Intelligent reflecting surface (IRS) has been deemed as an energy and spectral-efficient technology, that can potentially enhance network coverage and transmission reliability, with minimum impact on transceivers' complexity. Motivated by this, we develop a comprehensive analysis on the performance of integrating IRS into full-duplex (FD) cellular or Internet of Things (IoT) networks in both realistic Rician and Nakagami fadings. Firstly, in the context of reciprocal channels in Rician fadings, we derive the closed-form approximations of the users' outage probability (OP) and ergodic capacity (EC), under the non-central Chi-square distribution assumption on the signal-to-interference-plus-noise ratio (SINR). Further following by the Gamma distribution assumption on the SINR, we derive the cumulative distribution function (CDF) expression of the user's SINR, which is then leveraged to obtain simple yet effective closed-form expressions in terms of OP and EC. Subsequently, in Nakagami fading scenarios with the reciprocal and non-reciprocal channels, the closed forms of both users' OP and EC are obtained. Finally, the correctness of all the theoretical expressions is verified through substantial Monte Carlo simulations. The results indicate that the OP and EC deduced from Gamma distribution exhibit the fairly precise results for the arbitrary number of IRS elements, especially in Nakagami fadings.INDEX TERMS Full-duplex, intelligent reflecting surfaces, non-reciprocal, reciprocal, Rician and Nakagami fadings. Nakagami fading environment. In [22], Lu and Wang focused on the OP for an arbitrary IRS reflecting coefficient in an IRSaided two-way FD system, over correlated Rayleigh fading. Atapattu et al. [23] addressed the outage performance and spectral efficiency analyses for IRS-assisted two-way communication systems over Rayleigh fading channels. Apart from these, other literature relevant to IRS/RIS FD is summarized in Table 1, where the complex Gaussian (denoted as CN) assumptions are basically made about residual self-interference (RSI) or hardware impairment (HI). It is also noted that user, access point (AP) or relay can be in FD mode, allowing one or more FD nodes to coexist with other half-duplex(HD) nodes. Generally, one-way FD decode-and-forward (DF) relay is available for cooperative IRS/RIS FD systems [24], [25]. The papers [26], [27], [28], [30] addressing two-way FD primarily focus on the reciprocal channel which facilitates the received energy maximization for all users through the identical IRS phase shift design. For more complex scenarios involving spatial correlation [30], [31], multiple users [29], [30], [32] or non-reciprocity [32], research has typically focused on performance optimization algorithms than the derivation of performance expressions due to mathematical intractability of the latter.