# Optical OFDM for SiPM-Based Underwater Optical Wireless Communication Links
## 1 Introduction  
The increasing need to explore underwater resources has given rise to the development of high-performance underwater equipment and robotics with data transmission capability. Underwater wireless data transmission is one of the key features for the efficient operation of such systems. Among the available communication technologies, underwater wireless optical communications (UWOCs) have received increasing attention in the past two decades because of their ability to transmit high data rates with high energy efficiency over short to moderate distances [1; 2; 3; 4]. The primary challenges for UWOC systems include extending the range and enhancing the data rate of such links. To address the former, silicon photo-multipliers (SiPMs), also called multi-pixel photon counters (MPPCs), have recently drawn particular attention thanks to their high internal gain, allowing a high receiver (Rx) sensitivity, and hence, operation over large distances. In addition,they offer many implementation and operational advantages over photo-multiplier tubes (PMTs) [6]. On the other hand, the data rate of UWOC links is mainly limited by the limited modulation bandwidth (BW) of the emitting device, which is either a laser diode (LD) or a light-emitting diode (LED), and that of the photo-detector (PD). One efficient approach to deal with channel frequency-selectivity is to use optical orthogonal frequency-division multiplexing (O-OFDM). However, the resulting high signal peak-to-average power ratio (PAPR) can cause a significant performance degradation, given the limited dynamic range (DR) of the transmitter (Tx) opto-electronic components (primarily the emitter and its driver). Our aim in this paper is to assess the limitation of highly sensitive SiPM receivers when using O-OFDM signaling. For this, we consider the use of LEDs at the Tx, which have the advantage of a relatively high output power and the flexibility of being arranged in arrays. The use of SiPMs at the Rx has the obvious advantage of allowing significant range extension compared to PIN or APD counterparts on the one hand, and operational robustness and implementation simplicity compared to PMTs on the other hand [6]. Given the limited DR of an SiPM, which primarily impacts Rx performance at relatively short ranges [6; 7], the use of O-OFDM signaling could impose further limitations in practice. To the best of our knowledge, the performance of an SiPM-based Rx with O-OFDM signaling, taking into account the limited DRs of the Tx and the Rx, has not been investigated in detail so far. More specifically, we quantify the performance of three O-OFDM techniques from indoor visible-light communication (VLC) systems to underwater settings, namely DC-biased O-OFDM (DCO-OFDM), asymmetrically clipped (ACO-OFDM), and layered ACO (LACO-OFDM). To compare the performances of these schemes, we mostly fix the electrical power at the Tx, as it impacts directly the power consumption of the underwater unit, which is of crucial importance in underwater missions. We take into account the required DC-bias (to minimize the clipping noise) for the three considered schemes, given the LED characteristics. Indeed, the required DC bias for ACO- and LACO-OFDM in practice is commonly neglected in the related theoretical works, which could affect the general conclusions on the choice of the appropriate transmission technique. Taking into account the effects of upper and lower signal clipping at the Tx, SiPM saturation at the Rx at relatively short ranges, and beam attenuation in water, we show that, overall, ACO-OFDM has an undeniable advantage over the two other schemes in terms of energy efficiency for low-to-moderate spectral efficiencies. However, DCO-OFDM allows a higher flexibility (i.e., provides a good tolerance) in terms of operational range when relaxing the constraint on the transmit power. Meanwhile, we show that LACO-OFDM makes a good compromise between energy efficiency and operational range flexibility. The remainder of this paper is organized as follows.