Abstract-A system using frequency offset based transmitreference (TR) modulation allows multiple nodes to transmit simultaneously and asynchronously without any mutual timing coordination. Thus, such a system provides inherent capabilities for a multiple access in the medium access control (MAC) layer to coordinate the shared use of the common wireless medium among the nodes of the wireless sensor network (WSN). However, certain characteristics of a frequency offset based system limits its performance, for example, the number of available frequency offsets is limited as it depends on several system parameters, and the number of simultaneous communications using different frequency offsets is limited due to inter-user interference. In this paper, we introduce an extended version of the performance model of a basic slottedAloha system, that captures the basic phenomena of a multichannel system with a limited set of channels and a limit to the number of simultaneously used channels. An analysis of this model reveals the potential of a MAC protocol for TR modulation with frequency offsets.