A key goal of 5G is to provide massive connectivity. This issue has gained tremendous interest in recent times due to the emergence of technologies like narrow-band internet of things (NB-IoT) and massive machine type communication (mMTC). This use-case aims to serve various applications such as factory assembly lines, traffic monitoring, smart metering, etc. NB-IoT is a suitable key technology for realizing mMTC in 5G. However, it is often difficult to deploy dedicated bandwidth for all NB-IoT application scenarios due to the explosive overall growth of communication systems. Non-orthogonal multiple access (NOMA) has emerged as a promising strategy to accommodate a large number of devices given limited bandwidth. Superposition coding at the transmitter and successive interference cancellation (SIC) at the receiver enables NOMA to allocate the same bandwidth to multiple devices simultaneously. With rapid advancements in semiconductor fabrication technology, SIC will likely be implementable even on low-end devices that fall under the mMTC use-case.

Motivated by this, we develop heuristic and optimal solutions that maximize the number of connected devices satisfying their quality of service (QoS) requirement using NOMA. First, an optimal joint sub-carrier and power allocation strategy assuming perfect channel state information (CSI) called Stratified Device Allocation (SDA), is developed to maximize the connectivity under data rate, power, and bandwidth constraints. Then, we generalize the connectivity maximization problem to the case of partial CSI, where only the distance-dependent path-loss component of the channel gain is available at the base station (BS). It is shown that this problem is a mixed integer and non-convex optimization problem.

We introduce a novel framework called the Stochastic Connectivity Optimization (SCO) framework. In this framework, a concave approximation (SCO-CA) algorithm that maximizes connectivity is derived that has a performance loss of at most compared to any possible optimal solution, where e-4S is the number of sub-carriers in the system. Furthermore, SCO-CA is implementable using any standard convex solver. Finally, the problem of connection density maximization with residual interference due to imperfect SIC is investigated. Under this model, an iterative algorithm based on solving a system of linear equations on each sub-carrier for power allocation is proposed. Moreover, the relationship between the service rate, the residual interference,and the device power consumption is analytically evaluated. Through computer simulations, the performance of the proposed solution under various cell sizes and QoS requirements is evaluated and compared with the state-of-the-art techniques.