Recently, a maximum-likelihood channel parameter estimator was proposed by the authors for joint communication and positioning. The parameters of the physical channel (e.g. amplitudes and propagation delays of the propagation paths) are estimated jointly with the channel coefficients of the equivalent discrete-time channel model by exploiting a priori information about pulse shaping and receive filtering. In this paper, the influence of oversampling on the proposed estimator is investigated. On the one hand, more samples can improve the performance of the estimator. On the other hand, the complexity of the estimator increases with oversampling and the noise gets more colored. The Cramer-Rao lower bounds (CRLBs) of the time of arrival for different channel models with different oversampling factors are compared. Taking into account the tradeoff between performance and complexity, it can be concluded that only an oversampling factor of two is reasonable. This design issue is different from satellite navigation receiver designs, where usually extensive oversampling is applied. Furthermore, the performance of the estimator is compared to the CRLB by means of Monte Carlo simulations.