Here we present the design of the fast-ion collective Thomson scattering receiver for millimeter wave radiation installed at ASDEX Upgrade, a tokamak for fusion plasma experiments. The receiver can detect spectral power densities of a few eV against the electron cyclotron emission background on the order of 100 eV under presence of gyrotron stray radiation that is several orders of magnitude stronger than the signal to be detected. The receiver down converts the frequencies of scattered radiation (100-110 GHz) to intermediate frequencies (IF) (4.5-14.5 GHz) by heterodyning. The IF signal is divided into 50 IF channels tightly spaced in frequency space. The channels are terminated by square-law detector diodes that convert the signal power into DC voltages. We present measurements of the transmission characteristics and performance of the main receiver components operating at mm-wave frequencies (notch, bandpass, and lowpass filters, a voltage-controlled variable attenuator, and an isolator), the down-converter unit, and the IF components (amplifiers, bandpass filters, and detector diodes). Furthermore, we determine the performance of the receiver as a unit through spectral response measurements and find reasonable agreement with the expectation based on the individual component measurements.