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The work deals with the problematics of receiving very weak radio signals and it is focused especially on systems for low rate telemetry with carrier-subcarrier modulation. The part of this work is dedicated to calculation the link budget of typicall telemetry data transmission system between the Mars and the Earth in respect of the receiving equipment, which could be developed in the Experimental sattelites laboratory on the Institute of radio electronics BUT. The main part of this work is dedicated to developing and testing the low rate telemetry data transmission system model. The model is developed for the purpose of study the effects of AWGN and phase noise on the whole system and also on its component parts. The model has been developed and described in the way of easy parameters modification. The design for each parameter of the model is described carefully. With the developed model, the study of the effects of AWGN and phase noise on the whole system and also on its component parts has been performed.