## 1 Introduction
Combining CPM with OFDM creates a hybrid modulation technique called OFDM-CPM [23; 24]. This approach leverages the strengths of both methods to enhance performance in wireless communication systems [25]. Bose-Chaudhuri-Hocquenghem (BCH) codes are a popular type of error-correcting code that are often used in wireless communication systems to enhance the reliability of data transmission [26]. BCH codes have been used in a variety of wireless communication systems, including cellular networks, Wi-Fi, and satellite communications. They are a valuable tool for ensuring that data is transmitted reliably and accurately. They are called block codes because they work on data in blocks, or groups, of binary bits. They can find and correct multiple errors within those blocks using a mathematical formula (polynomial) and the code's size, which is determined by the Galois field [27]. A direct linear relationship exists between the decoding complexity and the energy consumption of error-correcting codes. This dependency scales positively with both the code length and the number of errors to be corrected. Simply put, longer codes and a higher number of correctable errors necessitate significantly more complex decoding algorithms and, consequently, increase energy consumption [28]. In this paper, we propose a coded CPM modulator for OFDM in doubly-selective [29] UWA channels. Due to the complex nature of underwater channels and the high error rates in transmission, we observed that the presence of a block coder module significantly improves the error rate performance with regard to the spectral efficiency and smooth phase transitions of a CPM modulator. Since in a CPM, the data symbols are correlated, the receiver has more information when detecting the transmitted data [30; 31]. Hence, it is nat ural for CPM-OFDM to have a better error performance than conventional OFDM. Channel codes are an integral part of a typical communication system because the error performance isn't good enough for practical purposes. Hence, it is a normal practice to evaluate the performance of an established scheme with channel coding schemes. Some examples of papers that investigated the performance of OFDM with channel codes are [32; 33; 34; 35]. BCH codes are in use in underwater acoustic systems not only theoretically [36] but in industry as well [37]. The performance of CPM-OFDM with channel codes, especially BCH, has not been studied for underwater acoustic channels. Hence, investigation of CPM-OFDM with BCH codes is a natural extension. Moreover, in this work, we used a well-known statistical channel model [3] that closely resembles a real, practical underwater channel. The following are some of the key contributions of this work:  
* The performance evaluation of BCH-encoded CPM-OFDM over a statistical channel [38] that closely resembles a practical underwater channel. * A detailed complexity analysis of BCH-encoded CPM-OFDM that takes into account the complexity of BCH encoding, BCH decoding, and CPM detection, and compares it with a conventional OFDM system. * Simulation of a BCH-encoded CPM-OFDM system using 23 different values of the modulation index \(h\), comparison with a conventional OFDM system, and evidence of the clear superiority and effectiveness of the proposed scheme. * Simulation of a BCH-encoded CPM-OFDM system and performance evaluation by varying the transmitter-receiver distance from 100 m to 1000 m in steps of 150 m, and identification of the range for which the proposed system performs error-free transmission. * Identification of the best performing modulation indices \((h)\) as being \(\left(\frac{7}{16},\frac{9}{16},\frac{5}{8},\frac{3}{8},\frac{3}{8},\frac{5}{ 5},\frac{5}{16}\right)\). * Evaluation of the spectrum efficiency of the proposed scheme, where it is concluded that the proposed scheme does not degrade the spectrum efficiency of the system. The remaining paper is organized as follows. Section 2 details the state-of-the-art literature review. Section 3 explains the proposed coded CPM-OFDM scheme.