The capacity region of a two-user linear Gaussian compound Multiple Access Channel with common message (CMACC) and intersymbol interference (ISI) under an input power constraint is derived. To obtain the capacity region we first convert the channel to its equivalent memoryless one by defining an n-block memoryless circular Gaussian CMACC model. We then make use of the discrete Fourier transform (DFT) to decompose the n-block circular Gaussian CMACC into a set of independent parallel channels whose individual capacities can be found easily. Finally we derive the capacity of this n-block memoryless circular Gaussian CMACC (n-CGCMACC) based on the DFT decomposition. Since our channel is a special case of a synchronous multi-terminal channel, the capacity region of the Gaussian CMACC with ISI is the same as the capacity region of the n-CGCMACC in the limit of infinite block length. We also investigate the capacity regions for some special cases of the Gaussian CMACC with ISI using the obtained capacity region, and finally, provide some numerical results to show the loss in the rate caused by ISI.

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