Abstract The baseband digital pre‐distortion (DPD) signal processing technique is the most cost‐effective linearisation method among other techniques to address the nonlinearity effect of the power amplifier. For communication systems containing DPD and power amplifier, it is difficult to acquire performance metrics closed‐forms for any DPD architecture since there was no mathematical expression for each DPD coefficient. Usually, researchers look for more efficient DPD algorithms for DPD coefficients (compared to the existing ones) in terms of computational complexity, delay, power consumption etc. Consequently, performance is evaluated through intensive simulation. In this paper, it is shown how one can exploit the results of the recent work to mathematically model the indirect learning architecture DPD and efficiently derive important measures in communication systems. Expressions of the normalised mean square error (NMSE) and achievable rate for the OFDM communication system are derived. The DPD is modelled mathematically by exploiting the DPD coefficients closed‐form expressions. The derived expressions of the NMSE and achievable rate are verified through numerical simulations. Furthermore, closed‐form expressions for the NMSE and achievable rate bounds for the OFDM communication system are derived. The performance measures bounds are found assuming a perfect linearisation scenario. The analytical expressions are validated through numerical simulations.