Peak Intensity Constraints Research Articles

Capacity Bounds for the Two-User IM/DD Interference Channel

This paper studies the capacity of the two-user intensity-modulation/direct-detection (IM/DD) interference channel (IC), which is relevant in the context of multi-user optical wireless communications. Despite some known single-letter capacity characterizations for general discrete-memoryless ICs, a computable capacity expression for the IM/DD IC is missing. In this paper, we provide tight and easily computable inner and outer bounds for a general two-user IM/DD IC under peak and average optical intensity constraints. The bounds enable characterizing the asymptotic sum-rate capacity in the strong and weak interference regimes, as well as the generalized degrees of freedom (GDoF) in the symmetric case. Using the obtained bounds, the GDoF of the IM/DD IC is shown to have a ‘W’ shape similar to the Gaussian IC with power constraints. The obtained bounds are also evaluated numerically in different interference regimes to show their tightness, and used to study the performance of on-chip and indoor OWC systems.

Capacity Maximization for Reconfigurable Intelligent Surface-Aided MISO Visible Light Communications

This paper investigates the employment of reconfigurable intelligent surfaces (RISs) to improve the asymptotic capacity of the multiple-input single-output (MISO) visible light communication (VLC) system in the case of high signal-to-noise (SNR). For the RIS-aided MISO-VLC system based on mirror array, we regard the high-SNR asymptotic capacity with the input subject to peak-intensity constraints as a goal and formulate an asymptotic capacity maximization problem to find the optimal orientations of mirrors. As for the non-convex optimization problem, we convert it into a quadratic programming (QP) problem with hemispherical constraints and prove that it can be solved by computing the maximum eigenvalue of an equivalent matrix. Simulation results indicate that the asymptotic capacity is able to be improved significantly by adopting RIS in MISO-VLC systems. Meanwhile, we observe that the proper deployment scheme of RIS is able to enhance the degree of improvement through several simulations.

Capacity analysis of underwater visible light communication systems over a lossy channel in the presence of noises.

Absorption and scattering losses due to impurities and turbidity in the water affect the transmission quality of underwater visible light communication links, restricting the channel capacity. For the first time to our knowledge, this paper analytically studies the channel capacity of a point-to-point underwater visible light communication link in the presence of input-independent and -dependent noises along with absorption and scattering losses. This way, novel lower and upper bound expressions on channel capacity are derived when average and peak-intensity constraints are imposed on the channel input. Our proposed upper and lower bounds are tight at high optical signal-to-noise ratio. The derived analytic expression of capacity also helps to evaluate the available data rate in the presence of different types of noise and water. From the results, we can say that input-dependent noise causes more system capacity degradation than input-independent noise. The results show that good water quality is crucial for high-capacity communication links. Furthermore, it is shown that the attenuation of the optical signal is more in water when compared to air as a medium, and channel capacity decreases as the link range increases. The results reported in this paper provide valuable insight into the design of underwater visible light communication systems.

Tight Capacity Bounds for Indoor Visible Light Communications With Signal-Dependent Noise

Channel capacity bounds are derived for a point-to-point indoor visible light communications (VLC) system with signal-dependent Gaussian noise. Considering both illumination and communication, the non-negative input of VLC is constrained by peak and average optical intensity constraints. Two scenarios are taken into account: one scenario has both average and peak optical intensity constraints, and the other scenario has only average optical intensity constraint. For both two scenarios, we derive closed-from expressions of capacity lower and upper bounds. Specifically, the capacity lower bound is derived by using the variational method and the property that the output entropy is invariably larger than the input entropy. The capacity upper bound is obtained by utilizing the dual expression of capacity and the principle of “capacity-achieving source distributions that escape to infinity”. Moreover, the asymptotic analysis shows that the asymptotic performance gap between the capacity lower and upper bounds approaches zero. Finally, all derived capacity bounds are confirmed using numerical results.

Adaptive Power Allocation for Distortion Minimization in Generalized Polar Optical Wireless Communications

In this paper, we investigate adaptive power allocation for generalized polar optical wireless communications (OWC), where a general complex bipolar signal is converted into magnitude and phase signals for intensity modulation. Mean square errors (MSE) between the input complex signals and the re-constructed complex signals are derived to characterize signal distortion. Optimal power scaling factors and power allocation are investigated to minimize the distortion. Under a sole average intensity constraint, closed-form optimal power scaling factors are derived and found to be input-dependent. Specifically, they are determined by the first and second moments of the magnitude signals, the first moment of the phase signals as well as the channel state. Under both average and peak intensity constraints, the expression of MSE regarding the power scaling factors is derived but it is too complicated to find the optimal power allocation. Thus, we propose to use a small-scale numerical search for practical power allocation. As an example, we adopt the proposed power allocation to polar optical orthogonal frequency division multiplexing (P-OFDM) systems and analyze its achievable bit error rate (BER). Numerical simulations are presented to validate the analysis. It is shown that the proposed power allocation greatly improves the performance in terms of MSE and BER and the proposed power allocation-enhanced P-OFDM (EP-OFDM) outperforms existing optical OFDM schemes over various channels in the high signal-to-noise ratio (SNR) regime, especially in the systems with a peak intensity constraint.

Physical-Layer Security for Indoor Visible Light Communications: Secrecy Capacity Analysis

This paper investigates the physical-layer security for an indoor visible light communication (VLC) network consisting of a transmitter, a legitimate receiver and an eavesdropper. Both the main channel and the wiretapping channel have nonnegative inputs, which are corrupted by additive white Gaussian noises. Considering the illumination requirement and the physical characteristics of lighting source, the input is also constrained in both its average and peak optical intensities. Two scenarios are investigated: one is only with an average optical intensity constraint, and the other is with both average and peak optical intensity constraints. Based on information theory, closed-form expressions of the upper and lower bounds on secrecy capacity for the two scenarios are derived. Numerical results show that the upper and lower bounds on secrecy capacity are tight, which validates the derived closed-form expressions. Moreover, the asymptotic behaviors in the high signal-to-noise ratio (SNR) regime are analyzed from the theoretical aspects. At high SNR, when only considering the average optical intensity constraint, a small performance gap exists between the asymptotic upper and lower bounds on secrecy capacity. When considering both average and peak optical intensity constraints, the asymptotic upper and lower bounds on secrecy capacity coincide with each other. These conclusions are also confirmed by numerical results.

Optical Wiretap Channel With Input-Dependent Gaussian Noise Under Peak- and Average-Intensity Constraints

This paper studies the optical wiretap channel with input-dependent Gaussian noise, in which the main distortion is caused by an additive Gaussian noise whose variance depends on the current signal strength. Subject to nonnegativity and peak-intensity constraints on the channel input, we first present a practical optical wireless communication scenario for which the considered wiretap channel is stochastically degraded. We then study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be discrete with a finite number of mass points, one of them located at the origin. Moreover, we show that the entire rate-equivocation region of this wiretap channel is also obtained by discrete input distributions with a finite support. Similar to the case of the Gaussian wiretap channel under a peak-power constraint, here too, we observe that under nonnegativity and peak-intensity constraints, there is a tradeoff between the secrecy capacity and the capacity in the sense that both may not be achieved simultaneously. Furthermore, we prove the optimality of discrete input distributions in the presence of an additional average intensity constraint. Finally, we shed light on the asymptotic behavior of the secrecy capacity in the low- and high-intensity regimes. In the low-intensity regime, the secrecy capacity scales quadratically with the peak-intensity constraint. On the other hand, in the high-intensity regime, the secrecy capacity does not scale with the constraint.

Capacity Bounds and High-SNR Capacity of MIMO Intensity-Modulation Optical Channels

The capacity of the intensity modulation direct detection multiple-input-multiple-output channel is studied. Therein, the nonnegativity constraint of the transmit signal limits the applicability of classical schemes, including precoding. Thus, new ways are required for deriving capacity bounds for this channel. To this end, capacity lower bounds are developed in this paper by deriving the achievable rates of two precoding-free schemes: channel inversion and orthogonal-upper triangular matrix product decomposition. The achievable rate of a dc-offset singular-value decomposition-based scheme is also derived as a benchmark. Then, capacity upper bounds are derived and compared against the lower bounds. As a result, the capacity at high signal-to-noise ratio (SNR) is characterized for the case where the number of transmit apertures is not larger than the number of receive apertures, and is shown to be achievable by the QR decomposition scheme. This is shown for a channel with average intensity or peak intensity constraints. Under both constraints, the high-SNR capacity is approximated within a small gap. Extensions to a channel with more transmit apertures than receive apertures are discussed, and capacity bounds for this case are derived.

Low-SNR Asymptotic Capacity of MIMO Optical Intensity Channels with Peak and Average Constraints

The low-SNR asymptotic capacity of the multiple-input multiple-output (MIMO) optical intensity channel is studied under both average and peak intensity constraints. We focus on low SNR, which can be modeled as the scenario where both constraints proportionally vanish, or where the peak constraint is held constant while the average constraint vanishes. A capacity upper bound is derived and is shown to be tight at low SNR under both scenarios. The capacity achieving input distribution at low SNR is shown to be a maximally correlated vector-binary input distribution. Consequently, the low-SNR capacity of the channel is characterized. As a byproduct, it is shown that for a channel with peak intensity constraints only, or with peak intensity constraints and individual (per aperture) average intensity constraints, a simple scheme composed of coded ON–OFF keying, spatial repetition, and maximum-ratio combining is optimal at low SNR.

Low-SNR Capacity of Parallel IM-DD Optical Wireless Channels

The capacity of parallel intensity-modulation and direct-detection optical wireless channels with total average intensity and per-channel peak intensity constraints is studied. The optimal intensity allocation at low signal-to-noise ratio (SNR) is derived, leading to the capacity-achieving ON–OFF keying distribution. Interestingly, while activating the strongest channel is optimal if 1) the peak intensity is fixed, this is not the case if 2) the peak intensity is proportional to the average intensity. The minimum average optical intensity per bit is also studied, and is characterized for case 1) where it is achievable at low SNR. However, in case 2), the average optical intensity per bit grows indefinitely as SNR decreases, indicating that lower optical intensity per bit can be achieved at moderate SNR than low SNR.

On the Capacity of the Intensity-Modulation Direct-Detection Optical Broadcast Channel

The capacity of the intensity-modulation direct-detection optical broadcast channel (OBC) is investigated, under both average and peak intensity constraints. An outer bound on the capacity region is derived by adapting Bergmans’ approach to the OBC. Inner bounds are derived by using superposition coding with either truncated-Gaussian (TG) distributions or discrete distributions. While the discrete distribution achieves higher rates, the TG distribution leads to a simpler representation of the achievable rate region. At high signal-to-noise ratio (SNR), it is shown that the TG distribution is nearly optimal. It achieves the symmetric-capacity within a constant gap (independent of SNR), which approaches half a bit as the number of users grows. It also achieves the capacity region within a constant gap. At low SNR, it is shown that on–off keying (OOK) with time-division multiple-access (TDMA) is optimal. This is interesting in practice since both OOK and TDMA have low complexity. At moderate SNR (typically [0,8] dB), a discrete distribution with a small alphabet size achieves fairly good performance.

Fundamental Limits of Parallel Optical Wireless Channels: Capacity Results and Outage Formulation

Multi-channel (MC) optical wireless communication (OWC) systems employing wave-division multiplexing for outdoors free-space optical communications, or multi-user time-division multiple access for indoors visible-light communications, e.g., can be modeled as parallel channels. Multi-input multi-output OWC systems can also be transformed, possibly with some performance loss, to parallel channels using pre-/post-coding. Studying the performance of such MC-OWC systems requires characterizing the capacity of the underlying parallel channels. In this paper, upper and lower bounds on the capacity of constant parallel OWC channels with a total average intensity constraint are derived. Then, this paper focuses on finding intensity allocations that maximize the lower bounds given channel-state information at the transmitter (CSIT). Due to its nonconvexity, the Karush–Kuhn–Tucker conditions are used to describe a list of candidate allocations. Instead searching exhaustively for the best solution, low-complexity near-optimal algorithms are proposed. The resulting optimized lower bound nearly coincides with capacity at high signal-to-noise ratio (SNR). Under a quasi-static channel model and in the absence of CSIT, outage probability upper and lower bounds are derived. Those bounds also meet at high SNR, thus characterizing the outage capacity in this regime. Finally, the results are extended to a system with both average and peak intensity constraints.