A pilot study involving 14 overweight or obese adults (average age 56) on a calorie-restricted diet, found that those whose diet had higher levels of protein showed greater improvements in their sleep score, regardless of the source of the protein.
In a follow-up study, 44 overweight or obese participants followed a normal-protein or a higher-protein weight loss diet (either 0.8 or 1.5 kg of protein for each kg of body weight) for 16 weeks. Sleep quality improved for those on the high-protein diet, but not for those on the normal-protein diet.
Sleep quality was assessed using the Pittsburgh Sleep Quality Index (PSQI) questionnaire.
The sources of protein were beef and pork, or soy and legume.
Higher protein intake has also been linked to promoting body fat loss, retention of lean body mass and improvements in blood pressure.
http://www.eurekalert.org/pub_releases/2016-03/pu-lww032416.php
Zhou, J., Kim, J. E., Armstrong, C. L., Chen, N., & Campbell, W. W. (2016). Higher-protein diets improve indexes of sleep in energy-restricted overweight and obese adults: results from 2 randomized controlled trials. The American Journal of Clinical Nutrition, 103(3), 766–774. http://doi.org/10.3945/ajcn.115.124669