I have a specific case for this inquiry, but hopefully it can be generalized to anything else.I'm working with an aircraft simulator and have been tasked to implement a module whose goal is to improve the performance, if you will, of the existing module. After reading up about how to write proper requirements (and there's company procedure and all that), I'm still a little stumped about how to go about writing a requirement.The good news is that there's data from the aircraft being simulated, so for testing purposes there's at least some real data to compare to. And I'm aware of the FAA document AC-120-40B, but I don't believe we're trying to approach the FAA requirements since we're not trying to get FAA certification (It'd be nice to get there, but that hasn't been a stated goal)Still I don't think The [software component] shall perform better than [component] from versions prior to [version] when compared to [real data] would cut it as a good requirement.I suppose I'm concerned with what makes something objectively better. The FAA doc does have some scenarios that cover this module, but then there might be someone who goes but what about X scenario!?And then I feel like I'm trying to prove or disprove some substance causes cancer in a variety of situations.For others with this inquiry, the project does not have any existing performance requirements for the module. 
Writing requirements when the task is to improve an existing implementation
requirements
To start, I'd say you don't have sufficient information to write the requirements. Your task would be to gather specific details. When you're tasked to improve performance, the first thing you should probably do is measure what the current performance is and record these numbers. Then, you should decide together with the business what the target is. If you have this, you can write out the requirements. Here are a few examples:Component X should calculate Y within 2 secondsThe module should have a throughput of at least 100 requests/secondDoing this makes the subjective improve performance more objective and measurable. It also prevents later discussions where some say it's gotten worse, some say it stayed the same and others say it has improved. With real data and benchmarks you can prove the impact the changes had.