# Pilot-Based Adaptive Channel Estimation for Underwater Spatial Modulation Technologies
## 1 Introduction  
The enactment of UWA channels for reliable high data rate underwater wireless communication is very challenging due to the characteristics of the oceanic environment. The main communication technologies, including optical, magnetic induction, electromagnetic, and acoustic communications, are employed in UWCs. In optical communication, the salient features, including scattering, severe absorption, and LoS communication, make its applications limited to clean water only [1; 2]. In magnetic and electromagnetic waves, harsh attenuation occurs via ocean conductivity, and ultra-low frequency bands overcome this attenuation. Acoustic communication technology is a widely trusted physical layer technology used in the UWC to achieve long communication distances, i.e., a few meters totens of kilometers for low and high transmission frequencies. The acoustic wave is operated with limited bandwidth, ambient noise effects, propagation delay, and high Doppler shift [3; 4]. Despite the problems mentioned earlier, acoustic communication is the most trusted UWC technology. A MIMO system is deployed in underwater acoustic communication (UWAC) to overcome the UWC data rate limitations. In conventional UWA-MIMO systems, all transmission antennas are used in one time interval; hence, its performance depends on various parameters such as the distance between transmitter/receiver antennas [5; 6], transmitter IAS, and receiver ICI [7; 8]. The performance of the UWA-MIMO system can be degraded significantly due to incorrect IAS [7; 8]. Despite this, UWA-MIMO technologies have brought a significant increase in capacity and diversity gain for acoustic underwater wireless networks [9] but there are many limitations such as implementation complexity due to multiple transmitter antennas, and performance deterioration due to the multipath propagation environment. In most of the MIMO systems, the implementation of a few transmitter antennas is led by power-loss problems [10]. Therefore, the SM scheme has been proposed in which only one transmitting antenna is activated in each time interval, and the possible data rate is compensated for by using spatial domain [11]. SM [12; 13; 14] is a unique method that accomplishes high spectral efficiency through spatial domain in MIMO transmission systems and information bits transmitted by only one antenna, providing higher data rate instead of traditional SIMO systems. The elementary principle of the SM is that it uses additional bits to convey the information through antenna indices and signal constellations such as M-QAM and M-PSK, where M is the constellation size. At the receiver, the SM decoder jointly searches all the transmitting antennas and M-ary constellation points to determine both the transmitted antenna index and the symbol. Therefore, SM has less receiver complexity, it effectively removes ICI, and it does not require IAS of the MIMO link due to availability of one RF chain at the transmitter. Different SMTs are introduced [15; 16; 17; 18; 19; 20; 21; 22; 23] by allowing it to enable one or more RF chains using different techniques so that high throughput and enhanced SNR can be achieved. GSM [21; 22] is the most prevalent technique, in which the multiple antennas are active in each communication channel so that high data rate can be achieved. The activated antennas transmit the same symbol in each time interval to achieve transmitting diversity. Consequently, the available data rate of GSM is improved by activating a more significant number of transmitting antennas. FGSM has been proposed in [15; 16] where the antenna subsets are varying between the activation of a single antenna and the activation of multiple/all antennas. These variations in the number of activated transmission antennas enhance the realization of the communication channel, resulting in increased available data rate. An additional parameter is also used to map the information bits, i.e., data signal constellations [17].