## 1 Introduction  
Higher system throughput and greater system capacity are necessary for fifth-generation (5G) mobile communication systems to offer high connectivity for new applications and use cases. One of the key enabling techniques for 5G to improve throughput and capacity is multiple-input multiple-output (MIMO) [1,2] by performing spatial multiplexing of multiple signals. In order to support the growth of wireless communication, 5G New Radio (NR) standards were created by the 3 rd Generation Partnership Project (3 GPP) to enhance spectrum efficiency for mobile broadband [3]. One of the improvements that 5G NR introduces is the employment of orthogonal frequency division multiplexing (OFDM) as the signal waveform due to its beneficial properties such as high spectral efficiency and robustness to channel fading. More specifically, the multipath challenge in wide-bandwidth channels can be mitigated by employing OFDM that uses a series of narrow-band overlapping sub-carriers, which results in an improved spectral efficiency. Therefore, the demand for higher data throughput over longer distances or under conditions of interference, signal fading, and multipath has driven the development of the MIMO-OFDM communication system. [PERSON] has discovered a simple transmission scheme known as the space-time coding that uses two transmit antennas [4]. [PERSON] et al. has developed a generalization of the Alamouti transmission scheme based on the notion of orthogonal designs, which use more than two transmit antennas, leading to the concept of space-time block coding (STBC) [5]. More specifically, in an MIMO system, the STBC scheme allowed multiple copies of the same data stream to be transmitted using a number of transmitter antennas, which resulted in an improved data transfer reliability [6,7]. Therefore, the spatial and temporal variety gained from using STBC in MIMO-OFDM systems will lead to high-rate packet transmission without losing bandwidth, appropriate for high-throughput application [8]. An alternative to STBC in MIMO-OFDM systems is Space-Frequency Block Coding (SFBC), which provides diversity in both space and frequency by using multiple antennas and different sub-carriers. SFBC is especially beneficial in frequency-selective fading environments, offering robust performance with many antennas [9]. However, STBC is chosen in this work because it provides a simpler implementation with lower computational complexity compared to SFBC. In a fast-paced communication scenario, the channel condition fluctuates rapidly, resulting in an apparent Doppler shift [10]. Adaptive modulation and coding (AMC) is a technology that adjusts the modulation and coding parameters to the dynamic wireless channel condition, hence increasing spectral efficiency [11]. The authors of [12, 13, 14] investigated adaptive modulation techniques for MIMO-OFDM systems and achieved improved spectral efficiency. An evaluation of the signal-to-noise ratio (SNR) at the receiver can be used to assess the channel state, and the value can be transmitted back to the transmitter via the feedback channel [15]. Generally, SNR estimators can be categorized into data-aided SNR (DA-SNR) estimators and non-data-aided SNR (NDA-SNR) estimators. The DA-SNR estimator uses transmitted pilot data to estimate the SNR at the receiver. This method increases estimation accuracy at the cost of decreased system throughput [16, 17, 18, 19, 20]. However, the NDA-SNR estimator blindly estimates the SNR without prior transmitted data. Hence, it does not incur throughput penalty [14, 16, 19, 21, 22, 23, 24]. Despite data overhead, the DA-SNR system outperformed NDA-SNR in terms of estimation accuracy [25, 26]. However, some studies have offered methods for mitigating incurred throughput penalties in DA-SNR, such as utilizing OFDM synchronization preambles [17, 18, 20, 27, 28], also known as preamble-based SNR estimators. Numerous preamble structures have been proposed for time synchronization in OFDM systems [30, 31, 32].