Optical Power Constraints Research Articles

UOWC spatial diversity techniques over hostile maritime environments: an approach under imperfect CSI and per-source power constraints

Optical communication in submarine environments has emerged as a novel technology that enables high bandwidth and high data rate links. However, the unique characteristics of the underwater channel impose new challenges, such as mitigating the remarkable absorption and scattering of hostile maritime environments. For the first time, we consider a per-source optical power constraint based on eye-safety regulations, which has never before been taken into account in Multiple-Input/Single-Output (MISO) systems within underwater optical wireless communication (UOWC) scenarios. Hence, we introduce an innovative spatial repetition coding (SRC) system model, which enables the analysis of an SRC scheme operating under either a per-source or a per-transmitter power constraint. In addition, a tractable generalized transmit laser selection (GTLS) model is presented in order to consider the impact of erroneous selections of the best laser source due to imperfect channel state information (CSI) at the transmitter, prevalent in underwater scenarios with dynamic fluctuations from water currents. Novel bit error rate closed-form expressions and asymptotic results are derived. The presented results demonstrate that an SRC system, when appropriately designed under a per-source power constraint, outperforms the TLS system by effectively mitigating the adverse effects of underwater links. Conversely, in situations where compact transmitters necessitate constraints that significantly modify eye-safety, TLS schemes are superior.

Channel capacity and power allocation of MIMO visible light communication system

In this paper, the channel capacity of the multiple-input multiple-output (MIMO) visible light communication (VLC) system is investigated under the peak, average optical and electrical power constraints. Finding the channel capacity of MIMO VLC is shown to be a mixed integer programming problem. To address this open problem, we propose an inexact gradient projection method to find the channel capacity-achieving discrete input distribution and the channel capacity of MIMO VLC. Also we derive both upper and lower bounds of the capacity of MIMO VLC with the closed-form expressions. Furthermore, by considering practical discrete constellation inputs, we develop the optimal power allocation scheme to maximize transmission rate of MIMO VLC system. Simulation results show that more discrete points are needed to achieve the channel capacity as SNR increases. Both the upper and lower bounds of channel capacity are tight at low SNR region. In addition, comparing the equal power allocation, the proposed power allocation scheme can significantly increase the rate for the low-order modulation inputs.

New Bounds on Capacity Region of Multiple Access Channels in Visible Light Communications.

In this paper, we propose new inner and outer bounds of the capacity region for multiple access channels in visible light communication (VLC) networks under both peak and average optical power constraints. Specifically, the proposed inner bounds are established by employing the single-user capacity achieving input distribution for each user. The proposed outer bounds are derived by determining single-user capacities for each user and calculating a sum capacity upper bound by relaxing the input constraints. Numerical results show that the proposed new bounds are extremely tight and outperform existing bounds over wide ranges of SNRs.

Spectral and Energy Efficiency of DCO-OFDM in Visible Light Communication Systems With Finite-Alphabet Inputs

The bound of the information transmission rate of direct current biased optical orthogonal frequency division multiplexing (DCO-OFDM) for visible light communication (VLC) with finite-alphabet inputs is yet unknown, where the corresponding spectral efficiency (SE) and energy efficiency (EE) stems out as the open research problems. In this paper, we derive the exact achievable rate of the DCO-OFDM system with finite-alphabet inputs for the first time. Furthermore, we investigate SE maximization problems of the DCO-OFDM system subject to both electrical and optical power constraints. By exploiting the relationship between the mutual information and the minimum mean-squared error, we propose a multi-level mercury-water-filling power allocation scheme to achieve the maximum SE. Moreover, the EE maximization problems of the DCO-OFDM system are studied, and the Dinkelbach-type power allocation scheme is developed for the maximum EE. Numerical results verify the effectiveness of the proposed theories and power allocation schemes.

Signal clipping at transmitter and receiver of O-OFDM for VLC under optical power constraint

Visible light communications (VLC) is considered as an effective supplement technology for next-generation (6G) communications due to its abundant spectrum, high power efficiency and easy deployment. Optical orthogonal frequency division multiplexing (O-OFDM) is a common technology to obtain further promotion. In this paper, two typical O-OFDM schemes direct current biased O-OFDM (DCO-OFDM) and asymmetrically clipped O-OFDM (ACO-OFDM) are analyzed in terms of signal clipping at both transmitter and receiver under the constraints of maximum optical power and non-negative optical power. And effective electrical SNR models after signal clipping are proposed and verified by link simulation. Then a noise cancellation scheme is proposed based on received signal clipping and is proved to bring a significant gain for ACO-OFDM. By system simulation, we find that under a certain optical power limitation, most users can achieve above 4Gbps in indoor scenario when modulation bandwidth of the light emit diode (LED) or laser diode (LD) is 1GHz. Therefore, it can be expected that the throughput could reach tens Gbps when the LED/LD modulation bandwidth is increased and multiple LEDs/LDs are deployed.

Spectral and Energy Efficiency of ACO-OFDM in Visible Light Communication Systems

In this paper, we study the spectral efficiency (SE) and energy efficiency (EE) of asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) for visible light communication (VLC). Firstly, we derive the achievable rates for Gaussian distributions inputs and practical finite-alphabet inputs. Then, we investigate the SE maximization problems subject to both the total transmit power constraint and the average optical power constraint with the above two inputs, respectively. By exploiting the relationship between the mutual information and the minimum mean-squared error, an optimal power allocation scheme is proposed to maximize the SE with finite-alphabet inputs. To reduce the computational complexity of the power allocation scheme, we derive a closed-form lower bound of the SE. Also, considering the quality of service, we further tackle the non-convex EE maximization problems of ACO-OFDM with the two inputs, respectively. The problems are solved by the proposed Dinkelbach-type iterative algorithm. In each iteration, the interior point algorithm is applied to obtain the optimal power allocation.The performance of the proposed power allocation schemes for the SE and EE maximization are validated through numerical analysis.

On the Capacity of RIS-Assisted Intensity-Modulation Optical Channels

Using re-configurable intelligent surfaces (RIS) in optical wireless communication (OWC) systems to solve the signal obstruction and skip-zones dilemmas modifies the transmission channel. It is thus necessary to analyze the capacity of such a system. To this end, the capacity lower- and upper-bounds of RIS-assisted single-input single-output (SISO) OWC systems are discussed in this letter, focusing on the intensity-modulation and direct-detection scheme. This analysis considers two main constraints, namely peak-intensity and average optical power constraints. It also considers two types of structures: the single-layer structure (SLS) and multiple-layer structure (MLS). By exploiting the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$QR$ </tex-math></inline-formula> -decomposition, the analysis is extended to RIS-assisted multiple-input multiple-output (MIMO) OWC systems. As a result, the RIS-based cascaded channel capacities bounds and the achievable rate at a high signal-to-noise ratio are given for free-space RIS-based SISO/MIMO OWC systems. These results show that the channel exhibits a high capacity when the RIS module is closer to the data source, and that the MLS provides a higher achievable rate when compared to the SLS.

BER Performance Analysis for Downlink Nonorthogonal Multiple Access With Error Propagation Mitigated Method in Visible Light Communications

In order to mitigate the error propagation (EP) effect on the bit error rate (BER) performance due to the imperfect successive interference cancellation for the non-orthogonal multiple access (NOMA)-based visible light communication (VLC) downlinks, adjustable bit rate superposition coding (ABRSC) and sample-and-sum successive interference cancellation (SSSIC) decoding schemes are proposed in this paper. Based on the modified fixed-power allocation (MFPA) strategy, the closed-form expressions of BER are derived for the two-user case with on-off keying, and further extended to the multi-user scenario. The residual probability of EP is introduced and derived to theoretically assess the effectiveness of the proposed ABRSC and SSSIC schemes. Monte Carlo simulation is also conducted to validate the analytical BER results. The BER performance of the NOMA-based VLC system with multiple users is further analyzed and discussed in detail. It is found that under the total average optical transmission power constraint, the allocated average optical transmission power to current user should be higher than that to all rest of users, i.e., the power allocation factor (PAF) is supposed to be greater than 1/2, in order to avoid the error floor issue of current user, hence facilitating the successful implementation of SSSIC. Besides, increasing the bit-rate factor (BRF) could mitigate the effect of EP, and larger BRF leads to more efficient outcomes in alleviating the effect of EP.

Results on the Rate-Equivocation Region of the Degraded Signal-Dependent Noise Wiretap Channel

This letter studies the rate-equivocation region of a degraded signal-dependent noise wiretap channel (SDGN-WC), where the noise is Gaussian. This signal-dependent noise occurs in optical wireless communication (OWC) settings based on intensity modulation and direct detection (IM-DD). In this setup, the transmitted signals are nonnegative and are restricted by an average optical power constraint. We consider the rate-equivocation region of the degraded SDGN-WC and through solving a convex optimization problem, we establish that the support set of the optimal distributions must be countably infinite. Our result implies that when the transmitted optical signals are restricted by an average optical power: 1) the secrecy capacity is achieved by a distribution which has a countably infinite support set; 2) the channel capacity (the case with no secrecy constraints) is also achieved by a distribution having a countably infinite support set.

Achieving Channel Capacity of Visible Light Communication

In this article, we propose an efficient inexact gradient descent method to obtain the channel capacity-achieving input distribution of visible light communication (VLC). Under both a peak and an average optical power constraints, finding the channel capacity of VLC is formulated as a mixed continuous-discrete optimization problem without an analytical expression of the objective function. To solve this challenging problem, we first adopt the numerical integration method to approximate the objective function and its gradient. Here, we prove that the gaps between the original functions and the approximations can be arbitrarily small. Then, based on the approximated functions, we describe the method, and theoretically show that the obtained solution sequence converges to the channel capacity-achieving discrete distribution of VLC. We also provide simulation results to verify the effectiveness and optimality of the proposed method. More importantly, the simulations numerically reveal that on-off keying (OOK) modulation achieves the capacity of VLC channel at low signal-to-noise ratio (SNR), while pulse amplitude modulation (PAM) achieves the capacity at high SNR.

Capacity-Maximized Transmitter Precoding for MU MIMO VLC Systems With Bounded Channel Uncertainties

Considering imperfect channel state information (CSI), we study robust precoding design for multiuser multiple-input–multiple-output (MIMO) indoor visible-light communication systems, where one transmitter with several light-emitting diodes sends messages to multiple receivers each with several photodiodes. We model the imperfect CSI with bounded channel uncertainties by worst-case model, aiming to maximize the worst-case sum capacity of all receivers via optimizing the precoders at the transmitter under optical power constraints. The robust precoding problem is nonconvex and thus hard to solve. To overcome this difficulty, we first separate the logarithm function and the precoders in the objective function, then employ the sign-definiteness lemma to eliminate the channel uncertainties, and finally develop an effective iterative optimization algorithm to compute the precoders. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.

DC bias and power optimization for AV-DCO-OFDM in optical wireless communication

In this paper, we investigate the optimization of direct current (DC) bias, information-bearing power and subcarrier power allocation in absolute valued DC biased optical orthogonal frequency division multiplexing (AV-DCO-OFDM) systems. First, we analyze the effect of absolute value operation on the system performance using the Bussgang Theorem. Then, we consider the maximization of achievable rate under the optical power constraint. Using the optimality conditions, the optimization problem can be simplified and two efficient algorithms are developed to obtain the solutions in flat channels and dispersive channels, respectively. Simulation results validate the theoretical analysis and the effectiveness of the developed algorithms.

Energy Efficiency Optimization for MIMO Visible Light Communication Systems

Multiple-input multiple-output (MIMO) visible light communication (VLC) systems can support high data rates for indoor communications. In this letter, we focus on maximizing the energy efficiency (EE) of MIMO VLC systems, where the non-negativeness of the transmit signal, the optical and electrical power constraints, and the data rate and bit error rate (BER) requirements are taken into account. The formulated problem is a difficult nonlinear fractional program. We exploit the Dinkelbach’s algorithm and Lagrangian analysis to obtain a semi-closed form solution. The performance advantage of the proposed design is verified by simulation results.

Rate Region of the ZF Precoder in a $2\times2$ Multiuser Optical IM/DD Channel

We derive an achievable rate region (ARR) of the zero-forcing precoder in a 2 $\times $ 2 multi-user multiple-input single-output broadcast intensity-modulation/direct-detection channel. A per-light emitting diode (LED) peak optical power constraint along with a per-LED average optical power constraint with inequality (Type-I constraint) generally considered in optical wireless communication systems is imposed for which we analytically characterize the boundary of the proposed ARR. Then, we compare this ARR with that under a per-LED peak optical power constraint along with a per-LED average power constraint with equality (Type-II constraint), which is considered in visible light communication systems for constant illumination requirement. Our analysis reveals that when the ratio ( $\beta $ ) of the maximum allowed per-LED average optical transmit power to the per-LED peak power is less than or equal to half ( $\beta \leq 1/2$ ), the ARR under both the constraints is the same. However, Type-I constrained system is analytically shown to be more power efficient in terms of the required total average transmit optical power. When $\beta > 1/2$ , the ARR under the Type-I constraint remains constant with increasing $\beta $ , whereas the ARR under the Type-II constraint shrinks.

Constellation-Optimal Beamformers for Multiuser MISO Broadcast Visible Light Communications

In this paper, we design energy-efficient space constellations for multiuser multi-input single-output visible light communication broadcast systems with channel state information (CSI) at the receiver in the three scenarios: 1) with CSI at the transmitter (CSIT); 2) with statistical CSIT; and 3) without CSIT. By utilizing the cooperation of multiuser interference, optimal multidimensional additively uniquely decomposable constellation groups are designed to optimize the received worst case performance metrics of all users subject to two commonly used power constraints, i.e., average and peak optical power constraints. The resulting optimal designs are proved to be pulse amplitude modulated with an optimal beamformer, which can be efficiently attained by numerical search for Scenarios 1 and 2 and be given in a closed form for Scenario 3. One of the common significant advantages of these designs is the fast demodulation of the sum signal from a noisy received signal, since these optimal designs result in an equivalent ideal scalar AWGN channel. Comprehensive computer simulations demonstrate that our designs significantly outperform traditional zero-forcing, minimum mean square error, and time-division methods.

Non-Alternating Globally Optimal MMSE Precoding for Multiuser VLC Downlinks

We study the minimum mean-squared error (MMSE) precoding for multiuser visible light communication downlink systems. Different from radio frequency systems, this problem does not admit a closed-form solution due to the light-emitting diode optical power constraints. To handle the difficult non-convex problem, we transform it into an equivalent convex form via the Charnes–Cooper transformation. In this way, we are able to achieve the globally optimal MMSE precoder by solving only one convex problem, thus requiring much lower complexity than the existing alternating algorithm. The proposed non-alternating method is also extended to robust the MMSE precoder optimization in the presence of statistical channel-state information errors.

Multiuser Transmit Precoding Design for Dimming Compatible Visible Light Communications

In multiuser visible light communication (VLC) systems, many transmit precoding (TPC) techniques have been investigated to suppress multiuser interference. However, these conventional works restrict their modulation to the special case of zero mean, which inherently limits their application to some popular modulations associated with the non-zero mean in VLC, such as pulse position modulation (PPM). Since the modulation with non-zero mean leads to more intricate optical power constraints and design objective functions than the case of zero mean, the TPC design that can support a general modulation is still an open problem. In the paper, we conceive of a general solution of the TPC scheme combined with dimming control for multiuser VLC systems, which is capable of mitigating multiuser interference, while at the same time, achieving the desired dimming level. The proposed scheme is applicable to a wide range of modulations in VLC, such as pulse amplitude modulation (PAM), PPM, and so on. Simulation results demonstrate that the proposed scheme outperforms the traditional pseudo-inverse-based zero-forcing TPC in terms of bit error rate (BER).

Achievable Rates of Multi-Carrier Modulation Schemes for Bandlimited IM/DD Systems

In this paper, we comprehensively investigate the achievable rates of selected band-limited intensity modulation schemes, which are important for optical wireless communication applications, while accounting for the specific nature of their signal construction (non-negative, real, and baseband), and imposing identical bandwidth and average optical power constraints. Furthermore, we identify/devise methods to effectively trade between these parameters. Three variants of orthogonal frequency division multiplexing (OFDM), namely, asymmetrically clipped optical OFDM (ACO-OFDM), spectrally and energy efficient OFDM (SEE-OFDM), and dc-biased optical OFDM (DCO-OFDM), and single-carrier pulse amplitude modulation are studied. The clipping noise in ACO-OFDM and SEE-OFDM is found to consume a large excess bandwidth. The detrimental effects of this excess bandwidth on the achievable rate are evaluated. For SEE-OFDM, the problem of optimal power allocation among its components is formulated and solved using the Karush–Kuhn–Tucker method. For DCO-OFDM, the clipping noise is modeled and incorporated in the analysis. Among the existing schemes, DCO-OFDM yields the best overall performance, due to its compact spectrum. In order to improve the achievable rate, we propose and analyze two improved distortionless variants, filtered ACO-OFDM and filtered SEE-OFDM (FSEE-OFDM), which yield better spectral efficiency than ACO-OFDM and SEE-OFDM, respectively. FSEE-OFDM, being the most spectrally efficient, outperforms all schemes.

Intrinsic Robustness of MISO Visible Light Communications: Partial CSIT Can be as Useful as Perfect One

We consider a multi-input single-output visible light communication (MISO-VLC) system. For such system under both average and peak optical power constraint, an optimal space constellation maximizing the received minimum Euclidean distance is attained among all the feasible sets, respectively, for the case with or without channel state information at the transmitter (CSIT). These designs demonstrate that the optimal transmission only requires CSIT which is related to the possibilities of the echelon arrangement of the channel coefficients and jointly determined by the power regime and the ordering of channel coefficient values. Our findings point out that it is not necessary to probe the exact value of the MISO-VLC channel vector and limited CSIT can sufficiently guarantee the intrinsic robustness. In addition, the optimal designs admit low-complexity maximum likelihood detection. These properties make our proposed optimal designs especially attractive in such channels.

Optimal Hexagonal Constellations Based on a Two-Dimensional Signal Space for Peak-Limited Intensity-Modulated Channels

For high-rate peak-limited intensity-modulated optical systems, the two-dimensional time-disjoint signal space (TDSS) is proposed. Based on the TDSS, the optimal hexagonal constellations (OHCs) are proposed analytically under a peak optical power constraint. Both analytical and simulation results show that our proposed OHCs based on the TDSS have the asymptotical peak optical power gain of 0.753 dB over the baseline schemes at no extra bandwidth cost.