# Pilot-Assisted OFDM for Underwater Acoustic Communication
## 1 Introduction  
The UWA channel is doubly selective due to multipath fading and a Doppler shift [1]. When compared with radio waves, acoustic waves have lower speeds and the bandwidth is higher when compared with the carrier [2]. The channel is a time variant as Doppler shifts are induced due to the relative motion of the transmitter and receiver [3]. Furthermore, the underwater acoustic channel is wideband and, as fewer path components carry most of the energy, the channel is space. Among the multicarrier modulation schemes, OFDM has been shown to be effective against inter-symbol interference (ISI) because of its longer symbol duration. Due to the motion of transmitting and receiving nodes in a UWA channel, OFDM is prone to frequency offsets [3]. OFDM works by splitting the frequency selective channel into several flat fading channels. Moreover, an OFDM symbol contains a cyclic prefix (CP) whose length is kept equal to or greater than the delay spread of the channel to combat ISI [4]. When using OFDM in a UWA channel, the subcarrier spacing must be reduced as the bandwidth of the UWA channel is significantly small. However, this introduces ICI [5, 6]. Almost all OFDM receivers use a channel estimation technique to compute approximate values of the channel parameters. Several types of estimation techniques have been explored in the literature to accurately estimate the channel for OFDM. These include blind, semi-blind, and pilot-based channel estimation techniques. Out of these techniques, the pilot-based technique is widely used mainly because of the ease in its implementation alongwith a better performance. The downside of this technique is the bandwidth overhead, resulting in poor spectral efficiency [7; 8; 9]. For UWA channels, this type of technique is preferable because the underwater nodes have limited power and limited processing capabilities. In a typical pilot-based channel estimation scheme, a few known symbols--also called training symbols--are inserted into the transmitted OFDM symbols at prespecified locations. These known symbols are then extracted by the receiver and are used for the synchronization and determination of the channel parameters [10]. Several estimation techniques have been used with OFDM receivers such as maximum likelihood (ML), minimum mean square error (MMSE) estimation, and least squares error (LSE) estimation. With the rise in data rates in future UWA systems, the symbol duration will keep on decreasing with the increasing data rates making the equalization process complex [11]. As OFDM offers a higher data rate and one-tap equalization, it is an ideal candidate for UWA communication systems. Moreover, as the equalization is performed in the frequency domain, the fast Fourier transform (FFT) in the receiver of the OFDM further reduces the equalization complexity [12]. However, coping with Doppler shifts is a challenge as they affect the orthogonality of the subcarriers due to phase variations. Hence, the problem of equalization when using OFDM in UWA channels has been addressed and several solutions have been proposed in the literature. In radio-based systems, zero forcing equalizers have been used as they are simple to implement. However, they suffer from significant noise amplification near to the zeroes of the channel in an attempt to invert the channel completely. MMSE equalizers overcome the shortcomings of ZF equalizers at the cost of complexity. This paper adds to the body of research in two ways. We propose the investigation of a channel estimation algorithm based upon a least squares error estimation. This algorithm is applied to a typical OFDM system, in which pilot signals are used for a UWA channel. In this algorithm, the pilot signals are inserted at predefined subcarriers and the receiver estimates the channel using the LSE algorithm. Secondly, we compare LSE and ZF equalizers. Based upon the channel delay spread, we tune the position and number of pilots as well as vary the length of the cyclic prefix to improve performance.