Table 1: 
Comparison of DFHOCDMA and other OCDMA techniques for BER
degradation due to receiver sensitivity 

It is noted that the power control technique has only be discovered for prime code^{[5]} and FFH code^{[9,14,15]} even there would be more potential code that can be considered. This study therefore proposes and investigates on how much the improvement can be obtained in DFHOCDMA using power control especially when such system suffers the effects of nearfar problem. The importance of power control for DFHOCDMA: DFHOCDMA is chosen as the scope of this study because of the following considerations. In general, DFHOCDMA has been proposed as a solution to provide easy reconfiguration of the transmitter without the need for sophisticated encoder^{[6]}. The encoder varies the central frequency of optical pulse signal according to the functional code set to the controller. It can be realized using controlled Tunable Optical Filter (TOF) in each encoder and decoder sides with sinusoidal function given in Eq. 1^{[6]}:
Where:
K 
= 
The number of simultaneous users 
∆v 
= 
The bandwidth of the optical frequency 
f 
= 
The optical frequency 
θ 
= 
The phase shift between two successive codes 
Another advantage of DFHOCDMA is that, it can accommodate simultaneous users
as maximum as 169^{[6]}, in average, twice as much as compared to other
OCDMA techniques. Nevertheless, the BER deteriorated rapidly with the small
reduction of the threshold received power compared to other techniques. The
comparison of BER degradation between DFHOCDMA and other techniques is tabulated
in Table 1. It is shown that, a little change of threshold
received power (from 10 dBm to 12 dBm) yields great BER degradation from 10^{9}10^{6
}while the other techniques did not show significant changes. This phenomenon
may significantly occur in a DFHOCDMA network with nearfar problem as shown
in Fig. 1.
 Fig. 1: 
Star Network at Different Fiber Lengths for K users: (a):
At transmitter side; (b): At receiver side 
In order to solve these problems, distributed power control technique for DFHOCDMA is proposed that would strongly satisfy the target Signal to Noise Ratio (SNR) for all users. MATERIALS AND METHODS Distributed power control method: To apply power control with DFHOCDMA, we need to initially analyze the noisy received signal. The received signal at decoder side for K users can be divided into two parts: the signal coming from i^{th }user which include the data and noise and second part represented the MAI which come from other users K1, where K is the total active users. In DFHOCDMA case, the received signal (Sr) is given by: where S_{desired }is the desired signal, while MAI is the interference signal found from the Eq. 3^{[6]}:
Where:
Pr 
= 
The received power 
∆v 
= 
The bandwidth of the optical frequency, T_{b} bit time duration 
BW 
= 
Bandwidth of the TOF 
F_{j}, F_{i} 
= 
The functions in (Eq. 1) of users i and j respectively 
N_{i, j} 
= 
The intersecting points between users i and j which is depend on phase
shift between the users 
S and E=The start and end interference time between i and j users respectively
This code was extensively discussed in^{[6]}.
MAI in Eq. 3 is the major problem in OCDMA as it limits the network at lower SNR. Instead of MAI, PIIN and shot noises also affect on the value of SNR. Basically, the photocurrent variance due to PIIN is given by^{[10]}:
Where:
I 
= 
The average photocurrent, 
τ_{c} 
= 
The coherence time of the source 
B 
= 
The noise equivalent electrical bandwidth 
In DFHOCDMA, the PIIN variance for K users is represented by^{[6]}:
Meanwhile the basic variance of shot noise is represented as the following^{[11]}:
Where:
e 
= 
The electronic charge 
B 
= 
The noise equivalent electrical bandwidth 
I 
= 
The average photocurrent 
The value of I in DFHOCDMA also depends on the received power over the bandwidth
of TOF, (Pr/Δυ) and therefore, the shot noise variance in DFHOCDMA
is considered as:
The Eq. 3, 5 and 7 in^{[6]} assume that the received power is equallyvalue for all users. This is true only if all users transmit the signals at the same path length. Although the other parameters can be remained as constant since the bandwidth of TOF does not change with the power misdistribution, as far as the nearfar problem is concerned, the Pr value in Eq. 3 can not be considered uniform. So the MAI for simultaneous users are not similar, or: where, MAI_{1}, MAI_{2} and MAI_{K }are the multi access interference for first user, second user and last user respectively and K is number of simultaneous users. Noted that, the value of MAI for any user i is found to be linearly proportion with Pr at another decoder j, thus the Eq. 3 can be simplified as the MAI of user i, given by: where, A is a constant representing the design parameters of DFHOCDMA in Eq. 3. The value of A depends on the bandwidth of the system, light speed, bandwidth of TOF and code size of the function of users defined in Eq. 1. In the same way, the value of PIIN and shot noise variances in Eq. 5 and 7 respectively will take new equations as follows:
Where:
It is clear now; the MAI, PIIN and shot noises for all users are affected by received power of other users and varies linearly with Pr. Since the Pr_{j }in Eq. 9 and 10 are different based on nearfar problem, we need to take the sum average of Pr_{j} for all users. Rearranging Eq. 911, the variance of each of MAI, PIIN and shot noise can be represented by:
where, A1, B1 and C1 are constants that lead to linear proportion relationship between MAI, PIIN and shot noises and Pr respectively. The SNR in OCDMA can now be represented by: where, σ^{2}MAI, σ^{2}PIIN, σ^{2}sh are the variances of MAI, PIIN and shot noises as shown in Eq. 1315 respectively and σ^{2}th is the thermal noise which is equal to:
Where:
K_{b} 
= 
Boltzmann's constant 
T 
= 
Absolute receiver noise temperature 
B 
= 
The noise equivalent electrical bandwidth of receiver 
R_{L} 
= 
The receiver load resistor 
As a result, the SNR in DFHOCDMA at various Pr with constant values of A1,
B^{~}1, B^{~}2 and C1 is:
The main purpose of applying power control is to reduce all these noises by adjusting appropriate transmitted power of certain users in such a way that all users may obtain the target SNR. The SNR for i^{th} user in Eq. 17 represents the first parameter for PC algorithm in Eq. 18 and this value will be compared with target SNR (SNR_{tar}) to estimate appropriate transmitted power for the next iteration (if any), shown as follows^{[12]}:
where, n is the number of iteration of PC. The transmitted power is updated
by scaling the current power level by the ratio between the target SNR and the
current SNR. In the DFHOCDMA case, the SNR_{targ} must be equal to
16 dB to achieve BER =10^{9} . If for example, the obtained SNR for
i^{th} user is 15 dB at nth iteration, then the Pt_{i} (n+1)
= 1.06 × Pt_{i} at (n+1)th iteration, considering that the power vector
does not exceed the initial transmitted power. A flowchart shown in Fig.
2 summarizes the power control algorithm.

Fig. 2: 
Flowchart to Apply Power Control with DFHCDMA 
RESULTS AND DISCUSSION Numerical simulation has been conducted using Matlab® to model the proposed algorithm. The parameters used are: BW = 1.65 nm, f = 1550 nm, ∆v = 30 nm. The number of users considered is 100, starting with fiber length of 0.2 km for the first user, up to 20 km for the last user. In this case, the difference of fiber length among adjacent user is 0.2 km. The system is considered as fully supported if the system can support all simultaneous users. In Fig. 3, it was observed that without power control, the system was not fully supported (i.e., only 77 out of 100 users managed to obtain BER of 10^{9}). After the application of power control in the first iteration, the system has improved to support 94 number of users. It is then gradually supported 100% of users after the second iteration.
Meanwhile the distribution of random path length for 30 users is shown in Fig.
4a, resulting to unequal received power, shown in Fig. 4b.
Note that, some users have Pr less than 10 dBm and therefore affected these
users to have SNR lower than 16 dB (shown in Fig. 4c). Then
it is depicted in Fig. 4de that, all users
satisfy the target received power,
resulting to SNR that less than 16 dB (where the BERs are at acceptable value of 10^{9}). Taking into account the noise effects of Multiple Access Interference (MAI), Phase Induced Intensity Noise (PIIN) and shot noise, the system could support 100% of users with power control compared to 33% without power control when the initial transmitted power was 1 dBm among 30 simultaneous users.
 Fig. 3: 
Supported 100% users in the system with power control 
 Fig. 4: 
(a): Random path length for 30 users; (b): Received power
without power control; (c): Received power with power control; (d): SNR
with power control; (e): SNR without power control 
CONCLUSION The DFHOCDMA is a new technique which increases the capacity of the network, but it has severe nearfar problem. To control solve this problem, the power control method has been proposed to achieve optimum value for signal to noise ratio for all user. Using power control, the unwanted noises from other users could be reduced significantly. From the results, it has been shown that the system could maintain on supporting high number of users although despite of the nearfar problem. " target="_blank">View Fulltext
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