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The exact analysis of the tracking performances of adaptive filters are provided in a real context of mobile satellite communication systems. In such a context, the time-variations of the channel's "impulse response" are modeled by a discrete time finite states Markov chain. More over, the transmitted data belongs to a finite alphabet. In fact, the paper tackles the exact analysis of the tracking capabilities of the least mean square (LMS) algorithm in the above stated setup. The different performance measures are carried for a large step size and, most importantly, for correlated inputs. Thus, the exact analysis is done without using any constraints or unrealistic hypothesis. These results are expected to aid in the analysis and design of mobile communication systems.