Performance Analysis and Optimization of Grant-Free Random Access With Capture Effect for Cell-Free Massive MIMO

To accommodate the proliferation of Internet-of-Things (IoT) applications, next-generation wireless communication networks, particularly the sixth-generation (6G), are expected to offer excellent support for the massive access of machine-type communication (MTC). In this paper, we investigate the grant-free random access (GFRA) employing orthogonal preambles in cell-free massive multiple-input multiple-output (mMIMO), which shows immense potential for enabling massive connectivity. In particular, we take into account the capture effect, defined as successful decoding despite preamble collisions, when the received signal-to-interference-plus-noise ratio (SINR) exceeds a predefined threshold. To this end, we develop an analytical framework to model GFRA with the capture effect adopting stochastic geometry. Subsequently, approximate analytical expressions for the received SINR and the access success probability for the typical GFRA frame structure are derived. Furthermore, leveraging these theoretical expressions, we formulate an optimization problem to determine the optimal preamble length that maximizes effective throughput. Simulation results validate the accuracy of our theoretical analyses and demonstrate the superior access performance of the optimized frame structure, whereas a frame structure with a constant preamble length does not consistently attain maximum effective throughput across varying user densities.