## 4 ME-SSA Receiver Design
### Burst Demodulator  
In this section, we compare the burst demodulator architecture of the E-SSA receiver with a conventional SUMF front-end receiver with the ME-SSA architecture based on the linear MMSE detector implementation. Figure 7 shows the overall burst demodulator functional blocks for both E-SSA and ME-SSA receivers. The conventional SUMF-based burst demodulator used in E-SSA receivers attempts to demodulate each burst detected by the PS _independently_. As shown in Figure 7, when the SUMF is used, the MSD block is bypassed. It is assumed that \(K\) bursts are detected by the PS and the following processing is carried out independently on each of them. * For each of the \(K\) bursts, its samples are extracted by the memory window according to the time estimate of the PS and corrected by the associated frequency. * A Doppler rate and further coarse frequency estimation on the preamble is carried out. * The TFI is checked to tune the receiver parameters on the specific burst features. Figure 6: Non–coherent PS. Figure 7: The structure of the burst demodulator. * Input samples are despread recovering the received noisy symbols. * Fine Doppler rate, frequency and phase are estimated and corrected by exploiting the pilot symbols. * Finally, decoding is carried out and CRC is checked to assess if the burst is correctly demodulated. For the ME-SSA receiver, QPSK modulation is used. In this case, a better spectral efficiency (SE) performance is obtained by resorting to a burst demodulator based on a linear MMSE detector. In the MASSIVE project, a particular version MMSE detector was implemented, known as MSD [9]. In the case of the ME-SSA receiver, the MSD block depicted in Figure 7 is activated and attempts to _jointly_ demodulate all the \(K\) interfering bursts detected by the PS. This operation is carried out approximating the theoretical linear MMSE detector through a certain number of identical stages as show in Figure 8. The accuracy of approximation improves by increasing the number of stages. The Linear MMSE detector would require the inversion of the covariance matrix \(\mathbf{R}\). The MSD approximates the inverse of the covariance matrix, \(\mathbf{R}^{-1}\), by a polynomial expansion in \(\mathbf{R}\) of degree \(S\), i.e.,  
\[\mathbf{R}^{-1}\approx\sum_{n=1}^{S}w_{n}\mathbf{R}^{n} \tag{1}\]  
where \(w_{n}\) are the proper weight coefficients. In practice a number of stages \(S\) equal to 2 and 3 can already give a good approximation of \(\mathbf{R}^{-1}\). The coefficients \(w_{n}\) shall be chosen to approximate the MMSE detector \(\sum_{n=1}^{S}w_{n}\mathbf{R}^{n}\simeq(\mathbf{R}+N_{0}\mathbf{I})^{-1}\), being \(N_{0}\) the noise power. Several methods can be found in the literature for weight computation [16; 17]. In this project, the solution derived in [18] was chosen, as it provides a very good approximation of the linear MMSE detector, accounting for the power each symbol is received with, 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. Let us assume that \(K\) interfering bursts have been detected by the PS to be demodulated. First, these bursts are individually despread as in the SUMF case, obtaining, for each of them, the noisy version of the received symbols. Then, the MSD processing takes place, consisting of a sequence of \(S\) identical stages depicted in Figure 8. At each stage, the following processing takes place, as shown in Figure 9 and previously reported in [2; 9]. Figure 8: Multistage despreader architecture. The \(K\) vectors, containing the symbols of the \(K\) burst as described above, are input to the first stage, where they are re-spread and the estimated time, Doppler rate and frequency offset are restored. In practice, the received spread bursts are regenerated and then summed together.