# CPM-OFDM Performance over Underwater Acoustic Channels
## 2 Related Work  
In CPM, the continuity of the phase from symbol to symbol introduces memory and correlation among symbols [13]. Since the inception of this class of signals, several interesting and useful works have been published and are still being published [14; 15; 16]. Utilizing the favorable properties of CPM, the pioneering work to combine CPM and OFDM was first reported in 2002 [17]. In this type of scheme, the traditional mappers such as PSK, QAM, etc., are replaced by CPM. The proposed scheme was named OFDM-CPM. (In this work, we call it CPM-OFDM owing to the norm currently being followed in literature.) It was shown that these signals offered much superior performance over traditional OFDM signals in multipath fading channels. After introducing CPM-OFDM signals in [17], the performance of different types of optimum and suboptimum receivers for CPM was evaluated over multipath-fading channels and reported in [18; 19; 20]. Viterbi decoder--though suboptimum--when used to detect CPM signals, offers performance that is comparable to optimum CPM receivers at a much-reduced complexity. As a natural consequence, the performance of Viterbi decoder to detect CPM-OFDM signals was presented in [21]. The performance of these signals over indoor wireless channels has also been assessed and reported in [22]. In [23], authors have evaluated the performance of convolutionally encoded CPM based OFDM systems for aeronautical telemetry. MIMO CPM-OFDM was studied in [24]. Authors have employed L2-orthogonal space-time codes and a zero-forcing equalizer at the receiver. They have shown that by using their proposed scheme, the complexity of CPM decoding can be significantly reduced. In [25], authors have implemented a typical CPM-OFDM system using software defined radio and have evaluated its performance over AWGN channels. Authors have shown that a value of 0.75 for the modulation index gives the best performance among the three modulation indices evaluated. However, they have not evaluated the performance of their proposed system over frequency-selective fading channels, which is the main ground of implementation for such systems. Moreover, they only evaluated their system only for three values of the modulation index. High PAPR is one of the disadvantages of a typical OFDM system. By using multi-amplitude CPM, it was shown that the PAPR of CPM-OFDM can significantly be re duced [26]. Another way to reduce the PAPR of CPM-OFDM is to use constant envelope OFDM [27; 28]. It should be noted that constant envelope OFDM is a different type of CPM-OFDM than the one proposed in [29] and other subsequent works discussed in the previous paragraph. In constant envelope OFDM, phase modulation is done after taking the IFFT of the signal, which is contrary to what was proposed in [29] where the continuous phase modulation was done before taking the IFFT. Constant envelope OFDM becomes CPM-OFDM if the phase continuity is maintained. Otherwise, it is a memoryless phase modulation. The scheme was named constant envelope-OFDM (CE-OFDM) or OFDM-phase modulation (OFDM-PM), and it was shown that CE-OFDM yield 0 dB PAPR constant envelope signals. In another work, authors have evaluated CE-OFDM for various multi-path fading channels [30]. Two types of equalizers have been employed in the receiver: minimum mean square error (MMSE) and zero forcing (ZF) equalizers. Results presented show significant BER performance improvements over a traditional OFDM system. Moreover, authors show that through the optimum variation of the modulation index, improved bandwidth efficiency and BER performance can be achieved. The same authors have employed chaotic interleaving to CE-OFDM after doing continuous phase modulation [31]. Although authors claim that their system offers improvements in BER as compared to the one reported in [27; 28], the reported results show only marginal improvements. In [32], the authors have studied a CE-OFDM system and evaluated its performance for a 1 Gbps wireless link at 60 GHz frequency.