Blind Device Detection via Extended Sparsity Estimation-OMP in Grant-Free NOMA-IoT

Grant-free non-orthogonal multiple access (NOMA) enables communication without a scheduling process. Base station (BS) must detect active users without knowing their number, a challenge that also occurs in grant-free NOMA–Internet of Things (IoT). Device detection in grant-free NOMA-IoT can be considered as signal reconstruction in compressive sensing (CS). To address this limitation, we propose extended sparsity estimation- orthogonal matching pursuit (ESE-OMP) to detect active devices in single measurement vector (SMV) and multiple measurement vector (MMV) problems for grant-free NOMA-IoT systems, a reconstruction method in CS that operates without prior knowledge of the sparsity level, which corresponds to the number of active devices. The algorithm iteratively detects active devices by monitoring the absolute difference in l1-norm of successive residuals, terminating when the change falls below a predefined threshold ε. ESE-OMP is evaluated under various grant-free NOMA-IoT systems, irregular low-density spreading-orthogonal frequency division multiplexing (LDS-OFDM), regular LDS-OFDM, and pattern division multiple access (PDMA) systems. When the signal-to-noise ratio (SNR) is 10 dB for the SMV problem with static active device composition, the regular LDS-OFDM system achieves a bit error rate (BER) of 2.95×10−4, while irregular LDS-OFDM and PDMA systems achieve BERs of 3.78×10−3 and 1.79×10−2, respectively. The smaller the number of active devices, the better the performance of ESE-OMP.