3. Proposed systems' configurations

A CDS and non-adaptive LSMS are two widely studied configurations in the literature; therefore, they are modelled and used for comparison purposes in order to evaluate the improvements offered through the proposed configurations. More information about CDS and LSMS system can be found in Refs. [9–11].

#### 3.1. FAPA-hologram

higher reflections are highly attenuated [10, 11]. Hence, two bounces are considered in our calculations. All the proposed systems use an upright transmitter with 1 W optical power. Furthermore, the significant signal to noise ratio (SNR) improvement of the hologramproposed systems is used to reduce the transmit power to 80 mW reducing the power density

In OW communication links, intensity modulation with direct detection (IM/DD) is considered the most viable approach. The indoor OW IM/DD channel can be fully specified by its impulse

<sup>m</sup>¼<sup>1</sup> Rxðt<sup>Þ</sup> <sup>⊗</sup> hmðt, Az, ElÞ þX<sup>M</sup>

where I(t, Az, El) is the current instantaneous due to m reflecting elements, El and Az are the directions of arrival in the elevation and azimuth angles, t is the absolute time, x(t) is the optical power transmitted, ⊗ denotes convolution, M is the total number of receiving elements, R is the photodetector responsivity and n(t, Az, El) is the background noise. The delay spread is a good tool to measure signal spread due to multipath propagation. The delay spread can be

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

= <sup>X</sup> ∀i P2 ri

ðti � μÞ 2 P2 ri

where the time delay ti is associated with the received power Pri (Pri reflects the impulse

The delay spared is deterministic for a given stationary transmitter-receiver and reflecting elements' positions. The delay spread can change for a given transmitter-receiver location when the reflecting elements moves or an object is entering and leaving the environment. However, the impact of such a change is not considered in this work and has not been

The SNR of the received signal can be calculated by taking into account the powers associated

SNR <sup>¼</sup> <sup>R</sup>ðPs<sup>1</sup> � Ps0<sup>Þ</sup>

σ<sup>0</sup> þ σ<sup>1</sup> � �<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

bn <sup>þ</sup> <sup>σ</sup><sup>2</sup> s1

<sup>s</sup><sup>0</sup> and σ<sup>2</sup>

σ2 pr <sup>þ</sup> <sup>σ</sup><sup>2</sup>

q

and σ<sup>1</sup> ¼

pr represents the receiver noise, which is a function of the design used for the pream-

� �

<sup>m</sup>¼<sup>1</sup> Rnðt, Az, ElÞ: <sup>ð</sup>1<sup>Þ</sup>

: ð3Þ

ð2Þ

ð4Þ

ð5Þ

<sup>s</sup><sup>1</sup> represent the shot

response h(t), and it can be modelled as a baseband linear system given by

on the adaptive hologram and helping eye safety.

128 Optical Fiber and Wireless Communications

<sup>I</sup>ðt, Az, ElÞ ¼ <sup>X</sup><sup>M</sup>

DS ¼

response h(t) behaviour) and μ is the mean delay given by

X ∀i

<sup>μ</sup> <sup>¼</sup> <sup>X</sup> ∀i tiP<sup>2</sup> ri = <sup>X</sup> ∀i P2 ri

with logic 0 and logic 1 (PS<sup>0</sup> and PS1), respectively. The SNR is given by [14]:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

bn represents the background shot noise component and σ<sup>2</sup>

bn <sup>þ</sup> <sup>σ</sup><sup>2</sup> s0

σ2 pr <sup>þ</sup> <sup>σ</sup><sup>2</sup>

q

r

written as [12, 13]:

investigated by other researchers.

where σ<sup>2</sup>

plifier; σ<sup>2</sup>

σ<sup>0</sup> ¼

Power adaptation and beam angle can be considered as an effective approach, which helps to have an optimum power allocation and distribution of the diffusing spots. A single spot is produced by the adaptive transmitter to scan the ceiling and walls at approximately 8000 possible locations (2.86 beam angle increment [3]) in order to identify the best location. A liquid crystal device (IR hologram) is used to change the spot location at each step. Power adaptation technique can be used with angle adaptation to further enhance signal to noise ratio. The transmitter switches spots one by one and the receiver calculates the SNR (weight) associated with each spot. Then the feedback signal is sent by receiver at a low data rate to inform the transmitter about the SNR associated with each spot. The transmitter re-distributes the power among the spots based on their SNR weights [1] .The transmitter generates the hologram after finding optimum angles and power levels of spots. Intensive calculations and time are required from a digital signal processor (DSP). An adaptation approach is proposed where a finite vocabulary of stored holograms is used in order to get rid of computing the holograms at each step to identify the best location. The ceiling is divided into 80 regions (0.4 m 1m per region), see Figure 2. This large number of regions has been selected based on our recent optimisation in Ref. [17].


Table 1. Parameters used in simulation.

Holograms generated by means of a computer can produce spots with any prescribed amplitude and phase distribution. For FAPA-Holograms, all the spots have different weights (powers) and different phases. CGHs have many useful properties. Spot distributions can be computed on the

Figure 2. OW communication architecture of FAPA-Hologram system.

Holograms generated by means of a computer can produce spots with any prescribed amplitude and phase distribution. For FAPA-Holograms, all the spots have different weights (powers) and different phases. CGHs have many useful properties. Spot distributions can be computed on the

Bandwidth (BW) 50 MHz 2.5 GHz 5 GHz Bit rate 50 Mbit/s 2.5 Gbit/s 5 Gbit/s

(3,1,1), (3,3,1), (3,5,1), (3,7,1)

Parameter Configuration

130 Optical Fiber and Wireless Communications

Transmitter

Location (x, y, z) (1,1,1),(1,2,1),(1,3,1,),(1,4,1),(1,5,1),(1,6,1),(1,7,1)

Resolution

Number-of-spot lamps 8

Wavelength 850 nm

Location (x,y,z) (1 m, 1 m, 1 m) (2 m, 7 m,1 m)

Elevation 90 65 65 65 65 65 65 65 65 Azimuth 0 0 45 90 135 180 225 270 315

Time bin duration 0.5 ns 0.01 ns Bounces 1 2 Surface elements 32,000 2000

Preamplifier design PIN-BJT PIN-FET

Locations (1,1,1), (1,3,1), (1,5,1), (1,7,1)

Quantity 1

Elevation 90 Azimuth 0 Receiver

Width 4 m Height 3 m ρ x z wall 0.8 y-z wall 0.8 x-z op wall 0.8 y-z op wall 0.8 Floor 0.3

Quantity 9 Photodetector's area 10 mm<sup>z</sup> Acceptance semi-angle 12

Table 1. Parameters used in simulation.

basis of diffraction theory and encoded into a hologram. Calculating a CGH means the calculation of its complex transmittance. The transmittance is expressed as follows:

$$H(\boldsymbol{\mu}, \boldsymbol{\nu}) = A(\boldsymbol{\nu}, \boldsymbol{\mu}).exp[j\phi(\boldsymbol{\mu}, \boldsymbol{\nu})] \tag{6}$$

where H(u, v) is complex transmittance function, A(u, v) and φ(u, v) are amplitude and phase distribution, respectively. The parameters (u, v) are coordinates in the frequency space. The phase of incoming wavefront is modulated by hologram, whereas the transmittance amplitude is equal to unity. The analysis used in Refs. [18–20] has been employed for the design of the CGHs. The hologram H(u, v) is considered to be in the frequency domain and the observed diffraction pattern h(x, y) in the spatial domain. They are related by the continuous Fourier transform:

$$h(\mathbf{x}, y) = \iint H(\mathbf{u}, \nu) \exp[-i2\pi(\mu\mathbf{x} + \nu y)] du d\nu \tag{7}$$

The diffraction pattern of the hologram when it is placed in the frequency plane is given by

$$h(\mathbf{x}, \mathbf{y}) = \text{RSsim}(\mathbf{R}\mathbf{x}, \mathbf{S}\mathbf{y}) \sum\_{k=-\frac{M}{2}}^{\frac{M}{2}-1} \sum\_{l=-\frac{M}{2}}^{\frac{M}{2}-1} H\_{kl} \exp[i2\pi(R\mathbf{k}\mathbf{x} + \mathbf{S}gl)] \tag{8}$$

where sincða, bÞ ¼ sinðπa<sup>Þ</sup> sinðπbÞ=π<sup>2</sup>ab. The complex amplitude of the spots is proportional to some value of interest. But, the reconstruction will be in error because of the finite resolution of the output device and the complex transmittance of the resulting hologram. This error can be considered to be a cost function. Simulated annealing (SA) is used to minimise the cost function [21]. The phases and amplitudes of every spot are determined by the hologram pixel pattern and are given by its Fourier transform. The constraints considered in the hologram plane are to discretise the phase from 0 to 2π and a constant unit amplitude for the phase only CGH.

Let the desired spots in the far field be fðx ; yÞ¼jfðx ; yÞjexpðiϕðx ; yÞÞ . The main target is to find the CGH distribution g(v, u) that produces optimum reconstruction g(x, y) that is very close to the desired distribution f(x, y). The cost function (CF) is defined as a mean squared error which can be interpreted as the difference between the normalised desired object energy f"(x, y) and the scaled reconstruction energy g"(x,y):

$$\text{CF}\_k = \sqrt{\sum\_{i=1}^{M} \sum\_{j=1}^{N} \left( |f''(i,j)|^2 - |\mathbf{g''}\_k(i,j)|^2 \right)^2},\tag{9}$$

where f"(x, y) represents the normalised desired object energy and g}kði, jÞ represents the scaled reconstruction energy of the k th iteration. Simulated annealing was used to optimise the phase of the holograms offline in order to minimise the cost function. The simulating annealing algorithm can help jump from local optima to close to a global optimum (minimising the cost function close to zero). The transition out of a local minima to global one is accomplished by accepting hologram phases that increase the mean squared error of the reconstruction with a given probability. The probability of accepting these phases is expð�ΔCF=TÞ, where ΔCFis the change in error and T is a control parameter (the temperature of the annealing process). First, we start with a high value of T so that all the change in the hologram phases are accepted and then slowly lower T at each iteration until the number of accepted changes is small. This method is similar to melting a metal at a high value of T and then reducing the T slowly until the metal crystals freezes at a minimum energy. The changes of hologram phases relate to a small perturbation of the physical system, and the resulting change in the mean squared error of the reconstruction corresponds to the resulting change in the energy of the system. Therefore, this technique finds a hologram configuration, which has a minimum mean squared error (CF). For phase only CGHs, the constraints are constant amplitude and a random phase distribution ϕ<sup>0</sup> (M � N). In the first iteration, a random phase is applied to help in the convergence of the algorithm.

For a large room of 8 m � 4 m, the floor is divided into 80 regions. A library that contains 6400 holograms is optimised offline using SA. In order to accurately identify the receiver location, a large number of holograms are required [17]. The optimum diffusing spots were pre-calculated based on the power and angle techniques shown in Ref. [1]. A total of 80 holograms are stored in a library and allocated for each region, the transmitter should cover the 80 possible receiver positions in the room, which means 6400 holograms are required to cover the entire room. The total number of holograms required is N<sup>2</sup> , where N represents the number of regions into which the floor/ceiling is divided. Figure 2 illustrates one hologram when the receiver is present at (1 m, 6 m and 1 m) and the transmitter is placed in the middle of room at (2 m, 4 m and 1 m). SA is used to optimise the phase of the CGH. Figure 3 shows

Holograms in Optical Wireless Communications http://dx.doi.org/10.5772/intechopen.68408 133

considered to be a cost function. Simulated annealing (SA) is used to minimise the cost function [21]. The phases and amplitudes of every spot are determined by the hologram pixel pattern and are given by its Fourier transform. The constraints considered in the hologram plane are to discretise the phase from 0 to 2π and a constant unit amplitude for the phase

Let the desired spots in the far field be fðx ; yÞ¼jfðx ; yÞjexpðiϕðx ; yÞÞ . The main target is to find the CGH distribution g(v, u) that produces optimum reconstruction g(x, y) that is very close to the desired distribution f(x, y). The cost function (CF) is defined as a mean squared error which can be interpreted as the difference between the normalised desired object energy

where f"(x, y) represents the normalised desired object energy and g}kði, jÞ represents the scaled

of the holograms offline in order to minimise the cost function. The simulating annealing algorithm can help jump from local optima to close to a global optimum (minimising the cost function close to zero). The transition out of a local minima to global one is accomplished by accepting hologram phases that increase the mean squared error of the reconstruction with a given probability. The probability of accepting these phases is expð�ΔCF=TÞ, where ΔCFis the change in error and T is a control parameter (the temperature of the annealing process). First, we start with a high value of T so that all the change in the hologram phases are accepted and then slowly lower T at each iteration until the number of accepted changes is small. This method is similar to melting a metal at a high value of T and then reducing the T slowly until the metal crystals freezes at a minimum energy. The changes of hologram phases relate to a small perturbation of the physical system, and the resulting change in the mean squared error of the reconstruction corresponds to the resulting change in the energy of the system. Therefore, this technique finds a hologram configuration, which has a minimum mean squared error (CF). For phase only CGHs, the constraints are constant amplitude and a random phase distribution ϕ<sup>0</sup> (M � N). In the first iteration, a random phase is applied to help in the

For a large room of 8 m � 4 m, the floor is divided into 80 regions. A library that contains 6400 holograms is optimised offline using SA. In order to accurately identify the receiver location, a large number of holograms are required [17]. The optimum diffusing spots were pre-calculated based on the power and angle techniques shown in Ref. [1]. A total of 80 holograms are stored in a library and allocated for each region, the transmitter should cover the 80 possible receiver positions in the room, which means 6400 holograms are required to

number of regions into which the floor/ceiling is divided. Figure 2 illustrates one hologram when the receiver is present at (1 m, 6 m and 1 m) and the transmitter is placed in the middle of room at (2 m, 4 m and 1 m). SA is used to optimise the phase of the CGH. Figure 3 shows

cover the entire room. The total number of holograms required is N<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>j</sup> <sup>f</sup> }ði,jÞj<sup>2</sup> � jg}kði,jÞj<sup>2</sup>

th iteration. Simulated annealing was used to optimise the phase

�2 ,

ð9Þ

, where N represents the

f"(x, y) and the scaled reconstruction energy g"(x,y):

CFk ¼

reconstruction energy of the k

132 Optical Fiber and Wireless Communications

convergence of the algorithm.

X<sup>M</sup> i¼1 X<sup>N</sup> j¼1 �

r

only CGH.

Figure 3. The reconstruction intensity at the far field and hologram phase pattern at iterations 1, 5, 15, and 100 using simulated annealing optimisation. Different grey levels represent different phase levels ranging from 0 (black) to 2π (white).

phase distributions and hologram reconstruction intensity at the far field in four snapshots. When the number of iterations increases, the reconstruction intensities are improved. The desired spot intensity in the far field is shown in Figure 4. Figure 5 shows the number of iterations versus cost function.

Figure 4. The desired spots intensity in the far field.

Figure 5. Cost function versus the number of iterations.

Scanning 6400 stored holograms in the system required a full search among all stored holograms, in order to select the best hologram. However, high complexity in term of the computation time is introduced. To solve this issue, a fast search technique is proposed to enhance the SNR via selecting the best hologram while reducing the computational time. The proposed search technique is based on a divide and conquer (D&C) method. Using the D&C algorithm, the transmitter is able to select the best hologram that can achieve the optimum receiver SNR. The fast search algorithm of our proposed system is applied for a single transmitter/receiver scenario as follows:


The proposed system reduces the computation time from 64 ms (each hologram required 1 ms to scan) taken by the classic beam steering system to 13 ms (13 possible locations should be scanned in all iterations 1 ms).

#### 3.2. FDAPA-hologram

phase distributions and hologram reconstruction intensity at the far field in four snapshots. When the number of iterations increases, the reconstruction intensities are improved. The desired spot intensity in the far field is shown in Figure 4. Figure 5 shows the number of


Scanning 6400 stored holograms in the system required a full search among all stored holograms, in order to select the best hologram. However, high complexity in term of the computation time is introduced. To solve this issue, a fast search technique is proposed to enhance the SNR via selecting the best hologram while reducing the computational time. The proposed search technique is based on a divide and conquer (D&C) method. Using the D&C algorithm, the transmitter is able to select the best hologram that can achieve the optimum receiver SNR. The fast search algorithm of our proposed system is applied for a single transmitter/receiver

<sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>100</sup> <sup>0</sup>

Number of iterations

1. The stored holograms in the transmitter are first divided into four quadrants based on their transmission angles. The transmission angles associated with each quadrant are

2. A single middle hologram is used in each group (quadrant) in order to find the first sub-

δmax<sup>x</sup> to δmin<sup>x</sup> and δmax<sup>y</sup> to δmin<sup>y</sup> in the x-axis and y-axis, respectively.

iterations versus cost function.

134 Optical Fiber and Wireless Communications

> 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Cost function (CF)

Figure 5. Cost function versus the number of iterations.

Figure 4. The desired spots intensity in the far field.

scenario as follows:

optimum hologram.

To additionally enhance the performance of the IROW system, we introduce beam delay adaptation technique coupled with beam angle and power adaptation using hologram selection approach. The delay spread in a multi-beam spot IROW system is influenced by the spots' numbers and locations seen by each detector's FOV [3]. Therefore, switching all the beams simultaneously can introduce a differential delay between the neighbouring signals received at the receiver, hence spreading the pulse and limiting the 3-dB channel bandwidth. Instead of transmitting all the beams simultaneously, the delay adaptation algorithm sends the signal that has the longest journey first, and then sends the other signals with different differential delays (Δt) so that all the signals reach the receiver at the same time. A total of 10 μs time delay computation is carried out for each beam [8]. Therefore, a total of 1ms delay adaptation time is required for a beam. Our FDAPA-Hologram (delay, power and angle methods) requires only 14 ms adaptation time in order to select the best hologram. Assume the receiver initiates the adaptation every 1 s. This time is associated with a pedestrian speed of 1 m/s. Therefore, employing FDAPA-Hologram with a total 14 ms adaptation time introduces only 1.4%. Array element delayed switching is used to implement the delay adaptation method. The delay adaptation algorithm is explained as follows:


$$
\Delta t\_i = \max(t\_{i\\_max}) - t\_i \ 1 \le i \le N\_{spot} \tag{10}
$$

7. The transmitter sends the beams with different times associated with their differential delay estimated in Eq. (10) to help the beam arrive at the receiver at the same time

The differential delay depends on the distances among the beams. If all the beams touch each other on the ceiling, then the differential delay will be few nano seconds, hence requiring timing control to switch such a beam within the required time.

### 4. Simulation results and discussion

In this section, we evaluate the performance of the proposed support systems in an empty room in the presence of multipath dispersion, receiver noise, back ground noise (light units) and mobility. The results are presented in terms of delay spread and SNR.

#### 4.1. Delay spread

The delay spread of our adaptive proposed systems (FAPA-Holograms and FDAPA-Holograms) compared with CDS and LSMS system is shown in Figure 6. The results are presented when the transmitter is located near the room corner while the receiver moves along x = 2 m. The conventional pure diffuse system (CDS) has the largest delay compared with other systems. This is due to the diffuse transmission along with wide FOV at the receiver. Moreover, the delay spread of non-adaptive system LSMS is increased as the distance between the transmitter and receiver increases. The delay spread is almost independent of the distance between the transmitter-receiver in our hologram configurations, FAPA-Holograms and FDAPA-Hologram. This is due to beam angle adaptation technique where the proposed systems choose the hologram that has the best SNR. A significant reduction in the delay spread to 0.04 ns is achieved in our FAPA-Hologram system. Moreover, our delay adaptation method in FDAPA-Hologram reduces the delay spread of FDPA-Hologram by factor of 8. This improvement enhances the 3 dB channel bandwidth and increases the SNR at high transmission rates.

#### 4.2. SNR

The SNR results of our proposed systems are shown in Figure 7. The proposed systems are tested under the influence of background noise and transmitter/receiver mobility. The proposed adaptive holograms are compared with conventional CDS and multi-beam angle diversity LSMS system to facilitate the results with previous work published in Refs. [9–11]. The results are shown when transmitters operate at 50 Mb/s. High data rates of 2.5 and 5 Gb/s will be also considered in the next section. The transmitter is located near the room corner while the receiver moves 1 m step along x = 1 m and x = 2 m. The LSMS system provides better results than CDS with wide FOV receiver. This is due to providing direct link though spots and using non-imaging angle diversity receiver. Although the improvement has been achieved, there is

Figure 6. Delay spread of four configurations (a) CDS and LSMS, (b) FAPA-Holograms and APA-LSMS with angle diversity receiver, when the transmitter is placed at (1 m, 1 m, 1 m) and the receiver moves along x = 2 m line.

Figure 7. SNR of OW CDS, LSMS, FAPA-Holograms and FDAPA-Hologram at 50 Mbit/s, when the transmitter is located at (2 m, 7 m, 1 m) and (1 m, 1 m, 1 m) and the receiver mobiles along x = 1 m and x = 2 m lines.

degradation in the SNR results as LSMS transmitter move away from the receiver. For example, this is observed when the transmitter is moved towards the edge or the corner of the room at (2 m, 7 m and 1 m) and (1 m, 1 m and 1 m) while the receiver moves along x = 1 m and x =2m lines, respectively, as seen in Figure 7(a) and (b). In order to overcome this significant reduction as well as improve the system performance, fast adaptive hologram (FAPA-Hologram and FDAPA-Hologram) systems are employed. Our proposed FAPA-Hologram achieves around 24 dB over the traditional LSMS system; see Figure 7(b).

#### 4.3. High data rate mobile IROW system

Δti ¼ maxðti\_maxÞ � ti 1 ≤ i ≤ Nspot ð10Þ

7. The transmitter sends the beams with different times associated with their differential delay estimated in Eq. (10) to help the beam arrive at the receiver at the same time

The differential delay depends on the distances among the beams. If all the beams touch each other on the ceiling, then the differential delay will be few nano seconds, hence requiring

In this section, we evaluate the performance of the proposed support systems in an empty room in the presence of multipath dispersion, receiver noise, back ground noise (light units)

The delay spread of our adaptive proposed systems (FAPA-Holograms and FDAPA-Holograms) compared with CDS and LSMS system is shown in Figure 6. The results are presented when the transmitter is located near the room corner while the receiver moves along x = 2 m. The conventional pure diffuse system (CDS) has the largest delay compared with other systems. This is due to the diffuse transmission along with wide FOV at the receiver. Moreover, the delay spread of non-adaptive system LSMS is increased as the distance between the transmitter and receiver increases. The delay spread is almost independent of the distance between the transmitter-receiver in our hologram configurations, FAPA-Holograms and FDAPA-Hologram. This is due to beam angle adaptation technique where the proposed systems choose the hologram that has the best SNR. A significant reduction in the delay spread to 0.04 ns is achieved in our FAPA-Hologram system. Moreover, our delay adaptation method in FDAPA-Hologram reduces the delay spread of FDPA-Hologram by factor of 8. This improvement enhances the

The SNR results of our proposed systems are shown in Figure 7. The proposed systems are tested under the influence of background noise and transmitter/receiver mobility. The proposed adaptive holograms are compared with conventional CDS and multi-beam angle diversity LSMS system to facilitate the results with previous work published in Refs. [9–11]. The results are shown when transmitters operate at 50 Mb/s. High data rates of 2.5 and 5 Gb/s will be also considered in the next section. The transmitter is located near the room corner while the receiver moves 1 m step along x = 1 m and x = 2 m. The LSMS system provides better results than CDS with wide FOV receiver. This is due to providing direct link though spots and using non-imaging angle diversity receiver. Although the improvement has been achieved, there is

timing control to switch such a beam within the required time.

and mobility. The results are presented in terms of delay spread and SNR.

3 dB channel bandwidth and increases the SNR at high transmission rates.

4. Simulation results and discussion

136 Optical Fiber and Wireless Communications

4.1. Delay spread

4.2. SNR

The results of the SNR achieved with our proposed FAPA-Hologram and FDAPA-Hologram allow the systems to reduce the total optical power transmit while operating at high data rates of 2.5 and 5 Gb/s. At high data rates, we considered a small photodetector area of 10 mm<sup>2</sup> , in order to reduce the impact of high capacitance and improving receiver bandwidth. To the best of our knowledge, commercial photodetectors with a 10 mm<sup>2</sup> area and operating at high data rate are not common. However, researchers in Refs. [16, 22] have shown that the use of a small

Figure 8. The SNR of proposed FDAPA-Holograms and FAPA-Hologram systems when operated at 2.5 and 5Gb/s, with a total transmit power of 80 mW.

detector area reduces the impact of high capacitance. In large commercial area, high speed detectors are starting to be used in free space optical systems. For example, Ref. [23] indicates that areas as large as 10 mm<sup>2</sup> and rise time as low as 10 ps are starting to emerge; however, the combination of large areas and fast response remains a challenge in photodetectors design. A 1 mW per beam is used to address the eye safety requirement in our proposed systems. Furthermore, we limit the power adaptation method where each beam cannot increase the power beyond 0.5 mW. The beams travel from the transmitter as group and spread until it reaches the object (reach to the ceiling in our case). At 10 cm distance each beam travel with different angle which can help in eye safety where the human eye cannot see more than one beam at time. Therefore, we propose that the transmitter is contained within a 10 cm deep enclosure to ensure that the human eye cannot be placed next to the transmitter. This can be achieved for example by placing the transmitter at the bottom of a laptop back cover (screen) and letting the beams emerge from the top of the back cover (screen). The proposed FAPA-Hologram achieves 20.5 dB at 2.5 Gb/s, see Figure 8. Moreover, at 5 Gb/s, the proposed FDAPA-Hologram offers around 2 dB SNR improvement over the FAPA-Hologram. This improvement is due to the use of beam delay adaptation method which helps to reduce the delay spread and improve 3dB channel bandwidth, hence increasing the SNR at the receiver. In terms of practical implementation, it should be noted that the diffraction limit has to be considered when considering commercially available spatial light modulators as the smallest pixel size that can be manufactured and operating wavelength to determine the maximum range of angles over which the beam can be steered [24]. This warrants further study.

#### 5. Conclusions

The performance evaluation of the conventional CDS and non-adaptive LSMS can be significantly degraded by the transmitter/receiver mobility. In this chapter, the finite adaptive hologram using beam angle, power and delay adaptation techniques is introduced. All holograms are stored and pre-calculated in our adaptive system. A fast search algorithm based on the divide and conquer is reported. The fast algorithm reduced the time needed to generate hologram to select the best stored hologram in the system. The adaptive proposed system is combined with an angle diversity receiver. Nine beaches non-imaging angle diversity receiver was used to further improve the received optical signal in the presence of background noise and transmitter mobility. At 50 Mb/s, our simulation results show that the adaptive FAPA-Holograms system provides around 35 dB SNR gain over non-imaging diversity LSMS system. The proposed FAPA-Holograms system using beam angle and power adaptation methods is able to guide the spots nearer to the receiver location at each given transmitterreceiver location. The angles and powers associated with each hologram stored in the system are pre-calculated without adding any complexity at the transmitter to recomputed holograms. In order to further improve system performance and reduce the effect of multipath dispersion, beam delay adaptation method coupled was introduced when the system operated at high data rates. The proposed FDAPA-Holograms system was examined under eye safety regulations. A total transmit power of 80 mW was used. The SNR results of our 5 Gb/s FDAPA-Holograms system were around 13 dB, under the impact of mobility as well as background noise. A fast search algorithm based on the divide and conquer was proposed to reduce the time needed to generate a real hologram and select the best stored hologram in the system.
