## 1 Introduction
In [17], the authors put forward an MUD scheme that switches between traditional detection techniques and the CS-based reconstruction algorithm. The switching is conditioned on the sparsity level of the signals that are to be detected: when sparse signals are involved, the CS-base reconstruction mechanism is activated; however, when non-sparse signals are to be processed, the traditional estimation method kicks in. The major drawback of this approach is that it is highly computationally costly. In [18], CS-based detection and multicarrier access schemes are combined in the context of machine-type communication (MTC) systems. In this method, the authors exploit the inherent sparsity of sporadic transmission of MTC in the users' signals received at the receiver in the system. In [19], the authors propose an MUD based on the structured matching pursuit (SMP) algorithm for joint estimation of both users' transmitted signals and their corresponding activities in continuous time slots. Temporal correlation of the sets of active users is employed in [20] to construct a dynamic CS (DCS)-based MUD. This was employed to realize the detection of both user data and user activities in communication networks. In [21], the authors propose a combination of a channel estimation scheme and a multiuser detection (MUD) technique for scenarios in which users are either active or inactive in a frame in uplink GF-NOMA communication networks. In [22], a comparative study of three CS algorithm-based MUDs for uplink GF-NOMA communication networks is presented. In both [23] and [24], amended implementations of both subspace pursuit (SP) and orthogonal matching pursuit (OMP) are used by the author to develop the proposed MUDs. A newly developed iterative hard thresholding-based accelerated step-size (IHT_ASS) algorithm is used to construct the proposed MUD scheme documented in [25]. In [26], NOMA-based code domain networks are analyzed for both cases in which the networks are overloaded and cases where they are underloaded in an uplink GF-NOMA system in which the schemes are subjected to similar MUD schemes. In [27], two amendedclassical SP and OMP algorithms are jointly used to develop a new MUD scheme for uplink GF-NOMA. This is employed purposefully for both detection of user data and estimation of user activities. The authors in [28] develop two user activity detection algorithms by using the dynamic channel tap delays as prior information for detection purposes. In [29], the authors propose active user detection (AUD) based on the expectation propagation (EP) algorithm and combine it with the channel estimation method for massive machine-type communication (mMTC) networks. The proposed expectation propagation algorithm is a Bayesian framework that is highly costly in terms of computational complexity. An intelligent reflecting surface (IRS)-based MUD method is proposed for use in ultra-reliable and low-latency communications (URLLC) in [30]. Faster-than-Nyquist (FTN)-NOMA uplink is investigated in [31] in terms of random access, in which user activity detection is combined with user signal detection using a factor graph mechanism. The proposed method is based on the expectation-maximization (EM) algorithm, which is combined with the message passing algorithm. The multiuser detection using the proposed scheme requires a prohibitively high computational complexity cost. The same authors in [31] propose a receiver that executes the reconstruction of channel state information, detection of user activities, and decoding of transmitted user signals in [32]. In a bid to mitigate user interference in NOMA systems, the authors in [33] propose a multiuser detection (MUD) based on a demodulation-based minimum mean square error scheme together with a successive interference cancellation method. However, in [34], gradient information is used by the authors to develop a gradient descent-based gradient pursuit (GDGP)-based MUD for mMTC networks.