Heart failure with preserved ejection fraction (HFpEF) is the fastest growing form of heart failure with a high morbidity and mortality rate, and is associated with severe exercise intolerance. The mechanisms responsible for the reduced exercise tolerance remain poorly understood. The investigators propose a novel paradigm shift, focusing on peripheral limitations to exercise. In particular, the investigators will test the hypothesis that muscle sympathetic nerve activity (MSNA) is elevated in older HFpEF patients compared to healthy controls, and is associated with reduced exercise tolerance. The investigators will also test whether 16-weeks of exercise training will lower MSNA compared to attention control, and correlate with improved exercise tolerance in older HFpEF patients.