# Forward Link Optimization for the Design of VHTS Satellite Networks
## 3 Fundamentals and Analytical Models
### Technical and Commercial Requirements  
A set of technical and commercial requirements are defined separately for ground and space segments.  
The requirements of the ground segment for the feeder link affect the calculation of the minimum number of gateways, which also depends on the use of Ka or Q/V band in the feeder link.  
A mixed solution using Q/V band on the feeder-link and Ka band on the user link is recommended to maximize system capacity [2]. Since the available bandwidth in Q/V band is larger, more capacity can be obtained in the system, and thus a reduction in the cost of Gbps is achieved.  
Frequency reuse in the multibeam satellite is usually defined by four colors [17] with two frequencies and two orthogonal polarizations in the frequency plan. The relationship between the uplink and the downlink parameters in the forward link [27] are defined in (11) and (12):  
\[BW_{T}=\frac{N_{P}BW_{A}\,B}{N_{C}} \tag{11}\]  
\[N_{GW}=\left\lceil\frac{BW_{b}\,B}{p\,BW_{A}}\right\rceil \tag{12}\]  
where  
* \(N_{C}\) is the number of colors defined in the frequency plan,
* \(BW_{T}\) is the total system bandwidth in MHz,
* \(BW_{b}\) is the bandwidth per beam in MHz,
* \(BW_{A}\) is the bandwidth assigned to each gateway in MHz,
* \(N_{P}\) is the number of polarizations of the frequency plan, and
* \(N_{GW}\) is the number of gateways.  
For instance, in a scenario of 82 beams and a four color scheme (two polarizations and two frequencies) to provide coverage in Europe, and with a bandwidth of 250 MHz per beam, at least eight gateways would be needed if the Ka band is shared between user and feeder links; however, five gateways would be required if Q/V bands are used in the feeder link (assuming an available bandwidth of 1.3 GHz for the Ka band and 2.5 GHz for the Q/V bands [2]).  
According to [28], the cost of ground segment varies between 10% and 15 % of the total cost of system (\(Cost_{T}\)). The model in (13) is proposed to evaluate the cost of a gateway, which aggregates the cost associate with the number of user beams fed by the gateway (\(f(n_{GW})\)) and the cost of the antenna (\(g(n_{GW})\)).  
\[Cost_{GW}=f(n_{GW})+g(D_{GW})=k_{1}n_{GW}+k_{2}D_{GW}^{2,7} \tag{13}\]  
where \(Cost_{GW}\) is the gateway cost (in M\(\epsilon\)), \(n_{GW}\) is the number of user beams per gateway, and \(D_{GW}\) is the antenna diameter of the gateway. \(k_{1}\) and \(k_{2}\) are empirical constants to adjust the cost to money units. The total cost of the ground segment is the sum of the cost of the gateways [22].  
The space segment is limited by the maximum satellite mass imposed by the platform and launcher. The satellite mass \(M_{sat}\) (kg) depends on the number of beams (\(B\)) and can be modelled as (14), with a constant mass of 4000 kg as the minimum mass of a full-wideband satellite [16]:  
\[M_{sat}=4000+B^{0,2}912 \tag{14}\]  
Finally, an additional limit associated to the maximum total cost of the system can be defined. The satellite cost model (15) includes a constant cost of 180 ME [16], including an average launch cost of 100 ME and a fixed cost of 80 ME as the minimum price of a broadband payload. A corrective term has been added according to the number of beams (\(B\)) [16].  
\[Cost_{sat}=180+1.8\,B \tag{15}\]