Non-orthogonal multiple access (NOMA) is widely recognized to increase the number of users and enhance the spectral efficiency in fifth-generation (5G) wireless networks and beyond. NOMA is still in the theoretical analysis and simulation phases and fewer experimental works are reported to date. In this paper, we design and implement NOMA in software-defined radio, and evaluate its performance. This includes the real-time realization of the key components of NOMA, i.e., superposition and successive interference cancellation. The main novelty of this paper is to introduce constructing superimposed signals with varying symbol rates to enlarge the achievable rate region of the experimented NOMA. By applying varying symbol rates, the set of possible transmission rate pairs enlarges and we can reach higher data rates compared to existing modulation and coding schemes (MCS). We also propose an algorithm to efficiently find the rate pairs. Simulations and experiments demonstrate that NOMA with a varying symbol rate not only can reach higher data rates than orthogonal schemes such as time division multiple access, but it can also outperform existing MCS-based methods which have a fixed symbol rate. The experiments also show that there is a noticeable gap between NOMA in theory and practice. In addition to the new NOMA experiments, we review the state-of-the-art in experimental NOMA. We also discuss several directions for future experiments that can help bridge the gap between theory and practice and bring NOMA to practical communication systems.