In this paper, an affine frequency division multiplexing

aided grant-free random access (AFDM-GF-RA) system

is designed for low Earth orbit (LEO) satellite Internet of Things

(SIoT) networks, where users employ the GF-RA to access the

satellite concurrently by configuring the AFDM modulation. In

order to evaluate the system’s performance, average bit error

probability (ABEP) bounds are first derived by Cholesky decomposition,

which are verified by simulation results. Furthermore,

a block sparse prior expectation propagation detection (BSPEP)

is developed for joint active users detection (AUD) and data

detection (DD). User activity probability is considered as a prior

for joint detection. Concurrently, the accuracy of AUD is further

improved by combining the block sparsity characteristics of

the user transmission signals. Simulation results show that the

proposed detector outperforms the classical oracle least squares

(OLS) benchmark and approaches the theoretical ABEP bound

at high signal-to-noise ratio (SNR).