## 1 Introduction
The preamble-based SNR estimators that were proposed in [17, 18, 29] also made use of these preambles. The authors in [29] developed an SNR estimator for cooperative SISO-OFDM, which exploited the preamble structure proposed in [30]. However, in [18], an SNR estimator was developedfor MIMO-OFDM systems and utilized the synchronization preamble structure proposed by [PERSON] et al. in [31]. The three key elements to consider when using SNR estimators are estimation accuracy, computational cost, and data overhead. Most proposed SNR estimators for MIMO-OFDM systems in the literature thus far focus on frequency domain SNR estimation, which lowers system performance due to inter-carrier interference [17; 18; 33]. Frequency domain SNR estimators execute SNR estimates after the OFDM signals have been demodulated. As a result, the computation of the Fast Fourier Transform (FFT) would add computational complexity to SNR estimation. In the literature, SNR estimation algorithms for MIMO-OFDM systems have been developed utilizing two methods: maximum likelihood (ML) [19] and second-order moment (M2) criteria [16; 17; 18; 20]. The SNR algorithm based on these techniques was derived using probabilistic techniques, which are very complex and involve addition and multiplication operations. The ML method is more complex than the M2 approach because it requires optimization to maximize the likelihood function, which demands higher computational power. While ML can be more accurate, the M2 method is simpler and demands less computational power, providing a good balance of accuracy and complexity. In [34], the suggested SNR estimator took the benefit of the OFDM synchronization preamble structure presented in [32], which employed Constant Amplitude Zero Autocorrelation (CAZAC) sequences. The SNR estimation algorithm of the SNR estimator in [34] was derived using the autocorrelation function, and the SNR estimation was performed in the time domain. However, the proposed preamble-based SNR estimator was employed in an adaptive modulation of a single-input single-output (SISO)-OFDM system. Against this background, this study extends the application of the preamble-based SNR estimator in [34] to an adaptive modulation STBC-assisted MIMO-OFDM system. This adaptation leverages the preamble-based SNR estimator to work effectively with STBC-decoded signals, enhancing signal reliability and diversity in MIMO-OFDM systems, which was not explored in the previous work. While the algorithm in [34] utilized a time domain approach, this study develops a new algorithm to estimate SNR in the frequency domain using the modified CAZAC preamble structure and utilizing M2 criteria. Let us denote the time domain and frequency domain preamble-based SNR estimators as CAZAC-TD and CAZAC-FD SNR estimators, respectively. The performance of both SNR estimators is evaluated when invoked in a non-adaptive STBC-assisted MIMO-OFDM system and is contrasted to the frequency domain preamble-based SNR estimator for the MIMO-OFDM system in [18], which employs M2 criteria in the SNR expression. Let us denote this frequency domain SNR estimator as the Milan-FD SNR estimator. Both CAZAC-TD and CAZAC-FD SNR estimators' performances are also compared to the normalized Cramer-Rao bound (NCRB) to determine how well both SNR estimators may approach the theoretically best feasible performance, ensuring system efficiency is not compromised. The SNR estimator that exhibits superior performance is then invoked in an adaptive modulation STBC-assisted MIMO-OFDM system. Thus, the adaptive MIMO-OFDM system described in this paper combines the advantages of the preamble-based SNR estimator with the STBC technique. The contributions of this work are summarized as follows:  
* The adaptation of the CAZAC-TD SNR estimator to the STBC-decoded signal: This study extends the application of the CAZAC-TD SNR estimation algorithm to an adaptive modulation STBC-assisted MIMO-OFDM system.