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This paper presents closed-form capacity expressions for interfere-limited relay channels. Existing theoretical analysis has primarily focused on Gaussian relay channels, and the analysis of interference-limited relay deployment has been confined to simulation based approaches. The novel contribution of this paper is to consolidate on these approaches by proposing a theoretical analysis that includes the effects of interference and capacity saturation of realistic transmission schemes. The performance and optimization results are reinforced by matching simulation results. The benefit of this approach is that given a small set of network parameters, the researcher can use the closed-form expressions to determine the capacity of the network, as well as the deployment parameters that maximize capacity without committing to protracted system simulation studies. The deployment parameters considered in this paper include the optimal location and number of relays, and resource sharing between relay and base-stations. The paper shows that the optimal deployment parameters are pre-dominantly a function of the saturation capacity, pathloss exponent and transmit powers. Furthermore, to demonstrate the wider applicability of the theoretical framework, the analysis is extended to a multi-room indoor building. The capacity improvements demonstrated in this paper show that deployment optimization can improve capacity by up to 60% for outdoor and 38% for indoor users. The proposed closed-form expressions on interference-limited relay capacity are useful as a framework to examine how key propagation and network parameters affect relay performance and can yield insight into future research directions.