Item Type Article
Authors Na, Dong-Hyoun;Park, Kihong;Ko, Young-Chai;Alouini, Mohamed- Slim
Citation Na, D.-H., Park, K.-H., Ko, Y.-C., & Alouini, M.-S. (2022).
Beamforming and Band Allocation for Satellite and High-Altitude Platforms Cognitive Systems. IEEE Wireless Communications Letters, 1–1. https://doi.org/10.1109/lwc.2022.3202641
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DOI 10.1109/lwc.2022.3202641
Publisher Institute of Electrical and Electronics Engineers (IEEE) Journal IEEE Wireless Communications Letters
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Beamforming and Band Allocation for Satellite and High-Altitude Platforms Cognitive Systems
Dong-Hyoun Na, Graduate Student Member, IEEE, Ki-Hong Park,Senior Member, IEEE, Young-Chai Ko, Senior Member, IEEE,and Mohamed-Slim Alouini, Fellow, IEEE
Abstract—In this letter, we consider a cognitive radio network consisting of broadcast satellite service (BSS), high-density fixed- satellite service (HDFSS), and high-altitude platforms (HAPs) systems. The spectrum utilization within a satellite beam coverage is increased by deploying extra HAPs in the pre-determined hot- spot regions to existing cognitive systems in which the BSS and HDFSS share frequency bands. Since the multiple network nodes simultaneously employ the same frequency band, there exists a challenge to efficiently mitigate the interference between them.
Therefore, we propose an iterative precoding and band allocation algorithm for multi-antenna HAPs to maximize the network data rate. In addition, we present other low-complexity techniques and compare them through simulation results.
Index Terms—Cognitive systems, satellite communications, HAPs, band allocation, beamforming, sum-rate maximization.
I. INTRODUCTION
D
UE to the rapid growth of data on demand, it is expected that the existing terrestrial network will be overwhelmed.In addition, it is challenging to serve remote areas by us- ing only terrestrial networks. Accordingly, satellite commu- nications (SatCom) systems are being successfully deployed to cover networking in remote or sparsely populated areas.
However, the demand for broadband SatCom has been ever- growing due to the significant increment in data usage, which makes the given spectrum bands insufficient to satisfy the needs. To tackle this spectrum shortage, the cognitive radio (CR) technique that shares bands but guarantees incumbent links has been proposed as a promising solution [1], [2]. It allows SatCom systems to have extra bandwidth and higher throughput in Ka-band. In [1], [3], [4], several CR scenarios of SatCom under International Telecommunication Union Ra- diocommunication Sector (ITU-R) regulations are presented, showing substantial improvements in system throughput.
Along with SatCom, airborne communications using high- altitude platforms (HAPs) have been attracting considerable attention. HAPs are located about 20 km above the Earth, and as such HAPs communications (HAPCom) have wider coverage than terrestrial communications and can secure line- of-sight (LoS) with a high probability. Moreover, compared to
This work was supported in part by the KAUST Office of Sponsored Research and in part by the Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korea government (MSIT) (2021-0-00260, Research on LEO Inter-Satellite Links).
D.-H. Na and Y.-C. Ko are with the School of Electrical Engineering, Korea University, Seoul 02841, South Korea (e-mail: [email protected];
D.-H. Na, K.-H. Park, and M.-S. Alouini are with the Computer, Electrical, and Mathematical Sciences and Engineering Division, King Abdullah Univer- sity of Science and Technology, Thuwal 23955, Saudi Arabia (e-mail: donghy- [email protected]; [email protected]; [email protected]).
Fig. 1. Cognitive satellite network model with BSS, HDFSS, and HAPs.
SatCom, HAPCom have lower delay and attenuation, and are more flexible in positioning [5].
ITU-R presented frequency bands utilized for HAPCom in world radiocommunication conferences (WRC), which overlap with the bands already allocated for SatCom. Thus, spectrum sharing between satellites and HAPs has been suggested [6], [7]. One of the most critical issues in such systems is inter- system interference between SatCom and HAPCom. In [6], it was shown that both systems coexist in the same band by examining the interference between SatCom and HAPCom, but it calculated just interference from HAPs without em- ploying band allocation or beamforming. In [7], a realistic channel model for a shared band was presented but only a beamforming scheme was proposed. Still, a single HAP situation was considered without band allocation. Efficient bandwidth management and beamforming are necessary to mitigate the resulting interference. In [6], [7], only the satellite and HAPs downlinks were taken into account. However, we consider a CR network that includes a SatCom uplink as a primary link and allows HAPCom to secure additional bandwidth with band allocation and beamforming.
In order to increase the areal spectral efficiency over Sat- Com beam coverage, we suggest additionally deploying multi- ple HAPs to cover hot-spot users at the empty coverage areas of SatCom beam in a CR system where broadcast satellite service (BSS) feeder uplink and high-density fixed-satellite service (HDFSS) downlink share multiple frequency bands.
We aim to allow the three systems to share and utilize the frequency bands more efficiently. We propose the solutions to resource management and beamforming scheme to maximize sum rate using realistic system parameters.
II. SYSTEM ANDCHANNELMODEL
We consider a SatCom CR system in the 17.3-17.7 GHz band. As shown in Fig. 1, a BSS and HDFSS work together.
On the basis of this SatCom CR setup, several hot-spot regions
including multiple mobile stations (MSs) are additionally covered by multi-antenna HAPs. The three systems share the same band in the same area with a CR technique, where spectrum sensing should be performed to detect interference from BSS gateway (GW) and HDFSS satellite. HDFSS is a multibeam system that employs four-frequency reuse, but we take a representative beam into consideration and assume a GW of the BSS is at the center of the beam. The BSS feeder uplink is an incumbent link, and the HDFSS downlink and HAPs downlink are cognitive links. Due to the BSS feeder uplink, the GW interferes with earth stations (ESs) and MSs on the ground. The HDFSS satellite and HAPs interfere with each other’s target receivers, MSs and ESs, respectively. Interference from the HDFSS satellite to BSS satellite can be neglected because of the orbital separation of the two satellites and the directivity of antenna [1], [3], [4].
The shared band employed by all the three systems and the exclusive band used only by HDFSS are taken into account, similar to [3]. The shared and exclusive bands are divided into L1andL2 sub-bands, respectively. The HAPs exploit all shared bands, and the HDFSS satellite appropriately allocates the shared and exclusive bands to downlinks and transmits signals toL(=L1+L2)ESs. In addition,Khot-spot regions with multiple MSs are covered by HAPs withN(=Nx×Ny) uniform planar array (UPA).
The ESs and MSs receive desired signals and interference signals from the HDFSS satellite (S), respectively. Thus, hl and ˆhkm represent the channel coefficients from the satellite to the lth ES (ESl)and mth MS in the kth hot-spot region (MSkm), respectively, which are represented as
hl=rl
λc
4πd(S,ESl)cl
pGES(0)p
Gmax, (1a) ˆhkm = ˆrkm
λc
4πd(S,MSkm)ˆckm
pGMS
pGmax, (1b) where λc and Gmax mean the carrier wavelength and the maximum satellite antenna gain, respectively. Atmospheric attenuation rl and rˆkm are experienced by ESl and MSkm, respectively, and follow a log-lognormal distribution [8]. In (1),d(X,Y) denotes the distance betweenXandY. Besides, GX,{X = ES,MS} is the antenna gain of the ES or MS, whereGESis a function of the offset angle from the boresight direction of ESs to the satellite [9] and set to zero in this paper.
The satellite beam pattern cl and ˆckm are depending on the position of the users and 3 dB angle of the satellite [8].
The ESs and MSs go through interference from the GW, and the channel coefficients of ESl andMSkm from the GW can be expressed as
bl= λc
4πd(GW,ESl)
pGES(θl)p
GGW(ϕl), (2a) ˆbkm= λc
4πd(GW,MSkm) pGMS
r GGW
ϕˆkm
, (2b) whereθlis the offset angle from the boresight direction ofESl
to GW, and ϕl andϕˆkm are offset angles from the boresight direction of GW toESlandMSkm, respectively [4], [9], [10].
The channel coefficients fkl and ˆfkm from the kth HAP (HAPk)to the ESl andMSkm can be expressed as [7]
fkl= λc
4πd(HAPk,ESl)
pGES(φkl)p
g(pkl, qkl)
×ax(pkl, qkl)⊗ay(pkl, qkl), (3a) ˆfkm= λc
4πd(HAPk,MSkm) pGMS
pg(ˆpkm,qˆkm)
×ax(ˆpkm,qˆkm)⊗ay(ˆpkm,qˆkm), (3b) whereφkl is the offset angle of boresight direction ofESl to HAPk [9]. The UPA element pattern g(p, q)depends on the angle of departure, wherepandq(orpˆandq) are the verticalˆ and horizontal angles from departure of the HAP, respectively [7]. In (3),axandayare thex-axis andy-axis steering vectors of the UPA, respectively [7]. We suppose that LoS is dominant between HAPs and ground.
Thus, the signal-to-interference-plus-noise ratios (SINRs) of ESl andMSmk can be written as
ΓESl = PS|hl|2 PG
L1
X
i=1
αil|bl|2+
L1
X
i=1
αil K
X
k=1
βik Mk
X
m=1
fklHwkm
2+σ2l , (4a)
ΓMSkm=
ˆfkmH wkm
2
Mk
X
i̸=m
ˆfkmH wki
2
+PS
ˆhkm
2
+PG
ˆbkm
2
+ ˆσ2km , (4b)
where PG and PS are the transmit powers of the GW and satellite, respectively, andσl2andˆσkm2 denote the noise power of ESl andMSkm, respectively. In (4), Mk is the number of MSs covered by HAPk. The HAPs exploit beamforming to mitigate the interference, and wkm is a beamforming vector fromHAPk for MSkm. Since we assume the number of hot- spot regions is less than the number of shared sub-bands and all HAPs utilize different sub-bands, we do not consider inter- HAP interference. We introduce binary variablesαandβ for the band allocation of ESs and HAPs, respectively, where αij = 1 (βij = 1) means the ith sub-band is used for ESj
(HAPj), otherwiseαij= 0(βij= 0). Since the HDFSS system operates in both shared and exclusive bands, forαij,1≤i≤L1 is for shared sub-bands andL1+1≤i≤L1+L2is for exclusive sub-bands, whereas forβij, 1≤i≤L1. Note that we assume a centralized design where the connection between HDFSS system and HAPs system exists through their gateways or other satellite [8], [11].
III. PROBLEMFORMULATION ANDPROPOSEDSOLUTION
Our objective is to maximize the sum rate in the proposed CR system by optimizing the beamforming vector of HAPs and allocating bands for HAPs and HDFSS downlinks. There- fore, the optimization problem can be formulated as
max
w,α,β L
X
l=1
log2 1+ΓESl +
K
X
k=1 L1
X
u=1
βuk
Mk
X
m=1
log2 1+ΓMSkm (5a) s.t.PMk
m=1wHkmQnwkm≤PH,kn, (5b) αij ∈ {0,1},PL
i=1αij = 1,PL
j=1αij = 1, (5c) βuk ∈ {0,1},PK
k=1βuk= 1,PL1
u=1βuk≥Bk, (5d)
for ∀k ∈ {1,2,· · ·, K},∀n∈ {1,2,· · · , NxNy}, and ∀u∈ {1,2,· · · , L1}, where PH,kn is the maximum power of the nth antenna of HAPk. Constraint (5b) is on the maximum power of the HAPs antenna, and Qn is a matrix in which the nth diagonal component is 1, and the rest are 0. In (5d), Bk denotes the minimum number of the bands for HAPk
and should be chosen to ensure that all HAPs use at least one band. Note that we can additionally consider minimum SINR constraint for guaranteeing user fairness, while the optimization problem will be solved in the same manner. It is challenging to find the globally optimal solution of the problem (5) because it is a non-convex mixed-integer nonlinear programming (MINLP).
We propose to solve the problem by decomposing it. Since there are two binary variables for band allocation for HDFSS and HAPs downlinks, we first allocate the band for HDFSS.
Since each ES uses one sub-band, the shared and exclusive sub-bands should be appropriately allocated to minimize in- terference from the primary user GW [3]. In that process, we do not consider the existence of HAPs and calculate the SINR assuming that all ESs undergo interference from the GW as ΓESl =PS|hl|2/(PG|bl|2+σl2). The shared sub-bands are allocated to L1 ESs having larger SINRs, and the exclusive sub-bands are allocated to the remainingL2ESs. Problem (5) is still an intractable form albeit αis determined. Hence, we introduce slack variables {γ, µ,γ,ˆ µ}ˆ to change the problem to a more manageable form and problem (5) can be transformed into
max
w,β,γ,µ,ˆγ,ˆµ
PL
l=1µl+PK k=1
PL1
u=1βukPMk
m=1µˆkm (6a) s.t.PMk
m=1wkmH Qnwkm≤PH,kn, (6b) βuk−βuk2 ≤0, 0≤βuk ≤1, (6c)
PK
k=1βuk = 1, PL1
u=1βuk ≥Bk, (6d) ΓESl ≥γl, log2(1 +γl)≥µl, (6e) ΓMSkm≥γˆkm, log2(1 + ˆγkm)≥µˆkm, (6f) for all k, n, u, l, and m. The constraint (5d) can be written equivalently as (6c). Since problem (6) is optimal when the equality in (6e) and (6f) holds, problems (5) and (6) are equivalent, which can be proved by contradiction [8].
Subsequently, we propose to solve the problem (6) based on the block coordinate descent (BCD) method. We divide the problem (6) into sub-band allocation problem for HAPs under fixed beamforming vector and beamforming problem under fixed band allocation. The two problems are solved alternately until convergence.
First, when w is fixed and only the constraints on β are considered, the problem to obtain β can be written as
max
β,γ,µ
PL
l=1µl+PK k=1
PL1
u=1βukPMk m=1µˆtkm
−ρPK k=1
PL1 u=1
βuk−2βukt βuk+(βukt )2 (7a) s.t. 0≤βuk≤1, PK
k=1βuk= 1, PL1
u=1βuk≥Bk, (7b) 2PS|hl|2/γlt−PS|hl|2γl/ γtl2
≥PGPL1
i=1αil|bi|2 +PL1
i=1αilPK
k=1βikPMk m=1
fklHwtkm
2+σl2, (7c) γl+(ηtl−µl)≥ ||[γl−(ηlt−µl) 2p
δtl]||2, (7d)
for allu, k, andl, whereβukt ,γlt, andwtkmare the local values at thetth iteration. We can approximate the first constraint of (6c) to the last term of (7a) using the first-order Taylor series expansion around βukt because (6c) is a difference-convex function. In (7a),ρis a penalty parameter, which is introduced to make the problem feasible. Problem (7) is equivalent to problem (6) for β when the last term in (7a) becomes zero.
For the relaxation, ρ is initially set to a small value, and then it increases at every iteration byc. Since findingρmax is difficult,ρ increases until the last term of (7a) approximates to zero [12]. The first constraint of (6e) can be transformed to (7c) by simple algebraic operations and the first-order Taylor series expansion of a quadratic-over-linear function aroundγlt. Since log functions are preferred to be converted to more computationally efficient form for optimization software, the second constraint of (6e) is transformed into (7d), where ηlt=log2(1+γlt) +γtl/((1+γlt)ln 2) and δtl=(γlt)2/((1+γlt)ln 2) [8].
When we express the optimization problem for w withβ given, constraints (6e) and (6f) can be transformed in a similar way previously used for (7c) and (7d) as follows:
2PS|hl|2/γlt−PS|hl|2γl/ γtl2
≥PG L1
X
i=1
αil|bi|2+
L1
X
i=1
αil K
X
k=1
βikt
Mk
X
m=1
fklHwkm
2+σl2, (8)
γl+ ηlt−µl
≥
γl− ηlt−µl
2 q
δtl
2
, (9)
2Rn
wkmt HˆfkmˆfkmHwkmo.
ˆ γkmt −
ˆfkmHwtkm
2
ˆ γkm.
ˆ γtkm2
≥PMk i̸=m
ˆfkmHwkm
2
+PS
ˆhkm
2
+PG
ˆbkm
2
+ ˆσ2km, (10) ˆ
γkm+ ˆηkmt −µˆkm
≥
ˆ
γkm−ηˆtkm−µˆkm
2 qδˆtkm
2
, (11) where ˆγtkm represents the local point at the tth iteration. In (11), ηˆkmt = log2(1+ ˆγkmt ) + ˆγkmt .
((1+ ˆγkmt ) ln 2) and δˆtkm= (ˆγtkm)2.
((1+ ˆγkmt ) ln 2). Thus, the optimization problem for w can be written as
max
w,γ,µ,ˆγ,µˆ
PL
l=1µl+PK k=1
PL1
u=1βukt PMk
m=1µˆkm (12a) s.t. (6b),(8),(9),(10),(11), ∀k, n, l, m. (12b) We note that (7) and (12) are the second-order cone pro- grammings (SOCPs), which can be solved by interior-point method (IPM). Algorithm with BCD to solve problem (6) is summarized in Algorithm 1. As the problem is solved with BCD repeatedly, the objective function value increases monotonically, and converges due to the power constraint [13].
IV. LOWCOMPLEXITYTECHNIQUES
Since the proposed BCD-based band allocation and beam- forming (BBA-BF) technique in the previous section has high complexity, we propose several other low complexity methods that do not require solving for β and w alternately, which are weighted distance based band allocation and beamforming (WDBA-BF) and WDBA zero-forcing (WDBA-ZF).
Algorithm 1 Proposed Iterative Algorithm to Solve (6)
1: Sett:= 0;
2: Initialization: feasible starting points ofwtandβt,γt,γˆt, and penalty parameterρt;
3: repeat
4: Solve (7) to obtain optimal solutionβ∗andγ∗for given βt,wt, andγt;
5: Updateβt:=β∗ andγt:=γ∗;
6: Solve (12) to obtain optimal solution w∗, γ∗, and ˆγ∗ for givenwt,γt, andˆγt;
7: Sett:=t+ 1;
8: Updateβt:=β∗,wt:=w∗,γt:=γ∗, andγˆt:= ˆγ∗;
9: Updateρt:= min cρ(t−1), ρmax
;
10: untilConvergence;
A. WDBA-BF and DBA-BF for Low Complexity Band Alloca- tion
In order to lower the complexity, we separately optimize the beamforming vector and band allocation for HAPs. For WDBA-BF, we first obtainw that maximizes the data rate of hot-spot regions without considering ES. Successive convex approximation (SCA) is used in a similar way to problem (12). It can be expressed as
max
w,ˆγ,ˆµ
PK k=1
PMk
m=1µˆkm s.t. (6b),(10),(11), ∀k, n, m, (13) which is also an SOCP that can be solved with IPM. For band allocation with lower complexity, we maximize the distance from ES sharing the same band to mutually alleviate the interference. We consider the weighted distance to allocate more sub-bands to the hot-spot regions where a higher data rate can be obtained. Therefore, the optimization problem for β can be written as
max
β
PK
k=1wkPL1
u=1βukd HAPk,ESu2
s.t. 0≤βuk≤1,(6d), (14) for all uandk, where the weightwk=QMk
m=1 1+ΓMSkm . The weight can be calculated withwoptimized in advance. In (14), ESu denotes ES using theuth sub-band, which is determined withα. Since problem (14) is a linear programming, the first constraint of (6c) does not have to be considered. In DBA- BF, we do not consider the weight and find β with wk= 1 in problem (14). Finally, we optimizew with the obtainedβ, which is the same as problem (12). Although the problems can be solved in a decentralized way if the position of HAPs and α are known to HAPs in advance, we propose a centralized method for consistency with the scheme in Section III.
B. WDBA-ZF and DBA-ZF for Low Complexity Beamforming In this sub-section, we utilize ZF as a benchmark scheme for beamforming, and only the HAPs downlink band allocation is optimized. When obtaining β, as in the previous methods, the distances to the ESs that will use the same sub-bands are maximized. WDBA-ZF considers the weight as in (14), and DBA-ZF does not, as in DBA-BF.
TABLE I COMPLEXITYANALYSIS
Method BBA-BF WDBA-BF WDBA-ZF
Iterative OL31K3
, ON3K3M2 ON3K3M2
Onetime OL31K3
OM3 ,OL31K3
TABLE II SYSTEMPARAMETERS
PARAMETER VALUE
Shared / exclusive band 17.3-17.7 / 19.7-20.2 GHz
Sub-band bandwidth 36 MHz
Satellite / HAP height 35,786 (GEO) / 20 km Satellite / GW transmit power 21 / 18.9 dBW
Satellite / ES maximum gain 52 / 42.1 dBi Noise power of ES / MS -128.86 / -128.24 dBW Beam diameter of satellite / HAP 250 / 20 km
Satellite / HAP 3 dB angle 0.4◦/60◦and10◦ Antenna spacing / side-lobe level half of wavelength / 20 dB Rain attenuation mean and variance (−2.6,1.63)
C. Complexity Analysis
We compare the computational complexity for the proposed methods in Table I [14]. We assumeMk=M andN≫M. In BBA-BF, the two subproblems are alternately solved based on BCD, whereas in WDBA-BF (or DBA-BF), the beamforming subproblem based on SCA is iteratively solved and the other band allocation subproblem is solved only once. Thus, the complexity of BBA-BF is higher than WDBA-BF (or DBA- BF). The difference between WDBA-BF and DBA-BF (or WDBA-ZF and DBA-ZF) is in the weight calculation.
V. NUMERICALRESULTS
In this section, we present the simulation results with realis- tic system parameters to show the performance of the proposed methods. The shared and exclusive band are 17.3–17.7 GHz and 19.7–20.2 GHz, respectively, and divided into sub-bands L1 = 11,L2 = 14, and L = 25 by setting the size of each sub-band to 36 MHz [1], [3]. The number of UPA elements is Nx = Ny = 6 and the number of MSs simultaneously covered by a HAP is Mk = M = 6. The GW and beam center of HDFSS are located at the origin, and the beam radius is 125 km. The centers of the hot-spot regions and ESs are uniformly distributed within the beam. MSs are also uniformly distributed in the hot-spot regions with a radius of 20 km considering the coverage of HAPs. The other system parameters are listed in Table II. We refer to [7] and ITU- R documents (e.g., F.1609-1, M.2101-0, M.2135-1) for the parameters and antenna gains. The offset angles from the boresights can be calculated using trigonometric techniques [4]. We assume that the maximum power of all HAPs antennas is the same, i.e., PH,kn =PH.
Fig. 2a plots the total data rate versus the maximum power per antenna of HAPs. There are four hot-spot regions, and we setBk=⌊L1/K⌋= 2for fairness. AsPH increases, so does the total data rate for all methods. We use WDBA-ZF and DBA-ZF presented in Section IV-B as benchmarks. Although these can remove inter-user interference with ZF, they have
10 15 20 25 HAP maximum antenna power (dBm) 10
12 14 16 18 20 22
Total data rate (Gbps)
BBA-BF WDBA-BF DBA-BF WDBA-ZF DBA-ZF
14.5 15 15.5
15.5 16
(a)
4 5 6 7 8 9 10 11
Number of hot-spot regions 11
11.5 12 12.5 13 13.5 14 14.5
Total data rate (Gbps)
BBA-BF WDBA-BF DBA-BF WDBA-ZF DBA-ZF
(b)
4 5 6 7 8 9 10 11
Number of hot-spot regions 11
11.5 12 12.5 13 13.5 14 14.5
Total data rate (Gbps)
BBA-BF WDBA-BF DBA-BF WDBA-ZF DBA-ZF
(c)
10 20 30 40
Number of iterations 330
340 350 360 370 380 390 400
Objective function value
0 20 40 60 80 100
Penalty term value
Value at convergence Objective function value Penalty term value
(d)
Fig. 2. (a) Total data rate vs. HAP maximum power per antenna forK= 4, (b) total data rate vs. number of hot-spot regions forBk=⌊L1/K⌋, (c) Total data rate vs. number of hot-spot regions forBk= 1, and (d) convergence of Algorithm 1 over a random channel generation forK= 4andPH= 10dBm.
much worse performance than the proposed techniques op- timizing the beamforming vector. The cases where weights are applied in (14) have a higher data rate than the cases where they are not. The proposed method to solve the problem iteratively using BCD has the highest performance, while the low complexity method (WDBA-BF) using the weighed distance maximization performs fairly well.
Figs. 2b and 2c show the total data rate according to the number of hot-spot regions from 4 to 11. The maximum power per antenna of HAPs is fixed at 10 dBm. To compare the performance for the minimum number of bands, we set Bk= ⌊L1/K⌋ for Fig. 2b and Bk= 1 for Fig. 2c. When Bk is constant, the total data rate decreases as the number of hot-spot regions increases. This is because distance between MSs and GW or ES and the HAP using the same sub-band decreases and it causes higher inter-system interference. Also, sub-bands cannot be concentrated in regions with higher rate.
When there are 6 to 11 hot-spot regions, the results are the same for both situations because Bk = 1 in both cases. In case of 4 and 5 hot-spot regions, however, the results in Fig.
2b are lower than in Fig. 2c, because two or more sub-bands (Bk= 2)in Fig. 2b and one or more sub-bands (Bk= 1)in Fig. 2c can be used in each region, respectively. In Fig. 2b, the variation of tendency at the point from K= 5 to K= 6 is also caused by the transition of Bk from two to one. In Fig. 2b, reasonable fairness can be achieved between hot-spot regions, but in Fig. 2c, more sub-bands can be allocated to regions where higher data rates can be obtained, which is more advantageous in terms of total data rate. The increase of hot-spot regions is beneficial for user access owing to the higher number of connected MSs per channel use. On the other hand, some hot-spot regions are generated closer to GW, then MSs experience higher interference causing lower data rate.
The benchmark techniques still have the same tendency as the proposed techniques regardless of the minimum number of band constraint.
Finally, in Fig. 2d, we investigate the convergence of the proposed method, wherePH= 10dBm andK= 4. As can be seen, the objective function value increases with each iteration and converges after some iterations. Moreover, after a few iterations, the penalty term approaches zero, and the binary constraint holds.
VI. CONCLUSION
We investigated a spectrum sharing system in which BSS, HDFSS, and HAPs co-exist using a CR technique. Since the
frequency band determined by WRC for HAPCom overlaps with the existing SatCom band, HAPCom was applied to the CR systems of BSS and HDFSS. We formulated an MINLP to guarantee the HDFSS link and alleviate the interference between systems, and we proposed several band allocation and beamforming methods. Furthermore, through simulation results using realistic parameters, the performance of the proposed methods has been verified according to fairness and transmit power. In future work, band allocation and beamforming will be considered for dynamic networks such as moving HAPs.
REFERENCES
[1] S. Malekiet al., “Cognitive spectrum utilization in Ka band multibeam satellite communications,”IEEE Commun. Mag., vol. 53, no. 3, pp. 24–
29, Mar. 2015.
[2] ETSI TR 103 263 V1.1.1, “Electromagnetic compatibility and radio spectrum matters (ERM); System reference document (SRdoc); Cogni- tive radio techniques for satellite communications operating in Ka band,”
Jul. 2014.
[3] S. K. Sharmaet al., “Joint carrier allocation and beamforming for cogni- tive SatComs in Ka-band (17.3–18.1 GHz),” inProc. IEEE International Conf. on Commun. (ICC), London, UK, Sep. 2015, pp. 873–878.
[4] S. Malekiet al., “Cognitive zone for broadband satellite communications in 17.3–17.7 GHz band,”IEEE Wireless Commun. Lett., vol. 4, no. 3, pp. 305–308, Jun. 2015.
[5] X. Caoet al., “Airborne communication networks: A survey,”IEEE J.
Sel. Areas Commun., vol. 36, no. 9, pp. 1907–1926, Sep. 2018.
[6] C. Queiroz et al., “New spectrum bands for HAPS: Sharing with fixed-satellite systems,” in Proc. IEEE 89th Vehicular Technol. Conf.
(VTC2019-Spring), Kuala Lumpur, Malaysia, Jun. 2019, pp. 1–5.
[7] Z. Lin et al., “Robust multi-objective beamforming for integrated satellite and high altitude platform network with imperfect channel state information,”IEEE Trans. Signal Process., vol. 67, no. 24, pp. 6384–
6396, Dec. 2019.
[8] J. Wanget al., “Multicast precoding for multigateway multibeam satellite systems with feeder link interference,”IEEE Trans. Wireless Commun., vol. 18, no. 3, pp. 1637–1650, Mar. 2019.
[9] ITU-R S.465-6, “Reference radiation pattern for earth station antennas in the fixed-satellite service for use in coordination and interference assessment in the frequency range from 2 to 31 GHz,”Series of ITU-R Recommendations, Jan. 2010.
[10] ITU-R S.580-6, “Radiation diagrams for use as design objectives for antennas of earth stations operating with geostationary satellites,”Series of ITU-R Recommendations, Jan. 2004.
[11] D. Wanget al., “The potential of multilayered hierarchical nonterrestrial networks for 6g: A comparative analysis among networking architec- tures,”IEEE Veh. Technol. Mag., vol. 16, no. 3, pp. 99–107, Sep. 2021.
[12] Q.-D. Vuet al., “Max-min fairness for multicast multigroup multicell transmission under backhaul constraints,” inProc. IEEE Global Com- mun. Conf. (GLOBECOM), Washington, DC, USA, Dec. 2016, pp. 1–6.
[13] P. Tseng, “Convergence of a block coordinate descent method for nondifferentiable minimization,”J. Optim. Theory Appl., vol. 109, no. 3, pp. 475–494, Jun. 2001.
[14] M. S. Loboet al., “Applications of second-order cone programming,”
Linear Algebra Appl., vol. 284, no. 1-3, pp. 193–228, Nov. 1998.
