Until just the last couple of years virtually nothing has been done to analyze its performance and improve upon it. The square loop was the simplest and the first to be used. Yet, quads are popular for two reasons. First, they are cheap and construction materials are readily available throughout the world.
Spreaders can be of bamboo or fiberglass.
Second, there are claims of superior performance when compared to Yagis. It is alleged that a quad-based parasitic array can significantly outperform a much larger Yagi having more elements. Not only were the quads' gains inferior to Yagis with the same number of elements but they were not as rugged. The takeoff angle myth was also debunked. No, not at all.