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We consider the arbitrarily varying Gaussian relay channel with senderfrequency division. We determine the random code capacity, and establish lowerand upper bounds on the deterministic code capacity. It is observed that whenthe channel input is subject to a low power limit, the deterministic codecapacity may be strictly lower than the random code capacity, and the gapvanishes as the input becomes less constrained. A second model addressed inthis paper is the general case of primitive arbitrarily varying relay channels.We develop lower and upper bounds on the random code capacity, and giveconditions under which the deterministic code capacity coincides with therandom code capacity, and conditions under which it is lower. Then, weestablish the capacity of the primitive counterpart of the arbitrarily varyingGaussian relay channel with sender frequency division. In this case, thedeterministic and random code capacities are the same.

The Arbitrarily Varying Gaussian Relay Channel with Sender Frequency Division