This paper presents cochannel interference cancelling techniques in on-board processing satellite systems using orthogonal polarizations. The techniques, based on mean square error (MSE) criterion and convolutional coding/soft decision Viterbi decoding (SDVD), are introduced on board. The bit error rate (BER) is derived for the mixed detection of a desired signal and an undesired cochannel interference when the techniques are applied to binary phase shift keying (BPSK), and is compared to that of no compensation for the interference. Performance results, obtained theoretically, show that the techniques of both the MSE and SDVD processings realize excellent improvements of the BER, and the improvements become significant in a large interference environment.