## 3 Established Connection Phase
### Remark--Protocol Summary and Efficiency  
The scheme here presented considers that, despite the CS stage, lasting \(T_{a,\mathrm{CS}}+T_{e,\mathrm{CS}}=Q_{a}T_{f}+Q_{e}T_{f}\) seconds, being necessary, it is somewhat limiting from the point of view of transmission efficiency. Such a performance metric, referred as \(\eta\), can be measured by considering the ratio for an assigned number of bits to be transmitted, between the time spent for an (ideal) OFDM communication with no connection setup, no estimation or prediction, and the presented case. Once set, the frame duration \(T_{f}\), the number of slots composing a frame is equal to \(M_{f}=T_{f}/T_{s}\). We recall from Section 2.4 that \(T_{s}\) correspondsalso to the symbol duration, which, in turn, is dependent on the CP length \(T_{CP}\). For the sake of simplicity, let us initially consider \(T_{CP}\) as fixed (that is, the case where CP tuning is not performed), so that \(T_{s}\) and \(M_{f}\) result can be considered fixed as well. Hence, the time requested to transmit \(N_{b}\) data bits in the ideal case, given \(R\) as the transmission rate, is:  
\[T_{N_{b}}^{(ideal)}=\frac{N_{b}}{R} \tag{21}\]  
since no overhead information is considered during the communication. On the other hand, the use of the proposed protocol makes the data transmission time given:  
\[T_{N_{b}}^{(proposed)}=(Q_{a}+Q_{e})T_{f}+\frac{N_{b}}{R}+N_{occ}(M_{a}+M_{e})T_ {f} \tag{22}\]  
thus, taking into account the \((Q_{a}+Q_{e})\) frames used for CS and those related to EC, while \(N_{occ}\) refers to the number of times interference and channel estimation refreshing is performed, allowing a reliable prediction to take place (\(M_{a}\) and \(M_{e}\) are recalled as the number of frame slots dedicated to interference and channel statistics update during the EC stage, respectively). The proposed mechanism efficiency is calculated from the ratio between the terms in Equations (21) and (22) that, after some mathematical manipulation, is expressed as:  
\[\eta^{(proposed)}=\frac{1}{1+\frac{R}{N_{b}}[(Q_{a}+Q_{e})T_{f}+N_{occ}(M_{a}+M_{ e})T_{f}]} \tag{23}\]  
where it is possible to observe that \(\eta^{(proposed)}\) increases with the amount of data to be transmitted \(N_{b}\). This is due to the fact that the growth of \(N_{b}\) makes the CS stage duration ever shorter than the EC time. Hence, the proposed methods approaches the ideal case performance where no initial setup is considered. Furthermore, another aspect must be highlighted. By removing the initial assumption about fixed CP length, if \(T_{s}\) changes due to the tuning of \(T_{CP}\), the whole time to transmit data also changes. Specifically, independently of \(N_{b}\), the growth of \(T_{CP}\) leads \(R\) to decrease and, interestingly, \(\eta^{(proposed)}\) to increase. This is because a larger time is needed to transmit the information, and this growth is more important with respect to the time spent in CS. Another interesting result is the following. From Equation (22), the CS time is invariant, since \(Q_{a}\), \(Q_{e}\) and \(T_{f}\) are fixed. So, CP adaptation impacts only on data transmission time, and this is true for both the ideal and proposed cases. Moreover, Equations (21) and (22) show the same dependency on \(R\). The only difference regarding data transmission is given by the quantity \(N_{occ}(M_{a}+M_{e})\), that is only related to the proposed mechanism. Therefore, we can conclude from Equation (23) that the time spent in CS and re-estimating cannot be considered as marginal when \(R\) is very high with respect to the data to be sent. For the sake of comparison, we also discuss a reference case where channel estimation was systematically performed every frame, without resorting to prediction. Moreover, no CS and interference acquisition during EC were considered. Hence, at the beginning of each frame some pilots for channel estimation were sent and, due to the channel non-reciprocity, the transmitter had to wait for two-way propagation time \(2T_{prop}\) before CSI was available.