# Asynchronous Partial Gaussian Approximation Detection Algorithm for Uplink-Grouped MIMO-SCMA System
###### Abstract  
To relieve the impact caused by different arrival times of multiple users in the uplink MIMO-SCMA system, a grouped multiuser transmission model, according to different delays and its corresponding detection scheme, is proposed in this paper. Assuming perfect synchronization in one group, a message-passing algorithm based on serial propagation (SP-MPA) is proposed to reduce the bit error rate (BER), which could transfer the updated information to the next symbol as its initial probability. Furthermore, with a more practical case, the partial Gaussian approximation method (PGA) is designed to decrease the interference resulting from the imperfect synchronization in one group. As the result, the computing complexity of the proposed PGA method could be decreased by at least 20% compared with SP-MPA and the BER could be improved by about 10%. sparse code multiple access (SCMA); asynchronous; grouped; multiple input multiple output (MIMO); partial Gaussian approximation (PGA) +
Footnote †: journal: Electronics Letters  
**Citation:** [PERSON]; [PERSON]; [PERSON] Asynchronous Partial Gaussian Approximation Detection Algorithm for Uplink-Grouped MIMO-SCMA System. _Electronics_**2022**, _11_, 3356. [[https://doi.org/10.3390/electronics11213536](https://doi.org/10.3390/electronics11213536)]([https://doi.org/10.3390/electronics11213536](https://doi.org/10.3390/electronics11213536))  
Academic Editors [PERSON], [PERSON] and [PERSON] Received: 29 September 2022  
Accepted: 27 October 2022  
Published: 30 October 2022  
**Published:**  
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The methods mentioned above mainly focus on a synchronous SCMA scheme, in which all signals are considered to arrive at the base station at the same time. However, in a real uplink channel, signals come from users in different directions or with different distances, resulting in different delays of transmission. Moreover, a grant scheme produces significant signaling cost, so grant-free transmission is introduced as a competitive alternative in 3 rd Generation Partnership Project (3 GPP) Release 16 [13]. That means delays of signals are completely random, adding great difficulty for uplink detection. Thus, exploring useful asynchronous detection algorithms is essential. Some research paid attention to asynchronous detection. Ref. [14] devised a message-passing receiver for the uplink SCMA that uses expectation propagation to tackle the intractable distributions. Ref. [15] estimated a channel based on both received short pilot and data sequences and introduces auxiliary active-state indicators in joint detection. Ref. [16] proposed a blind detection algorithm for detecting user signals without the knowledge of a user codebook. Ref. [17] performed signal detection using deep learning with unknown channel information and system sparsity. Ref. [18] investigated an algorithm based on belief propagation and equal gain combining under asynchronous circumstances and effectively improves the system performance. It is noted that delays can be various when connections of users are massive, which means the contents of the mixed signal received can be too various to decode in one scheme. Although the algorithms above perform well in an asynchronous system, few of them consider the problem caused by the variety of delays. Thus, making a detection rule is very important to relieve the bad effects brought by interference between symbols. To further improve system performance, the multiple-input multiple-output (MIMO) technique is used to increase system reliability through diversity gain. Ref. [19] made a selection of receive antennas that minimizes the signal-to-interference ratio of the observed signal during the MPA calculations. Ref. [20] developed low-complexity iterative detection algorithms based on an expectation propagation algorithm. Ref. [21] studied spatial multiplexing (SMX), spatial modulation (SM) and space shift keying (SSK) techniques for the MIMO-SCMA systems. Ref.