1 Introduction

The OCDMA technique has garnered a considerable interest due to its ability to provide secure transport of information. One of the key advantages of OCDMA is its ability to enable multiple channels to transmit data simultaneously using the same spectrum, resulting in capacity enhancement (Aljunid et al. 2004; Stok and Sargent 2003). In OCDMA, data is transmitted on channels that employ different codes, composed of binary bits “1” and bits “0”. The bit “1” indicates the presence of light, while the bit “0” indicates the absence of light (Abd El-Mottaleb et al. 2018). By utilizing these codes, multiple users can transmit their data concurrently without interfering with each other, thereby increasing the overall system capacity. Several codes are used in OCDMA. The differences between these codes are code weight, cross-correlation, code length, and number of channels that can be utilized (Moghaddasi et al. 2015). Codes with zero cross-correlation can easily be detected using a direct detection (DD) scheme. However, the implementation in a real-system poses a critical challenge to achieve zero cross-correlation due to factors like noise and multi-path interference. Consequently, it is preferred to use codes that have unity cross-correlation. While these codes may introduce multiple access interferences (MAI), employing a suitable detection approach, such as single photodiode detection (SPD), can effectively mitigate these interferences (Al-Khafaji et al. 2013).

In recent years, there has been a growing interest in the exploration and utilization of UW environments, leading to the need for improved communication methods that can connect submerged ecosystems with human technologies (Schirripa Spagnolo et al. 2020). In response to this demand, the field of UOWC systems has gained a considerable interest as a potential solution for transmitting and receiving data in UW environments. UOWC systems are highly attractive in UW communication scenarios as they offer several advantages. First, a wide range of bandwidth is provided, which means they can efficiently transmit large amounts of data. This aspect proves beneficial in underwater environments, where conventional communication systems, like acoustic communication, frequently grapple with bandwidth constraints. Additionally, UOWC systems offer a confidential data transmission as optical signals are more difficult to intercept and decode when compared to acoustic signals (Zielinski et al. 1995).

Moreover, higher data rates can be transmitted over longer ranges in UOWC systems. This is attributed to the fact that light signals propagate in UOWC faster than acoustic signals that experience lower attenuation (Zhou et al. 2022). Furthermore, UOWC systems are immune to wave interference (Akyildiz et al. 2005). Although, UW communication systems based on radio frequency (RF) could provide data rates in Mb/s, they are not preferred compared to UOWC systems. This is due to the large attenuation they exhibit, which results in requiring large size transmitter and receiver antennas (Lloret et al. 2012; Akyildiz et al. 2004). Despite the several advantages offered by UOWC systems, the significant reduction in signal strength caused by the absorption and scattering phenomena inherent in the optical characteristics of water results in a decrease in the maximum achievable transmission distances (Doniec and Rus 2010; Lloret et al. 2012).

Nowadays, researchers integrate multiplexing techniques like orbital angular momentum (OAM) (Singh et al. 2023a, b), OCDMA (Abd El-Mottaleb et al. 2023; Al Hammadi and Islam 2020) using different codes, and orthogonal frequency division multiplexing (OFDM) (Hameed et al. 2023) in UOWC systems to enhance UW system capacity. Al Hammadi and Islam proposed an UOWC system integrated with OCDMA using optical orthogonal codes. The light source utilized was operating at 532 nm and the performance was discussed for PS, CL, and CS waterbodies (Al Hammadi and Islam 2020). Although the results showed longer ranges for these types of waterbodies when five channels were used, it is difficult to implement their technique. The five channels require a code length of 409 and to implement this system, a large number of light sources is required (Al Hammadi and Islam 2020). In Chancey (2005), authors utilized frequency modulation in an UOWC system, and a data rate transmission of 10 Mb/s over an UW range of 5 m was reported. Another UOWC system operated with 30 dBm transmitted power with a filtered OFDM was proposed in Hameed et al. (2023). The system reported an UW transmission range of 12 m for harbor water at 1 Gb/s data rate. The OAM multiplexing scheme was used in an UOWC system in Singh et al. (2023a, b) operating at 532 nm, and an overall capacity of 40 Gb/s for 4 channels were achieved for five types of waterbodies. A 16-quadrature amplitude modulation (16-QAM) with OFDM system was employed in UOWC transmission system operating at 450 nm at a rate of 4.8 Gb/s (Oubei et al. 2015). The study conducted by the authors in Shen et al. (2016) utilized a LD operating at a wavelength of 450 nm, delivering a power of 51.3 mW was employed in conjunction with non-return-to-zero (NRZ) on–off keying (OOK) modulation technique to transmit data at a rate of 1.5 Gbps over an UW range of 20 m.

In this work, we propose a new UOWC transmission system based on OCDMA that utilizes DPS codes for the first time, to the best of our knowledge. The DPS code is characterized by unity cross correlation and shorter code length compared to the optical orthogonal code used in Al Hammadi and Islam (2020). Three channels assigned by three different DPS code-sequences are used. Each of these channels carries a different information rate. In our proposed model, we use the data rates 2.5, 5, and 10 Gb/s. Thus, the overall capacity of the investigated system is (3 × 2.5 = 7.5 Gb/s, 3 × 5 = 15 Gb/s, 3 × 10 Gb/s = 30 Gb/s). additionally, the subsequent waterbodies PS, CL, CS, HA I, and HA II are studied. The Q-factor, BER, and eye diagram performance metrics are considered for evaluating the system performance.

The structure of the rest of the paper is as follows. Section 2 shows how to construct the DPS code. Section 3 discusses the impact of waterbodies’ attenuations in the UOWC system, followed by the design of the proposed UOWC system utilizing OCDMA/DPS code in Sec. 4. The achieved results are displayed and discussed in Sec. 5. Finally, the main conclusions and suggestions are reviewed in Sec. 6.

2 DPS code construction

In this section, the DPS code that is utilized in the OCDMA technique is explained. The DPS is like any OCDMA code is characterized by code weight, P, number of channels, N, and code length, L. The value of P can be any prime number greater than 2. Additionally, N can be expressed in terms of P as (Singh et al. 2023a, b)

$$N={P}^{2}$$
(1)

Moreover, L can be expressed in terms of both \(N\) and P as (Singh et al. 2023a, b)

$$L=N+P$$
(2)

To construct the DPS code-sequence, four processes must be followed sequentially, which are diagonal, permutation, shifting, and joining. When choosing \(P\) = 3, the four steps will be carried out as:

- Diagonal process.

Firstly, construct a primary diagonal sequence as (Singh et al. 2023a, b)

$${x}_{\mathrm{0,0}}=\left(0\times 0\right)mod3=0$$
(3)

Afterwards, a generated sequence based on diagonal sequence is constructed as (Singh et al. 2023a, b)

$${X}_{3}=\left[{x}_{\mathrm{0,0}} {x}_{\mathrm{1,1}} {x}_{\mathrm{2,2}}\right]=[0 1 1]$$
(4)

Permutation process.

In this process, a matrix of size 3 × 3 is constructed based on keeping the first row with the same elements of \({X}_{3}\). Then, perform permutation on it one time to get the elements of the second row and perform permutation again on the second row to get the elements of the third row as (Singh et al. 2023a, b)

$${Q}_{3}^{0}=\left[\begin{array}{c}{x}_{\mathrm{0,0}} {x}_{\mathrm{1,1}} {x}_{\mathrm{2,2}}\\ {x}_{\mathrm{2,2}} {x}_{\mathrm{0,0}} {x}_{\mathrm{1,1}}\\ {x}_{\mathrm{1,1}} {x}_{\mathrm{2,2}} {x}_{\mathrm{0,0}}\end{array}\right]=\left[\begin{array}{c}0 1 1\\ 1 0 1\\ 1 1 0\end{array}\right]$$
(5)

-Shifting process.

In this process, two matrices are constructed, which are \({Q}_{3}^{1}\) and \({Q}_{3}^{2}\). To construct the matrix\({Q}_{3}^{1}\), a value of 1 is added to each element in\({Q}_{3}^{0}\). Then, perform modulo 3 to the result as follows (Singh et al. 2023a, b)

$${Q}_{3}^{1}=\left[\begin{array}{c}\left(0+1\right)mod3 (1+1)mod3 (1+1)mod3\\ (1+1)mod3 (0+1)mod3 (1+1)mod3\\ (1+1)mod3 (1+1)mod3 (0+1)mod3\end{array}\right]=\left[\begin{array}{c}1 2 2\\ 2 1 2\\ 2 2 1\end{array}\right]$$
(6)

While for matrix \({Q}_{3}^{2}\), a value of 2 is added to each element in \({Q}_{3}^{0}\). Then, perform modulo 3 to the result as follows (Singh et al. 2023a, b)

$${Q}_{3}^{2}=\left[\begin{array}{c}\left(0+2\right)mod3 (1+2)mod3 (1+2)mod3\\ (1+2)mod3 (0+2)mod3 (1+2)mod3\\ (1+2)mod3 (1+2)mod3 (0+2)mod3\end{array}\right]=\left[\begin{array}{c}2 0 0\\ 0 2 0\\ 0 0 2\end{array}\right]$$
(7)

Joining process.

In this process, an extra column, V, is added to each of \({Q}_{3}^{0}\), \({Q}_{3}^{1}\), and \({Q}_{3}^{2}\) matrices, where V is a matrix of size 3 × 1 and has elements {0; 1; 2}. Then, the matrices are stacked together to make the DPS matrix as (Singh et al. 2023a, b)

$${M}_{D}= \left[\begin{array}{c}0110\\ 1011\\ 1102\\ 1220\\ 2121\\ 2212\\ 2000\\ 0201\\ 0022\end{array}\right]$$
(8)

Additionally, to create code sequences corresponding to individual rows within the matrix \({M}_{D}\), substitute "0" with the code "100," "1" with "010," and "2" with "001." For instance, the DPS code sequences corresponding to the initial five rows in matrix MD can be displayed as

$$M_{D} = \left[ {\begin{array}{*{20}c} {0110} \\ {1011} \\ {1102} \\ {1220} \\ {2121} \\ \end{array} } \right] \leftrightarrow \left[ {\begin{array}{*{20}c} {100 010 010 100} \\ {010 100 010 010} \\ {010 010 100 001} \\ {010 001 001 100} \\ {001 010 001 010} \\ \end{array} } \right]$$
(9)

In this work, three channels are considered assigned with the first three code-sequences in the \({M}_{D}\) matrix. As in OCDMA codes, bit “0” refers to absence of light (no wavelength) and bit “1” refers to presence of light (there is wavelength). So, the wavelengths corresponding to the DPS code sequences assigned to three channels are given in Table 1.

Table 1 Channels with code-sequences and their corresponding wavelengths
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3 UOWC channel attenuation

The transmission of optical signals in an UOWC channel is subject to the effect of seawater attenuation. Seawater exhibits a high concentration of solutes and particulate matter, which can vary significantly causing different attenuation for different waterbodies. These variations have discernible impacts on the optical properties of seawater. To ensure effective UOWC system design and performance, it is crucial to analyze the inherent optical characteristics of water, considering the scattering and absorption effects. Figure 1 illustrates a pictograph of the interaction between seawater and light beam depicted in a small volume (Δv) of seawater with thickness (Δr). Assume a light signal of power \({{\text{P}}}_{{\text{in}}}\) is incident to seawater of volume Δv and thickness Δr, a part of this power denoted by \({{\text{P}}}_{{\text{t}}}\) will pass directly though seawater, a part of \({{\text{P}}}_{{\text{in}}}\) is scattered (\({{\text{P}}}_{{\text{sc}}}\)) and its travelling direction will be changed, and the remainder part of \({{\text{P}}}_{{\text{in}}}\) is absorbed (\({{\text{P}}}_{{\text{ab}}}\)) by components existing in the water.

Fig. 1
figure 1

Impact of light beam on water

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Hence, the total attenuation, \(c\left( \lambda \right)\), in \({\text{m}}^{ - 1}\), can be expressed as the sum of the scattering and absorption coefficients, (\(\propto_{s}^{a}\)) and (\(\propto_{b}^{a}\)), respectively, as (Boluda-Ruiz et al. 2020)

$$c\left( \lambda \right) = \propto_{s}^{a} \left( \lambda \right) + \propto_{b}^{a} \left( \lambda \right)$$
(10)

Wavelength transmission, concentration of chlorophyll, existence of dissolved organic and inorganic substances are factors that affect both \({\propto }_{s}^{a}(\lambda )\) and \({\propto }_{b}^{a}\) (Arnon 2010; Gabriel et al. 2013). \({\propto }_{s}^{a}(\lambda )\) can be expressed as (Smith and Baker 1981; Gabriel et al. 2013)

$${\propto }_{s}^{a}(\lambda )={s}_{pw}\left(\lambda \right)+{s}_{small}\left(\lambda \right)+{s}_{large}\left(\lambda \right)$$
(11)

where \({s}_{pw}\left(\lambda \right)\) is the scattering coefficient of pure water and its value depends on transmission wavelength (\(\lambda\)) and is equal to \(0.005826{\left(\frac{400}{\lambda }\right)}^{4.322}\). \({s}_{small}\left(\lambda \right)\) and \({s}_{large}\left(\lambda \right)\) are scattering coefficients of small and large particles, respectively. Their values depend on \(\lambda\) and the amount of chlorophyll concentration in which they can expressed as (Haltrin 1999; Vavoulas et al. 2014)

$${s}_{small}\left(\lambda \right)=0.020002{\left(\frac{400}{\lambda }\right)}^{1.7}{C}_{ch}{\text{exp}}\left[0.11631\left(\frac{{C}_{ch}}{{C}_{ch}^{0}}\right)\right]$$
(12)
$${s}_{large }\left(\lambda \right)=0.260204{\left(\frac{400}{\lambda }\right)}^{0.3}4{C}_{ch}{\text{exp}}\left[0.03092\left(\frac{{C}_{ch}}{{C}_{ch}^{0}}\right)\right]$$
(13)

where \({C}_{ch}\) is the amount of chlorophyll concentrated in water and its value at \(\lambda\)= 532 nm for PS is 0.005 mg/\({{\text{m}}}^{3}\), CL is 0.31 mg/\({{\text{m}}}^{3}\), and CS is 0.83 mg/\({{\text{m}}}^{3}\), and \({C}_{ch}^{0}\) is a fixed value of 1 mg/\({{\text{m}}}^{3}\) (Gabriel et al. 2013).

As for \({\propto }_{b}^{a}\), it can be expressed as (Smith and Baker 1981; Gabriel et al. 2013)

$${\propto }_{b}^{a}(\lambda )={a}_{pw}\left(\lambda \right)+{a}_{ch}\left(\lambda \right){\left(\frac{{C}_{ch}}{{C}_{ch}^{0}}\right)}^{0.62}+{a}_{fulvic}\left(\lambda \right){C}_{fulvic}{\text{exp}}\left(-{q}_{fulvic}\lambda \right)+{a}_{humic}(\lambda ){C}_{humic}{\text{exp}}\left(-{q}_{humic}\lambda \right)$$
(14)

where \({a}_{pw}\left(\lambda \right)\) is the absorption coefficient of pure water, \({a}_{ch}\left(\lambda \right)\) is the spectral absorption of the chlorophyll and its value depend on \(\lambda\), so at 532 nm, it has value of 0.0127 \({{\text{m}}}^{-1}\) (Prieur and Sathyendranath 1981; Smith and Baker 1981). As for \({a}_{fulvic}\left(\lambda \right)\), \({C}_{fulvic}\), and \({q}_{fulvic}\) are specific absorption coefficient of fulvic acid and has value of 35.959 \({{\text{m}}}^{2}/{\text{mg}}\) at transmission wavelength of 532 nm, fulvic acid concentration and its value depends on \({C}_{ch}\) and is equal to \(1.74098{C}_{ch}{\text{exp}}\left(\frac{{C}_{ch}}{{C}_{ch}^{0}}\right)\), constant value of 0.0189 \({{\text{nm}}}^{-1}\), respectively (Haltrin 1999; Vavoulas et al. 2014). The other parameters \({a}_{humic}(\lambda )\), \({C}_{humic}\), and \({q}_{humic}\) denote specific absorption coefficient of humic acid and its value at \(\lambda\)= 532 nm is 18.828 \({{\text{m}}}^{2}/{\text{mg}}\), concentration of humic acid and is equal to \(0.19334{C}_{ch}{\text{exp}}\left(\frac{{C}_{ch}}{{C}_{ch}^{0}}\right)\), and constant has value of 0.01105 \({{\text{nm}}}^{-1}.\)

In this work, five types of waterbodies are considered, which are PS, CL, CS, HA I, and HA II. The differences and specifications of the different waterbodies are described in Table 2 (Zeng et al. 2017).

Table 2 Comparison between various types of water (Zeng et al. 2017)
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4 Design of UOWC system utilizing OCDMA/DPS code

The setup of the proposed UOWC system exploiting OCDMA/DPS code is illustrated in Fig. 2. Different data rates of 2.5, 5, and 10 Gb/s are generated using a pseudo random bit sequence generator (PRBSG). The bit sequence is carried over an electrical signal with a NRZ format. As for generating optical signals corresponding to three channels assigned with DPS code, four LD sources are used for each channel having wavelengths described in Table 1. To modulate the NRZ electrical signal into optical signals, a Mach–Zehnder modulator (MZM) is used for each channel. Further, a multiplexer is used to multiplex the optical signals from the various channels before propagating in the UOWC channel.

Fig. 2
figure 2

Lay out of proposed UOWC system utilizing OCDMA/DPS code. PRBSG: pseudo-random bit sequence generator; LD: laser diode; MZM: Mach–Zehnder modulator; FBG: fiber bragg grating; PD: photodiode; LPF: low-pass filter; BER: bit error rate

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The transmitted signal is divided at the receiver to three branches corresponding to the three channels. A single photodiode detector (SPD) is used to detect the signal in each branch after passing through a decoder and a subtractive decoder (S-Decoder). The decoder has a series of fiber Bragg gratings (FBGs) with Bragg wavelengths matching those of the used LDs at the transmitter.

As an example, the decoder of channel 1 has 4 FBGs centered at 532, 536, 538.4, and 540 nm. Since the DPS code is characterized by a unity cross-correlation, there is an interference in one bit between any two code-sequences. Accordingly, there is an interference between channel 1 and channel 2 in the \({8}^{{\text{th}}}\) bit corresponding to the 538.4 nm wavelength. To solve this issue, an S-decoder is used which has an FBG centered at the wavelength corresponding to the bit of interference, which is 538.4 for channel 1. Moreover, to detect the signal of channel 1 without MAI, an optical subtractor is used to subtract the S-Decoder signal from the signal of the decoder. Finally, the detected electrical signal is passed through a low pass filter (LPF) to reject the unwanted signal. A BER analyzer is used to measure the eye diagram and calculate the BER performance of the received data.

The output current from the photodiode (PD) is expressed as (Singh et al. 2023a, b)

$${I}_{PD-DPS}= \frac{{\mathcal{R}}_{PD} {P}_{rx}^{UW}{B}_{op}(P-1)}{L}$$
(15)

where \({\mathcal{R}}_{PD}\) and \({B}_{op}\), are the PD responsivity and optical bandwidth, respectively, while \({P}_{rx}^{UW}\) indicates the power received, which can be expressed in terms of the transmitted power, \({P}_{tx}^{UW}\), and underwater range, \({L}_{UW}\), as (Saeed et al. 2019; Arnon 2010)

$${P}_{rx}^{UW}={P}_{tx}^{UW}{\eta }_{tx}{\eta }_{rx}G\frac{{A}_{rx}cos\theta }{2\pi {{L}_{UW}}^{2}\left[1-{\text{cos}}({\theta }_{0})\right]}{\text{exp}}\left[-c(\lambda )\frac{{L}_{UW}}{cos\theta }\right]$$
(16)

where \({\eta }_{tx}\) and \({\eta }_{rx}\) are the optical efficiencies for the transmitter and receiver, respectively, \({A}_{rx}\) represents the area of receiver aperture, \({\theta }_{0}\) is the beam divergence angle, \(G\) is the beam concentrator gain, and \(\theta\) is the angle that occurs when there is misalignment in the axis between the transmitter and receiver telescopes.

In this model, three noise sources are considered when calculating the SNR; namely, shot, phased induced intensity, and thermal noise. These noises are expressed as (Singh et al. 2023a, b; Singh et al. 2022)

$${\text{Shot}}\,{\text{ noise }} = {\text{ 2e}}\,B_{e} {\mathcal{R}}_{PD} \left\langle { I_{PD - DPS} } \right\rangle$$
(17)
$${\text{PIIN }}\,{\text{noise }} = \frac{{\left( {P_{rx}^{UW} } \right)^{2} B_{e} B_{o} \left( {P + 1} \right)}}{L}$$
(18)
$${\text{Thermal noise}} = { }\frac{{4k_{B} TB_{e} }}{{R_{L} }}$$
(19)

where e and \({k}_{B}\) are constants referred to electron charge and Boltzmann constant, \({B}_{e}\) and \({B}_{o}\) are electrical and optical bandwidths, respectively, and \({R}_{L}\) and \(T\), are the receiver load resistance and receiver absolute temperature, respectively.

The received signal SNR is then expressed as (Abd El-Mottaleb et al. 2023; Hanson and Radic 2008)

$$SNR= \frac{{\left( {I}_{PD-DPS}\right)}^{2}}{\mathrm{Shot noise}+\mathrm{PIIN noise}+\mathrm{Thermal noise}}$$
(20)

The BER is given as (Ahmed et al. 2022)

$$BER=\frac{1}{2}erfc\left(\frac{1}{2\sqrt{2}}\sqrt{SNR}\right)$$
(21)
$$BER=\frac{1}{2} erfc\left(\frac{Q}{\sqrt{2}}\right)$$
(22)

where erfc is the error complementary function and Q is quality factor.

The Q-factor is a measure of signal quality that shows how well a signal can be received in presence of impairments like noise and water attenuation. It can be expressed as (Djir et al. 2022)

$$Q= \frac{{I}_{S}-{I}_{N}}{{\sigma }_{S}+{\sigma }_{N}}$$
(23)

where \({I}_{S}\) and \({I}_{N}\) are the signal and noise levels of the two received symbols “1” and “0”, respectively, \({\sigma }_{S}\) and \({\sigma }_{N}\) are the standard deviations of the signal and noise levels of two symbols “0” and “1”.

5 Results and discussion

The proposed UOWC system utilizing OCDMA/DPS code is simulated at different data rates (2.5, 5, and 10 Gb/s) per each channel using the OptiSystem software ver. 21. The values of the main parameters used in simulation are given in Table 3 (Singh et al. 2023a, b; Al Hammadi and Islam 2020; Singh et al. 2022; Kaushal and Kaddoum 2016; experimental data provided by vendor optisystem software under the governmentally Funded Project NSERC/Card1 538,408–18;OptiSystem: Nowy Sa˛cz, Poland, 2019).

Table 3 Proposed model parameters values (Singh et al. 2023a, b; Al Hammadi and Islam 2020; Singh et al. 2022; Kaushal and Kaddoum 2016)
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For simplicity, the results are discussed for one channel. The system performance is investigated in terms of Q-factor, BER, and eye diagrams metrics. The five waterbodies: PS, CL, CS, HA I, and HA II are considered in the simulations.

5.1 Q-factor performance for UOWC utilizing OCDMA/DPS code

In this subsection, Fig. 3 present the Q-factor values for the UOWC system utilizing OCDMA/DPS codes at data rates of 2.5, 5, and 10 Gb/s, considering various types of waterbodies. It is evident from this figure that as the data rate increases, the ability for the UOWC to achieve longer UW spans diminishes. Furthermore, it is observed that waterbodies with higher attenuation leads to shorter distances traveled by the optical signal carrying the information.

Fig. 3
figure 3

Q-factor for UOWC utilizing OCDMA/DPS code versus UW range at different data rates for a PS, b CL, c CS, d HA I, and e HA II

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Figure 3 illustrates the Q-factor versus underwater range for different waterbodies at different transmitted data rates utilizing OCDMA/DPS code. A Q-factor of 5 is achieved at an UW distance of 13 m when operating the system at 10 Gb/s in PS. However, for similar values of Q-factor and data rate, the UW span decreases to 10 m and 7.2 m in CL and CS waterbodies, respectively. Furthermore, the UW range further decreases, reaching the shortest distance of 3 m in HA II water while maintaining the same values of data rate and Q-factor. Moreover, when the UOWC system operates at 2.5 Gb/s, there is an improvement in the Q-factor performance. It is evident from Fig. 3d, which depicts the Q-factor versus UW link for the proposed system in HA I water, that the Q-factor increases from 6.24 to 12.22 when the data rate is reduced from 10 to 2.5 Gb/s.

Table 4 summarizes the Q-factor for the UOWC utilizing OCDMA/DPS code at 3 m for HA II, 4.3 m for HA I, 7.2 m for CS, 10 m for CL, and 13 m for PS at 2.5, 5, and 10 Gb/s.

Table 4 Q-factor at different data rates for the proposed UOWC utilizing the OCDMA/DPS
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5.2 BER performance for UOWC utilizing OCDMA/DPS code

This part presents the BER performance of the proposed UOWC system utilizing the OCDMA/DPS codes at data rates of 2.5, 5, and 10 Gb/s. The lg(BER) performance versus UW distance for the proposed UOWC system is depicted in Fig. 4, representing different water environments, including PS, CL, CS, HA I, and HA II, respectively. It is observed that the longest UW link between transmitter and receiver with best BER performance occurs at lower data rates and in water types that have lower absorption and scattering coefficients. It can be seen from Fig. 4a, b that at lg(BER) of \(\sim\) − 13.8, UW ranges are 13 for PS and 10 m for CL at data rate of 5 Gb/s. In contrast, as HA II has the highest attenuation, so, the lowest travelling range in UW that optical signal obtains is 2.82 at the same lg(BER) and data rate. Moreover, at the same ranges, the BER performance degrades when data rate enhances to 10 Gb/s as cleared from Fig. 4e.

Fig. 4
figure 4

lg(BER) for UOWC utilizing OCDMA/DPS code versus UW range at different data rates for a PS, b CL, c CS, d HA I, and e HA II

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The maximum distances are different because there are five different types of water which have different inherent optical characteristics that cause different absorption and scattering coefficients. These coefficients have impact on the maximum propagation range as, according to Eq. (12), there is a relation between received power, UW range and excitation coefficient. As these five types of water have different attenuations, so, the maximum UW range will be different. Accordingly, we select different ranges which differ from small to large ranges according to type of water used to make sure the plot is clear. As PS has a low excitation coefficient, so, a large UW range is selected for it. In contrast, HA II exhibits a large excitation coefficient, so, a small range of UW spans is chosen for it. Moreover, if we plot the ranges that are selected for PS to HA II, so, we will get lg(BER) = 1. Therefore, we discussed the BER performance for short ranges as to discuss that maximum range that will achieve for HA II smaller values than that achieved for other water bodies.

Table 5 tabulates the lg(BER) for the UOWC utilizing OCDMA/DPS code at different data rates and UW ranges of 3 m, 4.3 m, 7.2 m, 10 m, and 13 m, for HA II, HA I, CS, CL, and PS, respectively.

Table 5 lg(BER) at different data rates for the proposed UOWC utilizing OCDMA/DPS code
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5.3 Eye diagram for UOWC utilizing the OCDMA/DPS code

Eye diagrams are commonly used as a metric to assess the quality of a received signal. An eye diagram displays the signal waveform over multiple periods, with the time axis horizontally and the signal amplitude axis vertically. The characteristic "eye" pattern arises from the overlapping of these waveforms. In an eye diagram, the quality of the information is shown by how wide the opening of the eye is. A larger eye opening signifies that the received signal is of higher quality. Conversely, a narrower eye opening suggests a lower signal quality, which can lead to an increased BER. Consequently, a wider eye opening indicates a good signal reception and a reliable data transmission.

Figure 5 displays the eye diagrams for the proposed UOWC system utilizing the OCDMA/DPS code in PS water for a range of 13 m, showcasing various data rates. In addition, Fig. 6 presents the eye diagrams at different data rates for CL water with a UW span of 10 m. Furthermore, Fig. 7 displays the eye diagrams at an UW range of 7.2 m for CS water, considering data rates of 2.5, 5, and 10 Gb/s. Finally, Fig. 8 showcases the eye diagrams for the proposed UOWC system using OCDMA/DPS code at different data rates and an UW distance of 4.3 m in HA I water. Similarly, Fig. 9 illustrates the eye diagrams for the system at different data rates and an UW distance of 3 m in HA II water. The wider eye openings shown in Figs. 5–9 assure that all information sent are received successfully. As for the distinct red line plot inside the eye diagram it shows how the signal evolves over time and as in many digital communication systems, signal sampling decisions are made at the midpoint of the bit interval.

Fig. 5
figure 5

Eye diagrams for UOWC utilizing OCDMA/DPS at 13 m UW range in PS water at a 2.5 Gb/s, b 5 Gb/s, and c 10 Gb/s

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Fig. 6
figure 6

Eye diagrams for UOWC utilizing OCDMA/DPS at 10 m UW range in CL water at a 2.5 Gb/s, b 5 Gb/s, and c 10 Gb/s

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Fig. 7
figure 7

Eye diagrams for UOWC utilizing OCDMA/DPS at 7.2 m UW range in CS water at a 2.5 Gb/s, b 5 Gb/s, and c 10 Gb/s

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Fig. 8
figure 8

Eye diagrams for UOWC utilizing OCDMA/DPS at 4.5 m UW range in HA I water at a 2.5 Gb/s, b 5 Gb/s, and c 10 Gb/s

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Fig. 9
figure 9

Eye diagrams for UOWC utilizing OCDMA/DPS at 3 m UW range in HA II water at a 2.5 Gb/s, b 5 Gb/s, and c 10 Gb/s

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To demonstrate the capacity enhancement achieved by the proposed UOWC system, a comparative analysis is conducted with respect to previous published works (including experimental works), as outlined in Table 6. This comparison allows us to assess the advancements and improvements offered by our UOWC in overall capacity.

Table 6 Comparison between present work and previous works
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6 Conclusion

A new UOWC system based on using a DPS code is proposed in this paper. Three channels assigned with three different DPS code-sequences are used. Additionally, green spectrum is used in this proposed model to carry the modulated signals. Moreover, the proposed UOWC system performance is investigated at 2.5, 5, and 10 Gb/s. Five types of waterbodies are studied and the system performance is evaluated for the UOWC proposed system. The obtained results show that the system performance of the propagated signals at lower data rate offer better performance. Additionally, the waterbodies that cause low attenuation allow the transmitted signal over the UOWC system to propagate longer. In contrast, the worst performance is achieved when the system rate operating at 10 Gb/s and in HA II waterbody. At lg(BER) nearly − 6.6 at 10 Gb/s, an UW range of 2.93 m is achieved for HA II waterbody, while this range is extended to 13 m when transmission is applied in PS. Accordingly, the proposed model is suggested to be used in submarine applications that require high speed and in military services that need secure data transmission. As for a future work, we suggest discussing the turbulence effects on the UOWC system and integrating OAM with the proposed model for enhancing the transmission capacity.