Average Intensity Constraint Research Articles

Distribution Decomposition and Sum-Capacity Results of Two-User Optical Intensity Multiple Access Channels

This paper investigates the sum-capacity of two-user optical intensity multiple access channels with per-user peak-or/ and average-intensity constraints. By leveraging tools from the decomposition of certain distributions, we derive several lower bounds on the sum-capacity. In the high signal-to-noise ratio (SNR) regime, some bounds asymptotically match or approach the sum-capacity, thus closing or reducing the existing gaps to the high-SNR asymptotic sum-capacity. At moderate SNR, some bounds are also fairly close to the sum-capacity.

On the Capacity of MISO Optical Intensity Channels With Per-Antenna Intensity Constraints

This paper investigates the capacity of general multiple-input single-output (MISO) optical intensity channels (OICs) under per-antenna peak- and average-intensity constraints. We first consider the MISO equal-cost constrained OIC (EC-OIC), where, apart from the peak-intensity constraint, average intensities of inputs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equal to</i> arbitrarily preassigned constants. The second model of our interest is the MISO bounded-cost constrained OIC (BC-OIC), where, as compared with the EC-OIC, average intensities of inputs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">no larger than</i> arbitrarily preassigned constants. By leveraging tools from quantile functions, stop-loss transform and convex ordering of nonnegative random variables, we prove two decomposition theorems for bounded and nonnegative random variables, based on which we equivalently transform both the EC-OIC and the BC-OIC into respective single-input single-output channels under a peak-intensity and several stop-loss mean constraints. Capacity lower and upper bounds for both channels are established, based on which the asymptotic capacity at high and low signal-to-noise-ratio are determined.

Capacity and Optimum Signal Constellations for VLC Systems

In this article, the capacity of the point-to-point VLC system is investigated by means of a functional analysis subjected to amplitude constraint and average intensity constraint. It is proved that the capacity can be achieved by a unique probability density function (PDF). The necessary and sufficient condition for the capacity-achieving PDF is derived by the functional optimization theorem. Moreover, the capacity-achieving PDF is proved to be discrete and finite. Based on these properties, the capacity-achieving constellation optimization problems under amplitude constraint and average intensity constraint is formulated and an algorithm is proposed to solve the corresponding problem. To apply simple adaptive modulation in practical VLC systems, constellation optimization problem subject to an additional equal probability constraint is formulated and solved by maximizing the mutual information as well.

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.

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.

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.

Free-Space Optical Communications: Capacity Bounds, Approximations, and a New Sphere-Packing Perspective

The capacity of the free-space optical channel is studied. A new recursive approach for bounding the capacity of the channel based on sphere-packing is proposed. This approach leads to new capacity upper bounds for a channel with a peak intensity constraint or an average intensity constraint. Under an average constraint only, the derived bound is tighter than an existing sphere-packing bound derived earlier by Farid and Hranilovic. The achievable rate of a truncated-Gaussian input distribution is also derived. It is shown that under both average and peak constraints, this achievable rate and the sphere-packing bounds are within a small gap at high SNR, leading to a simple high-SNR capacity approximation. Simple fitting functions that capture the best known achievable rate for the channel are provided. These functions can be of practical importance especially for the study of systems operating under atmospheric turbulence and misalignment conditions.

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.