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The aim of the paper is to describe a well-known quantum key distribution GG02 protocol using multimode coherent states generated on subcarrier frequencies of the optical spectrum. In order to detect signal states, we use a method of coherent detection without the participation of a local oscillator directly but where power from a carrier wave is used as such. Within the framework of the modern GG02 protocol description and the secutity proof against collective attacks, we introduce the necessary amendments to reduce our model to a model of the common system.