Non-linear filtering using a DSP for estimating the optical carrier phase in a BPSK homodyne coherent communications system

Transcription

1 n-linear filtering using a DSP fr estimating the ptical carrier phase in a BPSK hmdyne cherent cmmunicatins system ARVIZU A., MEDIETA F.J, MURAOKA R., MITRAI D. Departament de electrónica y telecmunicacines CICESE Km. 17 Carretera Tiuana Ensenada, Ensenada, B.C. MÉXICO Abstract: In this wrk we describe a nn-linear filter used fr the estimatin f the ptical carrier phase in a hmdyne cherent cmmunicatins system with BPSK mdulatin. The nn-linear filter is implemented using a digital signal prcessr and is characterized in a self-hmdyne cherent ptical cmmunicatins system. Simulatin and experimental results are reprted. Key-Wrds:- cherent ptical cmmunicatins, hmdyne detectin, maximum-likelihd estimatin, nn-linear filtering, phase nise, carrier synchrnizers. 1 Intrductin The cherent ptical cmmunicatins systems have imprtant advantages ver the direct detectin systems. They have greater perfrmance sensitivity (up t db theretical imprvement) as a result f the peratin clse t the quantum nise limit [1], (making them very attractive fr the implementatin f bth fiber ptic lng-distance links and free-space links []). They als have enhanced frequency selectivity allwing an ptical frequency divisin multiplexing with narrwer channel separatins [3]. There exis hwever, several imprtant prblems fr the practical implementatin f such systems, i.e.; a) the frequency stability f the ptical surces, b) the phase nise inherent f the semicnductr lasers [4], amng thers. As is well knwn [5], the phase-shift-keying (PSK) mdulatins are the less sensitive t the additive nise f the mdulatins used n the cherent ptical cmmunicatins systems. Hwever, the PSK receivers are the mre sensitive t the phase nise in the ptical fields (in cmparisn with their ASK r FSK cunterparts); therefre, the carrier synchrnizatin prcess is crucial in the perfrmance f these systems. The carrier synchrnizatin in the cherent ptical cmmunicatin systems is cmmnly made with synchrnizing structures taken frm the radielectric cmmunicatin systems [4,5,6,7,8]. These structures, hwever, are n in general, ptimum (in a statistical sense) fr the synchrnizatin f ptical carriers [9]. In this wrk we reprt a nn-linear filter (synchrnizatin structure) synthesized specifically fr BPSK cherent ptical cmmunicatin systems. The synthesis f this structure (reprted in a previus wrk [1]) was made using the maximum-likelihd criteria and a variable state apprach, taking int accunt the ptical carrier phase nise and the additive pstphtdetectin nise [11]. The perfrmance f the nn-linear filter btained is evaluated with cmputer simulatins and implemented using a digital signal prcessr n a demnstrative experimental self-hmdyne ptical fiber cmmunicatin system with cntrlled phase nise and BPSK mdulatin. Filtering prblem Usually, fr carrier synchrnizing purpses it is necessary t made the phase carrier estimatin prcess [1]. It can be shwn [13] that if the parameter ( the carrier phase) t be estimated is unknwn but nt randm, the synchrnizer structures like the PLL and the Cstas lp are ptimum carrier phase estimatrs (in a statistical sense). This estimatin prcess is a particular case f a mre general prblem knwn as the filtering prblem which is present in a great variety f engineering areas [14]. On the filtering prblem a memryless nn-linear transfrmatin is made ver the stchastic signal x () t, getting the signal h [ t : x() t ] that is bserved with an

2 additive randm perturbatin n () t. The bservatins are available ver an interval [ t,t] that begins frm an arbitrary time t ending n the time t, that it is mving ver the tempral axis n real time as mre data arrive. The filtering prblem cnsists n determining an ptimum pint realizable estimate f x () t based n all the available data { r() : t τ t} [14]. τ. n-linear filtering In this wrk we have used the maximum-likelihd [15] as the ptimality criteria fr btaining the ptical carrier phase estimate xˆ () t (the estimate f x(t)). In the figure 1 is shwn the BPSK cmmunicatin system fr which the estimate is btained. The nn-linear filter (synchrnizer structure) was shintesized using, the s-called variance and estimatr equatins [14], with a Fkker-Planck descriptin f the carrier phase nise prcess and taking int accunt the pst-phtdetectin additive nise.on a previus wrk [1] we have reprted the synthesis f the phase estimatr used fr this experimen hwever, we rewrite belw, fr cnvenience, the variance and estimatr equatins and the slutin btained t them. dxˆ ( t) = E{ ( x xˆ ) S( x, I )}[ dy() t ES( x t I ),, dt] (1) where xˆ () t is the MMSE estimate f the prcess x(t) given the bservatin prcess, and assuming that the data I was sent. The variance equatin is: 1 dv ( t) = dt E{ ( x xˆ ) [ S( x, I ) ( ) ES x, I ]} tc [ dy( t) ES( x, I ) dt] E [( x xˆ ) S( x, I ) ]dt () where v(t) is the variance in the estimatin f x(t). The phtdetected signal V(t), with amplitude PH (that depends mainly n the ptical pwers f the ptical data signal and the lcal laser scillatr), has an additive amplitude nise nt (), with white spectral density [11]: S ( f) = (3) n ( ) V () t = P sin x I n() t (4) H k t c is the cherence time related t the laser linewidth by [1]: t c = 1 (5) πf L The slutin f the cupled equatins (1) and (), cnsidering that the errr phase ( x xˆ ) has a Gaussian distributin [9] are given by the fllwing equatins [1]: x (6) 8 P H * PH () t = v cs( x I ) r() t dt v sin( ( x I ) 1 8P v tc 4P H * * v cs( ( x I ))]dt H () t = v sin( x I ) r() t dt (7) 3 Carrier phase estimatr The mechanizatin f the equatins (6) and (7) shwn n figure give us the phase estimatr structure (nnlinear) filter t be implemented with the digital signal prcessr. 4 Simulatin results In rder t evaluate the perfrmance f the phase estimatr synthesized, we have made several simulatins under different signal-t-nise cnditins and with different levels f phase nise with and withut data mdulatin.in the figure 3 are shwn the wavefrms f the carrier phase nise X (a Wiener prcess) [9], the binary data and the estimates btained with the nn-linear filter and with the cnventinal PLL. It can be bserved that the nn-linear filter has an imprved perfrmance cmpared with the cnventinal PLL as is shwn n figure 4 where the phase errr f bth estimatrs is drawn. 5 Implementatin The nn-linear filter described by the equatins (6) and (7), was implemented using the digital signal prcessr ADSP-181 frm Analg Devices [16]. In rder t calculate the sin(x) functin we used the fllwing apprximatin [17]: sin x = x.6367x (8) x x 1.893x where the angle x is scaled as shwn: dt

3 value _ f _ the _ angle( rads) x = (9) π The apprximatin (8) is valid nly fr values f the angle x scaled n the first quadrant [17], hwever, using sin( x) = sin( x) and sin( x) = sin( π x) it is pssible t btain the sinus functin f any angle frm the values n the first quadrant. In rder t calculate the cs(x) functin we have made use f the trignmetric identity: π cs( x ) = sin x (1) The integrals needed fr the nn-linear filtering prcess, were calculated using an apprximatin f the trapezidal methd as indicated fr the fllwing difference equatin [18]: 1 y () n = y( n 1) [ x() n x( n 1) ](11) where x(n) is the signal t be integrated and y(n) is the value f the integral calculated. 6 Experimental results In rder t characterize the carrier phase estimatr, we have implemented an ptical self-hmdyne cherent cmmunicatins systems with BPSK mdulatin as shwn n figure 5. In the figure 6a is shwn the phase nise prcess (x) and its estimate (x * ) using the nnlinear filter implemented using the ADSP-181, while in the figure 6b is shwn the squared errr n making the estimatin. In the figure 7a is shwn an scilgram f the phase nise prcess, while in the figure 7b are shwn the phase estimate using the ADSP-181 fr implementing the nn-linear filter (the lighter signal) and the cnventinal PLL (the darker signal) respectively. In the case f the cnventinal PLL it can be bserved an inverted nisy signal. 7 Cnclusin In this wrk we have described the implementatin and characterizatin f a nnlinear filter fr use n the estimatin f the ptical carrier phase n a BPSK hmdyne cherent cmmunicatins system. The nnlinear filter was synthesized taking int accunt the perturbatins that exist n the ptical channel, then as expected it has a better perfrmance than the cnventinal synchrnizer structures. The implementatin f the nnlinear filter based n the use f a DSP has the advantage f being very versatile and easy t mdify but als has the disadvantage f the prcessing speed. References: [1]Ryu S.,Cherent lightwave cmmunicatin systems, Artech Huse, Inc., []F.David, C.Rapp, Breadbard mdel f a cherent ptical BPSK hmdyne system with virtual pilt tne (Vip)-based receiver and MRC auxiliary channel, Prceedings f SPIE Free-Space Laser Cmmunicatin Technlgies XII, San Jse, CA, anuary,. [3]Shimada S.,Cherent lightwave cmmunicatins technlgy, Chapman & Hall, [4]Kazvsky L., Benedett S., Willner A., Optical fiber cmmunicatin systems, Artech Huse, [5]Cvietic M., Cherent and nnlinear lightwave cmmunicatins, Artech Huse, Inc., [6]Lindsey W.C., Synchrnizatin systems in cmmunicatins and cntrl, Prentice-Hall,197.. [7]Kazvsky, L.G., A 13-nm experimental ptical phase-lcked lp: perfrmance investigatin and PSK hmdyne experiments at 14 Mb/s and Gb/s, IEEE Jurn f Ligthw. Techn., Vl. 8,. 9, 199. [8]Kazvsky, L.G., Balanced phase-lcked lps fr ptical hmdyne receivers: perfrmance analysis, design cnsideratins, and laser linewidth requirements, IEEE Jurn. f Ligthw. Techn., Vl. LT.-4,., [9]Arvizu, A., Phase estimatin in cherent ptical cmmunicatins, Dctrate Dissertatin, february,. [1]Arvizu, A., Mendieta, F.J., Optimum estimatin f a phase mdulating Wiener prcess with applicatins in cherent detectin systems, published in the bk Recent advances in signal prcessing and cmmunicatins, Wrld Scientific and Engineering Sciety Press, [11]Jacbsen, G., ise in digital ptical transmissin systems, Artech Huse, [1]Meyr H., Ascheid G., Synchrnizatin in digital cmmunicatins Vl.I, Phase-frequency-lcked lps, and amplitude cntrl, Jhn Wiley and Sns, 199. [13]Harris, F., Carrier and timing recvery techniques in digital mdems, One Day Tutrial, IEEE San Dieg Chapter Signal Prcessing Sciety, 6 th april [14]Snyder D.L., The state-variable apprach t cntinuus estimatin with applicatins t analg cmmunicatin thery, Research Mngraphy 51,The M.I.T. Press, [15]Van Trees, H.L., Detectin, estimatin and mdulatin thery Part I, Jhn Wiley and Sns,1968.

4 [16] Analg Devices, ADSP-1 family user s manual, [17] Analg Devices, n-linear circuits handbk, [18] Hrnbeck, R.W., umerical methds, Quantum Publishers, Inc, plarizatin maintaining ptical fiber ptical cupler regenerated data utput TRASMITTER RECEIVER semicnductr laser surce ASK, FSK r PSK mdulatr balanced phtreceiver carrier synchrnizatin and data regeneratin data signal lcal laser scillatr autmatic frequency cntrl sytem Figure 1 BPSK hmdyne cherent cmmunicatins system electrical bservable V(t) cs(.) gain G1 X - 1/S gain G phase estim at r x*(t) sin (.) Figure Mechanizatin f the equatins that describe the nn-linear filter fr the carrier phase estimatin

5 x data X*pll phase errr fr the cnventinal PLL X phase nise X* nnlinear filter phase errr fr the nn-linear filter x 1 [secs] x 1 [se cs] Figure 3 Typical wavefrms btained by simulatin Figure 4 Phase errr fr the nn-linear filter and fr the cnventinal PLL infrmatin signal data phase nise - laser signal ptical fiber cupler electrptical mdulatr ptical hybrid pin- FET differential amplifier V(t) A/D cnverter DSP based maximum-likelihd carrier phase estimatr DSP D/A cnverter estimated data lcal scillatr electrptical mdulatr - pin- FET high-vltage amplifier ( ) X * estimatr Figure 5 Self-hmdyne cherent cmmunicatins system with BPSK mdulatin and phase nise cntrl

6 3 1 x x* (a) (b) n n (x-x*)^ Figure 6 a)phase nise (x) and its estimate (x * ) using the ADSP-181; b) squared errr in making the estimatin prcess (a) (b) Figure 7 a) scillgram f the phase nise prcess; b) scillgram f the phase nise estimate with the nn-linear filter (lighter trace) and the cnventinal PLL (darker trace).