With the development of the mobile internet and Internet of things (IoT), the number of connected devices is increasing exponentially. Services that are required to support a large number of users, such as massive machine-type communications (mMTC), suffer from limited radio resources. Non-orthogonal multiple access (NOMA) is a promising access scheme for mMTC systems to meet the massive connectivity and heterogeneous network demands with low latency and high throughput. Motivated by the problems of an mMTC system, we propose a novel waveform that superimposes the users on the same resources with a family of orthogonal functions. The proposed model, which we call superimposed multi-user shared access (MUSA), is able to support more users than the conventional MUSA scheme. Furthermore, we combine the superimposed MUSA scheme with generalized frequency division multiplexing (GFDM) technique to achieve low latency with high overloading ratio. The performances of the superimposed MUSA and superimposed MUSA with GFDM are investigated over Rayleigh fading channel model. It is shown that the overloading ratio with three layers of superimposed orthogonal functions becomes three times that of the conventional MUSA scheme with low latency by using the GFDM structure. (c) 2019 Elsevier B.V. All rights reserved.