# Mixed-Numerology Channel Division for Wireless Avionics Intracommunications

Authors: Xianghui Fan; Shining Li; Wen Cui; Pu Yang; Changsheng Chen; Guan-Long Huang
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Increasing attention has been paid to the wireless avionics intracommunications (WAIC) on aircraft. The frequency band of 4200-4400 MHz is recommended to WAIC by the International Telecommunication Union Radio Communication Sector (ITU-R), which thereby comes with a new challenge of using the available frequency band effectively to cater for the massive communication needs in aircraft. To address this challenge, we propose the first channel design framework named mixed-numerology channel division (MNCD) specifically for WAIC. Furthermore, a general interference model has been proposed to better utilize the recommended frequency band. Extensive evaluations show that the proposed framework can be a promising solution for massive wireless communications in aircraft.


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## Body

## 1. Introduction

Current intracommunication system design for aircraft is dominated by cable-based communications. Although promising so far, this system design can be an obvious bottleneck for the next-generation aircraft which pursues less weight, high flying safety, and low maintenance cost. In particular, cables are heavy, which means more carbon footprints and uneconomical for commercial flights; furthermore, the plug-in-plug-out process of the cable is onerous and can be dangerous when the outlet is damaged unnoticed; at last, cables have introduced unbearable maintenance costs [1]. Many work have been presented to bring wireless communications as a solution to solve this problem [2, 3]; however, without the systematic top-down design from both the government agencies and industry partners, it can be inaccessible to implement the wireless solutions to practical aircraft intracommunication systems. Fortunately, an emerging technology named wireless avionics intracommunications (WAIC) was aimed at addressing this pressing issue by connecting the on-board systems in aircraft via short-range wireless communications [4–6]. More importantly, the International Telecommunication Union (ITU) and its partners officially recommended the frequency band of 4200-4400 MHz for WAIC applications in 2013 [1], and henceforth, there have been tremendous attentions from both industries and academics in replacing most of the heavy and expensive cables inside aircraft.Several past works have demonstrated the feasibility of implementing the WAIC on the newly recommended frequency band of 4200-4400 MHz. Specially, Raharya and Suryanegara [7] and Engelbrecht et al. [8] investigated the interference between the WAIC and radio altimeters on the 4200-4400 MHz band. Park and Chang [9] analyzed the performance of three typical industrial wireless networks, namely, low latency deterministic networks (LLDN) [10], wireless highway addressable remote transducers (HART) [11], and wireless interface for sensors and actuators (WISA) [12], when applying these networks on the WAIC recommended frequency band. Aerospace Vehicle Systems Institute (AVSI) [13] has announced a communication protocol based on IEEE 802.11a and IEEE 802.15.4. Although promising, their research was limited to a specific WAIC application and can hardly be extended. To see it more clearly, ITU has recommended vast avionics applications for WAIC systems as shown below; a limited design goal may prohibit the system to be truly implemented [13], i.e.,
(1)
High data rate communications, e.g., 300 Mbps, for high uplink peak data rates;(2)
Low data rate communications, e.g., 10 Kbps, for low uplink peak data rates;(3)
High reliability communications for ultralow latency and high reliabilityHowever, it is nontrivial to design a solution for all the mentioned applications, e.g., high transmission rates, low latency, high reliability, and ultraintensive scenarios at the same time. Until recently, a few works are working towards to this end. In particular, the most relevant work reported in [14] proposed a solution of transplanting the IEEE 802.11a protocol and the IEEE 802.15.4 protocol together to the targeted 4.2 GHz frequency band, catering for the high data rate and low data rate applications, respectively. It is foreseeable that simple protocol transplantation from existing work may cause unexpected problems in practice. To be specific, for IEEE 802.11a [15], the maximum transmission rate is only 54 Mbps, far from achieving the high data rate requirement of WAIC systems, i.e., 300 Mbps. By transplanting IEEE 802.11a, the valuable frequency band would have to be divided into small bands, thereby resulting in more wasted spectrum caused by the guard bandwidth between neighbor bands. For IEEE 802.15.4, it brings very low spectrum efficiency which makes it difficult to satisfy the communication need for high-density sensor nodes in aircraft.To fill this gap, in this paper, we propose a mixed-numerology channel division (MNCD) architecture for WAIC systems. The MNCD architecture is designed specifically for practical WAIC applications, in terms of various data rates, communication latency, and reliability. To conclude, the contributions of this paper can be summarized as follows:(1)
To the best of our knowledge, this is the first mixed-numerology-based channel design for WAIC systems to enable diverse avionics applications(2)
In the mixed numerologies, a general interference model is proposed particularly for aircraft scenarios. The proposed interference model is essential in determining key wireless communication parameters, e.g., cyclic prefix duration, frame length, subcarrier spacing, and the number of subcarriers(3)
Extensive evaluations have been conducted to evaluate the performance of the proposed methodThis paper is organized as follows: The preliminary of the MNCD architecture is introduced in Section2. In Section 3, the interference model is presented and the design of the waveform from a latency perspective is discussed. In Section 4, simulation results are illustrated and analyzed, as well as the parameter settings of MNCD. We conclude our work in Section 5.


## 2. Materials and Methods

### 2.1. Preliminaries

To begin with, after a careful examination of current avionic applications, we conclude that there are three critical communication services that need to be fulfilled: first, high data rate services that support up to 300 Mbps uplink peak data rates; second, aviation control services that require latency below 2 ms and high reliability; and third, dense sensing services that are constructed by massively deployed sensors, i.e., up to hundreds of devices per aircraft [6]. In summary, the goal of this paper is to propose a communication architecture that can fulfill all the mentioned critical services. To achieve that goal, straightforwardly, we divide the available 200 MHz bandwidth into three independent subbands and assign each subband with different numerologies based on the cyclic prefix-orthogonal frequency division multiplexing (CP-OFDM) technique. We plot the bandwidth division in Figure 1. To implement this design in practice, however, is a nontrial task, and we elaborate the challenges as follows.Figure 1
Three different numerologies in WAIC system.OFDM was proposed by Chang [16] and Saltzberg [17] in the 1960s and has been widely adopted by the most popular wireless communication standards, e.g., 5G and Wi-Fi 6, because of its tempting advantages, i.e., high spectrum efficiency and low implementation complexity. Moreover, wireless signals in genuine can easily be disturbed by channel environments; even human movements can affect the signal strength greatly [18], while OFDM signals are robust to channel variations [19]. Hence, we use OFDM as the fundamental building block in our design.To harness OFDM signals in our design, several practical challenges have to be addressed. Specifically, as a parallel signal transmission scheme, OFDM signals usually have high peak-to-average power ratios (PAPRs), which come from the nonlinear characteristics of power amplifiers (PAs) in communication systems. Furthermore, OFDM signals are composited by sinc-shaped subcarriers that are vulnerable to Doppler effects, resulting in high out-of-band (OOB) radiations. As a result, mishandling of the mentioned problems would severely degrade the communication performance and waste the spectrum. To this end, we present four major settings for OFDM signals, as these settings play direct influences on the communication performance. A better understanding of these settings would lead to an optimized design for intracabin wireless communication systems.


#### 2.1.1. First, the CP Duration

The CP duration is a critical parameter for OFDM systems [20, 21], owning to its capability in reducing the intersymbol interference (ISI) and increasing the robustness against the multipath effect when complicated channel environments are involved. Moreover, CP is an inseparable part of signal offsets estimation, synchronization, and channel estimation which matter greatly to the reception of RF signals. However, a poorly designed CP duration is harmful as a prolonged CP duration degrades the spectrum efficiency and introduces high latency, while a shortened CP duration increases the decoding error rate due to the unsolved ISI.


#### 2.1.2. Second, the Frame Length

For WAIC systems, many critical aviation-control-messages require low communication latency, which is enabled by a short frame length, while a communication system with many frames in a shorter length would saturate the whole system given a much lower spectrum efficiency and higher burden in frame processing. Therefore, to satisfy the latency requirement as well as to avoid the system saturation, the frame length needs to be carefully designed for WAIC systems.


#### 2.1.3. Third, the Subcarrier Spacing

The subcarrier spacing is closely related to the CP duration—shorter subcarrier spacing requires shorter CP duration and vice versa. Specifically, shorter subcarrier spacing is preferred for high spectrum efficiency and high data rate services. Meanwhile, larger subcarrier spacing relates to lower PARPs which make the communication system immune from ISI. To this end, a detailed channel model with respect to aircraft features is needed in order to obtain a suitable subcarrier spacing in practical systems.


#### 2.1.4. Fourth, the Number of Subcarriers

A high transmission rate deeply relies on operating bandwidth. Given settled subcarrier spacing, to increase the operating bandwidth, the number of subcarriers has to be increased, but higher PAPRs will be introduced as well due to more parallel transmitted signals. Therefore, to achieve a higher transmission rate and remain low PARPs, the number of subcarriers needs to be well-addressed.Overall, to address all the above-mentioned issues, in this paper, we discuss these four parameters, in terms of data transmission rate, reliability, and latency, in simulated aircraft environments, and we design different numerologies based on the analysis results.


## 2.1. Preliminaries

To begin with, after a careful examination of current avionic applications, we conclude that there are three critical communication services that need to be fulfilled: first, high data rate services that support up to 300 Mbps uplink peak data rates; second, aviation control services that require latency below 2 ms and high reliability; and third, dense sensing services that are constructed by massively deployed sensors, i.e., up to hundreds of devices per aircraft [6]. In summary, the goal of this paper is to propose a communication architecture that can fulfill all the mentioned critical services. To achieve that goal, straightforwardly, we divide the available 200 MHz bandwidth into three independent subbands and assign each subband with different numerologies based on the cyclic prefix-orthogonal frequency division multiplexing (CP-OFDM) technique. We plot the bandwidth division in Figure 1. To implement this design in practice, however, is a nontrial task, and we elaborate the challenges as follows.Figure 1
Three different numerologies in WAIC system.OFDM was proposed by Chang [16] and Saltzberg [17] in the 1960s and has been widely adopted by the most popular wireless communication standards, e.g., 5G and Wi-Fi 6, because of its tempting advantages, i.e., high spectrum efficiency and low implementation complexity. Moreover, wireless signals in genuine can easily be disturbed by channel environments; even human movements can affect the signal strength greatly [18], while OFDM signals are robust to channel variations [19]. Hence, we use OFDM as the fundamental building block in our design.To harness OFDM signals in our design, several practical challenges have to be addressed. Specifically, as a parallel signal transmission scheme, OFDM signals usually have high peak-to-average power ratios (PAPRs), which come from the nonlinear characteristics of power amplifiers (PAs) in communication systems. Furthermore, OFDM signals are composited by sinc-shaped subcarriers that are vulnerable to Doppler effects, resulting in high out-of-band (OOB) radiations. As a result, mishandling of the mentioned problems would severely degrade the communication performance and waste the spectrum. To this end, we present four major settings for OFDM signals, as these settings play direct influences on the communication performance. A better understanding of these settings would lead to an optimized design for intracabin wireless communication systems.


### 2.1.1. First, the CP Duration

The CP duration is a critical parameter for OFDM systems [20, 21], owning to its capability in reducing the intersymbol interference (ISI) and increasing the robustness against the multipath effect when complicated channel environments are involved. Moreover, CP is an inseparable part of signal offsets estimation, synchronization, and channel estimation which matter greatly to the reception of RF signals. However, a poorly designed CP duration is harmful as a prolonged CP duration degrades the spectrum efficiency and introduces high latency, while a shortened CP duration increases the decoding error rate due to the unsolved ISI.


### 2.1.2. Second, the Frame Length

For WAIC systems, many critical aviation-control-messages require low communication latency, which is enabled by a short frame length, while a communication system with many frames in a shorter length would saturate the whole system given a much lower spectrum efficiency and higher burden in frame processing. Therefore, to satisfy the latency requirement as well as to avoid the system saturation, the frame length needs to be carefully designed for WAIC systems.


### 2.1.3. Third, the Subcarrier Spacing

The subcarrier spacing is closely related to the CP duration—shorter subcarrier spacing requires shorter CP duration and vice versa. Specifically, shorter subcarrier spacing is preferred for high spectrum efficiency and high data rate services. Meanwhile, larger subcarrier spacing relates to lower PARPs which make the communication system immune from ISI. To this end, a detailed channel model with respect to aircraft features is needed in order to obtain a suitable subcarrier spacing in practical systems.


### 2.1.4. Fourth, the Number of Subcarriers

A high transmission rate deeply relies on operating bandwidth. Given settled subcarrier spacing, to increase the operating bandwidth, the number of subcarriers has to be increased, but higher PAPRs will be introduced as well due to more parallel transmitted signals. Therefore, to achieve a higher transmission rate and remain low PARPs, the number of subcarriers needs to be well-addressed.Overall, to address all the above-mentioned issues, in this paper, we discuss these four parameters, in terms of data transmission rate, reliability, and latency, in simulated aircraft environments, and we design different numerologies based on the analysis results.


## 2.1.1. First, the CP Duration

The CP duration is a critical parameter for OFDM systems [20, 21], owning to its capability in reducing the intersymbol interference (ISI) and increasing the robustness against the multipath effect when complicated channel environments are involved. Moreover, CP is an inseparable part of signal offsets estimation, synchronization, and channel estimation which matter greatly to the reception of RF signals. However, a poorly designed CP duration is harmful as a prolonged CP duration degrades the spectrum efficiency and introduces high latency, while a shortened CP duration increases the decoding error rate due to the unsolved ISI.


## 2.1.2. Second, the Frame Length

For WAIC systems, many critical aviation-control-messages require low communication latency, which is enabled by a short frame length, while a communication system with many frames in a shorter length would saturate the whole system given a much lower spectrum efficiency and higher burden in frame processing. Therefore, to satisfy the latency requirement as well as to avoid the system saturation, the frame length needs to be carefully designed for WAIC systems.


## 2.1.3. Third, the Subcarrier Spacing

The subcarrier spacing is closely related to the CP duration—shorter subcarrier spacing requires shorter CP duration and vice versa. Specifically, shorter subcarrier spacing is preferred for high spectrum efficiency and high data rate services. Meanwhile, larger subcarrier spacing relates to lower PARPs which make the communication system immune from ISI. To this end, a detailed channel model with respect to aircraft features is needed in order to obtain a suitable subcarrier spacing in practical systems.


## 2.1.4. Fourth, the Number of Subcarriers

A high transmission rate deeply relies on operating bandwidth. Given settled subcarrier spacing, to increase the operating bandwidth, the number of subcarriers has to be increased, but higher PAPRs will be introduced as well due to more parallel transmitted signals. Therefore, to achieve a higher transmission rate and remain low PARPs, the number of subcarriers needs to be well-addressed.Overall, to address all the above-mentioned issues, in this paper, we discuss these four parameters, in terms of data transmission rate, reliability, and latency, in simulated aircraft environments, and we design different numerologies based on the analysis results.


## 3. Interference Model

The interference models for WAIC applications are established for simulation experiments to study the impact of the CP duration, the subcarrier spacing, the frame length, and the subcarrier number. The aircraft channel simulates the propagation of OFDM signals in aircraft. The multipath fading and the ISI simulate the multipath propagation and the propagation delay and evaluate the influence, made by the CP duration, on the bit error rate (BER) of the signal. In addition, the PAPRs corresponding are used to test the effect of the number of subcarriers on PAPR. This model is used to test the CP duration, subcarrier spacing, frame length, and the number of subcarriers that most suitable for WAIC.It is worth noting that our model presented in this paper targets specifically on the intracabin scenarios. In doing so, the proposed solutions in the following sections are better towards to the optimized performance for intracabin scenarios. The underlying reason for this is twofold. First, general wireless models have been extensively studied in the past decades; however, very few of them were proposed for intracabin scenarios, resulting in a lack of design in this certain research area. Second, there are emerging interests upon the fast-growing airline industry to utilize the wireless method to tackle the overweight problem of planes and to better embrace the development of wireless technologies, e.g., wireless virtual reality (VR)/augment reality (AR) and wireless sensor networks. Hence, the use of a special designed intracabin wireless model can satisfy the requirement more specifically and be a key enabler for the next-generation airline industry. Moreover, the design strategy that we have used in this paper can be further applied to other application areas, such as factory wireless networks, and we leave it as our future work.Recall that the main difference between our work and the past work is that instead of proposing a method targeting on a specific application or transplanting existing wireless protocols directly to intracabin scenarios, we aim to introduce a general model that covers high data rate, low data rate, and high reliability intracabin applications simultaneously. In doing this, we study the critical factors accordingly in the flowing subsections, i.e., wireless channel model, multipath fading, ISI, PARP, and the number of subcarriers.


### 3.1. Wireless Channel Model in Aircraft

In this part, only the intracabin communication is considered. The gain/loss between the transmitter and the receiver is(1)GdB=hdBf,d+SdB+FdB,where GdB is a measure of the channel gain/loss and hdBf,d predicts the large-scale channel gain/loss shown as
(2)hdBf,d=C1d−nf−k,where n and k are the distance and frequency exponents and C1 is a constant offset as 2.45 and 2.00 [9, 22]; SdB presents the error due to shadowing effects, part of which is resulted by the variations in the propagation environment; FdB indicates small-scale channel gain/loss due to fading effects, caused by random channel fading and generally represents the largest variation in the channel gain/loss measurements.Note that the uniqueness of the intracabin wireless environment is the key contributor to the above-mentioned channel expression, considering the special structure of the plane and the material painted on the inner surface that truly set the intracabin wireless channel expression apart from traditional ones. This expression is close to practical real-world scenarios that have been verified by many existing literatures. In particular, extensive experiments were conducted through vector network analyzers, spectrum analyzers, and software-defined radios across different planes [23, 24]. We are also aware that the complicity of the intracabin wireless channel environment would make the parameter we used above less accurate given certain scenarios, and we see the search of a more general channel model for intracabin environment as a promising direction for future work.


### 3.2. Multipath Fading and ISI

The discrete-time baseband OFDM signal is given by(3)Dt=∑n=0M−1dnexppj2πfnt,where t∈0,Tp, dn represents the nth modulated symbol, Ts is the symbol period, Tp is the symbol period plus protection time, and δ:Tp=Ts+δ. The frequency of each subcarrier is fn=f0+n/T, where f0 is the lowest subcarrier frequency. Here, it is assumed that δ is greater than the channel impulse response. Then formula (3) be expressed as
(4)Dt=∑n=0M−1dnexpj2πMtexppj2πf0t=Xtexppj2πf0t,where Xt denotes the equivalent complex baseband signal, given by
(5)Xt=∑M−1M−1dnexpj2πMnt.Assume the sample toXt with the rate to be 1/T, then the Ts=kT, then,
(6)Xk=∑n=0M−1dnexpj2πMnk,where 0≤k≤M−1 and dn is the discrete Fourier transform of Xk shown as
(7)dn=∑n=0M−1Xkexp−j2πMnk.At the transmitting side, the OFDM signals pass through digital/analog (D/A), Nyquist filter, and radio frequency (RF) amplifier and then finally enter the wireless transmission channel. The wireless transmission channel is described by a linear filter model with complex low-pass equivalent impulse response described as(8)ht=∑k=0Np−1αkδt−τkejθk,where Np denotes the number of paths and αk, τk, and θk are random amplitude, propagation delay, and phase shift of the kth path, respectively.The physical model is equivalent to a channel model consisting ofNp different taps with τk (k=0,1,⋯,Np−1) delay. For the mth tap, the transmission process of OFDM is ISI free if τk≤δ. Then, the kth symbol received on the kth path is
(9)Y^n,k=αmexpj2πkτmMT·xn,k=G^k,mxn,k,where xn,k (k=0,1,⋯,M−1) is the vector in the modulation constellation. ISI is caused as part of the previous frame is included in the current OFDM frame, which damages the orthogonality of each subcarrier. It is worth noting that when the delay spread of the multipath signal is smaller than the length of CP, the ISI can be fully eliminated; however, when the delay spread is greater, the ISI would exist and cause unwanted effects on the signal [25, 26]. Here, we present the detailed mathematical description in the presence of ISI. Specifically, the kth symbol received on the mth path can be expressed as
(10)Y~n,k=αm∑l=0M−1xn−1,lλl,kτ+∑l=0M−1xn,lμl,kτ,where xn−1,l is for previous frame and xn,l for current frame and
(11)λl,kτ=τ−δMTexpj2πkMT−δ−τMT,l<k,sinπl−kτ−δ/MTπl−kexpjπ2lMT+δ−τ+l−kτ−δMT,otherwise,μl,kτ=MT+δ−τMTexp−j2πkτMT,l<k,−sinπl−kτ−δπl−kexpjπ−2lτ+l−kτ−δMT,otherwise.Inλl,kτ and μl,kτ, l means that the first lth taps are within the CP coverage, and the remaining Np−l taps are outside the CP coverage. According to formulas (10) and (11), the received kth symbol is
(12)Yn,k=∑j=1lY^n,k+∑j=l+1NpY~n,k.The wireless channel is time-varying. Radio signals are attenuated in different ways when they pass through a wireless channel. Generally, the attenuation of the received signal power is the ratio tod−nn=3or4. This means that greater transmission delay results in larger electromagnetic wave propagation distance d=c·τ;c=3×108m/s) and greater signal power attenuation. Meanwhile, wireless signals are characterized by high probability of low transmission delay and low probability of high transmission delay. The number of taps with larger delay is smaller and the received energy is weaker. Based on the above characteristics, it is unnecessary to set the CP duration because of the maximum transmission delay of the channel.


### 3.3. PAPR Corresponding to the Number of Subcarriers

For an OFDM complex band signalxt superposes with N continuous subcarriers, xt will exhibit the property of complex Gaussian when N is large enough. At this point, both the real part and the imaginary part of xt follow Gaussian distribution that the envelope of composite signal x(t) denotes Rayleigh distribution. The power distribution can be represented by the χ2 distribution with mean value of 0, variance of 1, and 2 degree of freedom. The probability density function of xt is exponential distribution fy=e−y, so the cumulative distribution function (CDF) is
(13)PrPower≤λ=∫0ze−ydy=1−e−z,where z is the probability of PARP [27].According to (13), assuming that Xk is an independent and identically distributed random variable, the PAPR upper limit of OFDM signals can reach N, which is enough to attract attention although it is a small probability event. Furthermore, probability statistics are generally utilized to measure the PAPR state of time domain information x, shown as
(14)PcPAPRx≤λ=∫0ze−ydyN=1−e−zN,where Pr means that, for signal x transmitted by N channels, the probability that its peak average ratio does not exceed the threshold λ is Pc. Based on the above definition, the complementary cumulative distribution function (CCDF) is introduced in this work, which is also known as cutting probability. This parameter is the most commonly used PAPR metric, defined as
(15)CCDFλ=PrPARRx>λ=1−1−e−zN=1−Pc,where CCDFλ shows the probability that the PAPR of time domain signal x exceeds the threshold λ, i.e., 1−Pc.


## 3.1. Wireless Channel Model in Aircraft

In this part, only the intracabin communication is considered. The gain/loss between the transmitter and the receiver is(1)GdB=hdBf,d+SdB+FdB,where GdB is a measure of the channel gain/loss and hdBf,d predicts the large-scale channel gain/loss shown as
(2)hdBf,d=C1d−nf−k,where n and k are the distance and frequency exponents and C1 is a constant offset as 2.45 and 2.00 [9, 22]; SdB presents the error due to shadowing effects, part of which is resulted by the variations in the propagation environment; FdB indicates small-scale channel gain/loss due to fading effects, caused by random channel fading and generally represents the largest variation in the channel gain/loss measurements.Note that the uniqueness of the intracabin wireless environment is the key contributor to the above-mentioned channel expression, considering the special structure of the plane and the material painted on the inner surface that truly set the intracabin wireless channel expression apart from traditional ones. This expression is close to practical real-world scenarios that have been verified by many existing literatures. In particular, extensive experiments were conducted through vector network analyzers, spectrum analyzers, and software-defined radios across different planes [23, 24]. We are also aware that the complicity of the intracabin wireless channel environment would make the parameter we used above less accurate given certain scenarios, and we see the search of a more general channel model for intracabin environment as a promising direction for future work.


## 3.2. Multipath Fading and ISI

The discrete-time baseband OFDM signal is given by(3)Dt=∑n=0M−1dnexppj2πfnt,where t∈0,Tp, dn represents the nth modulated symbol, Ts is the symbol period, Tp is the symbol period plus protection time, and δ:Tp=Ts+δ. The frequency of each subcarrier is fn=f0+n/T, where f0 is the lowest subcarrier frequency. Here, it is assumed that δ is greater than the channel impulse response. Then formula (3) be expressed as
(4)Dt=∑n=0M−1dnexpj2πMtexppj2πf0t=Xtexppj2πf0t,where Xt denotes the equivalent complex baseband signal, given by
(5)Xt=∑M−1M−1dnexpj2πMnt.Assume the sample toXt with the rate to be 1/T, then the Ts=kT, then,
(6)Xk=∑n=0M−1dnexpj2πMnk,where 0≤k≤M−1 and dn is the discrete Fourier transform of Xk shown as
(7)dn=∑n=0M−1Xkexp−j2πMnk.At the transmitting side, the OFDM signals pass through digital/analog (D/A), Nyquist filter, and radio frequency (RF) amplifier and then finally enter the wireless transmission channel. The wireless transmission channel is described by a linear filter model with complex low-pass equivalent impulse response described as(8)ht=∑k=0Np−1αkδt−τkejθk,where Np denotes the number of paths and αk, τk, and θk are random amplitude, propagation delay, and phase shift of the kth path, respectively.The physical model is equivalent to a channel model consisting ofNp different taps with τk (k=0,1,⋯,Np−1) delay. For the mth tap, the transmission process of OFDM is ISI free if τk≤δ. Then, the kth symbol received on the kth path is
(9)Y^n,k=αmexpj2πkτmMT·xn,k=G^k,mxn,k,where xn,k (k=0,1,⋯,M−1) is the vector in the modulation constellation. ISI is caused as part of the previous frame is included in the current OFDM frame, which damages the orthogonality of each subcarrier. It is worth noting that when the delay spread of the multipath signal is smaller than the length of CP, the ISI can be fully eliminated; however, when the delay spread is greater, the ISI would exist and cause unwanted effects on the signal [25, 26]. Here, we present the detailed mathematical description in the presence of ISI. Specifically, the kth symbol received on the mth path can be expressed as
(10)Y~n,k=αm∑l=0M−1xn−1,lλl,kτ+∑l=0M−1xn,lμl,kτ,where xn−1,l is for previous frame and xn,l for current frame and
(11)λl,kτ=τ−δMTexpj2πkMT−δ−τMT,l<k,sinπl−kτ−δ/MTπl−kexpjπ2lMT+δ−τ+l−kτ−δMT,otherwise,μl,kτ=MT+δ−τMTexp−j2πkτMT,l<k,−sinπl−kτ−δπl−kexpjπ−2lτ+l−kτ−δMT,otherwise.Inλl,kτ and μl,kτ, l means that the first lth taps are within the CP coverage, and the remaining Np−l taps are outside the CP coverage. According to formulas (10) and (11), the received kth symbol is
(12)Yn,k=∑j=1lY^n,k+∑j=l+1NpY~n,k.The wireless channel is time-varying. Radio signals are attenuated in different ways when they pass through a wireless channel. Generally, the attenuation of the received signal power is the ratio tod−nn=3or4. This means that greater transmission delay results in larger electromagnetic wave propagation distance d=c·τ;c=3×108m/s) and greater signal power attenuation. Meanwhile, wireless signals are characterized by high probability of low transmission delay and low probability of high transmission delay. The number of taps with larger delay is smaller and the received energy is weaker. Based on the above characteristics, it is unnecessary to set the CP duration because of the maximum transmission delay of the channel.


## 3.3. PAPR Corresponding to the Number of Subcarriers

For an OFDM complex band signalxt superposes with N continuous subcarriers, xt will exhibit the property of complex Gaussian when N is large enough. At this point, both the real part and the imaginary part of xt follow Gaussian distribution that the envelope of composite signal x(t) denotes Rayleigh distribution. The power distribution can be represented by the χ2 distribution with mean value of 0, variance of 1, and 2 degree of freedom. The probability density function of xt is exponential distribution fy=e−y, so the cumulative distribution function (CDF) is
(13)PrPower≤λ=∫0ze−ydy=1−e−z,where z is the probability of PARP [27].According to (13), assuming that Xk is an independent and identically distributed random variable, the PAPR upper limit of OFDM signals can reach N, which is enough to attract attention although it is a small probability event. Furthermore, probability statistics are generally utilized to measure the PAPR state of time domain information x, shown as
(14)PcPAPRx≤λ=∫0ze−ydyN=1−e−zN,where Pr means that, for signal x transmitted by N channels, the probability that its peak average ratio does not exceed the threshold λ is Pc. Based on the above definition, the complementary cumulative distribution function (CCDF) is introduced in this work, which is also known as cutting probability. This parameter is the most commonly used PAPR metric, defined as
(15)CCDFλ=PrPARRx>λ=1−1−e−zN=1−Pc,where CCDFλ shows the probability that the PAPR of time domain signal x exceeds the threshold λ, i.e., 1−Pc.


## 4. Design and Analysis

### 4.1. Numerical Analysis

In this section, the aircraft channel model and the multipath model are implemented, and different numerology performances with varying subcarrier spacing and CP duration are evaluated. To be more specific, as shown in Figure2, to reflect the various signals caused by intracabin environments, the transmitted signal would go through an intracabin channel model first, in which the distance and the frequency are the main signal variation factors. After that, the signal would be further altered by a detailed multipath model, in which the number of multipath and variations of each path, such as the amplitude attenuation, the propagation delay, and the phase shift, are included. By doing this, the critical parameters that we have discussed in previous sections can be determined and verified by simulations.Figure 2
The diagram of signal transmissions.Here, we use numerical analysis in determining the critical parameters. Specially, without loss any generosity, we define the subcarrier spacing as∆fi=2i×15 KHz (i∈1,2,3) and Tcp,i=k μs which is related to symbol duration, and the percentage of Tcp is fixed. Furthermore, in the experiment, we transmit signals modulated in 16-QAM modulation and on a 4.3 GHz channel which is defined by ITU.To begin with, we study the relationship between BER and the CP duration. Clearly, as shown in Figure3, the BER and CP duration are negatively correlated. When the CP duration is increasing, the BER is decreasing significantly. Note that, for different subcarrier spacings, i.e., 15 KHz, 30 KHz, and 60 KHz, the BER decreasing is plateaued when CP durations reach at 3 μs, 7 μs, and 13 μs, respectively. According to the result of this plotting, we can learn two things: (1) a lengthen CP would not be always helpful in decreasing BER while the overhead keeps increasing, and (2) a suitable CP duration varies with different subcarrier spacings.Figure 3
Three different numerologies in WAIC system.Next, asTsym=1/∆f represents the symbol duration and ∆f represents the subcarrier spacing, we can obtain numerical results as summarized in Table 1. We can learn from the table that a wider subcarrier spacing offers a shorter symbol duration. But a shorter CP duration does not always introduce low overhead.Table 1
Relationship between subcarrier spacing and CP.
Subcarrier spacing15 KHz30 KHz60 KHzOFDM symbol duration66.67μs33.33μs16.67μsCP duration13μs7μs4μsOFDM symbol including CP79.67μs40.33μs20.67μsOverhead16μs17μs19μsTo make a conclusion so far, according to our analysis result, we understand that the 60 KHz subcarriers achieve the lowest transmission latency and the 15 KHz subcarriers present the highest spectrum utilization. Henceforth, we see the 15 KHz subcarrier is the best candidate for high date rate services, while 60 KHz subcarrier is the best for critical control services.Furthermore, as for the control service, the aviation applications often require bidirectional control requests in each frame and enable the opportunity to both receive and transmit scheduling information, and hence, two control symbols per frame are required. However, with short frame lengths, large OFDM symbols mean large control channel overhead. To know this relationship better, we plot the control overhead verse the frame length in Figure4 along with different subcarrier spacings (SCS).Figure 4
Different control symbols overhead corresponding to different frame length in WAIC systems.It is noticed from the figure that although the transmission delay becomes lower when the frame length is shorter, but there is a great cost of the transmission. In fact, compared with high data rate scenarios, aviation control requires a shorter frame length to maintain lower latency. Given these results, we know that for the same frame length, the narrower SCS requires a higher proportion of control overhead, so the wider SCS is more suitable for the shorter frame length.Finally, we study the effect of the PARP. In Figure5, we illustrate the probability of PAPRs and PAPR0 over a different amount of carrier. When the number of subcarriers is increasing, PAPR will increase correspondingly. However, we can also observe that the probability of extreme PAPR is very low. When PAPR0 is greater than 12, CCDFλ will be less than 10−4, no matter N=128 or N=2048. As a result, we believe we can safely omit the influence of the number of subcarriers on the PARP problem. Besides, there are many algorithms that have been studied to further reduce PAPR. In other words, we consider that the number of subcarriers is not a bandwidth-limiting bottleneck.Figure 5
Different PAPR corresponding to different number of subcarriers in WAIC systems.


### 4.2. MNCD Parameter Design

According to the numerical analysis results presented in the previous section, and after applying our understandings of aviation wireless communication scenarios, the parameter scheme of MNCD has been concluded in this section. Specifically, we select three typical settings for the subcarrier spacing, i.e., 15 KHz, 30 KHz, and 60 KHz, as a result of the constrains from both the spectrum efficiency and the PARPs. In particular, the 15 KHz can be allocated to high data rate scenarios because of its spectrum occupancy, and the 60 KHz is the best for the aviation control given its ability in reducing the communication latency; at last, the 30 KHz can be designated to massive sensors as it balances the latency and spectrum efficiency together which is essential for the communication among large number of sensors. From the communication efficiency perspective of view, longer frame lengths are needed for high data rate and massive sensors and shorter frame lengths for aviation control scenarios. In addition, the setting of CP duration and the number of subcarriers can be further defined by specific WAIC applications. The final parameters of our design for WAIC systems are shown in Table2.Table 2
Parameters of MNCD.
ScenarioHigh data rateMassive sensorsAviation controlData rate307 Mbps250kbps∗10010kbps∗1000Spectrum occupancy90 MHz30 MHz60 MHzSubcarrier spacing15 KHz30 KHz60 KHzSymbol+CP duration79.67μs40.33μs20.67μsNum. of subcarriers600010001000Modulation16-QAM16-QAMBPSKCompared with the existing IEEE 802.11 architecture, for high-speed applications, MNCD improve the spectrum efficiency significantly. In particular, for high data rate scenarios, MNCD occupies only 90 MHz spectrum, while the existing IEEE 802.11 channel design architecture requires 120 MHz spectrum. MNCD’s spectrum utilization is improved by 25%. Moreover, in terms of low-speed applications, MNCD supports up to 100 pairs of devices at the same time with a bandwidth of 30 MHz, while the existing IEEE 802.15.4 architecture can only support 6 pairs [28], which improves the performance in supporting more users by 16 times. It is worth noting that by separately designing the parameter settings according to these three typical scenarios, we can provide more reliability for the whole communication systems, as the shorter messages for the aviation control can be readily completed with less latency and high data rate messages can be served by using a large volume of spectrum resources, and finally, the massive sensors can communicate with much less interference that may be caused by the other types of communication links.


## 4.1. Numerical Analysis

In this section, the aircraft channel model and the multipath model are implemented, and different numerology performances with varying subcarrier spacing and CP duration are evaluated. To be more specific, as shown in Figure2, to reflect the various signals caused by intracabin environments, the transmitted signal would go through an intracabin channel model first, in which the distance and the frequency are the main signal variation factors. After that, the signal would be further altered by a detailed multipath model, in which the number of multipath and variations of each path, such as the amplitude attenuation, the propagation delay, and the phase shift, are included. By doing this, the critical parameters that we have discussed in previous sections can be determined and verified by simulations.Figure 2
The diagram of signal transmissions.Here, we use numerical analysis in determining the critical parameters. Specially, without loss any generosity, we define the subcarrier spacing as∆fi=2i×15 KHz (i∈1,2,3) and Tcp,i=k μs which is related to symbol duration, and the percentage of Tcp is fixed. Furthermore, in the experiment, we transmit signals modulated in 16-QAM modulation and on a 4.3 GHz channel which is defined by ITU.To begin with, we study the relationship between BER and the CP duration. Clearly, as shown in Figure3, the BER and CP duration are negatively correlated. When the CP duration is increasing, the BER is decreasing significantly. Note that, for different subcarrier spacings, i.e., 15 KHz, 30 KHz, and 60 KHz, the BER decreasing is plateaued when CP durations reach at 3 μs, 7 μs, and 13 μs, respectively. According to the result of this plotting, we can learn two things: (1) a lengthen CP would not be always helpful in decreasing BER while the overhead keeps increasing, and (2) a suitable CP duration varies with different subcarrier spacings.Figure 3
Three different numerologies in WAIC system.Next, asTsym=1/∆f represents the symbol duration and ∆f represents the subcarrier spacing, we can obtain numerical results as summarized in Table 1. We can learn from the table that a wider subcarrier spacing offers a shorter symbol duration. But a shorter CP duration does not always introduce low overhead.Table 1
Relationship between subcarrier spacing and CP.
Subcarrier spacing15 KHz30 KHz60 KHzOFDM symbol duration66.67μs33.33μs16.67μsCP duration13μs7μs4μsOFDM symbol including CP79.67μs40.33μs20.67μsOverhead16μs17μs19μsTo make a conclusion so far, according to our analysis result, we understand that the 60 KHz subcarriers achieve the lowest transmission latency and the 15 KHz subcarriers present the highest spectrum utilization. Henceforth, we see the 15 KHz subcarrier is the best candidate for high date rate services, while 60 KHz subcarrier is the best for critical control services.Furthermore, as for the control service, the aviation applications often require bidirectional control requests in each frame and enable the opportunity to both receive and transmit scheduling information, and hence, two control symbols per frame are required. However, with short frame lengths, large OFDM symbols mean large control channel overhead. To know this relationship better, we plot the control overhead verse the frame length in Figure4 along with different subcarrier spacings (SCS).Figure 4
Different control symbols overhead corresponding to different frame length in WAIC systems.It is noticed from the figure that although the transmission delay becomes lower when the frame length is shorter, but there is a great cost of the transmission. In fact, compared with high data rate scenarios, aviation control requires a shorter frame length to maintain lower latency. Given these results, we know that for the same frame length, the narrower SCS requires a higher proportion of control overhead, so the wider SCS is more suitable for the shorter frame length.Finally, we study the effect of the PARP. In Figure5, we illustrate the probability of PAPRs and PAPR0 over a different amount of carrier. When the number of subcarriers is increasing, PAPR will increase correspondingly. However, we can also observe that the probability of extreme PAPR is very low. When PAPR0 is greater than 12, CCDFλ will be less than 10−4, no matter N=128 or N=2048. As a result, we believe we can safely omit the influence of the number of subcarriers on the PARP problem. Besides, there are many algorithms that have been studied to further reduce PAPR. In other words, we consider that the number of subcarriers is not a bandwidth-limiting bottleneck.Figure 5
Different PAPR corresponding to different number of subcarriers in WAIC systems.


## 4.2. MNCD Parameter Design

According to the numerical analysis results presented in the previous section, and after applying our understandings of aviation wireless communication scenarios, the parameter scheme of MNCD has been concluded in this section. Specifically, we select three typical settings for the subcarrier spacing, i.e., 15 KHz, 30 KHz, and 60 KHz, as a result of the constrains from both the spectrum efficiency and the PARPs. In particular, the 15 KHz can be allocated to high data rate scenarios because of its spectrum occupancy, and the 60 KHz is the best for the aviation control given its ability in reducing the communication latency; at last, the 30 KHz can be designated to massive sensors as it balances the latency and spectrum efficiency together which is essential for the communication among large number of sensors. From the communication efficiency perspective of view, longer frame lengths are needed for high data rate and massive sensors and shorter frame lengths for aviation control scenarios. In addition, the setting of CP duration and the number of subcarriers can be further defined by specific WAIC applications. The final parameters of our design for WAIC systems are shown in Table2.Table 2
Parameters of MNCD.
ScenarioHigh data rateMassive sensorsAviation controlData rate307 Mbps250kbps∗10010kbps∗1000Spectrum occupancy90 MHz30 MHz60 MHzSubcarrier spacing15 KHz30 KHz60 KHzSymbol+CP duration79.67μs40.33μs20.67μsNum. of subcarriers600010001000Modulation16-QAM16-QAMBPSKCompared with the existing IEEE 802.11 architecture, for high-speed applications, MNCD improve the spectrum efficiency significantly. In particular, for high data rate scenarios, MNCD occupies only 90 MHz spectrum, while the existing IEEE 802.11 channel design architecture requires 120 MHz spectrum. MNCD’s spectrum utilization is improved by 25%. Moreover, in terms of low-speed applications, MNCD supports up to 100 pairs of devices at the same time with a bandwidth of 30 MHz, while the existing IEEE 802.15.4 architecture can only support 6 pairs [28], which improves the performance in supporting more users by 16 times. It is worth noting that by separately designing the parameter settings according to these three typical scenarios, we can provide more reliability for the whole communication systems, as the shorter messages for the aviation control can be readily completed with less latency and high data rate messages can be served by using a large volume of spectrum resources, and finally, the massive sensors can communicate with much less interference that may be caused by the other types of communication links.


## 5. Conclusion and Future Work

In this paper, a newly proposed mixed-numerology channel design is presented to cater for different application scenarios in WAIC systems. The signal propagation features have been studied for intra aircraft wireless communications. Based on that, critical system parameters, e.g., subcarrier spacing, CP duration, frame length, and number of subcarriers, are evaluated for different practical scenarios. Compared with the existing channel settings, MNCD increases the spectrum utilization by 25% in high-speed applications. Meanwhile, MNCD supports 16 times more devices in both low speed and aviation control applications.For our future work, in order to apply our design into more practical scenarios, a large-scale implementation platform is needed. Based on this platform, we could conduct real-world experiments in different aircraft where complicated channel conditions are involved. To achieve this, the state-of-the-art software-defined radios (SDR) would be a better option to fulfil this target and we left it as future work. One thing comes into our attention is that our current scheme is aiming to harness the proposed channel for WAIC applications, especially from the physical layer design point of view, while for our next step, there are many promising solutions from the Internet of Things, and the wireless sensor networks can be further applied into our scheme, which target on high level design, such as network routing [29, 30] and data security [31–33]. At last, we see our design as a promising solution to future intracabin communication applications, e.g., on-board sensor networks, emergency communications, and reliability control services.



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*Source: 7981869-2022-04-26.xml*