Rate-Splitting Multiple Access (RSMA) has emerged as a potent and reliable multiple access and interference management technique in wireless communications. While downlink Multiple-Input Multiple-Ouput (MIMO) RSMA has been widely investigated, uplink MIMO RSMA has not been fully explored. In this paper, we investigate the performance of uplink RSMA in short-packet communications with perfect Channel State Information at Transmitter (CSIT) and Channel State Information at Receiver (CSIR). We propose an uplink MIMO RSMA framework and optimize both precoders and combiners with Max-Min Fairness (MMF) metric and Finite Blocklength (FBL) constraints. Due to the high coupling between precoders and combiners, we apply the Alternating Optimization (AO) to decompose the optimization problem into two subproblems. To tackle these subproblems, we propose a Successive Convex Approximation (SCA)-based approach. Additionally, we introduce a low-complexity scheme to design the decoding order at the receiver. Subsequently, the Physical (PHY)-layer of the uplink MIMO RSMA architecture is designed and evaluated using multi-user Link-Level Simulations (LLS), accounting for finite constellation modulation, finite length polar codes, message splitting, adaptive modulation and coding, and Successive Interference Cancellation (SIC) at the receiver. Numerical results demonstrate that applying RSMA in uplink MIMO with FBL constraints not only achieves MMF gains over conventional transmission schemes such as Space Division Multiple Access (SDMA) and Non-orthogonal Multiple Access (NOMA) but also exhibits robustness to network loads. The benefits of splitting messages from multiple users are also illustrated. LLS results confirm the improved max-min throughput benefits of RSMA over SDMA and NOMA.

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