Optical microwave generation using modified sideband injection synchronization with wide line-width lasers for broadband communications

Optik 125 (2014) 308–313

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Optical microwave generation using modified sideband injection synchronization with wide line-width lasers for broadband communications A. Banerjee a,∗ , N.R. Das b , B.N. Biswas c a

Department of Applied Electronics and Instrumentation Engineering, Academy of Technology, Adisaptagram, Hooghly 712121, West Bengal, India Institute of Radio Physics and Electronics, University of Calcutta, 92 A.P.C. Road, Kolkatta 700009, India c Education Division, SKF Group of Institution, Sir J. C. Bose School of Engineering, Mankundu, Hooghly 712139, West Bengal, India b

a r t i c l e

i n f o

Article history: Received 9 February 2013 Accepted 22 June 2013

Keywords: Broadband mobile communication Optical phase locked loop Optical phase modulator Pull-in range Noise bandwidth

a b s t r a c t In future generation space based phased arrays and in pico-cellular broadband mobile communication systems operating at microwave frequencies optical techniques for transport and generation of electrical signals are widely used. In general, there are two main classes of optical transmitting and generating microwave frequencies: (1) methods using direct or external intensity modulation of lasers and (2) heterodyning method using two coherent optical waves. The present paper dwells on the second method. The present paper overcomes the major practical limitations of optical sideband injection locking. Simulation results have been given in support of the analytical result. © 2013 Elsevier GmbH. All rights reserved.

1. Introduction In creasing demand for broadband mobile communication and limited atmospheric propagation at mm-waves has resulted in the need for high density pico-cells. And as such future cellular broadband mobile communication systems will comprise mmwave components for radio link between the mobile station (MS) and the numerous base stations (BS), which are remotely controlled by the central station (CS). Moreover, the base stations are widely separated from the central station, optical transport of the mmwave signal is the choice owing to the inherent low transmission loss coefficient of the optical fibers. This, in turn, requires the use of lasers and photo-detectors. The cost of numerous BS’s should be kept as low as possible. Therefore, generation and control of mmwave signals should be optically carried out at the control station [1–5], making use of the proposed optical devices needed for the purpose of transport of the mm-wave signals. This avoids the need for mm-wave oscillators and modulators in the numerous base stations. In achieving this purpose two approaches are adopted, viz., (1) single optical source technique and (2) multiple optical source technique.

∗ Corresponding author. E-mail addresses: [email protected] (A. Banerjee), [email protected] (N.R. Das), [email protected] (B.N. Biswas). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.06.062

The single optical source technique is the simplest approach for impressing microwave signal on an optical carrier. It can be realized either by direct current modulation of semiconductor laser or with an electro-optic modulator (Mach Zehnder Modulator (MZM)). Direct current modulation is limited to frequency range below 15.0 GHz and accompanied by a large microwave noise floor due to laser intensity noise RIN and large harmonic content due to laser diode non-linearity. Another disadvantage is non-flat frequency response. Although indirect intensity modulation method MZM enjoys the advantage of large bandwidth over the direct modulation scheme, it suffers from non-linear response, limited modulation depth, optical insertion loss, cost and complexity. At frequencies, above which direct modulation or external modulation has the limitation, one method [1,6], of accomplishing optical generation of electrical signal is obtained by mixing the outputs from two very narrow line-width lasers. But it is not commercially viable because of prohibited costs. Use of commercially available DFB lasers, although eliminates the cost, ends up with the generation electrical signal with large line-width due to inherent laser phase noise of the each source. The spectral purity of the electrical signal can be improved if the noise terms of the optical waves are correlated. The easiest way of to achieve this is to utilize the technique of sideband injection locking of two commercial laser diodes with line-widths in range of few megahertz. The master laser is frequency modulated to create sidebands in the laser optical spectrum. The slave lasers are synchronized to sideband components of the FM signal. The important point is that two slave lasers,

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309

Let the modulation bandwidth of the master laser is close to 10.0 GHz, and it is desired to generate 60.0 GHz mm-wave signal. Using the drive voltages with x = 3.843, the modulator output can be approximately written as



Ei (t) = EI 0.43 sin [(ωi ± 3ω) t + ˛ (t)] +0.114 sin [(ωi ± 5ω) t + ˛ (t)]



(4)

The third harmonic components have been picked up, because the output mm-wave signal is required to be of 60.0 GHz with modulating frequency of 10.0 GHz. Disturbing components are away by 20.0 GHz and 6.0 dB less in amplitude causing almost no pulling and pushing force on the slave laser. Fig. 1. Block schematic of proposed modified optical phase locking arrangement.

3. Governing equation of the system used as active high-Q circuits [7], are thus phase coherent with the master laser and each other, while their frequency separation equals the integer multiples of master laser frequency modulation. The main practical limitations are: (1) the locking range is small (typically a few hundred MHz) so that the laser temperature must be controlled with milli-kelvin precision, as the temperature sensitivity is typically 1.0 GHz/◦ K and (2) the disturbing effect of pulling and pushing effects due to the neighboring sidebands, and the deleterious effect of loop propagation delay. In this paper, we present a modified optical phase locking techniques which is shown in Fig. 1. This modified optical phase locking system overcomes the major practical limitations of optical sideband injection locking.

In the following, for the sake of simplicity, we assume that the two modified OPLL (as shown in Fig. 1) are identical. Let the output of the laser VCO after the phase modulator be E0 = cos[ω01 t + VCO (t) + PM (t) + ˇ1 (t)]

(5)

where ω01 is the free running frequency of the slave laser VCO, ˇ1 (t) is the phase noise of the slave laser, VCO (t) is the phase modulation produced due to the laser VCO frequency modulation and VCO (t) is given by

t



2. System description



Vf t  −  dt 

VCO (t) = 2k

(6)

−∞

Fig. 1 comprises three basic arrangements, viz., (i) sideband generation scheme, (ii) arrangement for phase locking with an additional phase modulator, and (iii) heterodyning of two outputs of the modified optical phase lock system at the photo-detector to generate the millimeter wave signal. The master laser is intensity modulated in such a way as to generate only two required sidebands as far as practicable in order to lock the two slave lasers to the sidebands without interference from the adjacent sideband components. The important point is that the two slave lasers, used as active high-Q circuits, are thus phase coherent with the master laser and each other, while their frequency separation equals the integer multiples of master laser frequency modulation. Let the input to the cascaded MZ modulator be Em cos(ωi t + ˛(t)), where ˛(t) is the phase noise of the master laser and Em is the field associated with the master laser. Assuming the applied modulating voltages (drive voltage) to the two MZMs as





v1 = V ⁄2 + xV sin (ωt)



(1)



v2 = 3V ⁄2 + xV sin (ωt)

(2)

where xV is the normalized amplitude of the modulating signal. Noting  that the  transfer function of an MZM as T = 1⁄2 1 + sin v⁄V , it is not difficult to show that the transfer function ofthe two-cascaded   MZM is T = 1⁄4 1 − cos2 v⁄V = 1⁄4 sin2 (x sin(ωt)), where v is the input drive voltage and V is the half-wave voltage. Therefore, the output optical field of the modulator is given by Ei (t) = 1⁄2E sin (x sin (ωt)) cos (ω t + ˛ (t)). That is, I i



Ei (t) = EI

J1 (x) sin [(ωi ± ω) t + ˛ (t)] + J3 (x) sin [(ωi ± 3ω) t + ˛ (t)] + J5 (x) sin [(ωi ± 5ω) t + ˛ (t)] + · · ·

where ωi is the incoming optical signal frequency.



(3)

where Vf (t) is the loop filter output signal, k is the VCO laser sensitivity in Hz/V and  is the loop propagation delay. In (5), PM (t) is phase modulation due to the phase modulator at the output of the laser VCO and is given by PM

(t) = kP Vf (t − )

(7)

where kp is the phase modulator sensitivity in rad/V. Assuming a balanced optical phase detector and neglecting shot noise, it is easily shown that the photo-detector output is given by

V (t) = A sin  (t) with





A = 2.r.R.



(8) Pr P0

and

 (t) = ˝t −

PM

(t) −

VCO

(t) +

˛ − ˇ1 , where  is the open-loop frequency error. Let the filter be used an integrating one (active low pass filter) with transfer function F (s) = (1 + s2 )⁄s1 . If its output is Vf (t), then it is related to its input, V (t), by the following equation:

1

dV (t) dVf (t) = 2 + V (t) dt dt

(9)

where  1 and  2 are the filter time constants. Now, the active LPF output can be expressed by Vf (t + t) = Vf (t) + V (t) .

t −  2

1

+

2 .V (t + t) 1 

(10)

where t is the sampling interval, Vf (t) and Vf (t+ t) are the loop filter output at t-th and (t+ t)-th instant of time, respectively, V (t) and V (t+ t) are the balanced phase detector output at t-th and (t+ t)-th instant of time, respectively.

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If a passive low pass filter with transfer function F (s) = 1 + s3 ⁄1 + s is utilized, then its output can be expressed by 4



4 Vf (t + t) = Vf (t) 4 + t + V (t + t) .



3 − V (t) . 4 + t

 + t 3

(11)

4 + t

The phase equations of the two modified OPLL’s are written in mixed notation [8]



d˚e1 ⁄dt



= ˝1 − kF(s) (1 + sP ) e −



d˚e2 ⁄dt





dˇ1 ⁄dt

−s



sin (˚e1 ) + d˛⁄dt

 (12)

= ˝1 − kF(s) (1 + sP ) e−s sin (˚e2 ) + d˛⁄dt



dˇ1 ⁄dt



−s





= s ˛ − ˇ1



= s ˛ − ˇ1

 

˚e s + kF (s) (1 + sP ) e

−s



= s ˇ1 − ˇ2



(14)

(16)

H1 (s) =

  ⁄ s + k(1 + sP )F(s)e−s





(21)

1    1 + ωn P ⁄ ωkn

(22)

Pull-in ranges are shown to be







0.5

˝p0 ⁄k = 1.475 ωn ⁄k pm

˝p ⁄k = 2 0.5 ωn ⁄k



(23) (24)

That is,



pm

˝p

⁄ =



2 0.5 k ⁄ωn 1.475

where ωn =



k⁄T

0.5

0.5 (25)





and 2 = ωn P + ωn ⁄k .

We see from (22) and (25) that the noise bandwidth decreases while the pull-in range increases with the increase of normalized hold-in range k⁄ωn . This is opposite to that observed in conventional OPLL system. Consequently upon inclusion of the phase modulator, the dynamic phase locking range is increased. 5. Phase-error variance The receiver performance is affected by two major noise interferences: laser phase noise and photo-detector shot noise. In the following we neglect the shot noise contribution to the phase error, as it is small over the range of the laser line-width (say, 10.0 MHz) with the laser power on the order of 100 microwatt. In this connection it is important to note that noise output is considered at the output of the laser VCO from where the reference signal is taken and not at the output of the phase modulator after the laser VCO. Thus, the loop phase-error variance can be expressed as +∝

2 ˚ = e

  1 − H(jω)2 Sph (ω)dω

(26)

−∝

where Sph (ω) is the power spectral density of the white frequency induced phase noise and is given by Sph (f ) =

(17) H(s) =

−∝

kF(s)e−s

AkF0



(19)

(20)

(15)

These parameters are vital for judging the merit of an optical tracking system. The pull-in range should be as large as possible in order to improve the tracking capability but at the same time the noise bandwidth needs to be as small as possible for improving the noise squelching properties of the system. In achieving the goal, one should not sacrifice the stability of the system. It is worthwhile to remember that in ordinary optical phase lock loop (OPLL), improving the pull-in range deteriorates the noise squelching properties [7,9]. But in this proposed system improvement of the pull-in range improves the noise squelching performance as well as stability. To illustrate let us consider a simple OPLL system with an imperfect integrating loop filter. These parameters viz., noise bandwidth (Bn ), and locking ratio ˝⁄K, are defined as [10]:



=

k

4. Pull-in range and noise bandwidth

where

  (1 + jωP )F(jω) dω

k⁄4 ω   ωn  n P⁄ 1+ k

=

Bn

Bn0

Before we evaluate the phase error variance of the heterodyned signal (rf. output), that determines the bit error rate of the phase locked loop we need to check the performance of the individual phase lock systems, regarding locking range, noise bandwidth and stability and these are discussed in the sections to follow.

⎞ ⎛ +∝

 2 1  Bn = ⁄2 ⎝ H1 (jω) dω⎠



˝−AkF0

Bn0 = k⁄4

pm

Therefore, after heterodyning the phase error ˚e = [˚e1 − ˚e2 ] is given by



   = 1⁄ ˝ − AkF0

where F0 = P ⁄T and F(s) = 1⁄(1 + sT ) . If one ignores the loop delay, then the noise bandwidths of the two lasers, viz., without and with the phase modulator are given by

(13)

˚e1 s + kF (s) (1 + sP ) e−s





Bn



˚e2 s + kF (s) (1 + sP ) e

˝ ⁄k

and thus



where ˝1 = (ωi + 3ω − ω01 ), ˝2 = (ωi − 3ω − ω02 ), P = k⁄kP . Under steady state operation (with the absence of ˛(t) and ˇ(t)), let us assume that the steady state phase error is zero. Therefore, the phase fluctuation in the presence of laser phase noise is





pm



−



and

 f 2



k(1 + sp )F(s)e−s

(27)

  ⁄ s + k(1 + sp )F(s)e−s

(28)

Substituting (27) and (28) into (26), we obtain (18)

2 ˚ = e

2 IPN fn

(29)

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311

∞ A2 dx B2 +C 2

In (29), IPN =

is the phase noise integral.

0

where A=–x









B = −x2 + 1 − 2 px2 . cos (xd) + x p + 2 . sin (xd)









C = x p + 2 . cos (xd) − 1 − 2 px2 . sin (xd) p = ωn P , d = ωn  6. Stability of the system For the loop to act as a reference signal source, it must satisfy the condition of deterministic stability as well as stochastic stability. For deterministic stability, the loop parameters are to be fixed in such a way that the loop does not break into oscillations in a noise free environment. Whereas stochastic stability means that the loop does not often steps out of synchronism due to random fluctuation.

Using (24), (25) and taking the value of Tav as 10 years, a value sufficient to give reliable operation in a practical OPLL [12], we obtain

6.1. (A) Deterministic stability It is known that the introduction of a delay element in a phase locked loop modifies the behavior of the loop in many ways. Of them the most serious is the phenomenon of false or spurious locking, in which the loop slips into false locking instead of locking to the instantaneous phase of the reference signal. The open loop gain of the modified OPLL, is given by kF (s) (1 + sP ) exp (−s) s

G (s) =

(30)

Considering an active LPF with transfer function F (s) = (1 + s2 )⁄s1 and applying Nyquist’s criteria in the frequency domain (i.e., s=jω) to (22), following equations are obtained [11]



1 + 4x2 2 x4

 ≤



ωn  ≤



1 1 + ωn2 P2 x2



(31)

x

(32)

6.2. (B) Stochastic stability Note that although the PLL has been assumed to be working in the linear mode by virtue of the small phase error, the PLL slips cycles (i.e. the phase error of the PLL at times exceeds /2). This happens because the phase fluctuation is a random process, thus there is always a certain probability that the phase error may exceed /2 radians. The exact analytical expression for evaluating the average time (Tav ) between such events cannot be found in this case of a second order PLL with delay. However, the exact expression is available for a delay less first order PLL [7,12]. And for a delay less second order PLL, certain experimental results indicate that the expression for Tav of a delay less first order loop can be applied, provided the corresponding expression for the loop bandwidth is used. The authors also feel that this concept can be applied to a loop with time delay. Thus, we write



2  exp 2⁄˚

4Bn

 =

4.0438f

z ⎡ ⎛ ∞ ⎞⎤

∞ 

2   1 − H (jy) ⁄y2 ⎣19.37 + ln ⎝f H (jy)2 dy⎠⎦ z 0

(34)

0

where fz is the frequency at which the open loop gain of a second order OPLL assumes 0 dB gain, and y = ω⁄ωn . Eq. (34) gives the maximum value of the summed line width to achieve the desired receiver performance. The dependence of the line width on the loop delay and how it can be controlled through a phase modulator are shown in Fig. 2. From this figure it is easily appreciated, the proposed system can be easily built with the help of commercial DFB lasers with line widths ranging between 2 MHz and 20 MHz.



tan−1 2 x + tan−1 (ωn P x)

where = ωn 2 ⁄2 and x = ω⁄ωn .

Tav =

Fig. 2. Maximum allowable laser line-width versus loop delay ␶ for three different normalized phase control parameter. “o” – ωn  P = 0, “*” – ωn  P = 0.2, “+” – ωn  P = 0.4.



e

(33)

7. Simulation results The accuracy of the proposed method is validated in this section by comparing results between theoretical analysis and computer numerical simulation in the MATLAB environment. The simulation results shown in this section are obtained by the time domain numerical model of the modified optical phase locked loop. The numerical model of the modified OPLL is based on (6), (7), (8), (10) and (11). In simulation experiment, the OPLL has been modeled considering strong nonlinearity of the loop and finite loop propagation delay. Phase noise is assumed to be white Gaussian noise, for which Polar Marsaglia method is utilized. The generated phase noise is incorporated to the phase part of both lasers signal. To obtain the value of VCO (t), the integration in (6) has been done applying 4th order Runge–Kutta method. In this procedure VCO (t) is evaluated for each step of the calculation and the filter output controls the frequency and phase of the VCO and slowly loop phase-lock is acquired. It is important to mention that the operating frequencies of the lasers are very high (∼ few hundred THz). Thus, for simulation study large number of sampling points is required in time domain analysis. For this purpose large number of computer memory is needed which is not available. To overcome this difficulty the operating frequency of the optical sources are scaled down to 100 KHz and so, laser line width is taken of the order of few KHz.

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Fig. 3. Loop noise bandwidth ratio and normalized pull-in ratio against the normalized hold-in range. ‘-’ analytical and ‘*’ simulation data for noise bandwidth plot. ‘–’ analytical and ‘+’ simulation data for normalized pull-in ratio plot.

Fig. 5. Variation of phase error standard deviation with laser line-width for three different normalized phase modulator sensitivities. ‘-’ analytical and ‘*’ simulation data for conventional OPLL (with out phase control); ‘–’ analytical and ‘+’ simulation data for ωn  P = 0.2; ‘-.’ analytical and ‘o’ simulation data for ωn  P = 0.4.

pm

Fig. 3 plots the variation of loop noise bandwidth ratio Bn ⁄Bn0



and normalized pull-in range ratio

pm ˝p

k



⁄

against normalized

hold-in range k⁄ωn for normalized phase control parameter ωn  P = 0.4. Passive LPF is considered and the loop delay time is, for simplicity, set to zero. Theoretical and simulation results show that as the normalized hold-in range k⁄ωn is increased, the performance of the modified OPLL improves in terms of noise bandwidth and pull-in range, i.e., the noise bandwidth decreases and pull-in range increases. Good agreement between the theoretical and simulation results is observed. In the simulation analysis, the phase error standard deviation is evaluated from the balanced phase detector output. The open loop frequency error is, set to zero. In Fig. 4, phase error standard deviation is plotted as a function of the loop delay  for three different normalized phase control parameters ωn  P . Referring to kikuchi’s work [13] it is seen that the required phase-error standard deviation is 10 deg in order to suppress the receiver sensitivity degradation at BER of 10−9 below 3 dB. We presume that the summed line-width of the lasers is 10 MHz. Here we have considered a second order optical phase locked loop (type I). We choose a natural frequency of 250.0 Mrad/sec and a damping factor of 2.0. It is seen that conventional phase locking arrangement (without external phase control) is applicable up to about 0.6 nsec loop-delay only. The modified loop with the phase modulator (ωn  P = 0.2) permits required operation up to a loop delay of

Fig. 4. Variation of phase error standard deviation with loop propagation delay for three different normalized phase modulator sensitivities. ‘-’ analytical and ‘*’ simulation data for conventional OPLL (with out phase control); ‘–’ analytical and ‘+’ simulation data for ωn  P = 0.2; ‘-.’ analytical and ‘o’ simulation data for ωn  P = 0.4.

Fig. 6. Normalized maximum allowable loop delay d as a function of normalized phase modulator control parameter p. ‘-’ analytical and ‘o’ simulation results.

about 3.6 nsec. Thus, there is an improvement of more than 500.0 percent. It is important to observe that by properly adjusting the value of phase modulator index, PESD can be kept small over a large value of the loop propagation delay. It seems that theoretical results closely match with the simulation value except in the large loop delay, where it slightly deviates from the simulation value. In Fig. 5, PESD is plotted as a function of laser line-width for three different normalized phase control parameter ωn  P . Here, we have considered a second order OPLL with a loop delay of 4 nsec. Theoretical and simulation results show that as the laser line-width is increased, performance of the modified OPLL detorites in terms of PESD, i.e., PESD increases. To realize the same phase error standard deviation (10 deg) for the two cases, namely with ωn  P = 0 and ωn  P = 0.4. The ratio of the summed line-widths of the lasers with and without phase control can be found to 300%. That is, with the modified OPLL, 3 times more line-width of the laser can be allowed. Good agreement between the theoretical and simulation results is observed. Normalized phase control parameter ωn  P variation with the normalized loop delay ωn  at absolute zero phase error condition is shown in Fig. 6. From Fig. 6 it is concluded that about 14% increase in the value of ωn  (i.e. 0.98 compared to 0.736) is possible with ωn  P = 0.4. That is, for the same value of the loop natural frequency the loop can accommodate a larger value of the loop delay without throwing the loop into unstable operation. It seems that theoretical results closely match with the simulation value.

A. Banerjee et al. / Optik 125 (2014) 308–313

8. Conclusion The modified dither optical phase lock loop, as suggested, overcomes the major practical limitations of optical sideband injection locking with the help of commercially available DFB lasers with wide line-width. This modified OPLL seems a realistic approach for generating reference signal for future advanced communication systems with active phased array antennas. This technique provides the advantage of low weight, small size, flexible and above low cost because the proposed technique significantly reduces the requirement of narrow line-width lasers. The modified OPLL contains an additional phase modulator in the phase locking branch. The addition of the phase modulator at the output of the VCO lasers reduces the effective phase error and consequently the improvements are: (1) the effective loop noise bandwidth becomes narrower resulting better noise rejection capability, (2) due to the reduction of the effective phase error, the possibility of exceeding a phase error 90◦ becomes less and so the frequency of cycle-slips is considerably reduced, and (3) the instability of the system due to the loop delay is considerably reduced. References [1] R.P. Braun, G. Grossskopf, D. Rhode, F. Schmidt, Fiber optic millimeter-wave generation and bandwidth efficient data transmission for broadband mobile

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