An improved optical costas loop PSK receiver: Simulation analysis

Journal of Scientific HELALUDDIN: & Industrial Research AN IMPROVED OPTICAL COSTAS LOOP PSK RECEIVER: SIMULATION ANALYSIS 203 Vol. 67, March 2008, pp. 203-208 An improved optical costas loop PSK receiver: Simulation analysis G M Helaluddin* Department of Physics, Durgapur Government College, Durgapur 713 214 Received 29 June 2007; revised 18 December 2007; accepted 24 December 2007 Simulation analysis of proposed optical costas loop has been investigated considering strong nonlinearity of loop and finite loop delay through phase subtraction. Prime attention has been given on inherent laser phase noise due to random spontaneous emission and shot noise related to photo detection process. The stringent laser linewidth requirements for promising receiver has been relaxed up to 8.0 MHz for each laser considering 3.3 RMS phase error and power sensitivity improvement is realized introducing an extra optical phase modulator at VCO laser output. Keywords: B (balanced phase detector), DFB (distributed feed back), OPM (optical phase modulator), Optical costas loop, PSK (phase shift keying), VCO (voltage controlled oscillator) Introduction Optical phase locking is fundamental technique for coherent optical homodyne/heterodyne detections of phase shift-keying (PSK) receivers. The studies are reported 1-3 on trade off between detector shot noise (SN) and laser phase noise (PN) in pilot carrier and optimization of loop natural frequency or loop bandwidth to minimize loop phase error. Balanced phase locked loop (PLL) and decision driven PLL have been investigated considering effect of SN and PN, and data-to-phase lock cross talk and effect of low frequency flicker noise. This condition is valid for the system with low laser linewidth (<100 KHz). However, for larger linewidth laser sources, where larger band width loops utilized, phase shift due to transit-time of error signal round the loop and its effect on phase error variance must be taken into account 4-5. Optical phase locked loops (OPLLs) that require extremely narrow linewidth lasers 6 (6x10-6 times bit rate) need to design an OPLL with broader linewidth laser diodes in cost aspect. Optical costas loop (OCL) with broad band width can tolerate a broader linewidth requirement by using a nonlinear technique as compared to pilot carrier OPLL 7-9. OCL also enjoys advantages of its electrical counter part, yet inherent *E-mail: g.helaluddin@yahoo.com disturbances in the system due to SN of photo detectors and PN, which degrades loop performance 10. Theoretical analysis shows that, condition of stable loop operation is ω n τ D d 0.736 5, which is modified to ω n τ D d 0.98 with an additional phase control arrangement with control parameter, ω n τ p =0.4 12 ; where ω n is normalized loop natural frequency, τ D normalized value of loop delay time and τ p normalized value of optical phase modulator sensitivity. Also, linewidth requirements for binary phase shift keying (BPSK) homodyne detection considering loop propagation delay is obtained theoretically 11. Linewidth requirements ignoring loop delay time are useful for low bit rate system. But linewidth requirement is limited by loop delay time in high-speed transmission system 12-17. Therefore, loop propagation delay is an inherent phenomenon in OCL. Proposed system has been designed incorporating an optical phase modulator (OPM) at voltage controlled oscillator (VCO) output to modulate phase of VCO signal to compensate loop delay and control phase of reference signal to offer better system performance with linear phase modulation characteristic. Proposed Optical Costas Loop PSK Receiver Proposed system for simulation investigation has been modeled using source laser, VCO laser with OPM at the output, two balanced phase detector (B)

204 J SCI IND RES VOL 67 MARCH 2008 B-1 V I DECISION OUTPUT V A SOURCE LASER E S E V OPM VCO LASER ACTIVE LPF LOOP AMPLIFIER MULTIPLIER MIXER λ/4 V G B-2 V Q λ/4 /4 λ/4 /4 3dB COUPLER 3dB COUPLER + - + - + - BALANCED PHASE DETECTOR (B) Fig.1 Block diagram of proposed optical costas loop PSK receiver at in-phase (B-1) and quadrature arm (B-2), multiplier-mixer, loop amplifier and active LPF (Fig. 1). Output controls phase and frequency of VCO laser automatically. VCO tracks frequency and phase of source optical signal by automatic phase controlled feed back loop. Since linear analysis of OCL has been investigated neglecting nonlinearity of loop, which is inherent characteristic of the system 17. For simulation analysis of phase shift keying (PSK) receiver, strong nonlinearity of loop and stringent laser linewidth requirements are taken into account. Loop parameters like, loop natural frequency that depends on filter time constants, dc loop gain, damping factor, carrier frequency of input source signal and central frequency of VCO signal are selected for optimum system performance.

HELALUDDIN: AN IMPROVED OPTICAL COSTAS LOOP PSK RECEIVER: SIMULATION ANALYSIS 205 System Analysis In proposed OCL (Fig. 1), output light wave fields of two DFB lasers (source & VCO laser) are presented as E S = (2P S ) m Sin[ω S t+θ S ]...(1) E V = (2P V ) Cos[ω V t+θ V + φ+ ψ]...(2) In-phase and quadrature arm balanced phase detectors output are expressed as V I = R{(r[(E S1 +E V1 )/ 2] 2 r[(e S1 -E V1 )/ 2] 2 ) -(r[(e SQ1 +E VQ1 )/ 2] 2 r[(e SQ1 -E VQ1 )/ 2] 2 )}+n I V Q =R{(r[(E S2 +E V2 )/ 2] 2 r[(e S2 -E V2 )/ 2] 2 )...(3) -(r[(e SQ2 +E VQ2 )/ 2] 2 r[(e SQ2 -E VQ2 )/ 2] 2 )}+n Q Loop amplifier output is represented as...(4) V A = K G V I V Q...(5) where, P S & P V, source & VCO laser power respectively; m, +1 or 1; θ S & θ V, phase modulation of source & VCO laser respectively; φ, phase modulation due to feed back control of the loop; ψ, phase modulation due to OPM; (E S1, E S1, E V2 ), in-phase power splitting of source laser & VCO laser field respectively; (E SQ1, E SQ2 ) & (E VQ1, E VQ2 ), quadrature power splitting of source laser & VCO laser field respectively; and n I, n Q, shot noise contribution to in-phase & quadrature arm respectively. Considering time domain analysis for loop filter transfer function [F(s)=(1+sτ 1 )/sτ 2 ], output of active LPF is represented as V FL (t+ t) = V FL V A [τ 1 /τ 2 ] V A (t+ t) [(τ 1 + t )/τ 2 ]...(6) Now, phase contribution φ due to feed back control of loop at the frequency modulating part of VCO laser is given by...(7) Phase modulation due to OPM at VCO laser output is ψ = SV FL (t-τ D )...(8) where, V A & V FL, loop amplifier & LPF filter output respectively; t, sampling interval. Specific value of parameters are as follows: frequency of source signal (f s ), 100 THz; source laser power (P S ), - 53.0 dbm; filter time constants τ 1 & τ 2, 0.1 µs & 0.16ns; VCO laser sensitivity (K V ), 300 MHz/volt; loop amplifier gain (K G ), 4.47x10 5 ; power division factor (K I ), 0.707; photo detector sensitivity (R), 1 A/W; detector trans impedance (r), 2.74 KΩ; loop delay (τ D ), 20 ns; OPM sensitivity (S), 12.0 rad/v. System Noises a) Lasers Phase Noise In OPLL systems, PN of lasers is very much important on loop performance. For commercially available distributed feed back (DFB) lasers, PN is large and a wide control bandwidth is required for the system. In most cases, PN consists of random-walk frequency noise, flicker frequency noise and white frequency noise etc 13. But in optical domain, first two components are negligible compared to white frequency noise due to large frequency of optical signals. One-sided power spectral density of white frequency noise is given by S PH (f) = δν/πf 2 rad/volt. δν = δν S + δν V...(9) where, δν S & δν V, source & VCO laser linewidth respectively. b) Photo Detectors Shot Noise SN is additive in optical systems, originated due to quantum detection process. The terms n I & n Q in Eqs (3) & (4) represent SN contribution of photo detectors at in-phase arm and quadrature arm respectively. Spectral densities of these noise terms are expressed as, S I (f)= 2eR[(1-K I2 ) 2 P S +K I2 P V ]r 2 V 2 /rad S Q (f)= 2eR[K I2 P S +(1-K I2 ) 2 P V ]r 2 V 2 /rad...(10) Photo detector sensitivity R is given by R = eη/hf...(11)

206 J SCI IND RES VOL 67 MARCH 2008 Table 1 Study of stability boundary (P S =-53.0dBm, P V =0.33dBm, δν S =5.0 MHz, δν S =5.0MHz) OPM sensitivity, rad/v 0.0 3.0 6.0 9.0 12.0 15.0 Loop delay, ns 67 76 84 92 98 82 Table 2 Lock-in range performance τ D = 0 ns τ D = 10ns S=0rad/V S=0rad/V S=10rad/V 46.60 MHz 8.82 MHz 10.52 MHz Fig.2 RMS phase error (σ) variation with laser linewidth at P S =-53.0dBm, P V =0.33 dbm, τ 1 =0.1µs, τ 2 =16ns, τ D =20ns where, η, quantum efficiency of photo detectors; e, electronic charge; h, Planck s constant; and f, detected optical frequency. In simulation experiment, both PN and SN are assumed to be White Gaussian noise, for which Polar Marsaglia method 15 is utilized. The generated SN is incorporated to B-1 & B-2 output and PN to the phase part of both lasers signal. Results and Discussion OCL is an important demodulation scheme for PSK coherent detection 11. Linewidth (approx. 1.0 MHz) is the state of art for DFB lasers. However, laboratory results indicate that linewidth as low as 250 KHz can be realized 8. Therefore, in order to design proposed system with commercially available DFB lasers (linewidth, ~2-5MHz) are preferable. As system bandwidth is very large and lasers linewidth ~few MHz, loop delay time is nonnegligible and absolute stability of system should be realized. Introduction of a delay element in an OCL modifies loop behaviors; most serious one is false locking, in which loop slips into false locking instead of locking to instantaneous phase of reference signals. Thus, to examine loop stability, variation of S with τ D is analyzed at absolutely zero phase error condition (Table 1), where τ D increases up to 98 ns for S at 12 rad/ V and after that τ D decreases with S. So, maximum allowable value of S is 12.0 rad/v within stable system boundary. Loop acquisition time is reduced, i.e. lock-in stage attains faster and lock-in range increases. Lock range falls sharply in presence of delay element but improves in proposed system due to OPM (Table 2). About 1.7 MHz lock-in range increases with S at 10.0 rad/v. As system bandwidth increases, large volume of information can be received by improved system In proposed system, loop delay effect is compensated by increasing S, lock-in range increases, loop bandwidth enhances and RMS phase error reduces. Moreover, loop performance is dependent on power splitting ratio used because SN arises within OCL due to quantum detection process and PN, inherent component of lasers, affect system seriously. Variations of σ is studied with source and VCO laser linewidth (Fig. 2). Also, dependence of σ on source & VCO laser power is determined (Figs 3 & 4) respectively. It is observed that σ increases with linewidth of source and VCO laser almost linearly and for a typical case, P S =-53dBm, P V =33 dbm, δν S = 5.0 KHz, δν V = 5.0 KHz, σ reduces to 1 with S=12 rad/v. Consider RMS phase error as 3.3, linewidth requirement is relaxed for source laser from 5.05 to 13.53 MHz and VCO laser from 5.02 to 13.7 MHz (Table 3). Proposed system may allow laser sources with linewidth ~13.0 MHz with same value of σ as that of ordinary system with linewidth ~5.0 MHz each. Improvement in power sensitivity of source and VCO laser is 1.47 dbm and 2.76 dbm respectively at same value of σ, 3.6 (Fig. 3). Therefore, commercially available DFB lasers with linewidth ~10-50 MHz can be easily used to design OCL with required linewidth requirements and optical

HELALUDDIN: AN IMPROVED OPTICAL COSTAS LOOP PSK RECEIVER: SIMULATION ANALYSIS 207 5.5 5.5 RMS phase error, 5 4.5 4 3.5 Without OPM Proposed system: VCO laser power = -0.33 dbm RMS phase error, 5 4.5 4 3.5 Without OPM Proposed system: Source laser power =-53.0 dbm 3 3 2.5-60 -59-58 -57-56 -55-54 -53 Source laser power, dbm 2.5-6 -5-4 -3-2 -1 0 VCO VCO laser laser power, power dbm dbm Fig.3 RMS phase error (σ) variation on Source laser power (P S ) at P V =0.33 dβm, δν S =5.0 MHz, δν V =5.0 MHz, τ 1 =0.1µs, τ 2 =16ns, τ D =20ns Fig.4 RMS phase error (σ) variation on VCO laser power (P V ) at P S = 53.0 dβm, δν S =5.0 MHz, δν V =5.0 MHz, τ 1 =0.1µs, τ 2 =16ns, τ D =20ns Table 3 Lasers linewidth requirements [P S =-53.0 dbm, P V =0.33 dbm] RMS Source laser linewidth, MHz VCO laser linewidth, MHz phase error (at δν V = 5.0 MHz) (at δν S = 5.0 MHz) σ Without Proposed Without Proposed OPM system OPM system 3.3 5.05 13.53 5.02 13.7 4.0 12.23 23.68 12.07 25.58 Table 4 Lasers power budget [δν S =5.0 MHz, δν V =5.0 MHz] RMS Source laser power VCO laser power phase requirement, dbm requirement, dbm error σ [at 0.33 dbm fixed VCO laser [at -53.0 dbm fixed source power] laser power] Without Proposed Without Proposed OPM system OPM system 3.6-55.78-57.25-1.07-3.83 4.5-58.45-59.16-4.06-5.65 sources with larger value of power sensitivity, which enhances power budget requirement for future optical PSK receiver (Table 4). Conclusions Computer aided design of OCL receiver (PSK), possess PN due to finite linewidth of lasers, SN contaminated to the system during quantum detection process and finite loop delay time. A new OCL has been proposed incorporating an OPM at VCO laser output. OPM has linear phase modulation characteristic, which controls phase and frequency of VCO laser. In presence of OPM, loop delay is compensated and loop achieves lock-in state very quickly and locks range increases. The

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