# Asynchronous Flipped Grant-Free SCMA for Satellite-Based Internet of Things Communication Networks
## 2 System Model  
The scenario under consideration in this paper consists of \(U\) wireless MTDs, where MTDs send data packets asynchronously via a shared wireless channel to a GEO satellite, as shown in Figure 1a. The packets received by the satellite are forwarded to the ground gateway station transparently with independent backhaul channels which are assumed to be error-free. Considering the relatively high complexity of SCMA decoding process, the procedures of signal detection and decoding are performed at the gateway station. The system overall traffic load is assumed to follow a Poisson distribution with parameter \(\lambda\) in one packet transmission duration \(\tau\) which is fixed and same for all the transmitted packets. Moreover, the acknowledgment (ACK) mechanism is used to inform the packets transmitted by each MTD are received correctly. If an MTD fails to receive ACK message for a period of time, it will retransmit the packet.  
For each MTD, original data bits are encoded by a powerful FEC coding scheme and then are further encoded by the SCMA encoder. Specifically, for the SCMA encoder, every \(log_{2}M\) bits are mapped to a codeword according to the codebook, where \(M\) is the size of the codebook [15]. Due to the sparsity of the codeword, the number of the non-zero entities \(N\) is less than the length of the codeword (i.e., \(N<K\)). In the system that adopts multi-carrier technique, such as OFDM, each entity  
Figure 1: Asynchronous flipped SCMA for satellite communication networks. Different shadowed chunks in (**b**) represents packets encoded with different SCMA codebooks. (**a**) Satellite communication scenario under consideration; (**b**) situation of packet arrivals at the gateway station.  
in a codeword is mapped to a subcarrier. Therefore, \(K\) subcarriers in the frequency domain make up an SCMA transmission block. In practice, the available bandwidth is separated into several blocks to reuse the codebook. Nevertheless, in this paper, we only focus on one SCMA transmission block, and codebook reuse is not taken into consideration.  
To mitigate the negative impact of codebook collisions, the proposed AF-SCMA scheme combined flipped diversity with SIC technique. As shown in Figure 1b, with the concept of flipped diversity, each MTD randomly selects two different SCMA codebooks from the codebook set with size of \(N_{CB}\) to encode the data, and the original encoded packet is transmitted with its flipped replica, which is encoded by the other SCMA codebook simultaneously on the corresponding subcarriers. Pilot sequences, which are used for user detection, codebook identification, signal acquisition, and channel estimation, are appended in front of the encoded data. The pilot sequences adopted by this system have the characteristic of constant amplitude zero autocorrelation, similar to Zadoff-Chu sequences and Golden codes sequences. The performance of pilot sequence detection will be discussed in Section 5.  
Packet detection and decoding procedures are performed in a detection window with the size of \(W\) at the gateway station. The uplink LMS channel is modeled as a block fading channel, which means the channel conditions will not change during one specific packet propagation time. Channel information is assumed to be always available, which can be acquired by the methods mentioned in [6; 30] with the aid of pilot sequences. Moreover, the design of AF-SCMA transmitter and receiver will be introduced in detail in the next section.