# Forward Link Optimization for the Design of VHTS Satellite Networks
## 2 Problem Definition  
The methodology presented in this paper aims to obtain an optimal VHTS system at a minimum cost per Gbps in orbit, and at a maximum capacity per beam, according to a set of technical and commercial requirements. The methodology can be applied to any service area and frequency plan and considers three different KPIs (Key Performance Indicator): channel capacity per beam, satellite capacity, and cost per Gbps in orbit.  
We focus on the _CINR_ calculation of the forward link, assuming that the fading in the feeder link uplink is controlled by fade mitigation techniques (e.g., uplink power control, gateway diversity), thus assuming that the uplink is not affecting the downlink (user link) performance.  
The number of beams required in a VHTS system depends on two important factors: the service area and the beamwidth of the beams.  
According to [16], the transmission channel in each beam can be considered as a Gaussian channel due to the central limit theorem taking into account co-channel interference and noise. This supports the fact that the channel capacity of each beam can be obtained analytically using the Shannon law as:  
\[C_{b}=BW_{b}\ \log_{2}(1+CINR_{b}) \tag{1}\]  
where  
* \(C_{b}\) is the Shannon capacity per beam in Gbps,
* \(BW_{b}\) is the bandwidth per beam in Hz, and
* \(CINR_{b}\) is the average of carrier-to-interference-plus-noise-ratio for each beam in dB.  
Once the Shannon capacity is obtained, the real capacity of each beam is taken into consideration and the required _CINR_ and spectral efficiencies of DVB-S2X ModCods when using CCM or VCM are used [21]. The cost per Gbps in orbit of a VHTS satellite network focuses on the analysis of the forward link according to the number of beams used, the _G/T_ of the user station and the annual availability. In this sense, the methodology achieves the optimal trade-off solution to minimize the cost per Gbps in orbit by obtaining the highest capacity per beam \(C_{b}\) according to a set of technical and commercial requirements and constraints for different scenarios. The optimization problem can be formulated as in (2):  
\[\begin{array}{l}\min\limits_{C_{\text{att}},\ C_{\text{ost}}}Cost_{\text{Gbps}} \\ C_{\text{att}}=f\big{(}B,\frac{G}{T},P\big{)}\\ Cost_{T}=f(B)\\ B\mathbb{N},\ \frac{G}{T}\in\Big{(}\big{(}\frac{G}{T}\big{)}_{1},\big{(}\frac{G}{T} \big{)}_{2},\dots,\big{(}\frac{G}{T}\big{)}_{N}\big{)},\ P\mathbb{R}\end{array} \tag{2}\]  
_subject to_  
\[a_{m}\in\ L_{m},\ \ m=1,\dots,M \tag{3}\]  
where  
* \(Cost_{\text{Gbps}}\) is the cost per Gbps in orbit in million euros (M&) per Gbps,\(Cost_{T}\) is the total network cost in MC (cost of satellite and gateways),
* \(C_{sat}\) is the total satellite capacity in Gbps,
* \(B\) is the number of beams,
* \(\frac{G}{T}\) is the figure of merit for the user terminal in dB/K. It is selected from a set of \(N\) values of commercially available options,
* \(P\) is the required link availability in the service area,
* \(a_{m}\) represents the \(m\)-th system constraint, such as the payload mass, the maximum total system cost and diameter of antenna satellite,
* \(L_{m}\) represents the \(m\)-th set of possible values to the \(m\)-th system constraint, and
* \(M\) is the number of system constraints.  
The cost per Gbps in orbit can be calculated using (4) and (5):  
\[Cost_{Gbps}=\frac{Cost_{T}}{C_{sat}}=\frac{Cost_{Sat}+Cost_{GS}}{C_{sat}} \tag{4}\]  
\[C_{sat}=\sum_{b=1}^{B}C_{b} \tag{5}\]  
where  
* \(Cost_{Sat}\) is the satellite cost in MC, and
* \(Cost_{GS}\) is the total ground segment cost associated to gateways in MC.