In this paper we consider the estimation of channel coefficients and frequency offsets for LOS MIMO systems. We propose that by exploiting the structure of the channel matrix, which is present due to the geometrical nature of the channel, the estimation process can be enhanced. If a single oscillator setup is used at transmitter and receiver, respectively, this structure is preserved and can be exploited. Some methods using this fact are discussed and their performance is evaluated with respect to estimation accuracy, revealing that with relatively short training sequences, estimation results close to the fundamental bounds can be achieved.