Compressed sensing multi-user detection (CS-MUD) algorithms play a key role in optimizing grant-free (GF) nonorthogonal multiple access (NOMA) for massive machine-type communications (mMTC). However, current CS-MUD algorithms cannot be efficiently parallelized, leading to computationally expensive implementations of joint activity detection and channel estimation (JADCE) as the number of deployed machine-type devices (MTDs) increases. To address this, the present work proposes novel JADCE algorithms that can be applied in parallel for different clusters of MTDs by exploiting the structure of the pilot sequences. These are the approximation error method (AEM)-alternating direction method of multipliers (ADMM), and AEM-sparse Bayesian learning (SBL). Results presented in terms of the normalized mean square error and the probability of miss detection show comparable performance to the conventional algorithms. However, both AEM-ADMM and AEM-SBL algorithms have significantly reduced computational complexity and run times, thus, facilitating network scalability.
I. INTRODUCTIOND ETECTION, channel estimation, and data decoding are fundamental operations performed by a receiver in a wireless communication network [1]-[3]. However, the majority of algorithms designed for these operations in previous wireless communication systems, i.e., fourth-generation (4G) and earlier, were tailored exclusively for downlink human-type communications (HTC) [4], [5]. In a turn of events, the new communication standards, i.e., the fifth generation (5G) and beyond (5GB), natively support a new set of devices termed machine-type devices (MTDs), which perform various sensing tasks in the Internet of Things (IoT) paradigm [6]- [8]. Notably, MTDs are energy constrained, yet in some cases, they need to be deployed in remote areas where they cannot be readily charged. For this reason, MTDs are designed to save energy by only switching to active transmission mode after sensing data and remaining in sleep mode in the absence of data. This