Generally any simple agent-based model where one assumes that one agent is a noise trader, an unsophisticated trader that generally has little predictive power in their trading behaviour, is a "noise trader model". Often these models are rather simple and backward engineered in order to derive a mechanical and behavioral understanding for what is observed in the market, e.g. market impact.
For instance, assume that there are two kinds of agents trading, one unsophisticated noise trader, and one sophisticated informed trader. Furthermore, assume that we observe that the market impact is a concave function of market order size, hence a small market order cause a larger impact per share than does large a size. If orders made by informed traders tend to be smaller, and better predict the future price (as per definition of being an informed trader) than orders from noise traders, then a concave impact function will follow since other informed agents will react. Note that the authors in the article you reference argue that this assumes that orders are not anonymous, but I would claim that this is not necessarily the case. I would argue that it is simply enough that informed agents know that historically, small sizes carries more information per share (relatively more likely to have an informed trader behind), and thereafter a positive feedback effect will occur when a small order is observed.
