# Is Satellite Ahead of Terrestrial in Deploying NOMA for Massive Machine-Type Communications?
## 5 Ongoing R&D
### The Massive Project  
The ESA funded the ARTES AT MASSIVE project involving MBI S.r.L. and AIRBUS Italia S.p.A. (ADSR), aiming at improving the spectral efficiency of the E-SSA random access scheme by employing a linear minimum mean square error (MMSE) detector rather than a conventional single-user matched filter (SUMF) at the receiver. The above approach is justified by the fact that BPSK modulation is optimal when an SUMF detector is used and provides robustness to carrier phase noise. The multiple access spectral efficiency is maximized by single-user coding and decoding, and by implementing the SIC process described above. In this way, the complexity increases linearly with the number of users. To further boost the spectral efficiency performance of the spread spectrum random access scheme, especially in the case of a reduced power unbalance, a linear MMSE (LMMSE) detector can be used prior the SIC process [22]. In this case, BPSK modulation is not optimal, while QPSK modulation shows asymptotic optimality [22]. The adoption of QPSK modulation requires a modification of the waveform design. In particular, the quadrature multiplexing between PCCH and PDCH is replaced by time domain multiplexing (TDM) between the two channels. In the following, such E-SSA access scheme employing MMSE will be referred to as ME-SSA for short. Starting from the analysis reported in [23], the MASSIVE project implemented the LMMSE detector in the form of a multistage despreader (MSD) [24; 25]. The latter actually approximates an LMMSE detector, with the accuracy of approximation improving with the number of stages. The LMMSE detector requires, in fact, the inversion of the covariance matrix \(\mathbf{R}\), which is prohibitive in a real-time scenario. The MSD approximates the inverse of the covariance matrix by a polynomial expansion in \(\mathbf{R}\), that is: \(\mathbf{R}^{-1}\simeq\sum_{n=1}^{N}w_{n}\mathbf{R}^{n}\). A number of stages \(N\) equal to 2 or 3 is shown to provide a good approximation for the most typical scenarios. The weight \(w_{n}\) is properly chosen to approximate the LMMSE detector, i.e., \(\sum_{n=1}^{N}w_{n}\mathbf{R}^{n}\simeq(\mathbf{R}+N_{0}\mathbf{I})^{-1}\), \(N_{0}\) being the noise power. Assuming \(K\) bursts to be demodulated, the MSD implementation consists of a sequence of \(N\) identical stages, as depicted in Figure 16. First, the \(K\) received noisy bursts are individually despread. Then, they are input to the first stage, where the symbols are respread, time and frequency offset are restored and the so-obtained bursts are summed together. The resulting signal is sent in parallel to \(K\) lines, one per burst, where the relevant burst time and frequency offsets are corrected, and then despreading is applied. The symbols obtained in this way for each burst are input to the following stage, which performs the same processing as the previous one, until all the stages have been processed. The output symbols of each stage are also weighted and summed together. Once the final stage has been executed, such weighted sum represents the \(K\) despread bursts as they were obtained by a linear MMSE detector. Different approaches are available in the literature for weight computation. In this project, the approach proposed in [24] was adopted, as it provides a very good approximation of the LMMSE, accounting for the power each symbol is received with and the pulse shaping used, other than the noise power and the system load, i.e., the ratio between the number of interfering bursts and the spreading factor. In conclusion, ME-SSA should provide an improved spectral efficiency (theoretically, up to 50%), especially with low SFs/a high bit rate where E-SSA performances are degraded, without increasing the complexity at the user terminal side. The complexity increase is at the gateway side, where, instead of performing one despreading per burst as in the SUMFcase, spreading and despreading operations are carried out for each burst at each stage of the MSD.