SCMA System
SCMA can be considered as a code division multiple access scheme, described by a sparse codebook. The codebook is constructed based on a multi-dimensional constellation and the shaping gain helps it to be superior to the traditional scheme based on extended code. In SCMA, multiple users will use different codebooks on the same resource block for transmission. The use of a sparse codebook reduces the conflict between users, so SCMA is resilient to inter-user interference. The sparsity also benefits the complexity of the receiver, and MPA can be applied to achieve near-optimal performance. SCMA is also a kind of LDS-CDMA system technology, and its difference lies in that SCMA technology replaces data modulation by selecting user code words, and each user has his own codebook (Moltafet et al.,2019). SCMA, as a promising 5G wireless air interface technology, is a non-orthogonal multiple access technology with better spectral efficiency based on the codebook. The existing SCMA multi-user detection algorithm is mainly MPA, which is a suboptimal multi-user detection algorithm with near-optimal maximum a posteriori (MAP) probability detection algorithm performance. The traditional MAP exhaustive detection algorithm must detect the codebook combination of all users, which greatly increases the complexity of the algorithm. Compared with the traditional MAP algorithm, the MPA algorithm based on the sum-product operation is a typical multi-user detection algorithm in the SCMA system. The algorithm is implemented through message transmissions and iterative updates between nodes in the factor graph. In essence, the algorithm is based on the idea of parallel strategy.
Figure 1 and Figure 2 are schematic diagrams of the sending ends of the LDS-CDMA system and SCMA system.
Figure 1. Schematic diagram of LDS-CDMA transmitter
Figure 2. Schematic diagram of SCMA sender
As shown in Figure 1, in the LDS-CDMA system, after channel coding, the user information passes through the modulator, then undergoes sparse spread spectrum, and finally, is transmitted. In the SCMA system in Figure 2, modulation and sparse spread spectrum are unified based on codeword selection in the user codebook, and the user codebook in this process needs to be designed in advance.
Compared with the LDS-CDMA system, the SCMA system has the following two basic characteristics (Abebe & Kang, 2019):
- 1.
SCMA system distinguishes different users by codebook and combines modulation in LDS technology with sparse spread spectrum technology to express them by sparse codebook. Based on codeword selection in the codebook, bit information sent by users can be directly mapped into codewords.
- 2.
The receiver multi-user detection algorithm of the SCMA system is also based on the sparsity of the codebook, that is, message transmission based on edge of factor graph, and the message transmission process of edge in factor graph is essentially the transmission process of codeword. Therefore, to detect a codeword message, the receiver of the SCMA system needs to know the codebook information of the sender.
Improved MAX-Log MPA Multi-User Detection Algorithm
In the actual communication system, it is difficult to achieve complete orthogonality and synchronization for the codewords between users, and multiple access interference between users is unavoidable. The application of multi-user detection technology can effectively weaken the multiple access interference, increase the system capacity, and improve the communication anti-interference ability of the system. In the multi-user detection process of the SCMA system, the MAX-Log MPA uses approximate calculation, resulting in partial message loss and poor detection performance. Therefore, the approximate method closer to the real value is derived theoretically, and an improved MAX-Log MPA algorithm is proposed.
Assuming that the channel estimation is perfect and the codebook can be used in the receiver, the detection of SCMA can be regarded as a problem of traditional multiple users’ decoder, which can be solved by joint optimal MAP. Because there is a Equation 1:
(1)A posteriori probability may be written as Equation 2:
(2)If we assume that the transmission probability of each codeword is equal, the maximum a posteriori probability detection MAP is simplified to maximum likelihood (ML), as shown in Equation 3:
(3)A decision tree algorithm is an algorithm in the field of machine learning. Its core idea is not a very complex mathematical formula but a simple logical if-then branch, which also makes it easier to understand. It is also the basis of subsequent algorithms such as random forest and gradient-boosted decision trees. The ML algorithm uses the exhaustive method to search all possible combinations of users and their codebooks (Wei et al., 2018), so the complexity of the algorithm is extremely high. The idea of the improved algorithm in this paper is to convert the EXP(exponential function) operation into the MAX(maximum value) operation and reduce the product operation to reduce the complexity of the operation. At the same time, an influence factor is added to reduce the BER of the detector by adjusting the value of the influence factor without affecting the complexity of the algorithm.
MAX-Log MPA algorithms include parallel and serial algorithms. The message-updating process from the resource node to the user node adopts the approximate calculation of max, as shown in Equation 4:
(4)Using the MAX-Log operation on the MPA algorithm will inevitably cause some information loss. In addition, the complexity of the algorithm will be reduced by taking log operations and converting multiplication into addition. To solve the poor detection performance of the MAX-Log algorithm and keep its low complexity, we can get Equations 5 and 6:
(5)(6)
Equations 5 and 6, respectively, represent improved message-updating formulas from parallel MAX-Log MPA and serial MAX-Log MPA resource nodes to user nodes.
The message lost by the improved MAX-Log MPA message update formula will be smaller, which makes the message obtained in the next iteration process more reliable and has better detection performance. Therefore, the method adopted in this paper will not burden the original MAX-Log MPA algorithm, but also keep its advantage of low algorithm complexity and improve its detection performance.