with CSI can improve communication performance using channel gain.However, we can still determine the effect of the OVE even after multiplying it by the channel gain, as shown in Fig. 7(b).When a large metric is generated on low-reliability data, the decoding performance degrades.To prevent the effect of the OVE, we propose a likelihood adjustment method for a Viterbi decoder with CSI.

TABLE 5. Parameters for Simulation
First, the likelihood calculated based on ( 5) is input into the likelihood adjustment function f (x).Here, the likelihood adjustment function must converge in both the positive and negative directions, and in particular, must converge to zero in the positive direction to suppress the effect of the OVE.As a likelihood adjustment function with such properties, the proposed method selects a complementary error function as expressed below: where x denotes the input value of the branch metric.The complementary error function can approach the staircase functions by increasing the value of a. Introducing the likelihood adjustment function, which can reduce the extremely large metric value to zero, can suppress the effect of the OVE.Only large positive metric values owing to the OVE are compensated for by the likelihood adjustment function.If the input value of the likelihood adjustment function is smaller than b, the output of the likelihood adjustment function is one (in other words, the input and output are similar).
In the Viterbi decoder, the path with the largest metric value is selected.Compensation for the metric calculation in the negative direction has little effect on the path selection.Thus, the adjustment of the path metric in the negative direction has a small impact on communication performance.Finally, the output metric value is multiplied by the channel gain |h i | 2 .

V. PERFORMANCE EVALUATION
In this section, PER performance evaluations are performed using computer simulations to demonstrate the effectiveness of the proposed channel estimation method and proposed likelihood adjustment method for the Viterbi decoder with CSI.For computer simulation, MATLAB codes for the transmitter and receiver of the OFDM were originally developed based on [20].The simulator was validated in [5] by comparing the PER in an AWGN environment with results reported in other publications [14], [29], [30].

A. CHANNEL MODEL AND PARAMETERS
Tables 1 and 5 present the parameters used in the evaluation.For a Wi-SUN system compliant with the SUN-OFDM Option 3, the bandwidth is 400 kHz [4].Hence, we assume a noise power of -118 dBm at room temperature.The center frequency was set to 920 MHz.According to ARIB STD-T108 [31], which defines the requirements for using 920 MHz bands in Japan, the required carrier sense level is -80 dBm.The scope of this article is focused on the extent to which the terminal movement speed can be improved, and coverage is not considered.Therefore, the target received signal power was fixed at -80 dBm, while the target SNR was set to 38 dB (E b /N 0 = 41.4 dB).The channel model used was GSM TU with multipath fading channels.The evaluation was reproducible because a sufficient number of trials were used to ensure that the amplitude of each delay path followed a Rayleigh distribution and that the phase followed a uniform distribution.Additionally, IEEE 802.15.4g/4x specifies the receiver requirements in terms of receiver sensitivity.The required receiver sensitivity in the SUN PHY is the received power that satisfies PER <10% when the PSDU length and data rate are 250 octets and or higher, respectively [2].Thus, the PSDU length was set to 250 octets.

B. PERFORMANCE EVALUATION OF DECODING AND CHANNEL ESTIMATION METHODS
Figs. 8 and 9 show the PER as a function of the moving speed for different channel estimation methods employing the Viterbi decoder and Viterbi decoder with CSI.When using normal Viterbi decoding, the channel estimation method with the highest moving speed that can achieve PER <10% is the linear method (CM3).However, when using the Viterbi decoding with CSI, the maximum moving speed that can achieve PER <10% is smaller than those of the coherent method (CM2), PM1, and PM2.This is because the channel fluctuation is not linear when the received signal is considerably attenuated.The use of the CM3 results in a large channel estimation error, particularly when the moving speed is high.
When CM2, PM1, and PM2 were used as channel estimation methods, when the moving speed was low (approximately 50 km/h or less), the PER performance of a normal Viterbi decoder was worse than when using CM1 and CM3.In a GSM TU environment with frequency-selective fading, the channel error owing to copying in the frequency domain is larger than that owing to interpolation in the time domain when the moving speed is not very fast.Hence, the characteristics of CM2, PM1, and PM2, which are the channel estimation methods that use coherent characteristics in the frequency domain, are degraded.However, when the Viterbi decoder with CSI is applied, the PER with CM2, PM1, and PM2 is better than that with CM1 and CM3 because CSI reduces the effect of the OVE.When using Viterbi decoding with CSI, CM3 performed best in low-speed fading.However, during high-speed fading, PM2 performed the best.

C. PERFORMANCE EVALUATION OF PROPOSED LIKELIHOOD ADJUSTMENT FOR VITERBI DECODER WITH CSI
In this section, we evaluate the performance of the proposed likelihood adjustment for a Viterbi decoder with CSI.First, the appropriate parameters (a and b in ( 16)) were determined via computer simulations.Further, the PER of the proposed scheme with the appropriate parameters was evaluated.

1) APPROPRIATE PARAMETER
First, we searched for the best parameters in (16).We evaluated the PER performances of seven complementary error functions, as shown in Fig. 10.Because the QPSK modulation is applied in this study, we can find max(s i s iμ ) = 1/2 if the transmission power is normalized to one.In the simulation, the speed was set to 45 km/h.Table 6 presents the PER when seven complementary error functions are utilized for the proposed likelihood adjustment.Consequently, we determined the parameters as a = 2 and = 3/2 , with the PER showing the best results.In the case of PM1 and PM2, the PER characteristics with the likelihood adjustment were better than those without the LA at all moving speeds.The improvement was particularly significant at speeds below approximately 100 km/h.However, CM2 did not show any improvement in the PER owing to the likelihood adjustment.The channel update frequency in CM2 is not large as compared to PM1 and PM2.Further, because the time-varying tracking limitation is the main cause of the PER performance degradation, we can consider that there is no likelihood adjustment effect when CM2 is applied.
Table 7 summarizes the maximum moving speeds that achieved a PER <10% for each method.By combining the proposed channel estimation method with the likelihood adjustment, a maximum moving speed of 216 km/h was achieved without antenna diversity or frequency spreading.This value means that the Wi-SUN will be able to communicate with mobile terminals such as high-speed railroads and European highways.

D. PER EVALUATION USING ANTENNA DIVERSITY
We evaluated the PER performance when using the twobranch receiver antenna diversity with the MRC.The PER performance of the coherent scheme (CM2), PM1, and PM2.Fig. 12 shows the PER performance of the normal Viterbi decoder, Viterbi decoder with CSI, and Viterbi decoder with CSI and likelihood adjustment as a function of the moving speed when antenna diversity is applied.

VOLUME 4, 2023
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.For any channel estimation method, the improvement in the Viterbi decoder with CSI can be confirmed.This implies that OVEs are generated if antenna diversity is utilized.This shows that it is important to introduce CSI into the calculation of the metric.
Next, we compared channel-estimation methods.The PER performance of PM1 was better than that of PM2.The reasons for this are discussed below: If the received signal is severely attenuated by fading, the channel fluctuation cannot be considered to be linear, thereby resulting in a larger channel estimation error.However, if the received signal power increases owing to fading, the channel estimation accuracy by linear interpolation improves.As the number of antennas increased, the probability of significant signal attenuation at all the branches decreased.Therefore, linear interpolation is considered an effective channel-estimation method when antenna diversity is employed.
Table 8 summarizes the maximum moving speeds that achieved a PER <10% for each method when MRC was applied.By applying the proposed channel estimation method (PM1) to a Viterbi decoder with CSI, a maximum moving speed of 720 km/h can be achieved without frequency spreading.

VI. CONCLUSION
In this study, we proposed two channel estimation methods to obtain an accurate CSI in a frequency selective fading environment with ultra-high-speed mobility (≥100 km/h).Further, we proposed a LLR adjustment method for low-speed mobility (<100 km/h) for next-generation Wi-SUN systems by employing SUN-OFDM.One of the proposed channel estimation methods (PM1) is a combination of the coherent method (CM2) and linear method (CM3).The second proposed method (PM2) considers temporal coherence and introduces the zero-order interpolation in the time domain of the CM2.Computer simulations were performed to evaluate the proposed methods.PM1 was particularly effective for MRC implementation using multiple receiving antennas, whereas PM2 was particularly effective for single-antenna reception.The Viterbi decoder with the proposed LLR adjustment method with CSI obtained by PM1 and PM2 can achieve the required PER of 0.1 at a maximum of 216 km/h when one receiving antenna is used, and at a maximum of 720 km/h when two receiving antennas are used for the MRC.The results of this study show that the Wi-SUN based on the IEEE 802.15.4 can provide sensing information to and from bullet trains, and can collect sensing information from automated vehicles and control them remotely.New applications of the Wi-SUN system will be considered based on this study.

6 .
Example UDE and OVE using QPSK modulation.

FIGURE 7 .
FIGURE 7. Relationship between the absolute value of the channel estimation error function and channel.

FIGURE 8 .
FIGURE 8. PER characteristics of the normal viterbi decoder using different channel estimation methods.

FIGURE 9 .
FIGURE 9. PER characteristics the viterbi decoder with CSI using channel estimation methods.

FIGURE 10 .
FIGURE 10.Complementary error functions with different parameters.

TABLE 6 . PER Performance Using Different Complementary Error Functions FIGURE 11. PER characteristics decoding viterbi decoder with CSI likelihood adjustment.
2) PER EVALUATION WITH LIKELIHOOD ADJUSTMENT Fig.11shows the PER performance of the Viterbi decoder with CSI and proposed likelihood adjustment (LA).For reference, the results of the Viterbi decoder with CSI and without likelihood adjustment are shown.As channel estimation schemes, we use the coherent scheme (CM2), PM1, and PM2, which have a high mobility tolerance.