Orthogonal frequency division multiplexing (OFDM) is an alternative technology that is constrained to keep up with the increasingly high data transmission rate due to its robustness against selective frequency fading and its resistance to intersymbol interference (ISI). This paper aims to study and optimize its performance, namely, its probability of communication failure and signal-tointerference-plus-noise ratio (SINR) metrics. The mathematical tool used to perform OFDM evaluation and analysis is the Fourier transform and its properties. The obtained results of those equations led to the demonstration of the probability of communication outage and to notice that the cutoff time occurs after the 10th iteration for values of λ less than or equal to 1. It could also be checked that this period is small if λ exceeds 1 by considering the sensitivity factor. Moreover, for the obtained results, in terms of bit error rate (BER) and SINR, the influence of the modulation on the error vector magnitude (EVM) shows the sensitivity factor Ω presents a key role in the transmission chain.

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Integration of wireless and mobile networks to new generations constitutes a heterogeneous system, this is the case of LTE and WiFi networks. In this paper, we study and analyze the optimal performances of this system regarding the SINR(Signal Interference Noise Ration), the blocking probability and the user communication loss. The user mobility is represented by random wayPoint(RWP) model and users terminals equipped with multiple accesses interfaces. We have established a Markov chain to assess and analyze the performances obtained from the heterogeneous networks system. So we have proposed an average value of the signal power emitted in down-ling voice, the blocking probability of system connections.