Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 39 Increasing Energy Efficiency in OCDMA Network via Distributed Power Control Fábio R. Durand, Bruno A. Angélico, Universidade Tecnológica Federal do Paraná, [email protected], [email protected] Taufik Abrão Universidade Estadual de Londrina, [email protected] AAAAbbbbssssttttrrrraaaacccctttt———— IIIInnnn tttthhhhiiiissss wwwwoooorrrrkkkk,,,, wwwweeee iiiinnnnvvvveeeessssttttiiiiggggaaaatttteeee tttthhhheeee uuuuttttiiiilllliiiizzzzaaaattttiiiioooonnnn ooooffff ttttrrrraaaannnnssssmmmmiiiissssssssiiiioooonnnn ppppoooowwwweeeerrrr ccccoooonnnnttttrrrroooollll aaaassss mmmmeeeecccchhhhaaaannnniiiissssmmmm ttttoooo iiiinnnnccccrrrreeeeaaaasssseeee tttthhhheeee eeeennnneeeerrrrggggyyyy eeeeffffffffiiiicccciiiieeeennnnccccyyyy iiiinnnn ooooppppttttiiiiccccaaaallll ccccooooddddeeee ddddiiiivvvviiiissssiiiioooonnnn mmmmuuuullllttttiiiipppplllleeeexxxxiiiinnnngggg aaaacccccccceeeessssssss ((((OOOOCCCCDDDDMMMMAAAA)))) nnnneeeettttwwwwoooorrrrkkkkssss.... 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TTTThhhheeee mmmmaaaaiiiinnnn rrrreeeessssuuuullllttttssss sssshhhhoooowwwweeeedddd tttthhhhaaaatttt iiiitttt iiiissss ppppoooossssssssiiiibbbblllleeee ttttoooo ssssaaaavvvveeee 77770000%%%% ooooffff tttthhhheeee ttttrrrraaaannnnssssmmmmiiiitttttttteeeedddd eeeennnneeeerrrrggggyyyy ppppeeeerrrr bbbbiiiitttt wwwwiiiitttthhhh tttthhhheeee ppppeeeennnnaaaallllttttyyyy ooooffff oooonnnneeee oooorrrrddddeeeerrrr ooooffff mmmmaaaaggggnnnniiiittttuuuuddddeeee ooooffff BBBBEEEERRRR.... IIIInnnnddddeeeexxxx TTTTeeeerrrrmmmmssss———— optical code division multiplexing access, distributed power control algorithm. I. INTRODUCTION The informatics and telecommunications industries have become a component of the economies from the nations. The growing of Internet, information and communications technology (ICT) infrastructures have been showing an exponential behavior and the electrical power consume has increasing in the same way. However, the energy resources available in the world are limited and the energy efficiency in all sort of industry has been encouraged. The energy efficiency in the ICT is represented by the energy consumption per bit of data transported and/or processed [1][2]. Nowadays, the ICT sector is responsible for approximately 5 % of the total electrical power consumption in developed national economies and especially the Internet consumes 1 % of this total electrical power consumption [1]. Recent studies have showed the importance of the consideration of energy consumption in optical communications design, considering the transmission infrastructure (transmitters, receivers, fibers and amplifiers) [3] and network infrastructure (switchers and routers) [4] aspects. In a global scale network, the energy consumption of the switching infrastructure is larger than the energy consumption of the transport infrastructure [2][4]. In this context, it is necessary to improve the energy efficiency of switching and to optimize the network design to reduce the quantity of switching and overheads. Low energy efficiency is observed mainly at access network, because the access equipment consumes almost 50% of energy consumed in Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 40 the core or metro equipment [3]. However, the amount of bits transported in core or metro network is larger than in the access network. Optical-code-division multiple access (OCDMA) based networks [5] have attracted a lot of interests due to various advantages including asynchronous operation, high network flexibility, protocol transparency, simplified network control and potentially enhanced security [5–9]. In OCDMA each different code defines a user and different code-users can share a common channel. In a common channel, the interference that may arise between different code-users is known as multiple access interference (MAI) and can limit the number of code-users utilizing the channel simultaneously. OCDMA can be divided into non-coherent (unipolar) and coherent (bipolar) systems. The non-coherent systems are based only on intensity modulation of optical power [7], and coherent systems are based on modulation of amplitude and phase [8]. The coherent code is true-orthogonal and non-coherent code is pseudo-orthogonal. As a consequence, the performance of coherent codes is higher than non- coherent codes when analyzing the signal-to-interference plus noise ratio (SINR) [8]. However, the main drawback of coherent OCDMA lies in the technical implementation difficulties, concomitant with the utilization of phase-shifted optical signals [6-8]. The non-coherent codes can be classified in one dimensional (1-D) and two dimensional (2-D) codes. In 1-D codes, the bits are subdivided temporally into many short chips with a designated chip pattern representing a user’s code. On the other hand, in 2-D codes the bits are subdivided into individual time chips, and each chip is assigned to an independent wavelength from a discrete set of wavelengths [9]. The 2-D codes have better performance than 1-D codes and can significantly enhance the number of active and potential users [9]. In the OCDMA, the near- far ratio increases the multiple access interference effects, because each active node in transmission mode contributes with MAI and the power penalty varies dynamically. Therefore, the static power budget design does not solve this problem [10][11]. Furthermore, if the distances between the nodes are quite different, as would be the case in practice, the power received from different nodes will be significantly different. Thus, considering as reference one OCDMA node, the performance of closer nodes is many orders of magnitude better than that of far nodes. Hence, an efficient power control is needed to overcome this problem and to enhance the performance and throughput of the optical network [12]. This could be achieved via signal-to- interference (SINR) optimization [12][13]. In this case, analogous to a wireless CDMA cellular system, the power control, centralized or distributed, is one of the most important issues since it has a significant impact on both performance and capacity; it is the most effective way to avoid the near-far problem and to increase capacity. Previously, this problem has been investigated in OCDMA networks to solve the near-far problem [10] and to obtain quality of service (QoS) at physical layer [11]; however this issue has not been investigated with focus on the energy efficiency. In this work, we study the utilization of distributed power control as mechanism to obtain energy efficiency improvement in OCDMA access network with non-coherent 2-D codes. The performance of this architecture networks is analyzed considering the loss characteristics of encoders, decoders and star coupler. Our objective consists in investigating the viability of Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 41 power control in order to increase the energy efficiency of the OCDMA network and to determine the best tradeoff between the energy efficiency and near-far mitigation. This paper is organized as following: Section II describes the architecture of the network for 2-D codes. Section III discusses the proposed methodology for increasing OCDMA energy efficiency. The performance of proposed methodology systems is developed in Section IV. Section V shows representative numerical results for the proposed approach; finally, in Section VI the main conclusions are presented. II. NETWORK ARCHITECTURE The OCDMA architecture considered in this work is formed by K nodes interconnected by passive star coupler, in a broadcast-and-select pattern as shows Fig. 1. For viability characteristics, we consider network equipment, such as code-processing devices (encoders and decoders at the transmitter and receiver) and star coupler. Such devices could be made using robust, lightweight, and low-cost technology platforms with commercial-off-the-shelf technologies [14], [15]. dtx drx Tx 1 1 Rx 1 1 dtx drx Tx i j Rx i j Star Coupler dtx drx Tx K K Rx K K Fig. 1. OCDMA network architecture. The transmitting and receiving nodes create virtual path based on the code and the total link length is given by d =dtx +drx, where dtx is the link length from the transmitting node ij i j i to the star coupler and drx is the link length from the receiving node to the star coupler. The j ( ) received power at a j-th node is given byP =a p exp −α d , where p is the transmitted rj star i f ij i power by i-th transmitter node, αf is the fiber attenuation (km-1) and astar is the star coupler attenuation (linear units). Considering deciBell units,a =10log(K)−[10log (K)log δ], star 2 10 where, δ is the excess loss ratio. The 2-D wavelength-hopping/ time-spreading code sequence is illustrated in Fig. 2. This 2-D code is transmitted and its destiny in the network is determined by a particular code sequence. The 2-D codes can be represented by N × N matrices, where N is the number of λ T λ rows, that is equal to the number of available wavelengths, and N is the number of columns, T that is equal to the code length. The code length is determined by the bit period T which is B subdivided in small units called chips, each of duration T = T/ N. In each code, there are w c B T short pulses of different wavelength, where w is called the weight of the code. An (N × N w, λ T, I, I) code is the collection of binary N × N matrices each of code weight w; I and I are a c λ T a c Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 42 nonnegative integers and represent the constraints on the autocorrelation and cross- correlation [8], respectively. WWaavveelleennggtthh TT CC NN λλ •• •• •• •••••• 22 11 11 22 •••••• NN TTiimmee tt TT BB Fig. 2. Schematic of 2D wavelength-hopping time spreading code sequence. The 2-D OCDMA utilizes multi-wavelength sources such light-emitting diodes, amplified spontaneous emission noise from erbium-doped fiber amplifier (EDFA), gain switched Fabry– Pérot lasers, and supercontinuum generation [15]. These sources avoid the need for rapidly wavelength hop according the wavelength-hopping pattern. The encoder essentially creates a combination of two patterns: a wavelength-hopping pattern and a time-spreading pattern. The common technology applied in encoders/decoders with delay lines are array waveguide gratings (AWGs), thin-film filters (TFFs), simultaneously as fiber Bragg gratings (FBGs), holographic Bragg reflectors (HBRs), chirped Moire gratings (CMGs) [16][17]. The schemes of encoders commonly utilized are based on AWG, TFF and FBGs, as are showed in Fig. 3. The losses associated with the encoders/ decoders are given by [15][16][17] C (dB)=2a +a AWG AWG Delay (1.a) ( ) C (dB)=6log N +a +a TFF 2 λ TFF Delay (1.b) C (dB)= N a +a Bragg λ Bragg Cirulator (1.c) where a is the AWG loss, a is the delay line loss, a is the TFF loss, a is the AWG Delay TFF Bragg FBG loss and a is the circulator loss. The loss usual value for these equipments are Cirulator a = 2.5 dB, a = 1dB, a = 0.5 dB, a = 0.5 dB and a = 3dB. The AWG AWG Delay TFF Bragg Cirulator encoder has approximately uniform loss (6 dB) independently of the number of wavelengths (N) [16]. For this characteristic, we will consider the AWG as encoder/decoder in the rest of λ this work. Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 43 Fiber delay lines (FDL) λ 1 λ 2 λ k AWG AWG (a) Fiber delay lines (FDL) Coupler Coupler λ 1 TFF λ 2 TFF λ k TFF (b) Delay λ ...., λ 1, k λ λ λ 1 2 k (c) Fig. 3. Schematic of 2-D encoders and decoders (a) Array waveguide gratings (AWGs), (b) Thin- film filters (TFFs), and (c) fiber Bragg grating (FBG). III. THEORETICAL ANALYSIS a. Energy efficiency and power allocation The necessary energy in each i-th node for the transmission of 1 bit can be expressed as [3], Ei = piTbit [J bit], i = 1,.., K (2) where K is the number of nodes, T is the time to transmit one bit over the network given by bit T =1/R, where R is the bit rate (bits/seconds) and p is the transmitted power. In order to bit i determine the energy per bit values it is necessary to define the individual node transmitting power (p). The p is obtained by power budget or power control and it is associated to a QoS, a i i SINR and a maximum bit error rate (BER) tolerated by the optical nodes. Under a power control situation, each optical node adjusts its transmitting power in an attempt to maximize the number of transmitted bits with minimum energy consumption. This concept can be formulated by the energy efficiency definition [18], Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 44 L f(γ) ε =R i , i = 1,.., K i (3) M p i where M is the number of bits in each transmitted packet, L is the number of information bits contained in each data packet and f(γ ) is the efficiency function, which approximates the i probability of error-free packet reception. It can be approximated by f(γ)=(1−BER )M , with i i γ being the SINR for the i-th node, given by [14][18], i g p γ ∝ ii i , i = 1,.., K i I +N (4) i i where g are the total loss in the path that connects i-th-Tx node to j-th-Rx node, I is the total ij i interference power level comes from the others transmitters nodes and N is the receiver i power noise level. Both terms I +N will be described in details in the next subsection, eq. (8). i i In the same way this concept is used to define a metric named utility that is the number of bits received per energy expended or the relation of the throughput and power dissipation [18]. Hence, for each i-th node, the maximum number of transmitted bits occurs at power level for which the partial derivative of ε with respect to p equals to zero, ∂ε ∂p =0. So, the i i i i derivative of energy efficiency can be obtained referring to efficiency function f(γ ) and eq. i (4), setting: ∂ε R L  ∂f (γ)  ∂pi = p2 M γi ∂γi − f (γi), i = 1,.., K (5) i i i From (5) assuming p > 0, the necessary condition to maximize the energy efficiency is i immediately obtained: ∂f(γ ) γi i − f(γi)=0, i = 1,.., K (6) ∂γ i So, adopting the widely accepted approximation for BER performance with uncoding system (M=L) and binary modulation, the bit error rate can be approximated asBER =e−γi . Hence, i ∂f (γ) we have: i = ∂ (1−e−γi )=e−γi . As a result, we can conjecture that the optimum ∂γ ∂γ i i power allocation criterion in terms of energy efficiency is given by pi =κ⋅Ii g+Ni ⋅eγi ⋅(1−e−γi)M , i = 1,.., K (7.a) ii whereκ is a constant of proportionality. Besides, further simplification can be obtained if the condition M=1 could be assumed: I +N p =κ⋅(eγi −1)⋅ i i , i = 1,.., K i g (7.b) ii b. Proposed scheme Note that in order to satisfies (6) it is necessary adjust the SINR at each received node equals to the target SINR, γ=γ*. In this context, we propose the utilization of power control i i iterative algorithm in order to establish the lower energy per bit according to the OCDMA Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 45 network QoS requirements. Fig. 4 shows the flowchart with the adopted scheme to assign the energy per bit transmitted in each node. This scheme aims to save energy per bit at each node and, as a consequence, decreases the total energy consumption overall the network. QoSrequirement –BER Network topology Power controlalgorithm -search thelowerenergyper bit Numberofiterations Energyper bit Fig. 4. Flowchart with the proposed scheme to save energy per bit. This scheme is based on the power control with the restriction of QoS requirement based on BER level. The entries are the BER level and the network topology, comprising the following parameters: node distances, links lengths, fiber parameters, EDFA preamplifiers value, OCDMA code parameters, and so forth. The iterative power control algorithm defines the transmitted power according to the number of active transmitting nodes aiming to establish individual target value of BER, and taking into account as low level energy per bit as possible. The outputs of the scheme are the necessary number of iterations of the iterative power control algorithm and the optimized value of energy per bit necessary for each node. In the next subsections we will illustrate BER computation, the main characteristics of the power control procedure, as well as the way to apply the power control in order to obtain a more energy efficient OCDMA network. IV. PERFORMANCE EVALUATION a. Signal-to-interference plus noise ratio (SINR) and Bit error rate (BER) In [11], Inaty et al. derive an expression for optical SINR in a multirate chip-synchronous 2D-OCDMA system. Assuming single-rate case, the SINR for the i-th node of a 2-D code OCDMA system can be precisely written as: N 2g p G T ii i amp γ = , i = 1,.., K i K ∑ (8) σ2G g p +2P amp ij j N j=1,j≠i where g and G are, respectively, the total loss and gain of the preamplifier in the path that ij amp connects i-th-Tx node to j-th-Rx node. σ2 is the average variance of the Hamming aperiodic cross-correlation amplitude [8], P is the spontaneous amplified emission (ASE) noise power N in the preamplifier considering the two polarization mode presented in a single mode fiber Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 46 and p is the other nodes transmitted power. Note that the usual receiver noise power includes j thermal noise, shot noise and optical preamplifier noise. However, ASE in the optical preamplifier will be the main limiting factor (in addition to the MAI), compared to thermal and shot noise at the receiver [10]. In our work, the receiver noise power is represented by ( ) PN =nSPhf G−1 Bo (9) where n is the spontaneous emission factor, typically around 2 to 5, h is Planck’s constant, f sp is the carrier frequency, G is the amplifier gain and B is the optical bandwidth. Ideally, in o order to reduce the ASE noise power, the optical bandwidth can be set to a minimum of B = o 2R. Assuming Gaussian noise approximation, the BER associated with the i-th node is related ( ) to its SINR by P =erfc γ 2 , where erfc(.) is the complementary error function. b,i i b. Power control The power budget analysis establishes the transmitted power necessary to reach the photodiode sensibility. The power budget in dB must satisfy the follow inequality, p ≤ p +G −C −αd −a −C −N [dB], i 1,.., K (10) s i amp Enc f ij star Dec MAI where p is the receiver power sensibility, N is the MAI interference variance, C is the s MAI Enc encoder losses and C is the decoder losses. The losses associated with the encoders/ Dec decoders are given by (1). We observe in (10) the static characteristics of the power budget design, mainly because the MAI varies with the number of active nodes transmitting simultaneously. The design based on static power budget results in a transmitting power higher or lower than the necessary;;;; as a result, an increase in the near-far problem occurs. To solve this problem, it is adequate to apply dynamic power control that defines the transmitting power according the number of active transmitting nodes. The power control in optical networks is an optimization problem aiming to establish individual target value of SINR, denoted byγ*;;;; hence, each node unit transmitting with power i p, has to be controlled in order to satisfy the relation γ ≥γ*. The maximum achievable SINR i i i at the receiving nodes is equal to the maximum achievable carrier to interference ratio (CIR) at the receiver output times NT2/σ2. Denoting Γi as the CIR at the required decoder input, in order to get a certain QoS which is associated to a maximum tolerable BER at the i-th optical node, and defining the K-dimensional column vector of the transmitted optical power pppp = [p, 1 p2,…… pK]T , then the optical power control optimization problem consists in finding the optical power vector pppp* that minimizes the following cost function [19]: K J(p)=1Tp =∑ p i (11) i=1 subject to the constraints: Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 47 g pG Γ = ii i amp ≥Γ* i K ∑ G g p +2P amp ij j N (12) j=1,j≠i P ≤ p ≤ P ∀i = 1,.., K min i max where 1111T = [1, ..., 1] and Γ*is the minimum CIR to achieve a desired QoS. The elements gij that represent the connections of transmitter-receiver pairs constitute the network attenuation matrix: g g L g  11 12 1K   g g L g G = M21 M22 O M2K (13)   g g K g  K1 K2 KK Using matrix notations, (12) can be written as, Ι−Γ*Hp≥u (14) where IIII is a K-dimension identity matrix, HHHH is the normalized interference matrix, whose elements can be evaluated by 0, i = j,  h =g ij ij , i ≠ j, (15)  g ii and the ith element of vector uuuu is given by: Γ*P ui = G gN (16) amp ij Note that in (15) we have a scaled version of the noise power. Solving (14), substituting inequality by equality, we get the optimized power vector solution through matrix inversion: p* = Ι−Γ*H−1u (17) This optical power vector represents the case of power equilibrium at the receiver node, and is the optimal power required achieving the target CIR. Increasing the value of the CIR would result in higher optical power values that could result in a maximum power higher than the allowed. In this case, a solution would be fixing or decreasing the target CIR value or removing (switching off) some users from the network. The centralized power control is obtained by matrix inversion, as illustrated in (17), and corresponds to an existence of a central node. The central node storages information about all physical network architecture like fiber length between nodes, amplifier position, regular updating about transmission establishment and dynamic of the optical traffic. These characteristics are the drawback of centralized control [10][19]. On the other hand, the distributed power control algorithm (DPCA) synthesis consists of the development of a systematic procedure for the vector pppp evolution in order to reach the optimum value, p* =Ι−Γ*H−1u based on theγi*, γi and pi values. The optimum solution for the power allocation problem satisfies the following iterative process [14][19] (For more details about the derivation of (18), see Appendix I): Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 11, No.1, June 2012 48  γ*  p [n+1]= p [n]−α1− i p [n], i = 1,.., K i i  [ ] i (18)  γi n  where n is the number of iterations and α is the convergence. Note that the convergence factor α in (18) is the numerical integration step to solve an ordinary differential equation, which with some minor alterations is also considered in many other studies of power control [10][14][19]. The algorithm represented by eq. (18) was evaluated for positive and no greater than 1 value of α, since it was shown in [19] that the algorithm divergence outside this interval. This parameter is responsible for the convergence speed: values close to 1 indicate fast convergence; however, the quality of the solution after convergence is not excellent when compared with values close to 0 [14]. There are more details about several aspects that we do not discuss here, such as, convergence, proximity to the optimum value, and sensibility to estimation errors as well, that are discussed in details in [14]. Observing the scalar equations in (18) we can infer that the transmitted power actualization of each node depends only on its own parameters. This apparent uncoupling among nodes follows from the fact that we are estimating the SINR directly and not calculating it from the equation (8). It is obvious that for obtaining the SINR from (8) it would demand an expensive procedure in order to estimate all channel gains (interferers and desired user), imposing a centralized implementation of the DPCA, and finally increasing the algorithm implementation complexity. So, we must avoid this approach. However, the recursion in eq. (18) can be effectively implemented in each (i-th) optical node because all necessary parameters (i.e., α, i the QoS level given by γ*, and the transmitted power p [n]), except γ [n], can be considered i i i known at the i-th node. Under the distributed power control approach, the SINR γ [n] is i obtained at the correspondent destination optical node that demodulates the signal from the optical user i-th. In this way, the destination optical node estimatesγ [n], quantizes it in a i convenient number of bits, and transmits this information to the optical user i-th through a return channel. Indeed, it is possible to measure γ [n] without the effective knowledge of the i information from all the optical interferer nodes, only sensing the i-th optical signal for a period of time at the destination optical node, following by a sensing of all (sum) interferer signals (in the absence of i-th transmitted signal) in a second period of time. In summary, (18) depends only on local parameters allowing the power control to work in a distributed manner, i.e., each one of the K links would be able to carry out separately the respective power control procedure. This brief explanation justifies the name distributed power control algorithm (DPCA) for the set of recursions implicit in (18). To cope with the SINR optimization, the minimum power constraint (which is also called sensitivity level) assures detection of the optical signal by all optical devices. On the other hand, the maximum power constraint guarantees the minimization of nonlinear physical impairments, because it makes the aggregated power on a link to be limited to a maximum value. The convergence characteristics of the transmitted power given by DPCA present an lim p(n)= p* asymptotic behavior for any strictly positive initial condition (p > 0) [19]. i n→∞ Therefore, the energy efficiency presents the same asymptotic behavior of the transmitting Brazilian Microwave and Optoelectronics Society-SBMO received 29 Aug. 2011; for review 2 Sept. 2011; accepted 24 Feb. 2012 Brazilian Society of Electromagnetism-SBMag © 2012 SBMO/SBMag ISSN 2179-1074