# Is Satellite Ahead of Terrestrial in Deploying NOMA for Massive Machine-Type Communications?
## 3 From S-MIM to F-SIM
### F-SIM Key Implementation Aspects and Laboratory Test Results  
This section summarizes some key demodulator implementation aspects and the laboratory test results for some F-SIM waveforms previously introduced, corresponding to different use cases of interest. Performance results are shown in terms of the aggregated throughput (bits/chip) vs. the average multiple access channel (MAC) offered load (bit/chip) and the packet loss ratio (PLR) vs. the average MAC offered load (bit/chip). One of the main challenges in achieving the excellent theoretical E-SSA performance is related to the gateway demodulator's ability to minimize implementation losses in the presence of user terminal carrier frequency errors and phase noise. In particular, the two most critical demodulator functions are as follows:  
* Packet preamble acquisition;
* Interference cancellation. As mentioned at the end of Section 2.2, the first demodulation block is the preamble searcher (PS). The PS detects bursts in the current sliding window, by performing a search over a time-frequency grid to find the timestamp (i.e., the sample corresponding to the beginning of a burst) and the coarse frequency offset estimation of the detected bursts. Such a search is carried out by performing a cross-correlation between the samples stored in the sliding window memory and a local replica of the preamble (efficiently carried out by means of the fast Fourier transform). The spacing between the frequency hypothesis is set to keep the correlation loss [18] very low (usually, 0.5 dB), given the coherent integration time. This value corresponds to the duration of a preamble symbol, and then the resulting \(N_{p}\) coherent integrations (one for each symbol of the preamble, whose length is \(N_{p}\) symbols) are combined non-coherently. Such a short coherent integration allows having a rather wide spacing between the frequency hypotheses, or, in other words, to have a limited and hence affordable number of frequency hypotheses to test given the maximum frequency offset a burst can be received with. This maximum value accounts for all the impairments the carrier frequency is subject to, mainly, the instability of the terminal local oscillator. Thus, the PS provides the time delay estimate and a first coarse frequency offset estimate. Then, the residual frequency offset is finely estimated by a data-aided frequency estimation algorithm, i.e., the Rife-Boorstyn (RB) algorithm working on the known preamble symbols and pilot symbols [19]. Finally, the phase of the received signal is estimated. This is carried out by the maximum likelihood phase estimation algorithm working on the pilot symbols within a sliding window which has a length of \(M\) pilot symbols and slides of \(K=1\) symbols at a time. The length \(M\) is tuned to have a good trade-off between the estimation accuracy and tracking of the phase variation due to the effect of the phase noise. To summarize, the combination of the several estimators described above allows the demodulator to be robust to the channel impairments, thus justifying the limited performance loss shown in the results. Concerning the detected packet cancellation, it is well known that the SIC process can be negatively impacted in the presence of an imperfect cancellation caused by channel estimation errors (carrier frequency, phase, amplitude and clock timing). Once a burst is successfully decoded, the physical burst is locally regenerated so that a refined channel estimation is carried out, exploiting all the burst payload symbols in a decision-directed mode. This allows a better estimate of the carrier amplitude and phase evolution over the packet, thus leading to a better cancellation from the sliding window memory. Then, the locally regenerated and corrected burst is subtracted from the sliding window memory. To summarize, the combination of the several estimators described above allows the demodulator to be robust to the channel impairments, thus justifying the limited performance loss.