# Pilot-Based Adaptive Channel Estimation for Underwater Spatial Modulation Technologies
## 1 Introduction
Therefore, the signal constellation type is also used to carry the transmitted data in addition to indices of the transmit antennas as in SM, GSM, and FGSM. The number of combinations between modulations and transmit antenna are increased by using the primary and secondary constellations. In this way, the receiver complexity is reduced, and performance gain of spectral efficiency is improved with high power saving. In the SMTs, the receiver detects both active antenna/antennas index/indices and the transmitted symbol because it transmits the antenna index and transmitted information through the modulated signal. In the literature, the symbol detection and the antenna index are estimated by sub-optimal and optimal detection methods [12; 24]. The error performance can be improved by using SM instead of V-BLAST in some cases, assuming that the receiver has complete CSI [24; 25]. Practically, the receiver does not have the CSI, therefore, channel estimation has been performed to estimate the channel. In [26; 27] SM-MIMO systems are tested to check the effect of rough channel estimation. In [26], MSE performance in MIMO systems is examined through LS estimation technique over quasi-static Rayleigh flat fading channels. Data detection with joint channel estimation is proposed with the assumption that the channel correlation matrix is available at the receiver [27]. To attain coherent detection performance, PSAM is applied in wireless communication [28]. The channel estimation for SM system through the RLS method based on pilots is investigated by assuming that for the duration of at least one length of frame the wireless channel is quasi-static [29]. In the case of the UWA channel, the channel estimation problem is more severe, where the union of a significant Doppler effects and long delay spread restrain UWA channels as doubly (time and frequency) spread channels [30; 31]. In this work SM, GSM, and FGSM techniques are used to transmit the pilots and data symbols at time instant where one or multiple antennas are active. Therefore, CSI of the active transmit antennas can be obtained at the receiver by employing pilot-based channel estimation using the RLS channel estimation method. The performance of RLS improves if more pilots are employed for underwater time-varying channels, but unfortunately that affected the spectral efficiency. The challenging design for the MIMO system is to make pilot-transmitted sequences transmit from each antenna orthogonally to avoid inter-antenna interference. Spatially modulated MIMO systems handle this problem easily because transmitting antennas are mutual disjoints all the time, which makes each transmitted pilot sequence surely orthogonal to each other. On the other hand, to the best of the authors' knowledge, no studies have been published to investigate the performance of SMTs with ML decoder using imperfect CSI in the UWA communication system. Therefore, in this paper, the RLS adaptive channel estimation is used in the ML optimal detector to detect the transmit data and antenna indices. Computer simulations are also performed to determine how the proposed adaptive channel estimation algorithm approaches the BER performance of P-CSI. For simplicity and ease for the reader, acronyms are mentioned in Table 1.  
The rest of the paper is managed as follows: The related work of SMTs is briefly explained in Section 2. Section 3 contains the ML optimal detector. The underwater channel model is presented in