lain the SCMA proces- sing stages. Let's assume that the system comprises K users whose information bits are spread over N resource elements. In an orthogonal scenario, K < N to ensure that each user is assigned to an orthogonal resource element, while in the non-orthogonal scenarios, K > N and the ratio K/N is defined as the overloading factor. The transceiver structure of SCMA can be mathematically modeled as follows. Let b=b = bk] denote the infor- mation bits transmitted by K uplink users and represent the transmitted symbols by the kth user. An SCMA encoder at the kth user is defined to be a one-to-one mapping fk:Bk Xk with E Bk and Xk E Xk, where the cardinality of Bk and Xk is 2NB where NB denotes the number of information bits in bk. Note that due to the sparse nature of SCMA scheme, Xk may contain zero symbols. The received signal at the base station y, after passing through a block fading multiple-access (uplink) channel, can be expressed as = where Hk = diag(hi h IN) represents the channel between the base station and the kth user, z=zz Z2 ZN] is the additive white Gaussian Chapter 3 Codebook 1 User 1 B11b12.. Baseband and FEC encoder 1 SCMA encoder MPA receiver/SCMA decoder RF processing User 2 Baseband and FEC encoder 2 SCMA encoder RF processing User 3 B. b32 Baseband and FEC encoder 3 SCMA encoder RF processing User 4 B41b42.. Baseband and FEC encoder 4 SCMA encoder RF processing User 5 B511552 Baseband and FEC encoder 5 SCMA encoder RF processing Function nodes User 6 Variable nodes Baseband and FEC encoder 6 SCMA encoder RF processing Codebook 6 Layer 1 Layer 2 Layer 6 (Codebook 1) (Codebook 2) (Codebook 6) (1,1) (1,0) Streams are mapped to (0, 1) codebooks 6 Sparse codebooks are MPA-based sent over 4 resources MUD receiver Figure 3.35 Example SCMA processing with K = 6, N = 4 and 150% overloading factor [52]. noise with zero mean and unity variance. Given the received signal y = y1 y2 and the channel knowledge H = {Hk|k = 1, 2, ., K}, the joint maximum-A-posteriori detec- tion18 18 of X = X1 X2 