# Asynchronous Flipped Grant-Free SCMA for Satellite-Based Internet of Things Communication Networks
## 3 Asynchronous Flipped SCMA Scheme
### AF-SCMA Receiver Design  
Similar with some asynchronous multiple-access schemes [9; 10], AF-SCMA receiver adopts a sliding window at the gateway station to resolve collisions and decode the packets, where the sliding window size is \(W\). Additionally, packet-decoding and interference cancellation (IC) processing are also executed in the sliding window, which can refer to the method mentioned in [32]. The receiver design of AF-SCMA can be summarized as follows:  
1. For a received signal, it is first filtered and sampled, and then it is stored in a memory. To store all the filtered samples, the memory size should be large enough.
2. Perform pilot sequences detection throughout the window memory adopting a correlator which is matched to the pilot sequences.
3. Once a specific pilot is detected, channel information is estimated according to the pilot sequence. In this paper, we assume channel estimation is perfect, which can be acquired by the algorithms mentioned in [6; 30]. Furthermore, the information of the packet location, the MTD identification and the codebook that is used to encode the data can also be got from the pilot sequence.
4. Based on the position information of the received packets with in the detection window, AF-SCMA receiver can estimate the interference conditions of a specific packet. Since the lengths of each packet and each chunk are fixed, the decoding process can start with the chunk with minimum interference and strongest in power.
5. For SCMA decoding process, we first subtract the pilot sequences for the received signals to reduce the interference. We adopt a sub-optimal but efficient algorithm called MPA [15] to approach the optimal maximum likelihood (ML) detection. Since the packet arrivals are asynchronous, the SJD method in traditional MPA is not applicable. Therefore, AF-SCMA decoder decodes only one chunk at a time. To improve the decoding accuracy, we add the original codebook \(\mathbb{C}_{j}\) with a length-K zero codeword \(\mathbf{0}\), where \(j=0,1,...,N_{CB}\). Thus, the extended codebook becomes \(\overline{\mathbb{C}}_{j}=\mathbb{C}_{j}\cup\{\mathbf{0}\}\). For the chunk that is partially interfered, the clean part can be seemed as other interference MTDs virtually transmitting the codeword of 0 (for more details refer to [19]). Moreover, the factor graph which is used for MPA decoding can be obtained based on the interference conditions of the decoding chunk, and the SCMA decoding process follows the MPA decoding rules.  
The decoded chunk is declared correctly decoding when it passes the CRC check. Then re-encode the payload of the chunk using its original codebook. Meanwhile, the AF-SCMA also regenerates the payload of the flipped chunk with the codebook information which can be found in the chunk payload. Please note that, the codebook information in the payload is not the same in the original chunk and its flipped replica. Channel information can be acquired from the according pilot sequences.
7. Both the re-encoded chunk and its flipped replica are subtracted from the memory.
8. When no more chunks can be decoded successfully, this packet-decoding round terminates. Then the receiver will update the interference conditions of the remaining signals, and starts a new packet-decoding round from the chunk with minimum interference and strongest in power (in step 4) until the maximum iteration number \(N_{iter}^{max}\) reaches.
9. When the finish processing the signals in current window, the detection window will shift by \(\Delta W\) and continue to decode the packets in the new generated detection window. For the case that the replica chunk location of a decoded chunk is not within current window, the receiver will temporarily store the information of the chunk until the replica chunk completely locates within the span of the sliding window. Finally, the data stored in the previous \(\Delta W\) memory will be discarded.