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We present a wideband land mobile satellite channel model based on a three-state Markov chain model valid for any kind of satellite constellation and for L, S, and Ka bands. Data from measurement campaigns was used to extract the parameters for the statistical distributions involved in the model. We also present a methodology describing how to use the proposed channel model to interface with system-level analysis. We use the time series generated by the model to parameterize power control (PC) imperfection as a function of the environment and user speed by acting upon the time series through a seven-level PC algorithm. We then apply the obtained parameterization to the analysis of a direct sequence-code division multiple-access scenario with users requiring different quality-of-service (QoS). It is shown that request of different QoS produces an unbalance in the users power distribution and less users can be served with the most demanding QoS. PC error worsens this effect and considerably reduces capacity efficiency which is highly dependent on the environment and mobile speed. Bit-error rate statistics are also investigated through the log-normal characterization obtained by using the channel model obtaining results on the effect of required Eb/(No+Io) of a particular user.