Power allocation is performed by maximizing the signal-to-noise ratio (SNR) metric at the output of the photodetector. The term BER is used to estimate the cost of a VLC system in terms of the number of LEDs required for optimal system performance.
Introduction
Related Work
To address this, recent literature has focused on power allocation along with flexibility in the LED source geometry to achieve uniform irradiation. An optimal LED arrangement to achieve uniform irradiation is investigated as a convex optimization problem in [22].
Research Contributions of This Thesis
Some of the above literature has focused on a regular geometry with equal power distribution for individual LED sources. In [5], a genetic algorithm is proposed to optimize the refractive indices of the concentrators in the receiver to achieve a uniform distribution of the received power.
Thesis Organization
We present the BER performance analysis of circle-square BPP and compare it with square BPP. While maintaining uniformity, the cost of the system can be reduced when arbitrary geometries are used.
Operation of Visible Light Communication Sys- tem
- Propagation of Light from LED
- Transmitters
- Receivers
The LEDs are chosen as the emitters or light sources in VLC because of the above advantages. In the case of mobility, the image sensor can be used in place of a photodiode due to its larger field of view (FOV).
Trans-receiver Model
- Noise at the photo-detector
- Modulation technique
- Detection technique
All LEDs are located vertically in the plane where the photodetector is placed. The noise in the photodetector is the sum of the contributions from the shot noise and the thermal noise, and expressed as [26].
Point process
- Square BPP
- Circular BPP
- Matern process of type II
Although the BPP process captures the uniform distribution of LEDs, any realization of the process can result in two LEDs in the same location, leading to high interference. In this point process, points are generated from a stationary parent Poisson point process (PPP) with intensity λppp and a random marker is associated with each point, and a point is removed from the parent Poisson process if another point exists within the hard point process. core distance δ with a smaller marker.
Performance metric
Recent research in LED-based VLC system has focused on achieving uniform irradiance over a planar surface with the aim of finding the optimal LED geometry at the light source to achieve uniform irradiance [4]. There is also a fair amount of focus on achieving uniform irradiance with a regular geometry with equal power allocation to individual LED sources [1-3, 12]. To address this, recent research has focused on power allocation, along with flexibility in the LED source geometry to achieve uniform irradiance.
To achieve this, various power allocation schemes have been proposed to achieve uniform radiation for visible light communication (VLC) applications. For example, a trial-and-error approach for power allocation for uniform radiation is used in [21] for a combination of circular-square geometry to illuminate the edges of the incident surface. In [5], a genetic algorithm is proposed to optimize the refractive indices of the concentrators on receivers to obtain a uniform distribution.
The optimization of the location of an irregular LED array for uniform radiation is discussed in [7, 23].
Cost-effective approach to achieve uniform il- lumination
Power allocation for a BPP array
- Algorithm for optimal α
The heuristic in (3.1) makes the power allocation sub-optimal. 3.2) where EΦ is the expectation with respect to the BPP.
Results
The SNR profile for N = 64 for two different BPP realizations with sub-optimal power distribution is given in Fig. 3.8, it is clear that the heuristic power allocation scheme in (3.1) results in a uniform SNR profile. Also, the FΛ value in Table 3.2 for the BPP in Fig. 3.1c is approximate to that of the circle-square array in Fig. Equal power Optimal power Equal power Proposed heuristics. that the PBB with even suboptimal power distribution performs as well as a fixed geometry with optimal power distribution.
A significant amount of research has recently been conducted on the use of traditional light sources for wireless communications. The angular diversity is obtained by placing multiple photodetectors on a receiver node with a curved surface [32].
Modeling light sources using stochastic geom- etry
Since each realization of a random geometry gives different SNR profiles, we look at an average SNR profile and BER. In [25], a heuristic power allocation was proposed and an average SNR was evaluated by calculating the average SNR of each realization over the BPP. For a stochastic geometry, the average BER is calculated by computing the average BER of each realization over the BPP process Φ, EΦ[Q(√).
The average BER for stochastic geometry appears to be close to that for a fixed geometry, indicating that stochastic geometry can be used for modeling a VLC and the average BER of a BPP can be used for estimating system parameters. In [25] the power allocation ensures the uniform illumination in the average sense, it would be interesting to find the optimal power allocation for a single realization of a random geometry. For a square BPP, which is the most suitable stochastic model for an indoor environment, an expression for the average asymptotic BER is obtained.
In [25], a heuristic power allocation scheme was proposed for a BPP-VLC and shown to provide uniform radiation on average.
Power Allocation for a BPP array
To include uniform radiation in the VLC model in this paper, the same scheme is considered and described in the next section.
BER Analysis
Asymptotic BER
Since n0 is AWGN, the conditional BER for the BPP can be obtained from (4.6) as Pe =Q RC1PN.
Results
Circular BPP with Power Allocation Circular BPP with Equal Power Square Array with Power Allocation Square Array with Equal Power. The shape of the simulated BER curves for circular and square geometries is also similar. Thus, the closed form BER expression for the asymptotic BER can be used to estimate the cost of the system in terms of the number of LEDs.
Appendix
- Proof for asymptotic BER
- Derivation of E Φ [V i ]
For a BPP distributed over a square area of region A, the pdf is of the distance to the i-th nearest node from the origin [28]. The asymptotic BER performance of square BPP and circular BPP has been analyzed in the previous chapter. Such cases can be modeled by approximating the square BPP with multiple non-overlapping circles.
In this chapter, the BER performance analysis of squared GDP and compared to squared GDP is presented.
CDF and PDF of distance distribution
BER Analysis
Results
As expected, the round-square geometry mimics the square geometry, both in terms of SNR and BER profile. It is clear from the figure that after N = 20, the BER performance is close to the asymptotic BER.
Appendix
- Proof for the CDF of Circle-square BPP
- Proof for Circle-square BPP
The expectation of the variable Vi must be estimated to derive the error probability Pe. In existing VLC systems, uniform illumination is achieved by finding the highest order partial derivatives of the received power at a point close to the origin and equal to zero [1, 2]. While a stochastic model based on a binomial point process (BPP) is a powerful resource allocation tool for VLC, it is useful to consider power allocation for a VLC based on a single realization of a stochastic point process .
Here, a Matern type II hard-core point process (HCPP) is desirable, as it accounts for minimum separation between two LEDs for better coverage. This allows the realizations of the point process to be more uniformly distributed than BPP. We have found that an appropriate power allocation for a random arrangement of the source LEDs in the BPP results in uniform illuminance in an average sense.
Optimal power distribution between light sources for uniform illumination for one point process realization is an important problem in VLC.
Problem Definition
Optimum Power Allocation
Results
It can be solved numerically by quadratic programming (QP) with the solvers.qp command using the CVXOPT solver in Python. It can be seen from Tables 6.2 and 6.3, the variance and quality factor of the realization of the HCPP model with 13 LED sources is close to the realization with 16 LEDs, thus reducing the system cost. We can see that the quality factor saturates as the number of source LEDs increases.
For an ideal VLC system, high quality factor should be achieved with the least number of source LEDs. For example, at the threshold value of 0.016, the quality factor is 14.02 and close to the saturated value.
Appendix
- Formulation of optimization problem
The total power of the LEDs is P watts, which is distributed among the source LEDs.
Conclusion
Future Research
As an immediate extension of the work, the performance of VLC in terms of BER when using HCPP for modeling LED arrangement would be a challenging problem. To solve this, we need to find the nth LED distribution from the origin. There are few practical challenges such as Non-line of sight (NLOS), modulation techniques, channel equalization, which are not considered in this dissertation.
Praneeth Varma, “Optimal power allocation for uniform illuminance in visible light communications,” in Proc. Some of the interesting mathematical results obtained during the course of this dissertation are presented here in this chapter. These theorems are relevant to stochastic geometry and are likely to be useful for research in this area of applied mathematics.
Distance distributions of square BPP
- Calculating g(r)
Finding the distribution from any random point is the same as finding the distribution of its projection in the first quadrant.
Approximations in stochastic geometry
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