Deep Learning Based End-to-End Optical Wireless Communication Systems With Autoencoders

The utilization of neural network-based autoencoders (AEs) for the implementation of the physical layer in communication systems has recently emerged as a promising technique for achieving end-to-end optimization of communication links. However, applying conventional AE architecture to intensity modulation/direct detection optical wireless systems is challenging due to positive real-value constraint, eye safety standards, and the limited dynamic range of light sources. To address these issues, in this letter we propose a practical architecture, namely differential AE, that incorporates the concept of differential signaling. This approach allows the transmission of negative encoder output elements. In a shot-noise limited scenario, we assess and compare the performance of the differential AE with state-of-the-art works in the optical wireless domain, highlighting the superior bit-error ratio achieved by the differential AE.


Deep Learning Based End-to-End Optical Wireless Communication Systems With Autoencoders
Hossein Safi , Iman Tavakkolnia , Member, IEEE, and Harald Haas , Fellow, IEEE Abstract-The utilization of neural network-based autoencoders (AEs) for the implementation of the physical layer in communication systems has recently emerged as a promising technique for achieving end-to-end optimization of communication links.However, applying conventional AE architecture to intensity modulation/direct detection optical wireless systems is challenging due to positive real-value constraint, eye safety standards, and the limited dynamic range of light sources.To address these issues, in this letter we propose a practical architecture, namely differential AE, that incorporates the concept of differential signaling.This approach allows the transmission of negative encoder output elements.In a shot-noise limited scenario, we assess and compare the performance of the differential AE with state-of-the-art works in the optical wireless domain, highlighting the superior bit-error ratio achieved by the differential AE.
Index Terms-Autoencoder, deep learning, end-to-end learning, modulation, neural network, optical wireless communications.

I. INTRODUCTION
F ROM the early stages of researching telecommunication systems, engineers have striven to reliably convey messages from a specific source to a desired destination through a channel characterized by random parameters [1].To this end, conventional communication systems utilize a series of independent blocks that are optimized for specific tasks, such as source/channel coding, modulation, channel estimation, and equalization.However, the divided architecture, where transmitter (Tx) and receiver (Rx) tasks are split into multiple processing blocks, is known to be suboptimal, as it lacks integrated end-to-end optimization [2].Consequently, the notion of achieving the optimal performance by comprehensively optimizing the entire communication system remains attractive for further exploration.
Digital Object Identifier 10.1109/LCOMM.2024.3387286particular performance measure and channel model [4].Within this framework, where the Tx and Rx are represented as neural networks (NNs), autoencoders (AEs) have emerged as a promising technique for end-to-end design of the physical layer in communication systems [5].An AE is a deep NN in which a low-dimensional representation of its input vector is constructed at the output layer with a specific error [ [6], Ch. 14].This arrangement allows for the joint optimization of both the Tx and Rx, unbounded by the constraints of individual component optimization.Motivated by these advantages, the field of optical communication has recently witnessed a surge in research focused on the integration of AEs within these systems.For instance, considering an intensity modulation/direct detection (IM/DD) system in [7], an end-to-end DL-based approach for designing optical fiber communication transceivers was introduced.The work in [8] provided a tutorial on machine learning for optical interconnects based on vertical-cavity surface-emitting lasers (VCSELs).The tutorial emphasizes end-to-end approaches and addresses the challenges associated with VCSELs in this context.Meanwhile, a few studies on DL-based systems on the domain of optical wireless communication (OWC) have been recently reported [9], [10], [11], [12], [13], [14], [15], [16].Particularly, a deep learning AE was proposed in [9] to provide an end-to-end model of space optical communications systems.More recently, the work in [9] was extended to deal with both perfect and imperfect channel state information [10].Also, the authors in [11] proposed an AE framework with batch normalization in the encoder and layer normalization in the decoders to increase the performance in terms of achieving a lower bit-error ratio (BER).Moreover, in [12], a study was conducted on an AE-driven OWC system, considering various orders of quadrature amplitude modulation.Further, the study presented in [13] proposed an AE-based optical intelligent reflecting surface (OIRS) system to jointly optimize the processing modules at transmitter, OIRS, and receiver in a visible light communication (VLC) link.The authors in [14] proposed a DL framework for emerging image sensor communication and verify its feasibility through performing simulation.Furthermore, in [15], the authors introduced an AE-based system for both single-user and multi-user scenarios, operating over an additive white Gaussian noise (AWGN) channel while adhering to non-negativity and peak power constraints.Additionally, [16] delved into an AE-based OWC system, taking into account the impacts of atmospheric turbulence.
The proposed structures for AEs in the RF domain cannot be straightforwardly applied in the optical domain due to the non-negativity requirement of the input signal.Positive real values, enforced in the conventional AE structure for IM/DD systems, pose challenges.Firstly, concerns arise about potential eye exposure to laser beams, especially in the nearinfrared range, requiring compliance with safety standards and limiting transmit laser power [17].Secondly, for high data rate communication, more levels are needed to support numerous transmit symbols, necessitating wideband high current laser/LED drivers.In addition to positive real-valued signalling issues, signal-dependent shot noise is unique to optical systems, warranting exploration of AE-based IM/DD systems in shot-noise limited scenarios.
Given these insights, it is vital to reconsider handling the technical restrictions imposed by optical wireless characteristics in an AE-based communication system.Thus, our goal is to create a new AE architecture that effectively addresses these challenges and assesses its performance.We can summarize the contributions of this work as follows.
• We introduce the novel integration of differential signalling [18] into the AE architecture.This allows transmitting negative encoder outputs, significantly expanding the constellation space and enabling more flexible shaping for noise mitigation.To the best of our knowledge, this marks the initial instance of suggesting and confirming such an architecture for AE-based OWC systems.• By optimizing the constellation points through the learning scheme, we minimize the impact of shot noise.This leads to improved performance in signal-dependent noise scenarios prevalent in OWC systems.• We further evaluate the proposed differential AE-based communication system in a signal-dependent shot-noiselimited scenario, demonstrating its superior performance compared to existing state-of-the-art approaches in this domain.

II. DL-BASED COMMUNICATION SYSTEMS
As depicted in Fig. 1, the AE consists of three main blocks, i.e., Tx, Rx, and channel. 1 The Tx receives an input message s ∈ M = {1, 2, . . ., M }, where M = 2 k with k denoting the number of bits per message.Next, the input message is converted into a one-hot vector s m of size M , and then passed through dense layers.Particularly, the one-hot vector is a binary representation of an input message of size M , where it contains a single "1" at position m while all other elements are set to "0".The one-hot vector proceeds to the dense layers where each layer applies an activation function to individual elements of the input vector.As the one-hot vector passes through multiple dense layers, the transformation f T x : R M → R L occurs, generating the transmitted codeword x = [x [1] , . . ., x [L]] for L channel uses.Hence, the system's data rate is calculated as r = k L (bit per channel use).Notably, in this architecture, the codewords generated by the encoder comprise both positive and negative elements.However, in a practical OWC system, the transmitted optical signal must adhere to nonnegativity and peak power constraints.Consequently, a constraint layer should be appended to the end of the Tx dense layers to ensure compliance with these constraints on the transmitted optical signal.As a result, AE-based OWC systems differ from the conventional utilization of AEs in the RF domain.In the prior works of the AE-based OWC systems [15], [16], the constraint layer is considered as a layer that restricts the elements of the encoded vector x ∈ R L as 0 ≤ x[i] ≤ A c , i = 1, . . ., L, using a weighted sigmoid activation function.In other words, the activation function of the last layer is A c × sigmoid(•), where A c is the peak power constraint.However, in this work, we propose a more practical AE-based architecture that accommodates negative encoder output elements, thus removing the need for adding extra layers which brings us a less complexity.
The channel is modeled by incorporating a set of layers having probabilistic (e.g., additive noise, fading), and deterministic (e.g., path loss when there is no mobility) behaviours.At the decoder side, the received codeword y is passed through multiple dense layers in which the transformation of f Rx : R L → R M is applied.At the last layer, a softmax activation function is applied whose output is an estimate of the corresponding posterior probability vector p ∈ R M over all possible messages.Finally, considering the maximum a posteriori (MAP) decision rule, the index of the element of p with the largest value is reverted to estimate transmitted message ŝ.The loss function of the training process is the mean square error (MSE), which is given as (1)

III. AUTOENCODER ARCHITECTURE BASED ON DIFFERENTIAL SIGNALING
In this section, we resort to the differential signaling technique in the domain of optical wireless and propose a new practical architecture for AE-based OWC systems.This approach enables transmission of negative encoder output elements.
Fig. 2 illustrates the block diagram of the proposed system for DL-based OWC with differential signaling.In this scheme, the ith element of the encoded vector is initially multiplied by coefficients d 1 and d 2 to create x + i and x − i , respectively.The coefficients d 1 and d 2 are determined as follows where sign (•) denotes the signum function.Subsequently, x + i and x − i drive two optical sources (OSs) operating at distinct wavelengths λ 1 and λ 2 .The OS outputs pass through a beam combiner (BC) before transmission over the channel.After passing through the channel, the received optical signal is passed through a beam splitter (BS) and optical filters (OFs) with center wavelength λ 1 and λ 2 to separate the received optical signals of the two OSs.Photodetectors (PDs) then transform OF output optical signals into electrical signals y 1 and y 2 .Finally, based on discrete signal model for the noisy channels, we have [ [19], eq. ( 1)] where R is the PD responsivity, h is the instantaneous channel coefficient, and P t denotes the transmit optical power.Moreover in 3, n is a zero-mean AWGN with variance σ 2 cn .Subsequently, the decoder directly processes the received signal difference, utilizing a learning-based approach for signal detection.This differs from classical methods like [18], which usually require channel state information (CSI) for optimal detection after computing the difference.The proposed architecture in Fig. 1 enables the transmission of negative codeword elements x over the optical wireless channel, eliminating the necessity for a constraint layer with A c ×sigmoid(•) activation.However, to meet the peak power constraint for this setup, one can utilize A d × tanh(•) within the constraint layer.
Next, we assess the proposed architecture's performance using learned constellation points (geometric shaping) and the average bit-error ratio (BER).We use Keras [20] with TensorFlow [21] in its back-end in order to build, train, and evaluate the AE.For training, we use a variant of stochastic gradient descent known as Adam [22] with widely accepted thumb rule for the parameter values as follows, learning rate η = 0.001, the first moment of estimate β 1 = 0.9, and the second moment of estimate β 2 = 0.99 [2].Also, Batch size equal to 45 is selected to efficiently utilize computational resources while preventing overfitting.Moreover, the number of epoch is set to 500 while the MSE loss converges to 10 −3 .

IV. PERFORMANCE EVALUATION
In this section, we assume a complete noise model for the OWC link and evaluate the performance of the DL-based communication system.Specifically, we consider receiver thermal and shot noise.Shot noise arises due to the quantum properties of light, as optical signals are composed of photons that impinge on the photodetector at random intervals.Accordingly, in the presence of signal-dependent shot-noise the average SNR is obtained as [ [23], eq. ( 3)] where σ 2 cn is the variance of the photo-current additive noise, and it can be obtained as [ [24], eq. ( 2)] where σ 2 s is the variance of the shot-noise.Furthermore, σ 2 th represents the noise variance attributed to receiver thermal noise, encompassing the contributions from both branches.Nonetheless, within the context of our analyzed shot noiselimited scenario, the predominant source of noise is the signal-dependent shot noise.As evident from eq. ( 5), the noise variance exhibits a direct proportionality to the transmit optical power.We first examine the MSE loss convergence for our proposed differential AE and the conventional AE (utilized in [3], [15], and [16]) in Fig. 3.The figure shows that our differential AE achieves an MSE loss of 10 −3 in just 50 epochs, outperforming the conventional AE, which hits 10 −2 in the same epoch range.This result provides an indication that our proposed approach is less complex compared to the conventional AE, as it eliminates the need for a non-zero centred layer, i.e., sigmoid, to enforce non-negativity constraints.
Multilevel pulse amplitude modulation (M-PAM) has undergone extensive study in recent years, aimed at enhancing the data rate of IM/DD systems.When operating at the same symbol rate, the information rate achievable with M-PAM significantly surpasses that of non-return-to-zero (NRZ) modulation.In the configuration under consideration, the optical signals of varying intensities within the framework of M-PAM exhibit distinct statistical characteristics that ultimately give rise to heightened levels of inter-symbol interference.To address this challenge, one can employ constellation shaping, which has gained prominence as an effective technique for enhancing the transmission performance of OWC systems.However, determining the optimal amplitudes for M-PAM signals within the framework of geometric shaping presents a challenging optimization problem to achieve input points that maximize capacity.For every modulation scheme utilized, within the context of the endto-end optimization of the transceiver, the transmitter learns signal constellation representations which are robust to the impairments of the optical channel.Therefore, in the sequel, we revisit the problem of determining robust constellation points for the M-PAM systems under a signal-dependent noise regime.
In this regard, we first plot the constellation points learned by the different AEs in Fig. 4. The set of parameters for each AEs is provided in TABLE I. We consider two different rates, i.e., r = 2 and r = 3 (bits per channel use), for both differential and coventional (utilized in [3], [15], and [16]) AE structures.Moreover, two classical PAM schemes, i.e., 4-PAM and 8-PAM, are provided for making a comparison with the learned constellation points in the DL-based scenario.
Fig. 4 reveals a distinctive feature in the AE structures' constellation points, differing from classical PAM schemes.Specifically, higher transmit power points exhibit larger Euclidean distances (EDs) in the DL-based communication system, addressing the influence of signal-dependent noise outlined in (5).This increase in EDs for high-power signal points serves to mitigate the impact of shot-noise on system performance, given that a higher signal level is associated with a higher shot-noise level, in contrast to [25], which advocate uniformly distributed PAM for maximizing worst-case ED in signal-independent AWGN channels.Moreover, despite both structures maintaining a consistent average transmit power, the minimum Euclidean distance (ED) for the differential AE is twice that of the conventional AE, and its peak power is lower than that of the others.Indeed, this emphasizes the superiority of the proposed differential AE, showcasing enhanced noise tolerance and overall system efficiency.
Furthermore, in Fig. 5, we present BER curves versus average SNR for the proposed differential AE structure at different rates (r = 2 and r = 3) in the presence of signal-dependent shot noise.These results are benchmarked against uniform constellation 4-PAM and 8-PAM schemes, as well as state-of-the-art AE structures in OWC systems, including the learning-based AE proposed in [11] (employing batch normalization (BN) in the encoder and layer normalization (LN) in the decoder), and the conventional AE [3], [15], [16].From this figure, it is evident that all AE structures, employing non-uniform constellations, consistently outperform the classical equidistant PAM schemes.The superior performance of AEs arises from their capacity to learn optimal transceivers, resulting in constellations with larger EDs at high-power signal points in the transmitter.This, coupled with the use of optimal threshold levels in the receiver, leads to enhanced performance.Furthermore, the proposed differential AE schemes exhibit a remarkable performance gain over the other AE structures.For instance, achieving a BER of 10 −6 yields an average SNR gain of 2.8 dB for r = 2 and 2 dB for r = 3.The key insight lies in the larger minimum ED of the constellation points in the differential AE, as discussed in Fig. 4., showcasing its potential for improved noise tolerance and overall system efficiency.
It is worth noting that, while BER is crucial, additional metrics, including peak power, constellation compactness and separation, complement the analysis, offering a more comprehensive evaluation of our proposed differential AE architecture in OWC systems.These metrics collectively emphasize safety, efficiency, and signal-dependent noise tolerance, providing a nuanced understanding of the scheme's practical viability and advantages in diverse communication scenarios.Furthermore, our proposed scheme uses two optical sources and two receivers, differing from conventional ones, which increases cost and complexity.However, this approach offers advantages such as reduced dynamic range requirements for the optical source, better eye safety, and improved receiver sensitivity.

V. CONCLUSION
The letter introduced a practical architecture for integrating AEs into the IM/DD-based OWC systems.We proposed differential signalling tailored for OWC, addressing challenges like positive real-valued signalling and signal-dependent shotnoise.Our differential AE scheme outperforms existing methods, achieving a lower BER compared to both state-ofthe-art AEs and classical M -PAM techniques.

Fig. 1 .
Fig. 1.The layered structure of an end-to-end DL-based OWC system.

Fig. 2 .
Fig. 2. Block diagram of the proposed differential AE for end-to-end learning in OWC systems.

Fig. 3 .Fig. 4 .
Fig. 3.The MSE loss convergence behaviour versus training epochs for the two different schemes.

Fig. 5 .
Fig. 5. BER versus average SNR for different AEs and two different rates a) r = 2, and, b) r = 3, under a signal-dependent noise scenario.
Through the utilization of DL-based techniques, it has become feasible to train the Tx and Rx in a holistic fashion, tailored to a Manuscript received 2 March 2024; revised 4 April 2024 and 8 April 2024; accepted 8 April 2024.Date of publication 10 April 2024; date of current version 12 June 2024.This work is a contribution by Project REASON, a UK Government funded project under the Future Open Networks Research Challenge (FONRC) sponsored by the Department of Science Innovation and Technology (DSIT).The authors also acknowledge partical financial support from the Engineering and Physical Sciences Research Council (EPSRC) under grant EP/X027511/1, "Green Optical Wireless Communications Facilitated by Photonic Power Harvesting (GreenCom)."The associate editor coordinating the review of this letter and approving it for publication was A. R. Ndjiongue.