Joint optimization based satellite handover strategy for low earth orbit satellite networks

Low earth orbit constellation satellite communication has the characteristics of low propagation delay, low path loss, low launch cost and wide range of applications. Due to the low orbital altitude and the short orbital period of low earth orbit satellites, the relative position between satellites and gateway stations changes fast. As a result, the links between gateway stations and satellites need to be switched continuously. Based on the minimum handover frequency algorithm, this paper considers the balance of satellite workloads, and proposes a load balanced satellite handover strategy. In the proposed handover strategy, a joint optimization algorithm is employed, and the power allocation of the satellite is optimized to improve the system capacity. In the multi-satellite connection model, an adaptive power allocation algorithm is proposed to guarantee the service quality of the system. Simulation results demonstrate the efﬁciency of the proposed satellite handover strategy.

satellites is low, which means that the cost of LEO satellites is low. Moreover, LEO satellite networks have relatively strong resistance to destruction, because even if some satellite nodes are destroyed, the communication system can be maintained [6].
In the LEO satellite networks, because of the low orbit altitude, the satellite is moving at a high speed and the satellite network topology changes fast. For example, in the classic LEO constellation, Iridium constellation, the satellite and the ground station are in a fast relative motion, and the speed of relative movement is about 7 km s −1 . For one gateway station, the visual time of each satellite is only 9 min [7,8]. Therefore, a gateway station needs to switch between different satellites to ensure continuous connection to the satellite networks. This means that the gateway station has to choose a proper handover strategy to optimize the handover times, satellite loads and quality of service.
The link layer handover in satellite networks, includes spotbeam handover, satellite handover and inter-satellite link handover [9]. At present, the satellite handover strategy of the LEO satellite networks mainly includes the handover strategy based on the maximum service time (minimum handover frequency strategy), the handover strategy based on the maximum number of idle satellite channels, and the handover strategy based on the shortest star-earth distance [10] . However, a single handover strategy has its inevitable drawbacks. For example, the maximum service time based handover strategy leads to an imbalance of the satellite loads and decreases the channel quality; the handover strategy based on the most idle satellite channels results in the connections that do not conform to star-earth distance, reduces the quality of service, and increases the number of handovers; the strategy based on the shortest star-earth distance leads to the overloads of some satellites, and increases the number of handovers [11,12]. On the other hand, the gateway station may be covered by more than one satellite at a specific instant [13]. The gateway station can take the advantage of the satellite diversity to improve the quality of service [14].
This paper focuses on the satellite handover strategy and proposes a joint optimization handover strategy to balance the workloads of different satellites based on the minimum handover frequency. In the proposed handover strategy, the trade-off between the handover frequency and the satellite workloads is achieved. Besides, the multi-satellite connection model is considered, and an adaptive power allocation algorithm is proposed to improve the service quality of the system.
The main contributions of this paper are summarized as follows.
• Based on the reduced switching frequency, the weight of the switching path is optimized to balance the loads of satellites. • Under the quality of service constraint of the connected gateway stations, this paper employs the multi-satellite connection model to ensure gateway stations with low QoS to connect more satellites. In the process, the forward and backward searching methods are adopted in two switching cases, respectively. • Adaptive power allocation scheme based on gradient descent algorithm is adopted to further improve the system capacity.

Table of satellite information
The model of the connection between LEO satellites and gateway stations is illustrated in Figure 1. During a time period of T, there are N LEO satellites and M gateway stations. The jth satellite is represented by S j ( j = 1, 2, … , N ) and the i-th gateway station is represented by U i (i = 1, 2, … , M ). Based on the ephemeris data on the website [15] and the method proposed in refs. [16,17], the moments when the satellite S j begins to cover and to leave the gateway station U i over a period of T can be calculated, respectively.
The coverage area of a satellite is illustrated in Figure 2, where the satellite height is h, the satellite projection point on the ground is C, and the radius of the satellite coverage area is R. The spotbeam of the satellite can be controlled to point to gate- Suppose that the satellite and projection point C move with a velocity ⃗ v relative to the ground, then the motion velocity of the gateway station relative to the coverage area is ⃗ v r = −⃗ v. Therefore, the time points of U i entering and leaving the coverage area of the satellite can be calculated, respectively. Figure 3 illustrates the procedure of U i entering and leaving the coverage area of the satellite S j . Let the unit vector parallel to the satellite velocity ⃗ v be ⃗ e 2 , and the unit vector perpendicular to ⃗ v be ⃗ e 1 . According to the motion trajectory of the satellite, the motion trajectory of the projection point C can be known, and the distance d between the motion trajectory of U i and the projection point C can be derived. The projection point is expressed as C in and C out , respectively, when U i enters and leaves the coverage area. The coordinates of these two points can be obtained according to Pythagorean theorem The corresponding times t in and t out can be obtained according to ⃗ x C in , ⃗ x C out and the ephemeris, which can be gotten on the website [15].
It is assumed that N satellites pass over the gateway station U i during the time period of T, thus the table of satellite information related to U i is defined as where the three columns of TaskSeq i are the index of passing satellites, the time that the satellite begins to cover U i , and the time that U i leaves the coverage area of the satellite, respectively. The indexes of the satellites are arranged in the order according to the entry time t in , that is, t in_i 1 < t in_i 2 < ⋯ < t in_i N < T . Figure 4 is the map of the satellite coverage time, which is related to the gateway station U 1 . By considering all gateway stations and all satellites, record all the moments and the corresponding events that a gateway where the first column is the time t k of the k-th event; the second column is the index of the corresponding gateway station; the third column is the index of the corresponding satellite; the fourth column is the event at that moment, where 1 represents that the satellite begins to cover the gateway station, and -1 represents that the gateway station leaves the service area of the satellite.

Minimum handover frequency algorithm
According to the satellite information TaskSeq i , the digraph Graph i of U i is defined, and it represents U i 's handover choice between satellites. In the digraph Graph i , the nodes are the satellites that the U i passes through during the time T. The gateway station U i can switch from satellite S j to satellite S k , if the time that U i leaves the service area of S j is behind the time that U i enters the service area of S k . In this case, the line from S j to S k in the digraph is a directed edge. Figure 5 illustrates the handover digraph of the gateway station U 1 .
For the gateway station U i , generate the adjacency matrix according to its handover graph. The rule of setting weight is as follows. If node S j can be switched to S k , the weight value of the directed edge from S j to S k is set to 1; otherwise, it is set to infinity, that is, For the adjacency matrix G i , dijkstra algorithm is applied to obtain the shortest path road i from the first satellite to the last satellite (for example, TaskSeq i (1,1) and TaskSeq i (N,1)) [18]. Since the weight of each switchable edge is 1, the obtained shortest path corresponds to the handover path with the minimum handover frequency.

JOINT OPTIMIZATION MODEL
In this section, based on the minimum handover frequency strategy, a joint optimization is proposed to balance the handover frequency and workloads of satellites. Moreover, the multi-satellite connection model is considered to further optimize the power allocation and improve the service quality of the system.

Calculations of connection matrix and load matrix
The connection matrix link is defined as: The matrix link represents the situation of the connection of all gateway stations and satellites at each time node, and the size of matrix link is M × N × num_of_time. The number of time nodes is less than the maximum possible combinations (i.e. less than 2MN). Because some time points in the timenode are the same and several events may occur at the same time. Another case is that S j may not be on the U i 's handover path road i , and the switch will not occur under the minimum handover frequency algorithm.
Deriving from the matrix link, the matrix load, which represents the workloads of satellite S j at the time t k , is calculated as The process of generating the connection matrix link and the workloads matrix load is shown in Table 1.

Weight optimization in handover digraph
In Section 2, the handover strategy based on the minimum handover frequency is provided. However, the load balance of different satellites is not considered. The minimum handover frequency strategy can easily result in imbalance where some satellites are overloaded and other satellites are idle. In this section, we will modify the weight of edges in the handover digraph G i according to the matrix load, and recalculate the handover path road i, connection matrix link and load matrix load, so as to balance the satellite workloads.
For the gateway station U i , we analyse the handover edge from S p to S q (p, q = 1, 2,…, N) in the handover digraph G i , where U i enters the service area of S p earlier. By employing the event matrix time_U_S, we can find the corresponding time nodes that U i enters or leaves the service area of S p and S q , and they are represented by t k1 , t k2 , t k3 , t k4, respectively. If U i is going to leave the service area of S p , and S q is still covering U i at time t k2 , the handover time is t k2 , and the handover edge weight is set as exponent ratio of the loads between S q and S p at t k2 . If the coverage time of S q is less than that of S p , then the handover time is t k3 , and the handover edge weight is set as exponent ratio of loads between S q and S p at t k3 . The two cases are shown in Figure 6(a),(b), respectively.
The weight value of the directed edge from S p to S q is set as 10 load(k2,q)−load(k2, p) switchable and t k 2 ≤ t k 4 10 load(k3,q)−load(k3,p) switchable and t k 2 > t k 4 ∞ otherwise .
The significance of adjusting the weight value is that, for those stations switching from a satellite with low load to a satellite with high load, the weight value is no longer only determined by whether the overlap of the coverage time. The larger the difference of the loads between two satellites is, the larger the weight of the handover edge will be. Therefore, the gateway station will choose a handover edge by considering the workloads of the satellites. In the new handover diagram G i (i = 1, 2,…,3), repeating the steps of the minimum handover frequency path algorithm cooperated with the proposed weight adjustment, the workloads of different satellites will be balanced gradually. Therefore, recalculate the shortest path road i, the connection matrix link, and the satellite load matrix load at each moment, and repeat these steps so as to achieve the trade-off between the handover frequency and the workloads.

Power allocation and channel capacity analysis
As shown in Figure 7, in the downlink transmission from the satellite to the gateway station, the satellite may connect to multiple gateway stations at each moment. Therefore, it is necessary to optimize the power allocation for the satellite under a constant transmit power constraint.
The half power beamwidth of the transmit beam of the satellite is expressed as 2 , which is small. The wave surface arriving at the gateway station is regarded as a plane wave. Assuming P s is the transmit power, the power density is given by [19] S = P s (r × tan ( )) 2 .
where r is the distance between the satellite and the gateway station.
The effective area of the receive antenna is A e = c 0 2 4 f c 2 . and the received power of the gateway station is where f c is the carrier frequency, c 0 is the speed of light. The magnitude of the channel impulse response can be expressed as According to the connection matrix link(∶, ∶, k), the connections between the satellites and the gateway stations at each moment can be obtained. Suppose that at the time t k , the satellite S j is connected with U i , and the received signal of U i can be expressed as where x i is the information transmitted from S j to U i , H i, j ,k and V i,j,k are the channel coefficient and the control factor from S j to U i at time t k , respectively, and n i is the noise component.
Assuming that E [|x i | 2 ] = P s and the noise power is P n , the SNR of the received signal is According to Shannon theorem, the channel capacity from S j to U i at the time t k is calculated as follows [19] With the same principle, the channel capacity corresponding to other stations at time t k can be deduced. It is assumed that the gateway station U i is only connected to one satellite, and the index of the satellite is denoted by j (i,k) . Therefore, the channel capacity of the satellite communication networks at the moment of t k can be obtained The signal power is normalized as E [|x i | 2 ] = P s = 1, and the transmit power of each satellite satisfies that where power j (i,k) is the total transmit power of S j (i,k) . According to the objective function and constraints, the optimal solution of V i, j (i,k) ,k can be solved by using the gradient descent optimization algorithm [20].

3.4.1
Channel capacity in multiple satellite connection For the case that the quality of service (for example, transmission rate) of U i still does not reach the preset threshold at a certain time, we can judge whether U i can connect to another satellite according to its handover digraph G i . Therefore, in this subsection, multi-satellite connection model is used to achieve diversity gain and improve the quality of service [21][22][23].
As shown in Figure 8, in the downlink transmission, each gateway station may be connected to multiple satellites. In subsection 3.3, the channel magnitude is known as (12).
Assume that at time t k , U i is connected to multiple satellites, and these satellites send the same information to U i . In order to ensure that the signal from different satellites can arrive at the station synchronously, that is, the phase of each signal received is consistent, the satellites need to carry out phase coordination for the transmitted signal. Therefore, the compensation factor of the i-th satellite S j can be expressed as where A i, j ,k is amplitude compensation factor, and Φ i, j ,k is phase compensation factor, which is equal to Therefore the signal y i received by the U i can be rewritten as (19) All satellites are taken into account, and H i,j,k is set as zero (i.e. H i,j,k = 0) if U i and S j are not connected. Therefore, the SNR of the received signal is According to Shannon theorem, the channel capacity of the gateway station U i at the time t k is calculated as follows .
The channel capacity of other stations at time t k can be calculated with the same principle. Therefore, the channel capacity of the satellite communication networks at the moment of t k can be obtained as subject to The problem is equivalent to If U i is not connected with S j at t k , set A i, j ,k = 0. Therefore, the constraint is The equality constraint can be eliminated by Then the equality constrained optimization problem can be transformed into an unconstrained optimization problem as [20] The gradient descent method is used to find the optimal power allocation coefficient A M×N at each t k in the model of the multiple satellite connection [20].

3.4.2
Adaptive power allocation algorithm in multi-satellite connection Now we consider multi-satellite connection for U i , whose quality of service still does not reach the preset threshold when switching from S q-1 to S q . The time nodes when U i enters and leaves the service area of S q-1 are defined as t k1 and t k2 , respectively. The time nodes when U i enters and leaves the service area of S q are denoted by t k3 and t k4 , respectively. First, search the corresponding time nodes in time_U_S. If t k2 < t k4 , the handover occurs at the time t k2 . Since the satellite S q-1 has passed, U i can only determine whether it has entered the service area of S q+1 and whether S q+1 has any remaining power. If t k2 > t k4 , the handover occurs at the time t k3 . Since the U i has not entered the service area of satellite S q+1 , U i can only determine whether it is still in the service area of S q-2 and whether there is any remaining power in S q-2 . If U i is not in the service area of S q-2 , repeat the above steps to determine whether U i has left the service area of S q-3 and whether there is any remaining power. The forward and backward searching methods adopted in two switching cases are shown in Figure 9(a),(b), respectively.
The criterion for judging whether the satellite S j has remaining power is as follows. Assuming the quality of service of U i does not reach the threshold at a specific moment, it wants to connect to another satellite S j. It can be known from the matrix link that, for example, at this time, S j has been connected to U a, U b, U c and U d , whose service quality all reaches the threshold value. The minimum required power P a,j , P b,j , P c,j , P d,j and P i,j are calculated according to the quality of service threshold of U a , U b , U c , U d and U i , respectively. If the sum of the required power does not exceed the total power of S j , there is remaining power at S j , and the U i can connect to it.
The above procedure is summarized as the algorithm 2 in Table 2. Note that the proposed optimization can be done offline and does not require any real-time computation. Repeat. //Repeat the above steps

The simulation settings
We employ the parameters of Iridium satellite, and set some parameters according to the development trend of LEO satellites [24]. In the simulation, there are M = 20 gateway stations and N = 11 satellites. The gateway stations are randomly distributed in the area of the earth. Without loss of generality, we give the satellite information of the gateway station U 1 . The corresponding satellite coverage time diagram of U 1 is shown in Table 3, and the remaining simulation parameters are shown in Table 4.

FIGURE 10
Load variation of satellite S 6 , S 7 , S 8 and S 9 over time Figure 10 shows the load variation of satellite S 6 , S 7 , S 8 and S 9 over time. It can be seen from Figure 10 that at the beginning, S 6 and S 8 have heavy loads under the minimum handover frequency strategy, while S 7 and S 9 are relatively idle. After the second iteration of load optimization, the load of four satellites is comparably balanced, and average load of each satellite is about 5. Figure 11 shows the variation of the standard deviation of workloads of each satellites over time. From the minimum handover frequency strategy to the first and the second load balancing, the standard deviation of the load generally decreases step by step, reflecting that the load tends to balance. The average channel capacity of the system over time is shown in Figure 12. After the step by step optimization, the channel capacity of the system increases step by step. In the initial minimum handover frequency strategy, the channel capacity under the average power allocation is the smallest, and the channel capacity with the optimized power allocation is improved. After calculating the load matrix and reweighting the handover digraph, the load balance strategy enables the idle satellites to FIGURE 11 The standard deviation of workloads of satellites over time

FIGURE 12
Average channel capacity of the system over time be used, and the channel capacity is improved. After applying the optimization of multi-satellite connection and adaptive power allocation algorithm, the achievable data rate continues to increase, and it is close to 0.6 bit s −1 . Figure 13 shows the variation of the achievable data rate of U 10 over time. In the simulation, the threshold of quality of service is set to 0.2 bit s −1 . The sharp peaks in Figure 13 are caused by the sudden entry of a satellite. It can be seen from Figure 13 that the achievable data rate is gradually increased through step by step optimization. Besides, the achievable data rate remains above the threshold 0.2bit s −1 with the multi-satellite connection.

FIGURE 13
Achievable data rate of U 10 over time

CONCLUSION
This paper proposes a joint optimization satellite handover strategy in LEO satellite networks. In the proposed handover strategy, the weight of the handover digraph is optimized according to the real-time workloads, and the proposed handover strategy makes the loads of different satellites balanced effectively at a small cost of handover frequency. In addition, the power allocation of the satellite is optimized, which improves the channel capacity of the satellite networks. Besides, the multisatellite connection model is employed to ensure gateway stations with low QoS to connect to more satellites. In the process, the forward and backward searching methods are adopted in two switching cases, respectively. Furthermore, adaptive power allocation algorithm is proposed to guarantee the quality of service of each gateway station.