We consider a continuous-time complex-valued (approximately) bandlimited additive white Gaussian noise channel with a fixed unknown carrier frequency offset. The frequency offset is assumed to lie within plus or minus of a maximum value around the origin. The transmitter and receiver are unaware of the exact value of the frequency offset but are aware of this maximum value. The lack of knowledge of the precise channel probability law, while knowing the family of transition probability laws to which it belongs, gives rise to a compound channel model. An expression for the capacity of this compound channel is derived and shown to be independent of the exact value of the frequency offset. We provide a proof of the achievability part of the coding theorem.
