We study wave measurements made by the FAST satellite at 4100-km altitude in the auroral region. Three electric and three magnetic wave field components are available, and wave emissions appear close to the local proton gyrofrequency (187 Hz) and at its harmonics. The particle observations reveal an electron beam as well as counterstreaming protons and oxygen ions. The plasma density is very low. We investigate the linear wave mode structure using a five-component bi-Maxwellian plasma model. The streaming electrons cause an instability at large perpendicular wave vectors. Using cross spectra and autospectra computed from the data, we reconstruct the wave distribution function (WDF). The results show that the observations are consistent with a linear description of the plasma. We find a good agreement between the reconstructed wave energy distribution, and the instability and our analysis gives a wavelength of ~2.5 km. The reconstructed WDF fits into a simple geometrical picture, where the satellite is passing through the outer edge of a region with precipitating electrons.