## 1 Introduction  
Underwater wireless optical communication (UWOC) has attracted great attention in recent years due to its high data rate, low latency, and solid reliability compared with other traditional underwater communication ways, for example, the acoustic and radio frequency (RF) communications [1, 2]. Unfortunately, in UWOC, the received signal suffers severe attenuation caused by the optical properties of underwater channel, namely, absorption and scattering, which is defined as channel loss in [3, 4] and inevitably degrades the system performance. Besides this, the optical beam needs also to be highly directive for a successful communication. Practically, however, due to the misalignment between the transmitter and receiver, the so-called pointing loss is incurred [4, 5]. Obviously, the pointing loss effect will impair the system performance. So far, many studies have been conducted on the effect of misalignment of the transmitter and receiver on the received intensity [4, 5, 6, 7]. However, in the above literature, the receiver planes were fixed and could not be inclined, which greatly limited the performance of the UWOC especially in a dynamic ocean environment. Although [8, 9] allowed for the tilting or movement of the receiver, no further considerations were given to theoretically optimize the performance of UWOC by tilting the receiver to overcome the deleterious pointing loss. Channel capacity is an important indicator for evaluating the performance of communication links. A closed-form expression for the average channel capacity of UWOC was studied based on the anisotropic ocean turbulence channel with Malaga fading in [10]; Reference [11] investigated both the capacity and bit-error-rate (BER) of underwater wireless optical links under weak and strong turbulence by deriving the expressions of the average capacity and BER. In [12], based on modeling the statistical characteristic of the pointing error's variance, the average channel capacity over weak turbulence distribution was established. However, all the literature mentioned above only discussed the channel capacity of UWOC in a traditionally input-independent noise scenario, that is, they adopted a positive-intrinsic-negative (PIN) photodiode as the receiver and did not consider the effect of other more powerful photodiode, for instance, an avalanche photodiode (APD), on the channel capacity of UWOC in practical application. Since APD can greatly outperform the traditional PIN diode due to its intrinsic average gain [13], people prefer to use APD instead of PIN to mitigate the channel loss and then to enhance the system transmission length in seawater [14]. Despite this, however, the signal model of APD is a little difficult to be analyzed because an excessive shot noise term relating to the input signal is introduced in signal modeling, and this complicates the performance analysis. Although References [15; 16] investigated the performance bounds of the channel capacity when the input-dependent noise term is introduced in a free space optical (FSO) communication situation, the key channel loss factor in the transmitting signal construction was neglected to simplify the system modeling and performance analysis. Obviously, this makes the receiving signal model of APD receiver in [15; 16] incomplete and the results about the capacity bounds derived in them could not be used directly. In fact, there are other effective ways to improve the performance of an optical communication system reported in recent literature.