Joint power and bandwidth allocation for beam-hopping user downlinks in smart gateway multibeam satellite systems

Abstract

To improve the efficiency of on-board resources utilization, two joint power and bandwidth allocation schemes are proposed to optimize power and timeslot allocation for beam-hopping user downlinks of the smart gateway system. By decomposing the two-variable optimization problem into two single variable optimization problems, the joint optimization problem is solved effectively. Moreover, two novel algorithms are proposed to solve the two subproblems. Extensive simulation results demonstrate that the efficiency of resource utilization can be effectively improved with the joint power and bandwidth allocation schemes in contrast with conventional allocation scheme.

Keywords

Space information network multibeam satellite smart gateway beam hopping joint power and bandwidth optimization user downlinks

Introduction

To solve the problems that different space systems cooperate inconveniently due to being built separately, the space information network (SIN) is proposed. It can provide communication, navigation, and remote sensing service simultaneously using various space platforms, for example, satellites, aerial vehicles, and terrestrial terminals.^1,2 The traffic demands for the satellite communications in SIN are continuously increasing with the development of SIN, thus higher frequency bands such as Ka (20/30 GHz) and Q/V (40/50 GHz) are employed in more and more satellite networks. Although more available spectrum can be achieved by migrating to higher bands, the signal will also experience more severe degradations. For example, the rain attenuation in Ka band may exceed 20 dB.^3,4 Meanwhile, power control and adaptive coding and modulation (ACM) techniques are not sufficient to compensate the severe signal degradations. In this context, a promising technique named smart gateway is proposed, which can ensure the dramatic increase in link availabilities while keeping the cost to reasonable levels.^5,6

To utilize the bandwidth resources efficiently, three resource allocation schemes are proposed in Kyrgiazos et al.,⁷ which consider the feeder uplink conditions and the traffic demands of user beams. These schemes only aim to optimize the resources of feeder uplinks, and the user downlinks are assumed to be ideal and identical. However, the user downlinks are usually different because of the geographical location difference of user beams. Moreover, the scarcity of on-board resources is more prominent than that in gateways. Therefore, we propose two novel resource allocation schemes to optimize the resources of user downlinks in this article.

To adapt to the smart gateway scheme and improve the efficiency of power and bandwidth resources utilization, beam hopping technique is commonly implemented for user downlinks,^8,9 where the key point is the design of efficient and reasonable beam hopping pattern. Therefore, several researches have focused on the design of beam hopping pattern. Genetic algorithms are used in bandwidth optimization in Angeletti et al.¹⁰ Two heuristic algorithms are proposed in Alegre et al.,¹¹ where the capacity resources are allocated based on the per-beam traffic demands. However, all these schemes only consider the optimization of bandwidth resources, whereas the power resources are allocated uniformly among the user beams, thus the efficiency of power utilization is not improved effectively. Motivated by this fact, power and bandwidth are allocated jointly in this article. Similarly, there are some precedents considering joint power and bandwidth. For example, a joint power and carrier allocation problem is discussed in Barcelo-Llado et al.;¹² however, it merely focuses on user uplink. In Lei and Vázquez-Castro,¹³ the optimization problem of power and carrier allocation is addressed, but managing the co-channel interference due to non-orthogonal frequency reuse increases the complexity greatly. Apart from the optimization problem with co-channel interference, a simplified problem without co-channel interference is solved by the Lagrangian approach.¹⁴ However, the non-uniformity of channel has not been considered. Additionally, the optimization problem of power and carrier allocation has been addressed in terrestrial networks,^15,16 but the conclusions cannot be directly extended to the satellite scenario.

In this context, we propose two joint power and bandwidth allocation schemes based on the inter-cluster orthogonal frequency reuse, which consider channel conditions and the traffic demands of user beams. In our proposed schemes, the total bandwidth is reused by beam clusters but not user beams. In addition, only a single beam of a cluster is active during a particular timeslot in beam hopping system, the active beams can use the full frequency allocated to their clusters thus. By this means, not only the co-channel interference can be mitigated but also the frequency band can be used efficiently. In other words, it gives a good compromise between efficiency of frequency bands utilization and co-channel interference mitigation.

Allocating power and bandwidth jointly is challenging and non-trivial since two variables need to be optimized simultaneously. To address this problem, we propose a two-step allocation method. In the first step, the power is optimized according to the channel conditions and the overall traffic demands in each cluster. Then, we design the beam hopping pattern to allocate timeslots to each beam based on the traffic demand of each beam. With the aid of this scheme, we can decompose the two-variable optimization problem into two single variable optimization problems, which effectively decreases the complexity. Simulation results indicate that in contrast with conventional resource management method where both power and timeslots are uniformly allocated, the traffic match ratio can be improved to 94.61% and 95.53%, respectively. In addition, the capacity waste is also avoided effectively. Thus, the system can achieve more 110 Mbps in actual capacity by introducing the proposed methods. The comparison between joint resource optimization and single variable resource optimization further verifies the efficiency of proposed joint power and timeslot allocation schemes.

The remainder of the article is organized as follows. In section “System architecture,” the smart gateway and beam hopping layout are discussed. The inter-cluster orthogonal frequency reuse scheme is presented in section “The inter-cluster orthogonal frequency reuse scheme.” Section “Joint power and bandwidth allocation” provides the formulation of joint power and bandwidth allocation problem and the proposed two-step methods. Section “Simulation and analysis” evaluates the performance of joint power and bandwidth allocation schemes through numerical results. Section “Conclusion” concludes this article.

System architecture

Smart gateway

As shown in Figure 1, in the considered smart gateway system, a number of gateway earth stations (GESs) are interconnected via terrestrial links to form a flexible routing of feeder link data, which can be applied in a diverse manner to combat fading on the gateway to satellite links.⁵ Particularly, the feeder links are in Q/V band and the user links are in Ka band, where rainfall is the dominant fading factor since it causes the highest attenuation among the related atmospheric effects.¹⁷ Furthermore, we assume the feeder links to be ideal and identical as we herein focus on the optimization problem of resources allocation in user links. And this assumption can be achieved in real-world systems by spreading the gateways over large distances as mentioned in Jeannin et al.¹⁸ In addition, the smart gateway scheme illustrated in Figure 1 is called N-active smart gateway, where user beams are served by a number of gateways in a time frame period or simultaneously. Specifically, the satellite user in this article is assumed as the fixed satellite service terminal.

Figure 1.

Architecture of the smart gateway systems.

As for the channel state information (CSI) of the user links, we assume a prior knowledge of the satellite terminal locations or spatial distribution through inquiring a geo-location database. In this regard, the perfect CSI can be obtained by combining the short-term prediction of the behavior and the relevant duration with referring to the long-term and yearly averaged statistics.³

Two options can be used in this scheme for transparent satellite systems: frequency multiplexing and time multiplexing. On one hand, frequency multiplexing increases the output back off (OBO) due to the multicarrier operation. On the other hand, the equipment in the payload (i.e. transponders) needs to be increased as the degree of diversity increases. However, both the issues can be avoided by time multiplexing, thus we adopt the time multiplexing smart gateway similar to the satellite-switched time-division multiple-access scheme (SS-TDMA), as described in Figure 2, where the bandwidth resources employed by user beams are separate over timeslots. In each timeslot period, the user beam is served by just one gateway. The system can operate by routing timeslots from any uplinks to any downlinks. The interconnectivity between all pairs can be performed by a high-speed microwave switching matrix, and the traffic matrix is stored on board. Additionally, the matrix is updated periodically.

Figure 2.

Time multiplexing smart gateways.

Beam hopping layout

In the beam hopping systems, all the beams are divided into a number of clusters. Only a single beam is active during a particular timeslot in each cluster. In other words, the active beam can use the entire power and frequency bands allocated to the cluster in this timeslot, which is the notable advantage compared with conventional multibeam systems. Moreover, since only limited beams are illuminated simultaneously with a regular repetition pattern, the number of amplifiers on board can be reduced effectively.

To simplify the operation of beam hopping systems, the clusters are usually divided uniformly, that is, the number of user beams is uniform in each cluster. If the number of user beams in the system is K and the beams are divided into N clusters, the number of user beams in each cluster is $M = K / N$ . For instance, if the value of parameter M is assumed to be 7, the beam layout of the beam hopping systems is illustrated as Figure 3. Herein, we assume that the channel conditions of user beams in the same cluster are identical due to their adjacent location aforementioned. However, the channel conditions for different clusters are assumed to be different.

Figure 3.

An example for beam layout of beam hopping user beams.

The inter-cluster orthogonal frequency reuse scheme

As mentioned above, beam hopping technique is used in user downlinks. And in real-world systems, the beam hopping technique can be implemented with full frequency or partial frequency reuse. In the case of full frequency reuse, the active user beams in each cluster can use the entire available frequency bands on board, which improves the efficiency of frequency band utilization effectively. However, when the illuminated beams in different clusters are adjacent, co-channel interference cannot be negligible in this case. To mitigate the co-channel interference, new constraints are introduced to avoid the case that adjacent beams in different clusters work simultaneously in designing beam hopping pattern, which increases the complexity of timeslot allocation. In the case of partial frequency reuse, the total bandwidth is segmented and each user beam is illuminated with a fraction of the total frequency bands, which can mitigate the co-channel interference at the cost of efficiency of frequency band utilization. To obtain a compromise between co-channel interference mitigation and efficiency of frequency bands utilization, we propose an inter-cluster orthogonal frequency reuse scheme, which belongs to the partial frequency reuse.

A recent study¹⁹ on designing high-throughput satellite systems in Ka band suggests to use a four-colored frequency reuse pattern as it gives a good compromise between throughput and inter-beam interference. To further mitigate the co-channel interference, we adopt a six-colored frequency reuse pattern. However, different from the conventional frequency reuse scheme where the frequency bands are shared among user beams, the frequency bands are reused in the cluster level. In addition, circular polarizations, that is, right-hand circular polarization (RHCP) and left-hand circular polarization (LHCP), are introduced in the scheme as they are capable of counteracting the effects of Faraday rotation.²⁰ The frequency reuse factor is equal to 3 (with six colors) in this frequency reuse scheme, which is depicted in the left part of Figure 4. The right part of Figure 4 demonstrates the frequency reuse scheme between beam hopping clusters of user downlinks. That is to say, if the total available frequency bands are denoted as $B_{total}$ , the bands allocated to each cluster are $B_{cluster} = B_{total} / 3$ .

Figure 4.

The inter-cluster orthogonal frequency reuse scheme.

Joint power and bandwidth allocation

Problem statement

Once the frequency reuse scheme is determined, we focus on the power and timeslots needed to be allocated to user beams. In this part, we formulate power and timeslot allocation problem and explain the notation in the problem. In the beam hopping scheme, let $N_{t}$ be the number of timeslots in each time window and $η_{j}$ be the spectral efficiency of the jth beam. According to Lei and Vázquez-Castro,¹⁴ the capacity can be offered to the jth beam $C_{j}$ is

C_{j} = \frac{N_{j}}{N_{t}} \cdot B_{cluster} \cdot η_{j} (j = 1, 2, \dots, K)

(1)

where $N_{j}$ is the number of timeslots allocated to the jth beam, which is a non-negative integer variable.

The system is assumed to be implemented with ACM. Thus, the spectral efficiency $η$ is a quasi-linear function in digital video broadcasting—satellite—second generation (DVB-S2)²¹ with respect to signal-to-interference plus noise ratio (SINR) $γ$ as below

η = f (γ)

(2)

Since the channel conditions in the same cluster are considered uniform and the feeder links are assumed to be ideal as mentioned before, the spectral efficiency of user beams in the same cluster is identical. Let the SINR of uplink and downlink be $SIN R_{up}$ and $SIN R_{down}$ , respectively, which can be calculated by link budget, then

γ^{- 1} = {SINR}_{up}^{- 1} + {SINR}_{down}^{- 1}

(3)

Let the requested traffic of the jth beam in the beam hopping window duration be denoted as $T_{j}$ . To match the offered capacity with requested traffic efficiently, two different objective functions are studied as follows.

Second-order difference cost function

min \sum_{j = 1}^{K} {(T_{j} - C_{j})}^{2}

(4)

Load balance function

max Π_{j = 1}^{K} \frac{C_{j}}{T_{j}}

(5)

Both the on-board resources and characteristics of the beam hopping should be taken into account. Denote $P_{total}$ and $P_{i}$ as the total power on board and the power allocated to the ith cluster, respectively. The constraints are formulated as

{\begin{matrix} C_{j} \leq T_{j} & (c 1) \\ \sum_{i = 1}^{N} P_{i} \leq P_{total} & (c 2) \\ \sum_{j = 1}^{K} N_{j} \leq N \cdot N_{t} & (c 3) \\ N_{j} \geq 0, N_{j} \in Integer & (c 4) \end{matrix}

(6)

where $(c 1)$ means that the offered capacity cannot exceed the requested traffic generated in each beam to prevent the unnecessary waste of resources, $(c 2)$ and $(c 3)$ imply that the power and timeslots should be allocated within total available aggregate power and timeslots, $(c 4)$ is introduced to guarantee that $N_{j}$ is a non-negative integer. To remark conveniently in the following paragraph, the methods corresponding to objective functions (4) and (5) are named as capacity difference allocation and load balance allocation, respectively.

Problem decomposition

Note that obtaining the solution of equations (4) and (5) is complex since two variables complying with different constraints need to be optimized simultaneously. Thus, we adopt a two-step allocation scheme where equations (4) and (5) are decomposed into two subproblems.

In the first step, the on-board power is optimized according to the channel conditions and the overall traffic demands in each cluster. By solving the Subproblem 1, the power allocated to each cluster $P_{i}$ can be determined. In the second step, the available timeslots in each cluster are allocated to their user beams based on the outputs of Subproblem 1, that is, we allocate timeslots based on the power allocation consequence obtained in Subproblem 1. Specifically, we incorporate the inter-cluster power allocation with intra-cluster timeslot assignment to optimize the efficiency of on-board resources utilization. The formulation of the two subproblems is given as below.

Subproblem 1: inter-cluster power allocation

In this step, the overall requested traffic and offered capacity of user beams in the ith cluster are denoted as $T_{i}^{c}$ and $C_{i}^{s}$ , respectively. Since the power allocated to the cluster is shared by their user beams, the inter-cluster power allocation can be formulated as

\begin{matrix} \underset{P_{i}}{optimize} f_{1} (P_{i}) \\ s . t . {\begin{matrix} C_{i}^{s} \leq T_{i}^{c} & (p 1) \\ \sum_{i = 1}^{N} P_{i} \leq P_{total} & (p 2) \end{matrix} \end{matrix}

(7)

where $C_{i}^{s}$ is the function with respect to $P_{i}$ and $f_{1} (P_{i})$ is the objective function to be optimized. Corresponding to equations (4) and (5), $f_{1} (P_{i})$ is $min \sum_{i = 1}^{N} {(T_{i}^{c} - C_{i}^{s})}^{2}$ and $max Π_{i = 1}^{N} (C_{i}^{s} / T_{i}^{c})$ , respectively.

Subproblem 2: intra-cluster timeslot assignment

Based on the solution of equation (7), the timeslots in each cluster are assigned to the user beams in them. That is to say, $P_{i}$ is constant in this step. Let $T_{ik}$ and $C_{ik}$ be the requested traffic and offered capacity in the kth beam of the ith cluster, respectively; and $T_{ik}$ complies with the constraint that $\sum_{k = 1}^{M} T_{ik} = T_{i}^{c}$ . In addition, the timeslots assigned to the kth beam of the ith cluster is denoted as $N_{ik}$ . We formulate the problem of intra-cluster timeslot assignment as below

\begin{matrix} \underset{N_{ik}}{optimize} f_{2} (N_{ik}) \\ s . t . {\begin{matrix} C_{ik} \leq T_{ik} & (t 1) \\ \sum_{k = 1}^{M} N_{ik} \leq N_{t} & (t 2) \\ N_{ik} \geq 0, N_{ik} \in Integer & (t 3) \end{matrix} \end{matrix}

(8)

$min \sum_{k = 1}^{M} {(T_{ik} - C_{ik})}^{2}$ and $max Π_{k = 1}^{M} (C_{ik} / T_{ik})$ are the objective functions to be optimized corresponding to equations (4) and (5), respectively, in this subproblem.

Inter-cluster power allocation

First of all, the offered capacity for the ith cluster can be calculated as below

C_{i}^{s} = B_{cluster} \cdot η_{i} (i = 1, 2, \dots, N)

(9)

According to the European Telecommunications Standards Institute,²¹ the function f in equation (2) is a step function, which is illustrated in Figure 5. It can be concluded that the function f is not continuous. Moreover, the span of the step in f is not uniform, making equation (7) difficult to be solved.

Figure 5.

The spectral efficiency function in DVB-S2.

Considering both the discontinuity of f and the non-uniformity of the step in f, we propose an inter-cluster power allocation algorithm based on the lookup table idea, which is shown in Table 1.

Table 1.

The inter-cluster power allocation algorithm.

1. Calculate all the threshold power values.

2. Obtain the available power values in each cluster according to

(p 1)

3. Set the initial value

{f_{1}}_{_initial}

f_{1} (P_{i})

and combination index

P_{index} = 0

4. forj = 1:

Π_{i = 1}^{N} N_{A_{i}}

5. if

\sum_{i = 1}^{N} P_{i} > P_{total}

6. continue;

7. end if;

8. calculate the

f_{1} (P_{i})

value

{f_{1}}_{j}

of the jth inter-cluster power allocation combination;

9. if

{f_{1}}_{j} \leq {f_{1}}_{_initial}

for (4) or

{f_{1}}_{j} \geq {f_{1}}_{_initial}

for (5)

10.

{f_{1}}_{_initial} = {f_{1}}_{j}

;

11.

P_{index} = j

;

12. end if.

13. end for.

14. Output

{f_{1}}_{_initial}

and

P_{index}

15. Look up the best inter-cluster power allocation combination according to

P_{index}

It is notable from Figure 5 that different signal-to-noise ratio (SNR) values correspond to the same spectral efficiency in each step of f. Although the power values fluctuate in the same step, the corresponding spectral efficiency would not change. From the perspective of improving the efficiency of on-board power resource utilization, the SNR value should be as small as possible in order to achieve the same spectral efficiency. The smallest SNR value in each step is named as threshold SNR and the corresponding power value is called threshold power.

Therefore, we can calculate all the threshold power values incorporating equations (2) and (3). And the value of $SIN R_{up}$ is assumed to be constant. The connection between $SIN R_{dow n_{i}}$ and $P_{i}$ in the ith cluster can be derived from link budget as shown below.²² The symbols in equation (10) are explained in Table 4, and $[x]$ denotes the dB value of x

\begin{array}{l} [S I N R_{d o w n_{i}}] = [P_{i}] + [G_{T}] + [G_{R}] - [L_{f r e e}] \\ - [T_{n}] - [k] - [B_{n}] - [L_{r a i n_{i}}] \end{array}

(10)

By this means, there is a one-to-one relationship between the spectral efficiency and allocated power in each cluster. After knowing the spectral efficiency, we can thus determine the corresponding power by looking up the table. In this article, the threshold power values are defined as the power candidate set, which includes all the possible allocated power values.

Therefore, the inter-cluster power allocation can be converted into selecting the optimal power combination from the power candidate set. Next, according to $(p 1)$ in equation (7), the available power values in each cluster are obtained. And the number of the available power values in the ith cluster is denoted as $N_{A_{i}}$ . In other words, there are $Π_{i = 1}^{N} N_{A_{i}}$ combinations complying with $(p 1)$ for inter-cluster power allocation. Finally, we select the combinations complying with $(p 2)$ and determine the corresponding best inter-cluster power allocation combination by searching the best value of $f_{1} (P_{i})$ from them. Therefore, the complexity of the inter-cluster power allocation method is $O (n^{2})$ .

Intra-cluster timeslot assignment

Since the variable $N_{ik}$ in equation (8) must be an integer, optimization equation (8) is a non-linear integer programming problem. And $C_{ik}$ can be calculated as

\begin{matrix} \begin{matrix} C_{ik} = \frac{N_{ik}}{N_{t}} \cdot B_{cluster} \cdot η_{i} \\ = N_{ik} \cdot \frac{B_{cluster} \cdot η_{i}}{N_{t}} \end{matrix} & (i = 1, 2, \dots, N; k = 1, 2, \dots, M) \end{matrix}

(11)

where $B_{cluster}$ and $N_{t}$ are constant system parameters, and in each cluster, the spectral efficiency $η_{i}$ is uniform. Therefore, $(B_{cluster} \cdot η_{i}) / N_{t}$ is denoted as $A_{c_{i}}$ for the convenience of simplicity in the following parts.

We propose a novel algorithm incorporating convex optimization²³ with branch-and-bound approach²⁴ to solve equation (8), which is displayed in Table 2. The algorithm can be divided into two steps:

Solve equation (8) in real domain.

Convert the real domain solution to integer.

Table 2.

The timeslot assignment algorithm for ith intra-cluster beams.

1. Solve (8) in real domain and obtain the solution

N R_{ik}

2. Obtain the lower bound integer

N L_{ik}

N R_{ik}

N L_{ik} = ⌊ N R_{ik} ⌋

3. Calculate the number of remaining timeslots

N r_{i}

4. Set the initial value

{f_{2}}_{_initial}

f_{2} (N_{ik})

and combination index

N_{index} = 0

5. for j = 1:

{(N r_{i} + 1)}^{M}

6. if

\sum_{k = 1}^{M} N_{ik} > N_{t}

or there are any beams satisfying

C_{ik} > T_{ik}

7. continue;

8. end if;

9. calculate the

f_{2} (N_{ik})

value

{f_{2}}_{j}

of the jth intra-cluster timeslot assignment combination;

10. if

{f_{2}}_{j} \leq {f_{2}}_{_initial}

for (4) or

{f_{2}}_{j} \geq {f_{2}}_{_initial}

for (5)

11.

{f_{2}}_{_initial} = {f_{2}}_{j}

;

12.

N_{index} = j

;

13. end if.

14. end for.

15. Output

{f_{2}}_{_initial}

and

N_{index}

16. Look up the best intra-cluster timeslot assignment combination according to

N_{index}

We first solve the problem in real domain by relaxing $(t 3)$ to $N_{ik} \geq 0$ . If the result complies with the constraint that $N_{ik}$ is integer, that is also the solution of equation (8). Otherwise, we must convert the result to integer by branch-and-bound approach.

Solve the problem in real domain

If $N_{ik}$ is real number, an important observation is that equation (8) can be regarded as a convex optimization problem.²³ The second-order difference cost function can be transformed into

\sum_{k = 1}^{M} {(T_{ik} - C_{ik})}^{2} = trace (D)

(12)

where D is a diagonal matrix with the kth diagonal element $D_{k} = (T_{ik} - C_{ik})^{2}$ . The $trace (D)$ is the sum of convex functions as $\nabla^{2} D \geq 0, \forall x \in dom D$ .

As for the load balance function, we can take the logarithm of the function and change the sign. Then

max Π_{k = 1}^{M} \frac{C_{ik}}{T_{ik}} \Leftrightarrow - min \sum_{k = 1}^{M} \ln \frac{C_{ik}}{T_{ik}}

(13)

This again is the sum of convex functions.²³

Since equation (8) is a convex optimization problem in real domain, there are many practical algorithms and software packages available to obtain the optimal solution. We employ the MATLAB CVX software package to solve the proposed convex optimization problems.

Convert the real domain solution to integer

If the solution obtained in real domain denoted as $N R_{ik}$ , is not integer, we must convert the solution to integer. Branch-and-bound approach is a widely used method to solve the integer programming, which can convert optimal real domain solution to integer. However, the approach is usually used to solve the linear integer programming problems and the number of subproblems that are required to be solved during the execution of the approach increases exponentially with the size of the problem.²⁴ Therefore, based on the characteristics of objective functions, we propose a novel regional branch search algorithm to get the optimal integer solution referencing the branch-and-bound approach. In this method, the complexity is fixed once $N R_{ik}$ is determined.

First, we convert $N R_{ik}$ to integer $N L_{ik}$ by rounding down as

N L_{ik} = ⌊ N R_{ik} ⌋

(14)

where $⌊ x ⌋$ is the largest integer not greater than x. Obviously, $\sum_{k = 1}^{M} N L_{ik}$ is less than $N_{t}$ , which satisfies $(t 2)$ .

Second, the number of remaining timeslots $N r_{i}$ is calculated as given below

N r_{i} = N_{t} - \sum_{k = 1}^{M} N L_{ik}

(15)

Third, the candidate interval of the kth beam is set in $[N L_{ik} : N L_{ik} + N r_{i}]$ . Therefore, the number of the combinations is $(N r_{i} + 1)^{M}$ . Then, we seek the optimal solution by searching in the feasible region as indicated in Table 2. Similarly, the complexity of the search method is $O (n^{2})$ .

Simulation and analysis

Parameter introduction

Herein, a simplified model is considered in which a multibeam geostationary satellite has 49 beams with user links operating at 20 GHz. And the beams are divided into seven clusters, that is, there are seven beams in each cluster as shown in Figure 3. The system parameters used in our simulations are summarized in Table 3. It is considered that the feeder links are ideal and identical since the aim is to evaluate the performance of the schemes on the user links. And the user link budget parameters are depicted in Table 4, where the rain attenuation in each cluster is generated randomly. Moreover, the feeder uplink $SN R_{up}$ is taken as 25 dB.

Table 3.

System parameters in the simulation.

Parameters	Values
K	49
N	7
M	7
$T_{i}^{c}$	[270, 300, 330, 360, 390, 420, 450] Mbps

Table 4.

User link budget parameters.

Parameters	Illustration	Values
$P_{total}$	Total on-board power	200 W
$L_{free}$	Free space loss	212 dB
$B_{n}$	Noise bandwidth	200 MHz
$T_{n}$	Noise temperature	200 K
$G_{T}$	Transmit antenna gain	40 dB
$G_{R}$	Receive antenna gain	50 dB
k	Boltzmann’s constant	−228.6 dB
$L_{rain}$	Rain attenuation of the cluster	[8.73, 4.03, 8.51, 3.95, 9.43, 4.80, 3.57] dB

In each cluster, there are 256 available timeslots during the beam hopping window, that is, $N_{t} = 256$ . The traffic demands of each cluster are randomly distributed among the beams in them, and the parameters used in the simulation are represented in Table 5.

Table 5.

Traffic demands among beams in each cluster.

Cluster number	Traffic demand distribution (Mbps)
1	[17, 21, 26, 32, 35, 57, 82]
2	[21, 32, 34, 38, 42, 65, 68]
3	[20, 26, 36, 46, 55, 61, 86]
4	[28, 32, 37, 49, 53, 70, 91]
5	[21, 37, 51, 61, 68, 75, 77]
6	[24, 32, 56, 60, 65, 76, 107]
7	[25, 37, 55, 62, 75, 91, 105]

Performance metrics

Capacity losses

The capacity losses are the parts of allocated capacity exceeding the requested traffic, which is defined as below. This metric implies the count of the capacity wasted by the system

L_{C} = \sum_{j = 1}^{K} max {C_{j} - T_{j}, 0}

(16)

Actual capacity

The actual capacity is the parts of the allocated capacity not exceeding the requested traffic

C_{A} = \sum_{j = 1}^{K} min {T_{j}, C_{j}}

(17)

Traffic matching ratio

To describe the satisfaction degree of the actual capacity with respect to the total requested traffic, the traffic matching ratio is defined as

ρ_{s} = \frac{C_{A}}{\sum_{j = 1}^{K} T_{j}}

(18)

Performance evaluation

Performance comparison of power allocation

In this section, we first compare the performance of two proposed joint power and timeslot allocation methods with that of conventional resource management by uniform power and timeslot allocation.

After allocating the power to each cluster, the allocated capacity distribution among the clusters is shown in Figure 6. It is noticed that allocated capacities by conventional allocation exceed the requested traffic in some clusters (2 and 4), whereas those in other clusters are not enough obviously (especially in cluster 3 and 5). Furthermore, we calculate the capacity losses for conventional allocation, capacity difference allocation, and load balance allocation, where the results are 231.25, 0, and 0 Mbps, respectively. That is to say, the capacity waste is significantly avoided by the proposed inter-cluster power allocation methods. In addition, the actual capacities of three methods are 2.2683, 2.3854, and 2.4098 Gbps, and the distribution is illustrated in Figure 7. Both of the proposed power allocation methods improve more than 110 Mbps for throughout compared with conventional power allocation scheme. Another conclusion is that load balance allocation achieves more actual capacities than capacity difference allocation. It is because the second-order difference cost function makes a compromise between proportional fairness and maximum total capacity,²⁵ that is, comparing with load balance allocation, capacity difference allocation improves proportional fairness at the cost of actual capacity.

Figure 6.

Allocated capacity distribution comparison between proposed and conventional resource allocation.

Figure 7.

Actual capacity distribution comparison between proposed and conventional resource allocation.

Performance comparison of timeslot assignment

Then, the actual capacity would be assigned to each beam. We select a random cluster to exhibit the performance comparison between two proposed schemes with conventional timeslot assignment. The allocated capacity and actual capacity distributions among beams in cluster 4 are shown in Figures 8 and 9, respectively. It is inferred that there are capacities wasted again during the timeslot assignment by conventional methods, whereas this is effectively avoided by proposed timeslot assignment schemes. Therefore, we need to calculate the actual capacity again, and the results are described in Figure 10. It is notable that the results in Figure 10 are different from those in Figure 7, this is because conventional timeslot assignment to beams in the same cluster leads to capacity waste as mentioned above. However, the proposed intra-cluster timeslot assignment can effectively avoid capacity waste. Thus, the actual capacities of two proposed schemes are the same as Figures 7 and 10.

Figure 8.

Allocated capacity distribution among beams in cluster 4.

Figure 9.

Actual capacity distribution among beams in cluster 4.

Figure 10.

Actual capacity distribution of three resource allocation methods.

Moreover, we can also verify the effectiveness of the proposed joint power and timeslot allocation methods from the perspective of traffic matching ratio. The traffic matching ratio of conventional resource management, capacity difference allocation, and load balance allocation are 79.1%, 94.61%, and 95.53%, respectively, which further certify the effectiveness of the proposed joint power and timeslot allocation.

Comparison between joint optimization and single variable optimization

At last, the performance of joint optimization and single variable optimization are compared. According to the variable to be optimized and optimization method to be selected, there are four single variable optimization schemes, which are listed below:

Capacity difference power allocation + uniform timeslot assignment.

Load balance power allocation + uniform timeslot assignment.

Uniform power allocation + capacity difference timeslot assignment.

Uniform power allocation + load balance timeslot assignment.

Scheme (I) and scheme (II) are only power optimization schemes, and scheme (III) and scheme (IV) are only timeslot optimization schemes. The actual capacity distributions of power optimization schemes and timeslot optimization schemes are displayed in Figures 11 and 12, respectively. It is easily observed that the proposed joint optimization methods outperform both power optimization and timeslot optimization schemes. Then, the traffic match ratios of four single variable optimization schemes are calculated, which are 79.97%, 80.32%, 88.93%, and 88.41%, respectively. The results further verify the effectiveness of proposed joint optimization methods. Moreover, the traffic match ratio results demonstrate that all single variable optimization schemes are superior to the conventional resource management, and timeslot optimization schemes apparently achieve better performances than power optimization schemes.

Figure 11.

Actual capacity comparison between joint optimization and power optimization schemes.

Figure 12.

Actual capacity comparison between joint optimization and timeslot optimization schemes.

Conclusion

To improve the efficiency of on-board resource utilization in beam-hopping user downlinks, we propose two joint power and timeslot allocation schemes for smart gateway systems. These schemes introduce a two-step method to reduce the computation complexity by dividing the joint optimization problem into two single variable optimization subproblems: inter-cluster power allocation and intra-cluster timeslot allocation. Moreover, two novel algorithms are proposed to solve the two subproblems, respectively. Simulation results clarify that both the actual capacity and traffic match ratio are improved effectively in contrast with conventional resource management scheme. Moreover, the resource waste is also avoided by the proposed joint resource allocation methods. Eventually, the performance comparison between joint optimization methods and single variable optimization schemes further verify the effectiveness of the proposed methods.

Footnotes

Academic Editor: Haibo Zhou

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by National Natural Science Foundation of China (grant nos 61571464, 61601511, 91338201, 91438109, and 61401507).

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