## Optimization of spot pattern in indoor diffuse optical wireless local area networks

Optics Express, Vol. 13, Issue 8, pp. 3000-3014 (2005)

http://dx.doi.org/10.1364/OPEX.13.003000

Acrobat PDF (395 KB)

### Abstract

In this paper, a simulated annealing (SA) algorithm is proposed to be used in the optimization of the spot pattern for the indoor diffuse optical wireless network application. The channel response is analyzed using conventional grid-based patterns and a field of view (FOV) of 30° is found to give a good performance balance in the uniformity of the received power distribution and multipath dispersion. Using the algorithm to determine the spot pattern for the minimum standard deviation of the received power, an improvement of more than 85% is realized. To optimize the spot pattern at 30° FOV, a merit function is incorporated into the algorithm for two parameters, and the SA algorithm is run to obtain optimized spot patterns for both a 4.5m and 6m extent of the spot pattern. Various weights are used, and a performance improvement of 39% and 78% is observed for the 4.5m and 6m spot pattern sizes respectively which shows that the approach can be used to effectively optimize the spot pattern in the indoor optical wireless application.

© 2005 Optical Society of America

## 1. Introduction

2. W. A. Arbaugh, “Wireless security is different,” Computer **36**, 99–101, (2003). [CrossRef]

3. F. R. Gfeller and U. H. Bapst, “Wireless in-house data communication via diffuse infrared radiation,” *Proc. IEEE* , **67**, 1474–1486, (1979). [CrossRef]

6. V. Jungnickel, T. Haustein, A. Forck, and C. von Helmolt, “155Mbit/s wireless transmission with imaging infrared receiver,” Electron. Lett. **37**, 314–315 (2001). [CrossRef]

7. G. W. Marsh and J. M. Kahn, “50-MB/s Diffuse Infrared Free-Space Link Using On-Off Keying With Decision-Feedback Equalization,” *IEEE* Photon. Technol. Lett. **6**, 168–1270, (1994). [CrossRef]

8. M. Karpipinen, K. Kataja, J.-T. Mäkinen, S. Juuso, H. J. Rajaniemi, P. Pääkkönen, J. Turunen, J. T. Rantala, and P. Karioja, “Wireless infrared data links: ray-trace simulations of diffuse channels and demonstration of diffractive element for multibeam transmitters,” Opt. Eng. **41**, 899–910, (2002). [CrossRef]

9. P. L. Eardley, D. R. Wisely, D. Wood, and P. McLee, “Holograms for optical wireless LANs,” Proc. IEE Optoelectron. **143**, 365–369, (1996). [CrossRef]

10. J. P. Yao, G. Chen, and T. K. Lim, “Holographic diffuser for diffuse infrared wireless home networking,” Opt. Eng. **42**, 317–324, (2003). [CrossRef]

11. M. Kavehrad and S. Jivkova, “Indoor broadband optical wireless communications: optical subsystems designs and their impact on channel characteristics,” IEEE Wireless Commun. **10**, 30–35, (2003). [CrossRef]

13. A. G. Al-Ghamdi and J. M. H. Elmirghani, “Analysis of diffuse optical wireless channels employing spot diffusing techniques, diversity receivers and combining schemes,” IEEE Tran. Commun. **52**, (2004), 1622–1631. [CrossRef]

14. Y.A. Alqudah and M. Kavehrad, “MIMO Characterization of Indoor Wireless Optical Link using a Diffuse-Transmission Configuration,” IEEE Tran. Commun , **51**, (2003), 1554–1560. [CrossRef]

15. J. B. Carruthers and J. M. Kahn, “Angle diversity for nondirected wireless infrared communications,” IEEE Trans. Commun. **48**, 960–969, (2000). [CrossRef]

## 2. Mathematical model and parameters

### 2.1 Mathematical Model

16. J. R. Barry, *Wireless Infrared Communications*, (Kluwer Academic Publishers, Norwell, 1994). [CrossRef]

*where n*is the Lambertian mode number of the source,

*ϕ*is the angle between the source normal and the line connecting the source to the receiver,

*dΩ*is the solid angle subtended by the receiver at the source,

*θ*is the angle between the receiver normal and the line connecting the receiver and the source,

*FOV*is the half-angle of the receiver

*FOV, r*is the distance between the source and the receiver, and c is the speed of light in a vacuum. The effective result of (1) is that the impulse response is simply a scaled and delayed delta Dirac function. By multiplexing the application of (1), the impulse response between a source and a receiver off any number of reflecting surfaces can be obtained.

*FOV*limits the number of paths reaching the receiver by ignoring paths whose angle at the receiver is more than

*FOV*.

### 2.2. Design Parameters

^{2}active area photodetector directed vertically at the ceiling is used. The transmitter was placed at the center of the room and directed vertically at the ceiling, with a total power of 1W directed into the diffusing spot patterns at the ceiling. The simulation is carried out in a ‘dark’ environment without any illumination from light sources or from windows. A metric to determine the performance of a wireless mobile network is the RMS delay spread,

*τ̄*=Σ

*P*(

*τ*)·

*τ*/Σ

*P*(

*τ*).

*τ*is the delay associated with the signal, relative to the first arriving signal,

*P*(

*τ*) is the associated power of the signal,

*τ*̄ is the mean delay spread, and

*Γ*. This data rate does not take into account equalization and other forms of signal conditioning which could be used to increase the data rate.

## 3. Conventional grid-based diffusing spot designs

### 3.1. Impulse Response Graphs

^{nd}order bounces from the walls to be received by the detector and thus the generally lower receiver power. The Lambertian pattern results in more signal power being received as the wider coverage of the pattern allows some of the 1

^{st}order signals from the ceiling to be reflected onto the detector. The highest power detected was when the ceiling was uniformly illuminated using Fig. 1(h), giving a substantially higher power as compared to the other patterns. This is due to the uniform illumination of the ceiling which increases the number of sources within the FOV. However, the tradeoff is that the impulse response is longer compared as to when other patterns are used. When the 10° FOV detector is placed at the room center, the limited FOV only allows 1

^{st}order signals from the ceiling to be received. As the 2×2 and 4×4 patterns do not have spots that are within the receiver FOV, no signal is received resulting in a lost connection at the center when these 2 patterns are used. When a single spot lies within the FOV, such as in the 10×10 design, a negligible delay spread results due to the restriction of multi-paths entering the detector. The greatest amount of power is received when a single spot is used. This is since all the power is concentrated within that single spot and when the single spot falls within the receiver FOV, a large contribution to the received power is from the direct path. However, a single spot is unsuitable for use due to the inherent susceptibility of the single spot transmitting pattern to LOS blocks and the relatively large amount of power contained within that single spot.

### 3.2 Survey of results

*σP*, is taken into consideration. From the earlier results, particularly at the narrower FOVs, certain positions may be unable to receive any signals if no sources, either 1

^{st}order from the ceiling or 2

^{nd}order from the walls falls, within the receiver FOV. This is particularly prevalent at the corners, which tend to suffer a sharp drop-off in power as compared to positions near the room centre. A low standard deviation relative to the average received power would imply that the signal power distribution throughout the receiving plane, in this case the floor, would be more uniform than a high relative standard deviation, and would reduce the drop-off at the corners. Furthermore, a more uniform signal distribution would simplify the design of the receiver electronics by reducing the required dynamic power range of the electronics. Also, the average of the RMS delay spread across all the detector positions,

*µ*is calculated to for the overall delay spread performance.

_{t}*µP*), standard deviation of the average received power (

*σ*), the average delay spread (

_{P}*µ*) and the standard deviation of the RMS delay spread across all the locations (

_{t}*σ*) are shown in Fig. 2(a), 2(b), 2(c) and 2(d). The receiver FOV has a large impact on the system performance. As the FOV is reduced, the number of multipaths reaching the detector is reduced, which reduces the delay spread, limiting multipath dispersion effects and increasing the possible data rates. However, the tradeoff is that with a reduction in FOV, few paths reaching the detector means that the average received signal power is also reduced accordingly. The smaller gradient in Fig. 3(a) between the 45° and 90° FOV can be attributed to the type of signals that are prevented from reaching the receiver. At 90°, as earlier mentioned, all signals reaching the detector are accepted. When the FOV is reduced to 45° however, the weaker 2

_{t}^{nd}order signals from the walls are rejected more than the stronger 1

^{st}order signals from the ceiling. For example, when the receiver is placed at the room centre, a 45° FOV describes a circle of radius 3m at the ceiling. Effectively this means only 1

^{st}order signals from the ceiling is accepted. When the FOV is increased to 90° at the same position, the additional power at the receiver is due to the acceptance of 2

^{nd}order signals from reflections off the room walls.

*σ*, with a variation of more than 50% of the standard deviation values, particularly at narrower FOVs. At an FOV value of 10°,

_{P}*σ*is as much as

_{P}*µ*. A large variation in received power implies that some locations are not receiving any signals. Although an extremely low delay spread of less than 1ns is possible at this FOV, alignment is needed for the spot distribution with the room size to ensure that the receiver is able to receive signals, which may be difficult to ensure practically. The single point and 2×2 spot patterns are clearly unsuitable for use at narrow FOVs as

_{P}*σ*is larger than

_{P}*µ*.

_{P}*σ*relative to

_{P}*µ*to be achieved. However, the tradeoff is a higher

_{P}*µ*due to a larger number of multipaths being allowed to reach the detector. A maximum RMS delay spread of 1.85ns is used as a cutoff value. Using a conservative estimate of 1/(10×

_{t}*σ*), this delay spread value gives a maximum data rate of approximately 54 Mbit/s. Use of equalizers and other communication techniques such as diversity can be used to increase the data rate further but this value will be used as a performance benchmark within the scope of this paper. From the graphs shown in Fig. 3(c), the maximum FOV within this benchmark is seen to be 30°.

_{τ}*σ*implies a larger variation in the delay spread performance. Furthermore, at 30°, the larger FOV results in a 100% increase in

_{t}*µ*as well as a lower

_{P}*σ*as observed from Fig. 3(a) and Fig. 3(b), with the tradeoff being a 20% increase in

_{P}*µ*. A larger FOV would also simplify the design of the spot pattern. Using a 20° FOV, for a detector placed at the corner to be able to see a spot, the spot must be less than 2.5m away from the corner. If a 30° FOV detector is used, the spot need only be less than 6.5m away from the corner, reducing the likelihood of a dropped link if the transmitter is offset from the centre. Based on the arguments given above it can be concluded that a receiver FOV of 30° would give a good balance of delay spread and signal power distribution performance.

_{t}*σ*, but at the expense of higher

_{P}*µ*and the lowest

_{t}*µ*. The 4×4 and 6×6 spot patterns result in the

_{P}*σ*, with the 4×4 pattern performing marginally better in terms of consistency when the ratio of the

_{P}*σ*over the

_{P}*µ*is determined.

_{P}## 4. Optimization of spot pattern

### 4.1. Simulated Annealing Technique

18. S. Kirkpatrick, C. D. Gerlatt Jr., and M. P. Vecchi, “Optimization by Simulated Annealing,” Science **220**, 671–680, (1983). [CrossRef] [PubMed]

*P*=

*exp*(-

*df/T*), where

*P*is the probability of accepting an undesired result

*df*, and

*T*is the current temperature. The technique uses a random search process. If a desired result is obtained, the technique accepts the change as the best obtained result. If an undesired result is obtained, that undesired result is accepted with a probability of

*P*. This avoids the algorithm from working on the assumption that the first minimum is the global minimum, as can be the case when a simple iterative minimization (IM) process is utilized, which simply only accepts desirable results with no probability of accepting undesired results. After a number of iterations,

*T*is reduced by a factor of 0.95 [19]. The initial temperature

*T*should result in an average acceptance probability

_{0}*χ*

_{0}of about 0.8 [20

20. S. Kirkpatrick, “Optimization by Simulated Annealing - Quantitative Studies,” J. Stat. Phys. **34**, 975–986, (1984). [CrossRef]

*df/ln(χ*

_{0}).

10. J. P. Yao, G. Chen, and T. K. Lim, “Holographic diffuser for diffuse infrared wireless home networking,” Opt. Eng. **42**, 317–324, (2003). [CrossRef]

*df*, where an undesired result may or may not be accepted depending on

*P*. The iterations are repeated till the end of one cycle, whereby the annealing temperature is reduced, and the cycle of iterations begins anew for the new temperature. The process can run till either no improvement can be observed or until a set number of cycles have been reached.

*σ*and the plots of the results for the IM and the SA methods are shown in Fig. 4, which plots the number of cycles required against the normalized

_{P}*σ*. On the plot for the IM approach, the minimum value is obtained after about 2300 cycles. The graph also reflects the hard optimization nature of the algorithm, which only moves downwards. From the plot of the graph obtained using the SA technique, there is a higher probability of accepting undesired results in the early cycles when the temperature is high. As the number of cycles increase, the temperature drops and the probability of accepting undesired results drops. The obtained standard deviation using the SA algorithm is an improvement of 19% over the IM approach. However, the tradeoff is that the SA algorithm requires approximately twice the computing time than the simpler IM method.

_{p}*σ*that can be achieved using the SA method, five runs were conducted using the various FOV values that were described in the earlier sections to obtain the specific pattern that gives the minimum

_{P}*σ*for each value of the receiver FOV. A comparison is made between the graphs of the conventional grid designs and the optimized results in Fig. 5, and the accompanying spot patterns are shown in Fig. 6. Using the SA technique, a reduction of the

_{P}*σ*by a factor of 7 can be achieved. It can be generally observed that this is achieved by having a higher spot density at the edges and corners rather than at the centre. However, the tradeoff is a slightly higher

_{P}*µ*than the conventional designs which is more apparent at the larger FOVs for 45° and 90°. At 30° FOV, the SA obtained pattern is still able to achieve a delay spread of 1.77ns, less than the benchmark of 1.85ns, still achieving a 93% reduction in the

_{t}*σ*below that of the conventional grid designs, and 87.5% reduction over the uniform illumination pattern.

_{P}### 4.2. Optimization of Spot Patterns at an FOV of 30°

*σ*only, the corresponding

_{P}*µ*was found to still be below the benchmark of 1.85ns. To determine the tradeoff between

_{t}*σ*and

_{P}*µ*at the 30° receiver FOV, another round of optimization was performed. Instead of optimizing for only one parameter, a merit function was assigned to the SA algorithm to take into account the optimization of

_{t}*µ*(W2) as well as

_{t}*σ*(W1). With a normalized total weight of 1.0, various combinations of weights for the two parameters can be run to obtain the spot patterns. The optimization was also performed for two sizes of the overall extent of the spot pattern. For the first size, the spot pattern was allowed to cover the entire ceiling surface and for the second spot size, the extent of the pattern was limited to only a 4.5m×4.5m extent, which is 56.25% of the total ceiling surface area. The 6m extent simulates an ideal condition in which the hologram pattern matches the size of the ceiling, while the 4.5m extent spot pattern simulates a hologram projection and ceiling size mismatch, as well as the extent of the conventionally sized grid holograms shown earlier. In Fig. 8, the obtained spot distributions using the SA algorithm for the various conditions are shown. Figure 7(a) shows the results for

_{P}*µ*and

_{P}*σ*on the same graph, and likewise, Fig. 7(b) shows

_{P}*µ*and

_{t}*σ*. In the graphs, the normalized weight for

_{t}*µ*is the complement of the described power standard deviation weight i.e. W1+W2=1. Results from the 4×4 and uniform spot patterns have also been included in the graphs to serve as a basis of comparison.

_{t}*µ*and

_{P}*σ*drop while

_{P}*µ*increases. This is because a larger weight is placed on the SA algorithm in optimizing

_{t}*σ*over the

_{P}*µ*, resulting in a tradeoff. By optimizing for a more uniform power distribution via emphasis on W1, the RMS delay spread is adversely affected since a greater number of multipath signals reach the detector and this is evident from the graphs. The drop in

_{t}*σ*with the increase in W1 also shows that a more consistent delay spread performance is achieved. When the system is optimized for a higher value of W2, a delay spread of less than 1ns is obtained. However, the high

_{t}*σ*relative to the low average RMS delay spread implies a large variation in the actual delay spread values, which may be undesirable. It is also observed from the graphs that the extent of the size of the spot pattern affects the obtained results. When the spot pattern is limited to an area of 4.5m×4.5m, there is a drop in the metrics for the received power by a factor of at least 2.5 as compared to the larger spot pattern. Although the smaller pattern is also able to achieve a better delay spread performance, the relatively higher

_{t}*σ*also indicates a larger variation in the delay spread performance.

_{t}*R*is defined as

_{P}*σ*over

_{P}*µ*, and

_{P}*R*is defined as

_{t}*σ*over

_{t}*µ*, and the graphs are shown in Fig. 9. For the 4.5m x 4.5m sized spot pattern the spot pattern obtained that optimized only

_{t}*σ*gives the best performance of the other results in terms of the ratio i.e. the consistency of the performance of the system. When compared to the 4×4 spot pattern, it is interesting to note that the absolute results are 6.5% more and 1.3% more for the

_{P}*µ*and

_{P}*µ*respectively, use of the SA algorithm has reduced the

_{t}*R*and

_{P}*R*by a factor 39% and 23% respectively. Furthermore, in comparison with the results from the uniform signal power distribution, it is observed that the performance is similar with respect to both absolute and relative values. However, while the uniform pattern required illumination of the entire ceiling, the 4.5m×4.5m pattern only required illumination of 56.25% of the room ceiling. For the 6m×6m sized pattern, a value of 0.15 for W1 reduces

_{t}*R*by more than 78% as compared to the 4×4 pattern, while still maintaining a comparable absolute and relative RMS delay spread performance. The higher uniformity of the signal power results is due to the larger extent of the spot distribution, and it can be observed that the optimized spot patterns has a high concentration of spots at the corner to compensate for the lower corner power. In comparing the optimized pattern for the 6m extent with the uniform illumination pattern, it is observed when W1=1,

_{P}*R*and

_{P}*R*are less than that of uniform illumination pattern by 79% and 14% respectively, with the tradeoff being a 4.7% increase in the average delay spread.

_{t}### 4.3 Analysis when spot pattern is not centered on the ceiling

### 4.4. Q-factor and Bit Error Rate performance

20. S. Kirkpatrick, “Optimization by Simulated Annealing - Quantitative Studies,” J. Stat. Phys. **34**, 975–986, (1984). [CrossRef]

_{on}-I

_{off})/(σ

_{on}-σ

_{off}), where I

_{state}refers to the signal current in the ON or OFF state, and σ

_{state}refers to the sum of the shot noise and thermal noise in the ON or OFF state, the corresponding bit error rate (BER) can be found from expression BER=0.5erfc(Q/√2). In this model, it is taken that there is no received power in the OFF state. Furthermore, the shot noise current due to ambient lighting is taken to be 25dB more than the corresponding signal noise current [15

15. J. B. Carruthers and J. M. Kahn, “Angle diversity for nondirected wireless infrared communications,” IEEE Trans. Commun. **48**, 960–969, (2000). [CrossRef]

_{on}=σ

_{off}. The results of the BER analysis for the optimized pattern for W1=1 is shown in Fig. 12. For the purposes of calculation of the noise, the data rate is taken as 155Mbits/s.

^{-6}, with more than 90% having a BER value of less than 5×10

^{-6}. The highest obtained BER is 10

^{-5}. The system performance can be further improved by using multiple receiver branches in a diversity scheme to increase the signal to noise ratio and the corresponding BER, though at the cost of increased system complexity. [14

14. Y.A. Alqudah and M. Kavehrad, “MIMO Characterization of Indoor Wireless Optical Link using a Diffuse-Transmission Configuration,” IEEE Tran. Commun , **51**, (2003), 1554–1560. [CrossRef]

## 5. Discussion

## 6. Conclusions

## References and links

1. | O. Kyas and G. Crawford, |

2. | W. A. Arbaugh, “Wireless security is different,” Computer |

3. | F. R. Gfeller and U. H. Bapst, “Wireless in-house data communication via diffuse infrared radiation,” |

4. | D. Heatley and I. Neild, “Optical wireless — the promise and the reality,” |

5. | K. Akhavan, M. Kavehrad, and S. Jivkova, “Wireless Infrared In-House Communications: How to Achieve Very High Bit Rates,” |

6. | V. Jungnickel, T. Haustein, A. Forck, and C. von Helmolt, “155Mbit/s wireless transmission with imaging infrared receiver,” Electron. Lett. |

7. | G. W. Marsh and J. M. Kahn, “50-MB/s Diffuse Infrared Free-Space Link Using On-Off Keying With Decision-Feedback Equalization,” |

8. | M. Karpipinen, K. Kataja, J.-T. Mäkinen, S. Juuso, H. J. Rajaniemi, P. Pääkkönen, J. Turunen, J. T. Rantala, and P. Karioja, “Wireless infrared data links: ray-trace simulations of diffuse channels and demonstration of diffractive element for multibeam transmitters,” Opt. Eng. |

9. | P. L. Eardley, D. R. Wisely, D. Wood, and P. McLee, “Holograms for optical wireless LANs,” Proc. IEE Optoelectron. |

10. | J. P. Yao, G. Chen, and T. K. Lim, “Holographic diffuser for diffuse infrared wireless home networking,” Opt. Eng. |

11. | M. Kavehrad and S. Jivkova, “Indoor broadband optical wireless communications: optical subsystems designs and their impact on channel characteristics,” IEEE Wireless Commun. |

12. | Y. Alqudah and M. Kavehrad, “Assessing the feasibility of new diffused configuration for broadband wireless infrared links,” |

13. | A. G. Al-Ghamdi and J. M. H. Elmirghani, “Analysis of diffuse optical wireless channels employing spot diffusing techniques, diversity receivers and combining schemes,” IEEE Tran. Commun. |

14. | Y.A. Alqudah and M. Kavehrad, “MIMO Characterization of Indoor Wireless Optical Link using a Diffuse-Transmission Configuration,” IEEE Tran. Commun , |

15. | J. B. Carruthers and J. M. Kahn, “Angle diversity for nondirected wireless infrared communications,” IEEE Trans. Commun. |

16. | J. R. Barry, |

17. | T. S. Rappaport, |

18. | S. Kirkpatrick, C. D. Gerlatt Jr., and M. P. Vecchi, “Optimization by Simulated Annealing,” Science |

19. | S. Kirkpatrick, C. D. Gerlatt Jr., and M. P. Vecchi, “Optimization by Simulated Annealing,” IBM Research Report RC 9355, (1982). |

20. | S. Kirkpatrick, “Optimization by Simulated Annealing - Quantitative Studies,” J. Stat. Phys. |

21. | G. Keiser, |

**OCIS Codes**

(060.4250) Fiber optics and optical communications : Networks

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 19, 2005

Revised Manuscript: March 27, 2005

Published: April 18, 2005

**Citation**

Damon W. K. Wong, George Chen, and Jianping Yao, "Optimization of spot pattern in indoor diffuse optical wireless local area networks," Opt. Express **13**, 3000-3014 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-8-3000

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### References

- O. Kyas and G. Crawford, ATM Networks, (Prentice-Hall, Upper Saddle River, 2002).
- W.A.Arbaugh, �??Wireless security is different,�?? Computer 36, 99-101, (2003). [CrossRef]
- F. R. Gfeller and U. H. Bapst, �??Wireless in-house data communication via diffuse infrared radiation,�?? Proc. IEEE, 67, 1474�??1486, (1979). [CrossRef]
- D. Heatley and I. Neild, �??Optical wireless �?? the promise and the reality,�?? in Proceedings of the IEE Colloquium on Optical Wireless Communications, (Institute of Electrical Engineers, London, 1999), 1/1-1/6.
- K. Akhavan, M. Kavehrad and S. Jivkova, �??Wireless Infrared In-House Communications: How to Achieve Very High Bit Rates,�?? in Proceedings of IEEE Conference on Wireless Communications and Networking, (Institute of Electrical and Electronics Engineers, New York, 2000), 698- 703.
- V. Jungnickel, T. Haustein, A. Forck and C. von Helmolt, �??155Mbit/s wireless transmission with imaging infrared receiver,�?? Electron. Lett. 37, 314-315 (2001). [CrossRef]
- G. W. Marsh and J. M. Kahn, �??50-MB/s Diffuse Infrared Free-Space Link Using On-Off Keying With Decision-Feedback Equalization,�?? IEEE Photon. Technol. Lett. 6, 168-1270, (1994). [CrossRef]
- M. Karpipinen, K. Kataja, J.-T. Mäkinen, S. Juuso, H. J. Rajaniemi, P. Pääkkönen, J. Turunen, J. T. Rantala and P. Karioja, �??Wireless infrared data links: ray-trace simulations of diffuse channels and demonstration of diffractive element for multibeam transmitters,�?? Opt. Eng. 41, 899-910, (2002). [CrossRef]
- P. L. Eardley, D. R. Wisely, D. Wood and P. McLee, �??Holograms for optical wireless LANs,�?? Proc. IEE Optoelectron. 143, 365-369, (1996). [CrossRef]
- J. P. Yao, G. Chen and T. K. Lim, "Holographic diffuser for diffuse infrared wireless home networking," Opt. Eng. 42, 317-324, (2003). [CrossRef]
- M. Kavehrad and S. Jivkova, �??Indoor broadband optical wireless communications: optical subsystems designs and their impact on channel characteristics,�?? IEEE Wireless Commun. 10, 30-35, (2003). [CrossRef]
- Y. Alqudah and M. Kavehrad, �??Assessing the feasibility of new diffused configuration for broadband wireless infrared links,�?? Proceedings of the IEEE Conference on Wireless Communications and Networking, 1, (Institute of Electrical and Electronic Engineers, New York, 2003), 673-677.
- A. G. Al-Ghamdi and J. M. H. Elmirghani, �??Analysis of diffuse optical wireless channels employing spot-diffusing techniques, diversity receivers and combining schemes,�?? IEEE Tran. Commun. 52, (2004), 1622-1631. [CrossRef]
- Y.A. Alqudah and M. Kavehrad, �??MIMO Characterization of Indoor Wireless Optical Link using a Diffuse-Transmission Configuration,�?? IEEE Tran. Commun. 51, (2003), 1554-1560. [CrossRef]
- J. B. Carruthers and J. M. Kahn, �??Angle diversity for nondirected wireless infrared communications,�?? IEEE Trans. Commun. 48, 960-969, (2000). [CrossRef]
- J. R. Barry, Wireless Infrared Communications, (Kluwer Academic Publishers, Norwell, 1994). [CrossRef]
- T. S. Rappaport, Wireless Communications, Principles and Practices, (Prentice-Hall, Upper Saddle River, 2002).
- S. Kirkpatrick, C. D. Jr. Gerlatt, and M. P. Vecchi, �??Optimization by Simulated Annealing,�?? Science 220, 671-680, (1983). [CrossRef] [PubMed]
- S. Kirkpatrick, C. D. Jr. Gerlatt, and M. P. Vecchi, �??Optimization by Simulated Annealing,�?? IBM Research Report RC 9355, (1982).
- S. Kirkpatrick, �??Optimization by Simulated Annealing - Quantitative Studies,�?? J. Stat. Phys. 34, 975-986, (1984). [CrossRef]
- G. Keiser, Optical Fiber Communications, (McGraw-Hill, New York, 2000).

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