System-Level Evaluation of Beam Hopping in NR-Based LEO Satellite Communication System

This paper considers a LEO satellite communication system, where satellites work with a regenerative payload allowing on-board processing of baseband signals. The system is assumed to operate at two frequency bands for downlink transmission, with a center frequency of 2 GHz and 20 GHz at S band and Ka band, respectively. The system bandwidth is 30 MHz with the subcarrier spacing of 15 kHz for S band, while the bandwidth is 200 MHz and subcarrier spacing is 120 kHz for Ka band.

Furthermore, the LEO system is assumed to follow a walker constellation, composed of $M$ satellites that are distributed in $P$ planes inclined at $55^{\circ}$, with an orbital altitude equal to 600 km. Each satellite intends to cover the service area via generating at most $K$ spotbeams on the ground, and a maximum number of $I_{\mathrm{max}}\leq K$ beams are assigned at each time slot to illuminate a portion of the coverage area. Details for the designing beam hopping scheme will be elaborated in the next section. Furthermore, a visualization demonstration of one time slot in the considered communication system, which comprises $M=2400$ satellites in $P=60$ planes, for serving parts of the world under $I_{\mathrm{max}}=40$ is plotted in Fig. 1, where satellites and illuminated spotbeams on the ground are represented by yellow points and white circles, respectively.

In the LEO satellite communication system, each satellite is assumed to be equipped with phased array antenna, which can steer multiple beams on the ground and change their directions in real-time. Specifically, the elements of planar array are arranged on a square grid, and the geometry is obtained by placing 28 elements along both the x-axis and y-axis with equal spacing of $0.46\lambda$, where $\lambda$ is a wavelength. The satellite transmit gain $G_{T}$ is 24 dBi and 30.5 dBi for S band and Ka band, respectively.

By following [3], the LEO system is assumed to serve handheld UEs and very small aperture terminal (VSAT) UEs in S band and Ka band, respectively. In particular, the handheld UE is equipped with omni-directional antenna with receive antenna gain $G_{R}=0$ dBi, while the VSAT UE is equipped with a circularly polarized antenna with 60 cm equivalent aperture diameter and receive antenna gain $G_{R}=39.7$ dBi.

The system-level evaluation of the LEO system is performed in a 5G NR simulator with a full protocol stack. For example, radio link control entity is configured in acknowledge mode to support error-free transmission; channel-quality indicator (CQI) information is fed back by UEs for the scheduling of satellite resources; adaptive modulation and coding is employed for the transmission of UEs; retransmissions are processed by adaptive hybrid automatic repeat request (HARQ) protocol.

Typically for a UE on the ground, a certain number of satellites are visible above the minimum elevation angle and might provide service to it. In this paper, we assume that satellites employ the earth-fixed beams and each UE can only be served by one satellite at one snapshot such that the satellite can direct its beams towards its associated UEs and interference received from neighboring satellites is reduced. With these assumptions, it is thus essential to find an appropriate association between the layout of satellites’ spotbeams and UEs to ensure that beamforming gains are fully exploited. In the following, we propose an efficient approach to find a proper association.

After receiving global navigation satellite system (GNSS) signals of UEs, each satellite will assign its spotbeams towards UEs in an order from near to distant until all $K$ spotbeams are utilized or all reporting UEs are covered. Besides, during the assignment, if a UE has already been covered by an existing spotbeam, no new spotbeams will be directed towards it. With the above procedures, UEs are always served by their closest satellites such that they are more likely to enjoy better communication links. Furthermore, we assume a full spectrum reuse across all spotbeams.

In this subsection, we design a beam hopping scheme to meet the time-varying traffic demands of UEs. Firstly, we denote the satellite set as $\mathcal{M}=\{1,\cdots,M\}$. The corresponding spotbeam set of satellite $m$ is denoted as $\mathcal{K}_{m}=\{1,\cdots,K_{m}\}$, with $|\mathcal{K}_{m}|=K_{m}\leq K$, $m\in\mathcal{M}$. A set of $\mathcal{J}=\{1,\cdots,J\}$ UEs are distributed requesting communication service.

For ease of exposition, the time horizon $T$ is equally discretized into $N$ equal time slots, indexed by $n=1,\cdots,N$. The elemental time slot length $\delta=T/N$ generally depends on the scheduling requirement of the LEO communication system, which can be flexibly set as the duration of several slots within a frame or the duration of several frames. The traffic demand of UE $j$ at the beginning of each time slot is denoted as $d_{j}[n]$, $j\in\mathcal{J}$, which is assumed to vary over time. During each time slot, only a maximum number of $I_{max}\leq K_{m}$ beams of each satellite are assigned. Let $I_{m,k}[n]$ denote the binary scheduling of beam $k$ of satellite $m$ at time slot $n$, where the corresponding spotbeam is illuminated if $I_{m,k}[n]=1$ and dimmed otherwise. We thus have the following constraints

Denote by $p_{m,k}[n]$ the transmit power for beam $k$ of satellite $m$, $k\in\mathcal{K}_{m}$, $m\in\mathcal{M}$ at time slot $n$. We have the following constraints

where $P_{{\mathrm{max}}}$ is the maximum transmit power of the satellite. The received power for UE $j$ from its serving satellite can be expressed as

where $h_{m,k}^{j}[n]$ is the power gain from satellite $m$ to UE $j$ and is given by

where $G_{t}(\theta_{m,k}^{j}[n],\phi_{m,k}^{j}[n])$ is the beam gain with $\theta_{m,k}^{j}[n]$ and $\phi_{m,k}^{j}[n]$ respectively representing the elevation angle and azimuth angle for UE $j$ at time slot $n$ [10], $G_{T}$ and $G_{R}$ are satellite transmit gain and UE receive gain, respectively, as described in subsection II-B, and $d_{m,k}^{j}[n]$ is the slant path distance between UE $j$ and satellite $m$, and $PL(d_{m,k}^{j}[n])$ denotes the corresponding path loss as specified in [2].

As a result, the overall signal-to-interference plus noise ratio (SINR) of UE $j$ at time slot $n$ is calculated as

where $N_{0}$ is the noise power determined by noise figure and antenna temperature, $\hat{I}^{j}_{m,k}[n]$ and $\check{I}^{j}_{m,k}[n]$ are the intra-satellite interference from beams currently transmitted by satellite $m$ and the inter-satellite interference from beams transmitted by satellite $m^{\prime}\neq m$ in $\mathcal{M}$, respectively, and are given by

It is observed from (6) that designing the beam hopping scheme is in general challenging as it entails high computational complexity with both integer variables $\{I_{m,k}[n]\}$ and non-integer variables $\{p_{m,k}[n]\}$ involved. It can also be found that illuminated spotbeams on the ground should be geographically far from each other to reduce interference so as to increase SINR and thus the offered throughput. Motivated by the aforementioned discussion, we propose an efficient greedy algorithm for the beam hopping scheme while considering the interference and time-varying traffic demands of UEs.

Specifically, at the beginning of each time slot for each satellite, define an empty set as $\mathcal{I}_{m}[n]$ to contain beams that will be assigned, i.e., $\mathcal{I}_{m}[n]\triangleq\{k|I_{m,k}[n]=1\}$. In each iteration, to maintain fairness, a spotbeam $k$ whose maximum UE traffic demand is the largest in $\mathcal{K}_{m}$ will be firstly selected. To reduce the interference, a distance limit constraint is imposed to ensure adjacent spotbeams are not illuminated concurrently. In particular, if and only if the distance $d_{k,k^{\prime}}$ between the spotbeam $k$ and all other spotbeams $\forall k^{\prime}\in\mathcal{I}_{m}[n]$ is larger than a pre-specified distance limit $D$, the spotbeam $k$ will be illuminated via setting $I_{m,k}[n]=1$ and moved from set $\mathcal{K}_{m}$ to set $\mathcal{I}_{m}[n]$. Otherwise, the spotbeam $k$ will be directly removed from $\mathcal{K}_{m}$. The process continues until set $\mathcal{K}_{m}$ becomes empty or $|\mathcal{I}_{m}[n]|=I_{\mathrm{max}}$. After determining all illuminated spotbeams, the transmit power of the satellite is evenly distributed among them, i.e., $p_{m,k}[n]=$ $P_{\mathrm{max}}/|\mathcal{I}_{m}[n]|$, $k\in\mathcal{I}_{m}[n]$. The detailed procedures of the proposed beam hopping scheme are summarized in Algorithm 1.

To draw useful insights about the system full capacity, we firstly consider the full-buffer traffic model, where a new packet of the same size 0.5 Mbytes arrives at the satellite for every UE within each time slot.

The downlink SINR and throughput performance with different beam hopping schemes at Ka band are shown in Fig. 2. As can be seen, the SINR of UEs gradually decreases with the increase of the maximum number of illuminated beams $I_{\mathrm{max}}$ under the beam hopping scheme w/o distance limit and the round robin scheme in Figs. 2(2(b)) and 2(2(c)), whereas SINR only decreases when the value of $I_{\mathrm{max}}$ is small and almost remains unchanged thereafter for the beam hopping scheme w/ distance limit in Fig. 2(2(a)). This is expected, since with the increasing value of $I_{\mathrm{max}}$, the transmit power of each beam is decreased due to a given total satellite power budget, thus leading to the degradation of SINR. Whereas for the beam hopping scheme w/ distance limit, where spotbeams within distance $D$ should not be illuminated simultaneously, the number of illuminated beams at each time slot almost remains unchanged even when $I_{\mathrm{max}}\geq 40$, resulting in a similar performance of SINR. Moreover, it is found that SINR of UEs under the beam hopping scheme w/ distance limit is always higher than that under the other two beam hopping schemes, since the inter-beam interference is greatly alleviated.

The average throughput of each satellite for different maximum number of illuminated beams $I_{\mathrm{max}}$ achieved by three beam hopping schemes is compared in Fig. 2(2(d)). It is firstly observed that for a small value of $I_{\mathrm{max}}$, the average satellite throughput increases for all three beam hopping schemes with $I_{\mathrm{max}}$. This is expected, since with the increase of $I_{\mathrm{max}}$, more beams are assigned at each time slot such that higher throughput can be achieved. And the beam hopping scheme w/ distance limit always outperforms the other two schemes due to the suppression of inter-beam interference. Moreover, it is noted that when the maximum number of illuminated beams $I_{\mathrm{max}}$ is relatively small, the round robin scheme slightly outperforms the beam hopping scheme w/o distance limit. The reason is that for UEs with insufficient link budgets, fewer bits are transmitted at each time slot and their accumulated traffic demands are generally larger than other UEs. As a result, spotbeams covering these UEs are illuminated more often to achieve fairness under the beam hopping scheme w/o distance limit, thus achieving a lower average throughput as compared to the round robin scheme.

When the maximum number of illuminated beams $I_{\mathrm{max}}$ is large, it can be observed from Fig. 2(2(d)) that the average throughput of satellites under the beam hopping scheme w/ distance limit almost remains constant, due to the distance limit constraints on the number of illuminated spotbeams. Moreover, even when $I_{\mathrm{max}}=100$ and all spotbeams are illuminated at each time slot under the beam hopping scheme w/o distance limit and the round robin scheme, the beam hopping scheme w/ distance limit still outperforms the other two. This further demonstrates effectiveness of the distance limit constraint and illustrates that assigning more beams at each time slot is not necessarily needed in designing the beam hopping scheme.

The downlink SINR and throughput performance with different beam hopping schemes at S band are shown in Fig. 3. It is observed that UEs in the S band system in general experience a lower SINR than UEs in the Ka band system due to the limited antenna gains. Furthermore, it is noted that the SINR and throughput performance of the three beam hopping schemes at S band follow a similar pattern as the Ka band, and the details are thus omitted for brevity.

In this subsection, to capture the fact that UEs in the communication system are not always requiring services, a more practical traffic model, file transfer protocol (FTP) model 3 as described in [11], is considered to evaluate the performance of the proposed beam hopping scheme. Packets of sizes 0.5 Mbytes and 0.05 Mbytes are assumed for the Ka band system and S band system, respectively, and they arrive for the same UE according to a Poisson process with arrival rate 8. Two additional performance metrics, which reflect quality of service (QoS) experienced by UEs, are used: packet life time, which is defined as the duration from the time when the packet arrives at satellite to the time when the packet is completely received at UE, and UE’s satisfaction, which is defined as the ratio between the offered throughput and demand throughput. The maximum number of illuminated beams is set as $I_{\mathrm{max}}=40$ during the simulation time of $T=1$ s.

For Ka band, Fig. 5(4(a)) depicts the life time of all packets completely received at UEs under different beam hopping schemes, while Fig. 5(4(b)) shows the satisfaction of UEs. It is observed that the beam hopping scheme w/ distance limit always outperforms the other two schemes. This further demonstrates the promising benefits of not simultaneously scheduling adjacent spotbeams. For S band, the performance comparison between different beam hopping schemes in terms of packet life time and UEs’ satisfaction are shown in Figs. 5(4(c)) and 5(4(d)), respectively, where the proposed beam hopping scheme w/ distance limit enjoys better performance.

Table I gives the system satisfaction, achieved by different beam hopping schemes. Similarly, it is observed that most traffic demands are satisfied by the proposed beam hopping scheme.