UAV-aided maritime communication over the Pacific Ocean using the elevated duct toward future wireless networks (2025)

Over the past few years, we have witnessed a tremendous explosion in the Public Land Mobile Network, with a plethora of new applications and use cases emerging driven by the modern economy, social interactions, physical infrastructure, and more. Researchers have already begun envisioning the future sixth-generation (6G) communication network, which is expected to bring about a disruptive transformation by deeply integrating deep-sea ocean communication, aviation communication, and satellite communication into the traditional cellular network. This integration will provide combined communication capabilities for land, sea, air, and space on a truly global scale. The maritime communication network, aiming towards 5G and beyond¹, will amalgamate coastal public networks, satellite communication networks², underwater communication networks³, and various other supplementary networks based on flexible platforms such as UAVs⁴. These low-altitude platforms (LAPs) have been identified as crucial components of 6G networks⁵, designed to meet the requirements for reliable, cost-effective, and on-demand wireless communication solutions across diverse real-world scenarios. UAVs-based networks have been invoked as an appealing assistance for terrestrial communication networks⁶, and can efficiently extend the network coverage unfeasible by ground base stations. Moreover, enabling network connectivity has been recognized as pivotal for 6G, with current research focusing on realizing the long-range communication capabilities of LAPs⁷.

Various technologies, including high-frequency (HF), microwave, and satellite radio links have facilitated limited land-to-ship or ship-to-ship radio communication⁸. However, these communication methods come with significant speed, capacity, range, and cost limitations⁹. An atmospheric duct, which often occurs at the sea surface, can lead to anomalous effects on the propagation of electromagnetic energy in a radio transmission system¹⁰. Simultaneously, recent unprecedented advancements in drone technology have made widespread deployment of UAVs possible, extending the potential for maritime communication links based on the elevated duct. While the evaporation duct has been extensively studied in the realm of beyond-line-of-sight communication research, the transmission mechanism of the elevated duct remains largely unexplored¹¹. This is due to early research on atmospheric ducts primarily concentrated on modelling methods of radio wave propagation and observations of anomalous propagation¹², and previous research outcomes primarily centred on communication utilizing evaporation ducts due to their high occurrence. The maturation of UAV technology has emerged as a catalyst for communication under elevated ducts, and this newly explored ducting communication application offers a viable avenue for future transmissions of 6G and beyond.

To explore innovative maritime communication solutions, we provide a UAV-aided communication method utilizing elevated ducts informed by statistical findings that consider structural characteristics. This approach facilitates high-speed, large-capacity, long-range, and reliable LAP-to-LAP and ship-to-LAP radio communication. Initially, we delve into the attributes of atmospheric ducts. Subsequently, we offer insights into a typical communication scenario within elevated duct layers through simulations using the parabolic equation (PE) method. Ultimately, we draw significant conclusions regarding over-horizontal, GHz-bandwidth microwave radio communication in the northern Pacific Ocean, while addressing the accompanying challenges. This paper marks the inaugural design and simulation of the system performance of UAV wireless communication based on elevated ducts, presenting a promising outlook for the future of UAV-aided maritime communication.

Spatiotemporal characteristics of elevated duct over the Northern Pacific Ocean

Radio meteorological data is fundamental to elevated duct communication. According to the determining method of elevated duct (see Method 1), we get the monthly occurrence distribution of the elevated duct over the past 11 years, as shown in Fig.1, based on the radiosonde dataset from the Brownsville site (25.9°N, -97.43°E) in the American coastline from 2010 to 2020¹³. The annual occurrence of the elevated duct at the Brownsville site exceeds 90%, with the highest monthly occurrence reaching 100%.

Furthermore, Figs.2 and 3 demonstrate the distribution of the height and strength of the elevated ducts in the Brownsville site during different seasons from 2015 to 2020. As shown in Fig.2, the strength of the elevated duct is mainly distributed at 10M-units in autumn, while the strength of the duct in other seasons is slightly inferior. In Fig.3, except for the higher duct height in winter, the duct heights in other seasons are mainly concentrated around 1000m.

These above conditions are conducive to establishing a communication system based on the elevated duct and the basis for determining the trapped frequency, transmission angle, and power for the optimum propagation of a communications signal. Given the occurrence of elevated ducts in the northern Pacific Ocean, thus we utilize a UAV wireless communication system within the ducting layer, presenting a promising solution for swiftly establishing an auxiliary maritime communication system.

UAV-aided communication over the Pacific Ocean using the elevated duct

Figure4 presents a scenario illustrating the use of the elevated duct as a communication medium, demonstrating its capability for over-horizontal transmission beyond the coverage provided by terrestrial communication networks. A ground-to-air relay terminal positioned along the shoreline is established using a stationary airship, capable of consistently transmitting signals to the surrounding maritime area for extended durations. Conversely, at the opposite end of this network, a UAV can swiftly ascend into the ducting layer, serving as an aerial base station. This UAV provides autonomy, flexibility, and wide-ranging connectivity for maritime services within a communication radius spanning tens of kilometres. Moreover, UAVs operating within the elevated duct can serve as relay stations for one another. This arrangement mitigates the impact of adverse meteorological conditions on the network, ensuring reliable communication.

Regarding the selection of communication frequency, the minimum frequency is 200MHz, and the radio wave trapping capability of the given meteorological environment is 154.45MHz. A maximum frequency of 20GHz was selected considering the communication capability of operating equipment, which can also efficiently avoid the maximum value of around 22GHz in specific attenuation due to atmospheric gases¹⁴.

According to the Parabolic Equation method (see Method 2), Fig.5 shows the simulation result in a real scenario over the Pacific Ocean, which is a link with Zhoushan, Zhejiang Province, China (30.02 °N, 122.21 °E) as the transmitting position and San Francisco, California, USA (37.78 °N, 122.47 °W) as the receiving point, with a great-circle distance of 9919.45km. While the simulation parameters of the maritime UAV communication network based on elevated duct are shown in Table 1, thus the network can facilitate a long-range transmission link with a path loss budget of 189 dB consequently.

The propagation phenomenon of guided waves for the frequencies at 200MHz, 10GHz, and 20GHz is pronounced separately; signals can be trapped in the ducting layer and transmitted over the Pacific Ocean. The path loss budget of 189 dB is marked with black isoline in Fig.5, implying that the receiver at the other end of the UAV communication system in the ducting layer can receive and demodulate microwave signals with 1GHz bandwidth. The right side of Fig.5 uses the Blue line and Orange line to indicate the transmission loss in the duct layer (at antenna height of 1050m) and out of the duct layer (at antenna height of 400m), respectively. The transmission loss within the range of the elevated duct is significantly lower than that outside the duct height, validating the use of elevated ducts for long-range wireless communications over the ocean without relaying.

To discuss the communication effect more specifically, we selected and analyzed the required jamming-to-signal ratio (JSR), bit error ratio (BER), and bandwidth efficiency (BE) of high-quality communication services with six digital modulations of 2FSK, BPSK, QPSK, MSK, 16-QAM, and 64-QAM¹⁰. As shown in Eq.(8), JSR is the ratio between the total interference and noise in the communication system and the strength of the useful signal. Generally, a lower JSR value indicates better communication quality and higher transmission data rates. According to method 3 (Evaluating the Performance of Communication), the communication effect under different modulations is shown in Fig.6.

Figure6 delineates the experimentally determined performance boundaries of each modulation scheme, revealing distinct critical JSR thresholds:

1. (1)

   No effect on the normal operation of the communication system (BER < 10^− 5).

   • 2FSK: JSR > -13.3 dB.

   • BPSK/QPSK/MSK: JSR > -9.6 dB.

   • 16-QAM: JSR > -14.0 dB.

   • 64-QAM: JSR > -18.6 dB.

2. (2)

   Message communication can be realized but the quality of packet communication is poor (10^− 5 ≤ BER < 10^− 3).

   • 2FSK: -13.3 dB ≤ JSR < -9.8 dB.

   • BPSK/QPSK/MSK: -9.6 dB ≤ JSR < -6.8 dB.

     See Also

     Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer

   • 16-QAM: -14.0 dB ≤ JSR < -11.6 dB.

   • 64-QAM: -18.6 dB ≤ JSR < -16.2 dB.

3. (3)

   Message communication is barely realized and packet communication is not possible (10^− 3 ≤ BER < 10^− 2).

   • 2FSK: -9.8 dB ≤ JSR < -7.3 dB.

   • BPSK/QPSK/MSK: -6.8 dB ≤ JSR < -4.3 dB.

   • 16-QAM: -11.6 dB ≤ JSR < -9.6 dB.

   • 64-QAM: -16.2 dB ≤ JSR < -14.2 dB.

4. (4)

   Message and packet communication systems cannot be implemented (10^− 2 ≤ BER < 10^− 1).

   • 2FSK: -7.3 dB ≤ JSR < -2.2 dB.

   • BPSK/QPSK/MSK: -4.3 dB ≤ JSR < -0.8 dB.

   • 16-QAM: -9.6 dB ≤ JSR < -6.2 dB.

   • 64-QAM: -14.2 dB ≤ JSR < -11.0 dB.

5. (5)

   Unable to work normally and communication interrupted (BER > 10^− 1).

   • 2FSK: JSR ≤ -2.2 dB.

   • BPSK/QPSK/MSK: JSR ≤ -0.8 dB.

   • 16-QAM: JSR ≤ -6.2 dB.

   • 64-QAM: JSR ≤ -11.0 dB.

The bandwidth efficiency under different modulations shows the opposite tendency in Fig.7 according to Eq.(11). When BER is 10^− 5 (communication is no error), the bandwidth efficiency of 2FSK, BPSK, QPSK, MSK, 16-QAM, and 64-QAM is 1bps/Hz, 1bps/Hz, 2bps/Hz, 4/3bps/Hz, 4bps/Hz, 6bps/Hz.

According to the above theory and relative analysis, the mapping relation between different modulations and JSR, bandwidth efficiency, and ease of implementation can be obtained and shown in Fig.8. The optimum bandwidth efficiency is 6 bps/Hz with 64-QAM when BER is 10^− 5 (communication is no error), which also shows the most challenging hardware implementation. Modulations of 2FSK and BPSK are relatively simple in hardware implementation, corresponding to the lowest bandwidth efficiency. Combined with the statistics in Fig.8, QPSK stands out for its relative compromise in bandwidth efficiency and hardware implementation difficulty. Furthermore, it shows the lowest requirement for JSR that does not affect the communication system. As a result, an adaptive selection function of optional modulation mode may improve communication link performance.

As a result, a maritime microwave radio link employing a method of implementing a no-relay, long-range, and GHz-bandwidth radio communication system via the UAV wireless network in the elevated duct is investigated in this work. The optimum working parameters and the maximum range were simulated using the PE method. In contrast with the ground-to-air communication network based on the elevated duct, the UAV wireless system can provide various solutions of flexible accessibility, wide-area coverage, and extensive spectrum resources for maritime applications, which may supply efficient support for naval communications and play a critical component of the 6G networks.

This research holds significant theoretical significance and practical application value in developing new communication methods and systems, particularly for maritime military purposes. The findings suggest that ducting layer communication could emerge as the predominant radio wave propagation mechanism in the lower troposphere. Future communication endeavours are poised to address specific challenges linked to conventional long-range radio communication methods, such as sluggish HF communication rates and exorbitant satellite communication costs.

Determining the appearance of the atmospheric duct

To analyze the characteristics of the atmospheric duct, we selected the modified refractivity M, which is defined by radio refractivity N and the height above the Earth’s surface¹⁷:

With

where z is the height above the ground (m), N is radio refractivity (N-unit/km), T is the atmospheric temperature (K), p is pressure (hpa), q is specific humidity (g/m³), A_N is 77.6N-unit/KhPa, B_N is 7733K^− 1, n is the atmospheric refraction index¹⁷:

where c and v are the transmit speed of the electromagnetic wave in free space and the medium (m/s), respectively; ε is the dielectric constant (F/m).

To sum up, the occurrence of the atmospheric duct means that there is a negative vertical gradient of modified refractivity M due to strong gradients of temperature and humidity in the atmosphere. Namely, dN/dz<-157 or dM/dz < 0 when the atmospheric duct occurs^17,18.

Predicting of radio propagation in atmospheric duct

Here, we used the PE method to investigate the feasibility of communication utilizing atmospheric ducts in the northern Pacific Ocean. The objective of the simulation was to determine the optimal operating frequency and antenna height. The PE method is favoured for addressing radio propagation prediction issues related to tropospheric ducting^19,20. Based on this method, a series of simulations of radio propagation above the ocean was conducted based on statistical characteristics such as the height, thickness, and strength of atmospheric ducts over the ocean²¹. Specifically, the PE method can estimate large-scale propagation losses within ducting layers under varying refractivity conditions, polarization, and surface types. Therefore, this study utilized the PE method for the numerical simulation. The parabolic equation approximates the wave equation and can simulate propagation in the conical region along the paraxial direction.

For tropospheric radio wave propagation, the Standard Parabolic Equation (SPE) can be expressed as²²:

where \(\psi (x,z)\) is the electric field under horizontal polarization or magnetic field under vertical polarization; n is the atmospheric refraction index; x and z are the propagation distance and height in the rectangular coordinate system, respectively; \(k={\text{2\varvec{\uppi}}}/\lambda\) is the wave number in free space, u(x, z) is the path loss function related to x.

The PE in free space can be solved either analytically or numerically based on the Fourier transform. Hardin and Tapert proposed the Split-Step Fourier Transform (SSFT) method^23,24,25; the distance step can be large, and matrix operation is not required; great solving speed can be achieved with the Fast Fourier Transform (FFT).

Using the SSFT method to solve the parabolic equation numerically, we start from the transmitting antenna and solve within the computational range. By utilizing the field from the previous step and setting appropriate boundary conditions, we obtain the vertical field within the given range. The wide-angle split-step solution for the equation is given as^26,27:

where F denotes the Fourier transform, p = ksinθ is the transform variable, and θ is the horizontal propagation angle.

The SSFT method provides a numerical way of solving the Parabolic Equation: transform the initial field u(0, z), multiply it by the spectral domain propagation term, and then take the inverse Fourier transformation. Path loss L_p is the ratio of the axial equivalent omnidirectional radiated power of the actual antenna to the received power of the equivalent omnidirectional receiving antenna. Thus, the path loss can be expressed by the field function u(x, z)²²:

where a is the Earth’s radius.

Evaluating the performance of communication

In analyzing the communication system performance, JSR is the ratio between the total interference and noise power and the useful signal strength.

where \({P_{{\text{signal}}}}\) is the signal power, \({P_{{\text{interference}}}}\) is the interference power, and \({P_{{\text{noise}}}}\) is the noise power.

Assuming that the external electromagnetic environment is broadband and additive white Gaussian noise, the BER characteristics against six modulations can be obtained:

According to the Shannon’s theory, the bandwidth efficiency (η) can be defined as:

where C and B are the channel capacity and bandwidth, respectively.

At the same time, according to the Nyquist first criterion for binary transmission conditions, the signal bandwidth is twice that of the baseband signal, and Eq.(10) can be converted as:

where R is the symbol rate, and M is multiple modulation schemes.

Authors and Affiliations

1. School of Microelectronics, Tianjin University, Tianjin, China

   Jian Wang,Wenlu Liu&Cheng Yang

Contributions

J. W. and C. Y. developed the key idea for this paper. J. W., W. L. Liu, and C. Y. conducted the numerical experiments. J. W. and C. Y. designed the study. J. W., W. L. Liu, and C. Y. performed the simulations. J. W. and C. Y. extracted the data and coded the analyses. J. W., and C. Y. wrote the draft of the manuscript. All authors discuss the results. J. W., W. L. Liu, and C. Y. edited the manuscript and reviewed the manuscript.

Corresponding author

Correspondence to Cheng Yang.

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions