Coverage Ratio–Based Evaluation of Antenna Omnidirectionality for a Pair of Microstrip Patch Antennas on a 6U CubeSat

Abstract

CubeSat missions increasingly rely on microwave-band communication systems, whose antennas often exhibit directional radiation patterns. As a result, multiple antennas are commonly used to improve coverage; however, a quantitative method to evaluate their performance across all spacecraft attitudes has been lacking. This paper introduces the Coverage Ratio of CubeSat Attitude (CRCA), a metric that quantifies the proportion of orientations for which the antenna gain exceeds a required threshold. CRCA is introduced and demonstrated using the S-band command antenna system of the 6U CubeSat VERTECS. The proposed metric is then used to quantitatively compare multiple antenna placement configurations, clarifying the effect of mounting faces on attitude-dependent coverage. Electromagnetic simulations and three-dimensional radiation pattern measurements using a metal CubeSat enclosure show good agreement when splitter and cable losses are taken into account. The combined radiation pattern achieves greater than $-8.0$ dBic in 90% of attitudes in simulation, and greater than $-10.0$ dBic of attitudes in 90% in measurement. Furthermore, a CRCA-based link budget analysis demonstrates that sufficient uplink margin can be conservatively maintained under tumbling conditions. The proposed CRCA framework provides a practical and generalizable approach for evaluating antenna omnidirectionality and attitude-dependent communication performance in CubeSat missions.

1. Introduction

CubeSats have become an established platform for space missions due to their standardized form factor, modular subsystems, and the ability to support rapid and cost-effective development [1]. As CubeSat missions increasingly incorporate higher-performance payloads and more complex operational requirements, the reliability of their communication subsystems has become a critical determinant of mission success. In particular, the command uplink plays a central role during early operations, when the spacecraft state is uncertain and attitude stabilization has not yet been completed.

These characteristics also align well with the principles of the Lean Satellite (LeanSat) philosophy, which emphasizes low-cost development, extensive use of Commercial-Off-The-Shelf (COTS) components, and simplified testing processes [2]. LeanSat-oriented missions often operate under tighter resource constraints and shorter development cycles, making the communication subsystem—especially its robustness during early operations—even more critical. Thus, methods that quantitatively evaluate communication performance across all possible spacecraft attitudes are valuable not only for CubeSats in general but are particularly relevant for missions developed under LeanSat principles.

CubeSats are increasingly adopting microwave communication bands such as the S-band and X-band to support higher data volumes and more demanding mission operations [3]. However, antennas operating in these frequency bands often exhibit directional radiation characteristics, making it difficult to maintain sufficient gain across all possible spacecraft orientations. As a result, many CubeSat missions employ multiple antennas mounted on different faces of the spacecraft to improve overall coverage.

While the use of multiple antennas can mitigate coverage gaps, it also raises a fundamental question for CubeSat communication system design: how can the combined omnidirectional performance of such antenna configurations be quantitatively evaluated? Existing studies have demonstrated various antenna arrangements—including wide-beamwidth patch antennas [4], antennas mounted on opposite CubeSat faces [5,6,7], and other compact designs—but have not established a systematic metric for assessing how frequently the required gain is achieved over all possible attitudes.

In contrast, the mobile communication industry has established standardized methods for three-dimensional (3D) radiation assessment, such as the spherical coverage specifications defined by the 3rd Generation Partnership Project (3GPP) [8]. Metrics based on the fraction of solid angle exceeding a required gain have also been discussed in the antenna literature, such as the coverage efficiency proposed by Helander et al. [9]. Zhao et al. [10] further introduced a spherical coverage characterization framework for 5G user equipment based on 3GPP specifications. This perspective highlights the importance of assessing antenna performance not only by peak gain or pattern shape but also by how reliably a required gain is satisfied across the entire orientation space—an aspect highly relevant to CubeSat communication design. However, these metrics do not explicitly account for spacecraft attitude as a state variable, which plays a critical role in CubeSat command uplink scenarios, particularly during early mission phases.

Motivated by this gap, this study introduces the Coverage Ratio of CubeSat Attitude (CRCA), a metric that quantifies the proportion of CubeSat orientations for which the antenna gain exceeds a specified threshold. CRCA provides an intuitive and quantitative measure of uplink robustness when multiple antennas are used to improve omnidirectionality and complements conventional link budget analysis. We apply CRCA to the S-band command uplink system of the 6U CubeSat VERTECS, which employs two patch antennas mounted on opposite faces and a COTS-based S-band receiver. Through electromagnetic simulations and three-dimensional radiation measurements, we demonstrate that the proposed system provides robust uplink performance across a majority of possible attitudes. Although this study focuses on VERTECS, the proposed methodology is broadly applicable to CubeSat and small satellite communication systems across various frequency bands, particularly for missions that require reliable communication performance independent of spacecraft attitude. Although this study focuses on an S-band uplink system as a representative case, the proposed CRCA framework itself is independent of frequency and antenna type. It can be applied to any radiation pattern obtained through simulation or measurement, including those at higher frequency bands such as X-band.

The remainder of this paper is organized as follows. Section 2 overviews the VERTECS mission and its S-band command system. Section 3 describes the uplink subsystem configuration. Section 4 presents electromagnetic simulations, and Section 5 introduces the CRCA formulation. Section 6 applies the proposed CRCA to a comparative study of antenna placement configurations. Section 7 details the 3D radiation pattern measurement system and compares measured and simulated patterns. Section 8 applies CRCA to the uplink link budget. Section 9 discusses related CubeSat antenna studies. Finally, Section 10 concludes the paper and outlines future work.

2. VERTECS: Visible Extragalactic Background Radiation Exploration by CubeSat

2.1. Mission Overview

VERTECS is a 6U CubeSat designed to observe the Extragalactic Background Light (EBL) in the visible wavelengths ($0.4$–$0.8$ $\mathrm{\mu }\mathrm{m}$) [11]. By capturing multi-wavelength data, VERTECS aims to reveal the origin of the EBL, which is critical for understanding the overall star formation history of the universe.

This mission builds upon the experience gained through previous CubeSat developments at Kyushu Institute of Technology, including KITSUNE [7,12], which served as a technology demonstration platform for optical payloads. A computer-aided design (CAD) model for the VERTECS is shown in Figure 1.

2.2. Mission Objectives

The primary objective of VERTECS is to reveal the origin of the EBL at visible wavelengths. In the near-infrared region, previous measurements show that the intensity of the EBL is several times higher than that of the integrated light of galaxies. To explain this discrepancy, possible contributions from the first stellar objects in the early universe or intra-halo light in the local universe have been suggested. The radiation spectra of these objects are expected to exhibit large differences in the visible wavelength. VERTECS is designed to observe the EBL in multiple visible wavelengths to identify the origin of the high-intensity EBL [11].

2.3. CubeSat Design

VERTECS is based on the BIRDS Standard CubeSat Bus [13], leveraging advancements from the KITSUNE 6U CubeSat. The CubeSat is equipped with a visible camera for EBL observations, a high-data-rate communication system, and an advanced attitude control system to ensure precise pointing stability during observations.

A key feature of VERTECS is its adoption of an S-band command system, which marks the first satellite that Kyutech has implemented an S-band command and telemetry system instead of the conventional UHF-based system. This transition aligns with the increasing demand for higher data rates and compatibility with established ground station networks. The key components of the CubeSat include:

• Bus system: 6U CubeSat platform based on Kyutech’s standardized bus [12].
• Telescope: Visible-light telescope with a 3k × 3k CMOS image sensor optimized for multi-band EBL observations within a 3U volume [11].
• Communication system: X-band downlink (10 Mbps) for mission data and S-band uplink/downlink for telemetry and command, implemented using commercial transceiver units (Addnics Corp., Tokyo, Japan) [14].
• Attitude control: XACT-15 unit (Blue Canyon Technologies, Boulder, CO, USA) for high-precision pointing [15].
• Power system: Deployable Solar Array Paddle (DHV Technology, Malaga, Spain) for large power generation.
• Orbit: Sun-synchronous orbit (SSO) at an altitude of 500–680 km.

2.4. Launch Plan

VERTECS was selected for the JAXA-Small Satellite Rush (JAXA-SMASH) program and is scheduled for launch in FY2025. Flight Model (FM) development is ongoing, and environmental testing is currently in progress.

3. S-Band Command Uplink System for VERTECS

3.1. System Overview

VERTECS employs an S-band command uplink system with two patch antennas to ensure a robust and reliable command reception under various attitude conditions [16]. These antennas feed signals into an S-band command receiver, which demodulates telecommands. This system receives and processes telecommands from the ground station using a single assigned channel within a frequency range of $2.025$ GHz to $2.110$ GHz [17]. For security reasons, the specific center frequency of the S-band uplink is not disclosed in this paper. Photographs of the receiver and antenna, along with a simplified block diagram, are shown in Figure 2.

3.2. S-Band Command Receiver

The S-band command receiver (ADD1443BM) was developed by Addnics Corporation [14,18]. It demodulates PCM-PSK-PM signals, supporting data rates of 1 kbps and 4 kbps, and operates within a single assigned frequency channel in the $2.025$–$2.110$ GHz range. The receiver features two input ports, which are combined internally by a built-in splitter to support an omnidirectional radiation pattern. The key specifications are listed in

Table 1. Specifications of the S-band command receiver [14,18].

Parameter	Specification
Receiver name	A88 SRX
Model number	ADD1443BM
Operating frequency	Single channel within $2.025$–$2.110$ GHz
Modulation scheme	PCM-PSK-PM
Subcarrier frequency	16 kHz
Data rate	1 kbps/4 kbps
Carrier tracking range	$\pm 50$ kHz
Input level range	$-40$ dBm to $-130$ dBm (Carrier acquisition level)
Sensitivity (BER = ${10}^{-4}$)	$-122$ dBm (1 kbps, mod. index = 1 rad) $-116$ dBm (4 kbps, mod. index = 1 rad)
Operating voltage	$+5$ V to $+12$ V
Power consumption	≤1 W
Operating temperature	$-20 °\mathrm{C}$ to $60 °\mathrm{C}$
Dimensions	80 mm × 80 mm × 16 mm
Weight	≤140 g

.

3.3. Antenna Configuration

The VERTECS system employs two identical S-band patch antennas mounted on the ±Y faces of the CubeSat. This antenna configuration minimizes communication dropouts caused by CubeSat tumbling, ensuring reliable uplink performance. The antenna system is designed to meet the following key requirements:

• Operating frequency: A single channel within $2.025$ GHz–$2.110$ GHz
• Polarization: Right-Hand circular polarization (RHCP)
• Radiation pattern: Near-omnidirectional coverage as an antenna system, ensuring command reception in over 90% of all possible CubeSat attitudes.

For antenna measurement purposes, an external power splitter (Mini-Circuits ZX10-2-332-S+ [19]) was employed instead of the built-in splitter to facilitate accurate characterization of the antenna system.

4. Electromagnetic Simulation for S-Band Uplink Antenna

4.1. Modeling

To verify that the combination of two patch antennas provides omnidirectional performance, an electromagnetic field simulation was conducted using the Finite Element Method (FEM). The antenna geometry shown in Figure 3 represents the electrically relevant dimensions used in the simulation, while minor mechanical details not affecting radiation characteristics were omitted for clarity and reproducibility. As shown in Figure 4, the CubeSat model consisted of a 6U aluminum structure with deployable solar array wings.

Table 2. Main parameters of the simulation model.

Parameter	Modeling	Remarks
Main body	Aluminum box ($102\times 226.5\times 325$ mm)	6U CubeSat
Wings	Aluminum plate ($207\times 318\times 1.5$ mm)	Deployable Solar Array Paddle (DSAP)
Antennas	See Table 3 and Figure 4
Simulation area	Sphere of 1 m radius	Free-space boundary conditions applied
Feeding	Port 1 (−Y): 1V $\angle 0°$ Port 2 (+Y): 1V $\angle 0°$

summarizes the main parameters used in the simulation setup, including CubeSat dimensions, antenna placement, and feeding conditions.

Table 3. Antenna design requirement of single patch antenna.

Parameter	Value or Description
Frequency	Single channel within $2.025$–$2.110$ GHz
Material of patch antenna	Rogers RT5880 (Dielectric thickness $t=1.575$ mm)
Antenna size	70 mm × 70 mm × $1.575$ mm (excluding SMA connector)
Feeding method	Coaxial probe feed
Polarization	RHCP generated by a corner cut on the patch element
Antenna gain	>6 dBic
Input impedance	50 $\mathsf{\Omega }$
Reflection coefficient	$|S_{11}|<-10$ dB at center frequency
Bandwidth	>50 MHz
Radiation pattern	Broadside
Axial ratio	<3 dB

Table 3. Antenna design requirement of single patch antenna.

Parameter	Value or Description
Frequency	Single channel within $2.025$–$2.110$ GHz
Material of patch antenna	Rogers RT5880 (Dielectric thickness $t=1.575$ mm)
Antenna size	70 mm × 70 mm × $1.575$ mm (excluding SMA connector)
Feeding method	Coaxial probe feed
Polarization	RHCP generated by a corner cut on the patch element
Antenna gain	>6 dBic
Input impedance	50 $\mathsf{\Omega }$
Reflection coefficient	$|S_{11}|<-10$ dB at center frequency
Bandwidth	>50 MHz
Radiation pattern	Broadside
Axial ratio	<3 dB

4.2. Simulation Results

Reflection coefficient and radiation patterns were analyzed to evaluate the performance of the patch-antenna system. The reflection coefficient was visualized using an S11 plot and the radiation pattern was examined in a two-dimensional plot.

4.2.1. Impedance Matching

The impedance matching is evaluated using an $S_{11}$ plot, as shown in Figure 5. For security reasons, this graph is plotted with the horizontal axis as the difference from the uplink frequency used by VERTECS. Because the antennas mounted on the ±Y panels had identical designs, the impedance characteristics of both antennas were nearly identical. To avoid visual clutter in Figure 5, only the result for the antenna mounted on the −Y panel is presented. These reflection coefficients were observed to be $18.5$ dB and $19.2$ dB at the uplink frequency for the −Y and +Y panels, respectively, indicating good impedance matching.

Furthermore, the S-parameters measured with a prototype antenna (as shown in Figure 2b) attached to a CubeSat mockup are indicated by the red dotted lines. The simulated and measured S-parameters are in good agreement, differing by only $5.25$ MHz when compared at the center of the range where $S_{11}$ is below $-10$ dB. This is an error of only $0.26\%$ for an uplink frequency of about 2 GHz. The simulated bandwidth is $55.0$ MHz, while the measured bandwidth is $52.5$ MHz, an error of only $10\%$.

4.2.2. Radiation Pattern Analysis

The simulated two-dimensional radiation patterns were presented in three principal planes: XY-plane (0°: X-axis, 90°: Y-axis), YZ-plane (0°: Z-axis, 90°: Y-axis), and XZ-plane (0°: Z-axis, 90°: X-axis). The results are shown in Figure 6. The results demonstrate that the combined radiation from the two patch antennas achieves an omnidirectional pattern in the XY-plane and YZ-plane, which is critical for maintaining a stable uplink communication at various CubeSat attitudes.

4.3. Discussion

The simulated radiation patterns confirmed that the combination of the two patch antennas achieved near-omnidirectional coverage in most of the directions. In the XY-plane (Figure 6a) and YZ-plane (Figure 6b), the gain remains above −5 dBic in the majority of CubeSat attitudes, ensuring stable uplink communication. However, in the XZ-plane (Figure 6c), the gain drops below $-5$ dBic in certain regions. This is attributed to the broadside radiation pattern inherent to patch antennas, which results in a weaker signal strength along specific axes.

To further analyze these characteristics, we evaluated the maximum gain at 1° intervals for both $\varphi$ and $\theta$. The highest simulated gain was found to be $4.8$ dBic at $(\varphi ,\theta )=(95°,97°)$. Theoretically, the maximum gain is expected at $(\varphi ,\theta )=(90°,90°)$ and $(270°,90°)$, corresponding to the broadside directions of the two patch antennas. In this study, the azimuthal angle $\varphi$ was measured in the plane perpendicular to the CubeSat Z-axis, starting from the positive X-axis and increasing counterclockwise. The zenith angle $\theta$ is defined as the angle between the Z-axis and the observation direction. However, this deviation is considered to be influenced by antenna placement, feed position, and CubeSat structure.

These results indicate that a purely two-dimensional analysis does not fully capture the gain variations across all possible CubeSat attitudes. Motivated by this limitation, we developed a three-dimensional radiation pattern measurement system to obtain a more comprehensive understanding of the coverage of the antenna system. This approach accounts for variations across all possible CubeSat attitudes, and enables a more holistic assessment.

Building on these simulation results, we introduce the Coverage Ratio of CubeSat Attitude as a quantitative metric to evaluate the proportion of attitudes that meet a given required gain threshold. This provides deeper insight into the robustness of the communication link under realistic operational conditions, as discussed in the next section.

In the actual VERTECS project, although the ±Y faces are selected based on the CRCA-based evaluation, the antenna positions are adjusted to accommodate other onboard instruments. The final antenna layout adopted for VERTECS is shown in Figure 1.

5. Coverage Ratio of CubeSat Attitude (CRCA)

In this section, we propose a new metric for assessing the communication performance of CubeSats under tumbling conditions: the Coverage Ratio of CubeSat Attitude (CRCA). This metric is defined as the proportion of all possible CubeSat attitudes in which the antenna gain exceeds a specified threshold. Intuitively, it represents how often the satellite can maintain a communication link under tumbling conditions. The CRCA formulation assumes a uniform distribution of spacecraft attitudes, which corresponds to early mission phases or contingency scenarios where the attitude motion is not actively controlled. Although actual attitude dynamics may deviate from a perfectly uniform distribution, this assumption provides a conservative and practical baseline for evaluating communication robustness under uncertain conditions. This evaluation is critical for ensuring reliable communication between the CubeSat and ground station.

5.1. Gain Map from Simulation Results

First, we introduce the gain map derived from the simulation results, where the vertical axis represents the azimuthal angle ($\varphi$) and the horizontal axis represents the zenith angle ($\theta$). This map visually illustrates the gain of the antenna system across the various CubeSat attitudes.

The gain map of the simulation result is shown in Figure 7. As shown in the map, the antenna system achieves a gain of −10 dBic or higher over a wide range of angles. This suggests that omnidirectional coverage is possible across a significant portion of the CubeSat attitude range. However, this visual representation alone does not provide a quantitative assessment of expected antenna gain under tumbling conditions. This is because each sample point in the gain map corresponds to a different solid angle. Therefore, we propose calculating the Coverage Ratio of CubeSat Attitude, which represents the proportion of attitudes that meet the required gain.

5.2. Definition of the Coverage Ratio of CubeSat Attitude (CRCA)

The coverage ratio of CubeSat attitude was computed by determining the solid angle corresponding to the required gain and normalizing it by the total solid angle, $4\pi$. Specifically, the solid angle $\mathrm{\Delta }S$ for a given required gain is calculated as follows:

$$\mathrm{\Delta }S=|sin\theta |\mathrm{\Delta }\varphi \mathrm{\Delta }\theta$$

(1)

where $\mathrm{\Delta }\varphi$ and $\mathrm{\Delta }\theta$ are the step sizes of azimuthal angle $\varphi$ and the zenith angle $\theta$.

By summing the solid angles corresponding to all attitudes that satisfy the required gain, we obtain the total solid angle coverage. This was then normalized by $4\pi$ to determine the proportion of attitudes that met the gain requirement. In summary, the Coverage Ratio of CubeSat Attitude (CRCA) is expressed as:

$$\mathrm{CRCA}\left(G_{\mathrm{r}}\right)=\sum _{G(\theta ,\varphi )>G_{\mathrm{r}}}{\displaystyle \frac{\mathrm{\Delta }S}{4\pi }}=\sum _{G(\theta ,\varphi )>G_{\mathrm{r}}}{\displaystyle \frac{|sin\theta |\mathrm{\Delta }\varphi \mathrm{\Delta }\theta }{4\pi }}$$

(2)

where:

• $G_{\mathrm{r}}$ is the required gain threshold.
• $G(\theta ,\varphi )$ represents the antenna gain at a given attitude ($\theta ,\varphi$).
• $\mathrm{\Delta }S$ is the solid angle corresponding to each gain sampling point.
• $\theta$ and $\varphi$ are the zenith and azimuthal angles, respectively.

It should be noted that the CRCA formulation itself does not depend on operating frequency. Once the three-dimensional radiation pattern is obtained, either through simulation or measurement, the CRCA can be computed in an identical manner regardless of the frequency band. Therefore, although this study validates the CRCA framework using an S-band uplink antenna as a representative case, the proposed metric is equally applicable to antenna systems operating at other frequency bands, such as X-band.

The mathematical meaning of the CRCA formulation can be understood by interpreting the antenna gain over all possible CubeSat attitudes as a random variable defined on the unit sphere. Under the assumption of a uniformly distributed attitude, each infinitesimal solid angle element represents an equal probability mass. When the radiation pattern is discretized with uniform angular steps in $\theta$ and $\varphi$, the probability associated with each sampling point is proportional to the corresponding solid angle element, given by $|sin\theta |\mathrm{\Delta }\theta \mathrm{\Delta }\varphi$.

From this perspective, CRCA corresponds to a weighted complementary cumulative distribution function (CCDF) of the antenna gain with respect to the attitude distribution. Specifically, for a given required gain $G_{\mathrm{r}}$, the CRCA represents the probability that the gain random variable $G(\theta ,\varphi )$ exceeds $G_{\mathrm{r}}$, where each sample is weighted by its solid angle contribution. The $sin\theta$ term arises from the spherical surface element and ensures that attitudes near the poles, which represent smaller solid angles, are not overrepresented in the evaluation.

This solid-angle weighting is essential for correctly reflecting the physical distribution of spacecraft attitudes on the sphere. Without this weighting, simple point counting would bias the coverage evaluation toward regions with higher sampling density in angular coordinates, leading to an incorrect estimation of attitude coverage.

In this study, the CRCA is calculated under the assumption of a uniform attitude distribution, which corresponds to random tumbling conditions without preferred spin axes. This assumption is particularly relevant to early mission phases or contingency scenarios, where active attitude control is not yet available or temporarily lost. Although non-uniform attitude distributions may occur in practice, their evaluation requires attitude dynamics simulations coupled with antenna radiation characteristics and is therefore left for future work.

It is important to clarify the distinction between CRCA and existing spherical coverage metrics discussed in the antenna and mobile communication literature. Metrics based on the fraction of solid angle exceeding a required gain have been previously proposed, such as the coverage efficiency introduced by Helander et al. [9], which focuses on characterizing antenna radiation performance over a sphere. In addition, spherical coverage characterization frameworks based on 3GPP specifications have been developed for mobile communication devices, where metrics such as the cumulative distribution function of EIRP are evaluated assuming optimal beam selection through beamforming [10].

In contrast to these approaches, CRCA is specifically formulated to evaluate CubeSat communication performance by treating spacecraft attitude itself as a state variable. Rather than assessing coverage over a solid angle under fixed device orientation or beam control assumptions, CRCA represents the fraction of possible CubeSat attitudes for which the antenna gain exceeds a required threshold. This formulation directly reflects the probability of successful command uplink establishment under attitude-uncertain or tumbling conditions, particularly during early mission phases when active attitude control or beamforming cannot be assumed.

5.3. Coverage Ratio of CubeSat Attitude (CRCA) from Simulation Results

Figure 8 shows the coverage ratio calculated from the simulation results. This figure represents the proportion of CubeSat attitudes that achieve the required gain at different levels. As expected, the coverage ratio decreases as the required gain increases, illustrating a trade-off between gain requirements and attitude coverage. From this figure, we observe that the required gain corresponding to 90% of all possible CubeSat attitudes is $-8.0$ dBic.

In actual measurements, the step size of $\varphi$ may not always achieve fine angular resolution. To evaluate the influence of angular sampling on the CRCA, we computed the coverage ratio using various $\varphi$ step sizes ranging from 1° to 90°. As shown in Figure 8, CRCA values are nearly identical for step sizes of 15° or finer. However, when the resolution becomes too coarse, such as at $\mathrm{\Delta }\varphi =90°$, the accuracy of CRCA estimation degrades significantly.

Table 4. Maximum CRCA error for different $\varphi$ step sizes.

$\mathbf{\Delta }\mathit{\varphi }$	CRCA Error (% Point)
1°	Reference
5°	0.2
15°	1.1
45°	5.0
90°	12.4

summarizes the maximum CRCA error for each step size, using the 1° case as a reference. The error remains below 1.1 percentage points for step sizes up to 15°, confirming the validity of the chosen resolution in our simulation.

To further ensure the robustness of the CRCA metric, we investigated its dependence on the simulation coordinate system. The CubeSat coordinate system used in the simulation is shown in Figure 9. Specifically, we calculated the CRCA while aligning the simulation Z-axis with each of the mechanical X, Y, and Z axes of the CubeSat. As shown in Figure 10, the resulting curves are nearly identical, indicating that the CRCA metric is independent of the simulation axis definition.

These results indicate that CRCA can also be applied to measured data. Although the finer step size used in the simulations may not be feasible for practical measurements, the difference in step size does not significantly affect comparability. Applying the same criteria allows consistent comparison between the simulation results and experimental data.

Based on these results, the angular resolution settings used in the simulations and measurements are summarized in

Table 5. Angular resolution for simulations and measurements.

Condition	$\mathbf{\Delta }\mathit{\theta }$	$\mathbf{\Delta }\mathit{\varphi }$
Simulation	1°	1°
Measurement	1°	5°

. In both cases, the zenith angle ($\theta$) was sampled at 1° intervals, while the azimuthal angle ($\varphi$) was sampled at 1° and 5° intervals in the simulation and measurements, respectively. The coarser azimuthal sampling in the measurements was selected as a trade-off between measurement time and angular resolution.

It should be noted that CRCA is not intended to replace conventional communication performance metrics such as equivalent isotropic radiated power (EIRP), but rather to complement them. Metrics such as EIRP, G/T or peak antenna gain are effective for evaluating the maximum achievable link margin under favorable pointing or controlled attitude conditions. However, these metrics do not directly indicate how frequently such conditions occur when the spacecraft attitude is uncertain.

In contrast, CRCA explicitly incorporates spacecraft attitude as a probabilistic variable and evaluates the fraction of attitudes that satisfy a required gain threshold. This makes CRCA particularly suitable for assessing uplink robustness during early mission phases or contingency scenarios, where attitude control and beamforming cannot be assumed. On the other hand, CRCA does not capture information such as instantaneous peak performance, polarization mismatch, or achievable data rate, which are better evaluated using conventional link budget metrics.

Therefore, CRCA should be regarded as a complementary metric that bridges antenna radiation characteristics and attitude uncertainty, rather than a substitute for existing performance indicators.

In the next section, we compare the coverage ratio of CubeSat attitude obtained from both the simulations and measurements.

6. CRCA-Based Antenna Placement Design and Comparison

In this section, the proposed CRCA is used to compare several antenna placement configurations for a CubeSat with solar panels deployed from the $\pm X$ faces. The antenna placement is evaluated from the viewpoint of attitude-dependent coverage using the CRCA metric. Although the antenna configuration of VERTECS is used as a reference, this placement study focuses on a generalized comparison of antenna mounting faces using CRCA, independent of the final mechanical layout.

6.1. Antenna Placement Configurations

Several antenna placement configurations are considered to investigate the effect of antenna location on attitude-dependent coverage. In this study, antenna pairs are placed on the ±X, ±Y, and ±Z faces, as well as on non-opposing face combinations such as +Y & −Z and −Y & +Z. For all configurations, the antenna position on each face is fixed at the center to enable a fair comparison among different faces. Figure 11 shows the antenna placement configurations used for the CRCA evaluation. Although the ±X faces are not suitable for mounting a critical uplink antenna due to solar panel deployment, they are included here for a comprehensive comparison. In all configurations, the antenna geometry, excitation conditions, and feed structure are kept identical, and only the mounting faces are varied. The antenna simulation parameters are identical to those described in Section 4.

6.2. Comparison of CRCA Results

Figure 12 shows the CRCA curves for different antenna placement configurations. For all configurations, the CRCA is calculated under the same evaluation conditions and angular resolution as defined in Section 5, where both $\theta$ and $\varphi$ are sampled with a resolution of 1°.

As shown in Figure 12, the antenna placements on the ±Y and ±Z faces achieve higher coverage ratios over a wide range of required gain values than the other configurations. These opposing-face placements maintain high CRCA values even for relatively stringent required gain levels, indicating robust attitude-independent coverage.

In contrast, the ±X placement exhibits lower CRCA values across most of the required gain range. This degradation is attributed to the interaction with the deployed solar panels, which affects the radiation characteristics and polarization purity. The non-opposing face configurations (+Y & −Z and −Y & +Z) also show reduced CRCA values compared with the opposing-face cases.

For a quantitative comparison, the required antenna gain corresponding to a CRCA of 90% is extracted for each configuration. The results are summarized in

Table 6. Required antenna gain for 90% CRCA under different antenna placement configurations.

Antenna Placement	Required Gain for 90% CRCA [dBic]
±X	−13.9
±Y	−8.2
±Z	−8.7
+Y & −Z	−13.8
−Y & +Z	−13.4
VERTECS (±Y)	−8.0

. For reference, the CRCA of 90% for the final VERTECS antenna configuration is also included. The 90% CRCA value for VERTECS is in good agreement with that of the ±Y case with the antenna placed at the center, suggesting that the choice of antenna mounting faces plays a dominant role in achieving robust attitude-dependent coverage.

6.3. Design Insights from CRCA-Based Comparison

The CRCA-based comparison demonstrates that antenna placements on opposing faces provide superior attitude-dependent coverage compared with non-opposing configurations. Among the evaluated cases, the ±Y and ±Z placements achieve higher coverage robustness as quantified by CRCA.

Although the ±Z placement exhibits coverage performance comparable to that of the ±Y placement, the $-Z$ face of the VERTECS satellite is reserved for star sensors and the telescope. Therefore, the ±Y antenna placement is selected as a reasonable configuration for the uplink antenna system when both communication performance and mission constraints are taken into account.

These results indicate that CRCA can serve as a practical design tool for selecting antenna mounting faces at an early design stage, before detailed mechanical integration is finalized.

7. 3D Radiation Measurement System

Based on the CRCA-based antenna placement study presented in Section 6, the selected antenna configuration is experimentally validated through three-dimensional radiation pattern measurements. To evaluate the coverage ratio of CubeSat attitude through actual measurements, we developed a three-dimensional radiation pattern measurement environment. This section describes the measurement system, setup process, and obtained results, along with a comparison with simulation data.

7.1. Measurement System Overview

To achieve three-dimensional radiation pattern measurements, we constructed a system consisting of the following components:

• Full anechoic chamber: A shielded room designed to eliminate reflections and external electromagnetic interference, ensuring accurate measurements.
• Base and roll turntable: A system comprising a base rotation turntable and an additional roll-angle turntable to achieve full three-dimensional measurements (Figure 13b).
• Absorber material: Near metallic structures in the test area to minimize reflections and unwanted interference.
• Reference antenna: A well-characterized standard-gain antenna was used as the receiving antenna to ensure consistent and repeatable measurements. Gain calibration was performed prior to the measurements using another reference antenna to ensure accurate received power levels.
• Signal generator and spectrum analyzer: The signal generator provides the input signal, whereas the spectrum analyzer records the received power for each orientation.
• Control software (LabVIEW 2024): Automated system control using LabVIEW that manages turntable movements and synchronizes data acquisition.

Table 7. 3D radiation pattern measurement equipment.

Equipment	Model or Description
Full anechoic chamber	Manufactured by Riken Environmental System Co., Ltd., Japan; working volume: 5 m × $6.4$ m × $5.6$ m
Base turntable	TUA series (Riken Environmental System Co., Ltd., Tokyo, Japan)
Roll turntable	HQ303-EL (TSS Japan Co., Ltd., Tokyo, Japan)
Reference antenna	CLSA0110 RHCP antenna (Schwarzbeck Mess-Elektronik, Schönau, Germany)
Signal generator	SMR20 (Rohde & Schwarz GmbH & Co. KG, Munich, Germany)
Spectrum analyzer	FSQ26 (Rohde & Schwarz GmbH & Co. KG, Munich, Germany)
Control software	In-house developed software on LabVIEW 2024 (National Instruments, Austin, TX, USA)

lists the primary equipment used in the three-dimensional radiation pattern measurement system. Figure 13 presents a block diagram of the measurement system, the turntable for the roll angle and a photograph of the measurement setup inside the anechoic chamber. The distance between the CubeSat under test and the reference antenna was set to 3.8 m. The validity of the far-field condition was evaluated using the Fraunhofer distance. The minimum far-field distance $R_{\mathrm{FF}}$ is given by

$$R_{\mathrm{FF}}={\displaystyle \frac{2D^2}{\lambda }},$$

(3)

where D is the maximum dimension of the antenna-under-test including the deployed solar panels, and $\lambda$ is the wavelength.

In this study, the maximum CubeSat dimension is approximately $D=0.52$ m. The uplink center frequency of $2.11$ GHz corresponds to the shortest wavelength within the operational band and therefore represents the most stringent condition for far-field verification. At this frequency ($\lambda \approx 0.142$ m), the Fraunhofer distance is approximately $3.8$ m. Since the measurement distance was set to $3.8$ m, the far-field condition is satisfied for all frequencies within the uplink band.

It should be noted that the measurement distance of 3.8 m is close to the maximum achievable separation in the anechoic chamber at Kyushu Institute of Technology. For higher frequency bands, such as X-band, the required far-field distance increases due to the shorter wavelength, and satisfying the Fraunhofer condition may become impractical within the same facility. In such cases, additional techniques such as near-field to far-field transformation or compact antenna test range (CATR) methods would be required. The integration of CRCA evaluation with these advanced measurement techniques is left for future work.

While spherical near-field (SNF) [20] is widely used for antenna characterization, this technique is primarily beneficial when far-field conditions cannot be readily achieved, such as in the case of large satellite platforms or complex communication devices. In contrast, for small satellites like CubeSats, the physical dimensions allow for sufficient far-field measurements within a relatively short distance. Moreover, when a sufficiently large anechoic chamber and a turntable system are available, the proposed method can be implemented simply by adding a roll-angle rotation mechanism, enabling three-dimensional radiation pattern measurements with minimal additional cost and effort. This setup provides a practical and cost-effective solution specifically optimized for small satellite applications.

7.2. Measurement Result

Figure 14 illustrates the measured results of the three-dimensional radiation pattern. The figure shows that the main lobe is oriented along the $\pm Y$ axis.

To capture a complete three-dimensional radiation pattern, measurements were taken twice, with the CubeSat flipped by 180° between each measurement. This procedure was necessary to mitigate measurement obstructions caused by the roll turntable. The two datasets were then merged to generate a complete gain map, ensuring comprehensive coverage. Figure 15 presents the measured gain map of the CubeSat antenna system, obtained in the anechoic chamber. The color gradient represents the measured gain values across various CubeSat orientations. Two faint vertical lines at $\theta =\pm 90°$ indicate the regions where the measurement datasets were merged.

Measurement errors due to dataset merging were quantified by comparing the gain values before and after CubeSat flipping. The mean absolute error (MAE) between the pre- and post-flip measurements was 0.7 dB at $\theta =+90°$ and 1.2 dB at $\theta =-90°$. These deviations can be attributed to multiple factors, including residual scattering from the roll turntable, small positioning deviations during the flipping process, and calibration uncertainties between measurements. Since the observed errors are confined to a narrow angular region around the merging seam and remain on the order of 1 dB, their contribution to the solid-angle–weighted CRCA is limited. Such seam-related errors can be mitigated through improvements in turntable scattering suppression, positioning repeatability, and calibration procedures.

By comparing Figure 15 with the simulation results, it is evident that the resolution of the $\varphi$ angle is lower because of the use of a 5° step in $\varphi$. Despite this, the main characteristics were still preserved, and the measured gain map exhibited similar trends, confirming the validity of the measurement setup. However, slight deviations in certain regions can be attributed to the measurement uncertainties discussed above. Future work will include systematic chamber validation tests, such as quiet-zone field uniformity evaluation, together with these improvements, to quantitatively assess and minimize the associated measurement uncertainties.

7.3. Coverage Ratio of CubeSat Attitude (CRCA) from Measurement Results

A plot of the coverage ratio of CubeSat attitude derived from the measurement data is shown in Figure 16, with the simulation results included for comparison. To incorporate the measurement conditions into the simulation results, a loss correction was applied to the coverage ratio plot. Specifically, the transmission loss of the RF splitter and coaxial cables was measured using a vector network analyzer (VNA), yielding $S_{21}$ and $S_{31}$ values of approximately $-4.1$ dB. Since this measured loss includes both splitter and cable effects, it corresponds to an effective excess loss of about $1.1$ dB per output path. Therefore, the measured coverage ratio results were corrected by $1.1$ dB, as these losses were not considered in the initial simulation.

The measurement and simulation results exhibited strong agreement, with discrepancies within 1 dB in the coverage ratio of CubeSat attitude. This small deviation can be attributed to minor measurement uncertainties such as cable losses, positioning errors, and environmental factors within the anechoic chamber. These results confirm that the coverage ratio of CubeSat attitude serves as a reliable metric for both simulation and measurement.

According to the measured data, the antenna gain exceeds $-10.0$ dBic in 90% of all possible CubeSat attitudes. Given that the maximum gain is $3.4$ dBic, this corresponds to a pointing loss of $13.4$ dB.

It should be noted that the radiation characteristics presented in this study were measured under room-temperature conditions. The influence of extreme thermal environments in space was not explicitly evaluated. Thermal effects on antenna gain and impedance characteristics are important for flight qualification and are typically assessed through thermal-vacuum testing at the system level. The integration of CRCA evaluation with radiation pattern measurements under high- and low-temperature environments, as well as under ionizing radiation conditions, is an important subject for future work.

8. Link Budget Considering Coverage Ratio of CubeSat Attitude (CRCA)

By applying the coverage ratio of CubeSat attitude to the link budget, the feasibility of communication under tumbling conditions can be evaluated. As an example, we analyze the VERTECS S-band 1 kbps uplink system.

The coverage ratio of CubeSat attitude, derived from the measured data in Figure 16, shows that a gain of greater than $-10.0$ dBic is achieved in 90% of all possible CubeSat attitudes. We incorporated this value into the link budget analysis to assess the feasibility of uplink communication under tumbling conditions.

Table 8. Link budget calculation for S-band uplink of VERTECS.

Parameter	Value	Unit	Remark
Frequency f	2070	MHz	Center of allocated frequency for S-band uplink
Wavelength $\lambda$	145	mm	Calculated from $\mathrm{c}/f$ and $\mathrm{c}$ is the speed of light in vacuum.
Transmission power at ground station	20	W	Design requirement for manufacture
Transmission power in dBm	43	dBm	Converted from power value
Line loss at ground station	1	dB	Assumed value for ground station transmission line loss
Antenna diameter D at ground station	2.4	m	Kyutech ground station antenna specification
Aperture efficiency $\eta$ at ground station	50	%	Typical value for parabolic antennas
Antenna gain at ground station	31.3	dBic	Calculated from $10{log}_{10}\left(\eta ·{\left({\displaystyle \frac{\pi D}{\lambda }}\right)}^2\right)$
Pointing loss at ground station	3	dB	Estimated based on ground station tracking accuracy (Beamwidth $=4.3°$)
Altitude	680	km	Sun-synchronous orbit altitude
Elevation	10	°	Minimum operational elevation angle
Range R	2112	km	Calculated using orbital geometry and Radius of the Earth as 6378 km
Free Space Path Loss (FSPL)	165.3	dB	Calculated from $20{log}_{10}\left({\displaystyle \frac{4\pi R}{\lambda }}\right)$
Polarization loss	1.2	dB	Maximum polarization mismatch assuming both antennas have an axial ratio of 3 dB
Atmospheric loss	0.3	dB	Atmospheric gaseous loss at S-band and 10 ° elevation (ITU-R P.618/P.676) [21,22]
Ionospheric loss	0	dB	Ionospheric loss at S-band (ITU-R P.531) [23]
Rainfall loss	0	dB	Rainfall loss at S-band (ITU-R P.618) [21]
Antenna gain at CubeSat	3.4	dBic	Measured in this work
Pointing loss at CubeSat	13.4	dB	Equivalent to $-10.0$ dBic effective antenna gain
Line loss at CubeSat	1	dB	Assumed for internal CubeSat RF system
Receiving power at CubeSat	−107.4	dBm	Calculated using link budget equation
Sensitivity (Bit Error Rate (BER) = ${10}^{-4}$)	−122	dBm	From specification sheet of A88 SRX [18]
Hardware degradation	3	dB	Conservative margin for implementation loss and environmental effects [24,25]
Link margin	11.6	dB	Calculated as received power minus sensitivity minus hardware degradation

presents the link budget calculations based on worst-case operational values. The results confirm that the link margin remains positive, demonstrating that the antenna configuration for the VERTECS S-band command uplink ensures reliable communication across 90% of all the possible CubeSat attitudes.

In this calculation, the center frequency is 2.070 GHz as an example, which is near the middle of the range of 2.025 GHz to 2.110 GHz allocated for the S-band uplink. As mentioned above, this is because of security issues. In fact, the link margin remains unchanged across the 2.025–2.110 GHz range, because the frequency dependency of the ground station’s parabolic antenna gain exactly cancels out that of the free-space path loss.

It should be noted that the sensitivity value used in this link budget analysis was measured by the receiver manufacturer using a single input signal before the splitter, as illustrated in Figure 17. This measurement configuration can introduce a theoretical discrepancy of approximately 3 dB compared to the actual operational scenario, in which signals from both antennas are combined through the splitter.

However, since the link budget analysis adopts a conservative, worst-case assumption by directly using the specified sensitivity without compensating for potential combining gain, the reported sensitivity remains appropriate for evaluating robust communication performance under tumbling conditions.

9. Comparison with Previous Work

Several previous studies have investigated CubeSat antenna configurations aiming at omnidirectional coverage. Islam [6] and Abdullah [7] focused on antenna placement strategies for S-band communication, but their evaluations were limited to simulation or subsystem design without a systematic quantitative metric. Abele [8] reported measurement results of a 6U CubeSat antenna system, while Orger [13] demonstrated an on-orbit mission using C-band communication. Although these works confirmed that combining multiple patch antennas can enhance coverage, none provided a framework to quantify how frequently sufficient gain is achieved across all CubeSat attitudes.

As summarized in

Table 9. Comparison of CubeSat antenna studies with focus on omnidirectional coverage.

Ref.	Frequency	Antenna Type	Form Factor	3D Radiation Pattern	Quantitative Omnidirectionality Evaluation	Remark
[4]	2.285 GHz	2 TX on +X and +Y side	30 cm-class	Yes (Sim.)	No	On-orbit demo by HORYU-IV
[5]	2.0675 GHz 2.245 GHz	2 TX and RX on ±Z side	CubeSat (not specified)	No	No	–
[6]	2.05 GHz	2 RX on ±X side	6U CubeSat	Yes (Meas.)	No	–
[7]	5.65–5.67 GHz 5.84–5.85 GHz	2 RX on ±X 1 TX on –Z	6U CubeSat	No	No	On-orbit demo by KITSUNE
This Work	2.025–2.110 GHz	2 RX on ±Y side	6U CubeSat	Yes	Yes (CRCA)	On-orbit demo by VERTECS (planned)

, our study extends beyond these efforts in two key aspects. First, it combines both electromagnetic simulations and three-dimensional measurements to characterize the antenna system, ensuring consistency between modeling and experimental results. Second, it introduces the Coverage Ratio of CubeSat Attitude (CRCA) as a unified and quantitative metric, which can be applied to both simulation and measurement data. This dual approach not only validates the simulation model but also establishes a practical methodology for evaluating CubeSat communication performance under tumbling conditions, filling a gap left by previous research.

10. Conclusions

This study presented a quantitative evaluation of the omnidirectional antenna performance of a CubeSat S-band communication system using both electromagnetic simulations and three-dimensional radiation pattern measurements. Prior to this work, determining the appropriate antenna gain for link budget analysis under arbitrary CubeSat attitudes had not been addressed in a systematic manner. To overcome this limitation, we introduced the Coverage Ratio of CubeSat Attitude (CRCA), a metric that quantifies the proportion of spacecraft orientations for which the antenna gain exceeds a required threshold.

Using CRCA, we demonstrated that the combined S-band antenna configuration of the 6U CubeSat VERTECS achieves greater than $-8.0$ dBic in 90% of possible attitudes in simulation. Three-dimensional measurement results using a CubeSat metal enclosure showed good agreement with simulations after accounting for splitter and cable losses, confirming that more than $-10.0$ dBic is achieved in 90% of attitudes. A CRCA-based link budget analysis verified that sufficient uplink margin can be secured even under tumbling conditions, providing a more reliable basis for communication performance assessment than traditional peak- or worst-case-gain approaches. Furthermore, CRCA was shown to be effective for quantitatively comparing different antenna placement configurations, clarifying the impact of mounting faces on attitude-dependent coverage.

The CRCA framework offers a practical and generalizable method for evaluating attitude-dependent antenna performance in CubeSat missions. By enabling link reliability to be assessed independently of specific attitude control capabilities, the method also reduces the burden placed on the spacecraft’s attitude control subsystem—a feature that aligns well with the resource-efficient design philosophy of LeanSat missions.

Future work includes integrating attitude dynamics simulations to estimate communication availability under realistic motion profiles, as well as examining in-orbit communication data from VERTECS to verify consistency with CRCA-based predictions. Although demonstrated in the S-band context, the CRCA methodology itself is not frequency-specific and is directly applicable to higher frequency bands such as X-band and Ka-band. However, experimental validation at higher frequencies introduces additional challenges, as the required far-field distance increases with decreasing wavelength and may exceed the physical constraints of conventional anechoic chambers. In such cases, advanced measurement techniques such as near-field to far-field transformation or compact antenna test ranges will be required. Addressing these measurement challenges while extending CRCA-based evaluation to higher frequency bands remains an important subject for future research.