Capacity Bounds and Interference Management for Interference Channel in Visible Light Communication

Capacity Bounds and Interference Management for Interference Channel in Visible Light Communication Networks

Abstract: In this paper, we investigate channel capacity region of interference channel and develop both centralized and distributed interference management schemes for visible light communication networks. For a typical multiuser and multi- LED scenario, we derive both discrete inner and outer bounds of channel capacity region, and such proposed inner bound is numerically shown to be the highest among the existing inner bounds. Moreover, with the continuous input signals, we develop the channel capacity region bounds in closed-form, termed(ABG) inner bound and ABG outer bound, which are tight for the large amplitude-to-variance ratio. Then, based on the derived ABG inner bounds, we investigate a centralized beam forming design problem to minimize the total transmit power, under three practical constraints: peak optical power, average optical power, and average electrical power. By utilizing semi definite relaxation technique, we reformulate this NP-hard problem as a convex semi definite program, and obtain the optimal beam formers. Furthermore, to reduce the cost of channel station information exchange, we propose a distributed coordinated interference management scheme by adopting the alternating direction method of multipliers method. Finally,

numerical results are presented to evaluate the performance of the proposed interference management schemes in visible light communication networks.

Existing system: The aforementioned characteristics of VLC systems impose tremendous challenges on pursuing the capacity region of IC. So far, a great many of efforts have been made on studying the channel capacity and interference management for VLC networks. However, most existing works focus on the point to- point channel or broadcast channel (BC) , while IC is not well addressed. For the most typical point-to-point channels, the closed-form expression of channel capacity is yet unknown. In, the author proved that the optimal input of the point-to-point channels is a finite set of discrete points, but it needs the exhaustive search to find the optimal discrete points and the computational complexity.

Proposed system: In this paper, we investigate the capacity region of IC for VLC networks under peak optical power, average optical power and electrical power constraints.

Furthermore, we seek to find efficient inference management scheme under practical setups. To the best of our knowledge, the proposed inner and outer bounds are the first theoretical bounds of channel capacity region for VLC IC networks. Then, based on the proposed closed-form expression, we further propose interference management schemes for multi-LED VLC IC networks. The main contributions of this paper are summarized as follows: First, we derive both discrete inner and outer bounds of the channel capacity region for multi-user multiLED VLC IC of IC networks.

Advantages: Comparing to the radio frequency (RF), visible light has many advantages for indoor communication, such as huge available unlicensed bandwidth, no electromagnetic radiation, secure data transmission, and etc.

However, at the current stage, there are many fundamental issues that need to be resolved, where identifying the channel capacity region for the interference channel (IC) is one of the open problems.

Disadvantages: As a common multiuser communication scenario, IC is one the most important building blocks in wireless networks, where multiple transmitters communicate with their individual receivers while introduce interference on other receivers at the same time.

Note that even for RF, the IC capacity region is still a well-known open problem, and Shannon formula is only an approximation for achievable rate under the assumption that both input signal and interference follow Gaussian distributions.

However, the Shannon formula cannot be directly applied in VLC networks due to the unique features of VLC systems.

Modules: Visible light communication: With the ever-increasing spectrum demand for high data rate wireless communications, visible light communication (VLC), as a promising supplementary for traditional radio frequency (RF) communications in the future indoor wireless networking , has recently attracted great interests from both industry and academia. Comparing to the radio frequency (RF), visible light has many advantages for indoor communication, such as huge available unlicensed bandwidth, no electromagnetic radiation, secure data transmission, and etc.

However, at the current stage, there are many fundamental issues that need to be resolved, where identifying the channel capacity region for the interference channel (IC) is one of the open problems.

Intensity modulation and direct detection: As a common multiuser communication scenario, IC is one the most important building blocks in wireless networks, where multiple transmitters communicate with their individual receivers while introduce interference on other receivers at the same time. Note that even for RF, the IC capacity region is still a well-known open problem, and Shannon formula is only an approximation for achievable rate under the assumption that both input signal and interference follow Gaussian distributions. However, the Shannon formula cannot be directly applied in VLC networks due to the unique features of VLC systems. VLC adopts the intensity

modulation and direct detection (IM/DD) mechanism for information transfer.

Hence, unlike RF networks, the input signal of VLC is uni polar and non-negative.

Besides, the VLC system also needs to account the issues about eye safety and light brightness. Thus, both the peak and average optical power of VLC signal should meet certain requirement. Moreover, the electrical power of VLC signal is also constrained due to the electrical circuit limitations. The aforementioned characteristics of VLC systems impose tremendous challenges on pursuing the capacity region of IC. Minimum mean square error: As to the VLC IC, both the channel capacity region and the optimal input distribution are still open problems, which are the main bottlenecks for interference management. Currently, there are roughly two approaches for interference management for VLC IC networks: 1) the minimum mean square errors (MMSE) approach, in which the pre coders is designed to minimize the sum MMSE and approximate channel capacity formula approach, in which the power minimization problem or sum-rate maximization problem is investigated based on the approximate channel capacity formula. However, there are two main issues in existing approaches. The first issue is that the interference of VLC IC networks in is handled by adopting the classic Shannon capacity formula as the achievable rate expression. However, as discussed above, the Shannon capacity formula with Gaussian input does not fit for VLC networks. The second issue is that the approximate channel capacity formula in is derived only under the constraints of peak and average optical power while without average electrical power, and the input signal is assumed to follow uniform distribution.

Alternating direction method of multiplier: This problem is shown to be NP-hard. We reformulate this problem as a convex semi definite program (SDP) by using the semi definite relaxation (SDR) technique, which is proved to be tight for the original problem. Moreover, we develop a distributed coordinated beam former by adopting the alternating direction method of multiplier (ADMM) method, which does not need the central controller and significantly reduces the exchange of channel state information (CSI) of users. Note that, the capacity regions of the point-to-point channel and the

BC are derived in previous work, where the input signal follows the continuous distribution: the ABG distribution. Since IC is a typical communication scenario in multi-user multi-cell networks, we in this paper focus on both the channel capacity region and interference management schemes for the VLC IC networks, where we characterize the channel capacity region of VLC IC based on both the discrete and the continuous input distributions, respectively.