Indian Journal of Radio & Space Physics Vol. 30, February 200 I, pp. 53-58

An opto-microwave .phase-locked receiver for SCM signals*

B N Biswas, S Pal , A Bhattacharya, D Monda! & P Lahiri

Radion ics Laboratory, Physics Department, Burdwan University, Burdwan 713 I 04

Received 27 December 1999; accepted 8 August 2000

A broadband receiver for the recovery of the subcarriers of coherent subcarrier multiplexing (SCM) signals has been presented. Unlike its predecessors thi s receiver generates negligible inter-modulation noise, and is capable of reducing the effect of laser phase noise to a large extent. Numerical experiments agree well with the theoretical findings.

1 Introduction The subcarrier multiplexing (SCM) technique is an

attractive approach for multichannel di stribution of broadband signals using a s ingle optical carrier1

'2

• It utilizes the wide bandwidth of mono-mode optical fibres , uses electro-optic devices and exploits the advantages of microwave electronics. In addition, bandwidth allocation is very flexible and as such this technique is a current subject of great interest, particularly, in the field of broadcasting networks for broadband services and distribution of video signals .

Several SCM systems using direct-detection method have been used. It first combines the microwave subcarrier signals and then the combined signal is used to intensity-modulate a laser source. Thus, this technique requires laser source with an excellent linearity of the output power versus current characteristics and this severely constraints the number of multiplexed channels3

. In order to overcome thi s difficulty, coherent SCM techniques have been proposed4

'5

. Here the combined microwave subcarriers are used to phase-modulate the lightwave signals. The advantages are the following:

(i) It exploits the wide and flat frequency response of electro-optic phase modulator and thus, it does not require the linearity of the laser output power versus current characteristics and

(ii) It provides improved receiver sensitivity of coherent detection-about 10-15 dB improve­ment over direct detection scheme.

·Part of the paper was accepted for presentation at the International Topical Meeting on Microwave Photonics, Kyoto, Japan, during 3-5 Dec., 1996.

The disadvantages are: (i) adjacent channel cross­talk and intermodulation distortion at the detectors, and (ii) requirement of narrow linewidth lasers ( -10 kHz) at the receiver end. Thi s paper addresses some of these issues and overcomes these difficulties, to a large extent, with the use of a new type of hybrid optical phase-locked loops, called the opto­microwave phase-locked loop (OMPLL).

2 System mechanisation Figure 1 shows the block diagram of the coherent

SCM system that uses an opto-microwave phase­locked loop (OMPLL) at the receiver end . for

MODULATING SIGNALS

OUTPUT ~-------~---~~---L--~

Fig. !--Block diagram of the opto-microwave phase-locked loop. (It is basically a double phase- locked loop making use of optical heterodyning.]

54 INDIAN 1 RADIO & SPACE PHYS, FEBRUARY 2001

isolating the subcarriers. After being appropriately modulated by the modulating signals, the microwave subcarriers are power-combined to phase-modulate an optical carrier of narrow linewidth (of the order of 10 kHz). After transmission through the optical fibre, it is received by OMPLL as shown in Fig. 1. It consists of a local voltage-controlled laser source, an optical phase modulator, a photodetector, a microwave voltage-controlled oscillator, etc. The loop tracks the optical signal and the Jowpass filter output gives the demodulated subcarriers.

3 Analysis Assume the various signals in the loop such as the

incoming lightwave signal

... (I)

and the output of the local laser source after the phase modulator

... (2)

where, ?. is the powe!f of the incoming signal, P0

the

strength of the local laser source and

N

1/f,(t) = L,/3k cos [wkt + ak (t)] ... (3) k = l

wk is the sub-carrier frequency, /3k the optical modulation index, ak the modulating signal, 1JI0 (t) the laser VCO modulation and ~,(t) the phase modulation component due to the phase modulator of the OMPLL. It is apparent that the output of the local laser source is

Then the phase detector output is written as

V11

(t) =A sin if>(t) + n(t) ... (4)

where,

n(t) is the noise, R the responsivity, and r the receiver transresistance.

In deriving the above equations the output of the microwave VCO is taken as

. .. (7)

where, P,. is the power output oft e microwave VCO and r1 the matched load.

Before concentrating on the present system, Jet us briefly refer to the case of the receiver proposed by Olshanskl. Here, the transmitted SCM lightwave signal is detected by a heterodyne receiver and the electrical signal is demultiplexecl and processed to extract the desired signal. Assumi ng the output of the

local laser source as .J2P: cos (wi), the photodetec­

ted IF current can be expressed as

... (8)

where, ry(t) is the detected noise. If f3k' s are equal to /3, then

Therefore, the kth channel output is obtained by putting nk =- 1 and nFO for j :t k, and is given by

I k (t) = 2R~ PoP. l1 (/3)[1 0 (/3)t-1

X COS { ( W 1F - Wk )t - ak (t)} + 7](t) ... (10)

Therefore, the carrier-to-noise ratio (CNR) becomes

. .. (11)

where,

a?r =Shot noise variance= 2qRP,B1F .. . (12)

2 • . NF.kTB1F a,h =Thermal noise vanailce = ----

RL ... (13)

where, q is the electronic charge (1.6x10- 19C), B1F the filter bandwidth, k the Boltzmann constant (1.38x 10-23 J/K), NF the noise figure, T the tempera-

ture, RL the load resistance, a;, the variance due to

adjacent channel intelfference and a ~MP the variance

due to intermodulation products (IMP). The third order IMP's falling within the band of the kth channel is given by

BISWAS eta/ .: OPTO-MICROWA VE PHASE-LOCKED RECEIVER FOR SCM SIGNALS 55

... (14)

The factor h3 denotes the effect of filtering on the IMP's. The maximum value of h3 is unity. The parameter K3 is the number of third order IMP's that fall in the band. This parameter is bounded by 3N3/8. Observe that, for a power levels of 1.0 microwatt and 5 milliwatts, the effect of IMP's will be negligible up to the value of f3 = 0.1.

Let us now consider the proposed OMPLL and evaluate the CNR. Denoting the sensitivities of the laser VCO, microwave VCO and phase modulator by Kt. K111 and KP, respectively, it is easy to derive the governing equation of the system as (in mixed notation)

x[Asinif>+n(t)]+ dlJfs dt

.. . (15)

where, F(s) is the lowpass filter transfer function and n(t) is the loop noise comprising shot and thermal noise mainly.

Looking carefully into the governing equation and adjusting loop parameters it is possible to keep the phase error to a low value such that the loop behaves like a linear one. In that case

Sljf 5 (s)-(K L + K 111 + sK P )F(s)N(s) 1/>(s)=-------.:....__ __ _

s+A(KL +Km +sKP)F(s) ... (16)

The effect of the laser phase noise has been neglected.

From Eq. (16) it is seen that the (sub) carrier-to­noise ratio depends on the phase modulation index and the noise variance due to shot noise, thermal noise and relative intensity noise (RIN). Further, Eq.(l6) indicates the following. If the maximum hold­in range, A (K L + K

111 ), is small compared to the

frequency of the subcarrier and the filter bandwidth is large, then the signal component is

... (17)

and the expression for the locking range under this condition is obtained as6

... (18)

The locking range is an important parameter, as this signifies the maximum frequency error between the signal and the VCO up to which the loop is capable of locking.

On the other hand, when the subcarrier frequency is small compared to the loop natural frequency , it can be shown that the signal component is

.. . (19)

and the locking range is approximately A(K L + K111

) .

Equation (19) clearly indicates that the effective phase error is very small , provided we assume that A(K L + K m) is large compared to the subcarrier

frequency. This can be easily satisfied. That is, the spectral character of 1/>(t) is the same as

that of IJI(t), but its power is much less than that of IJI(t). Note also that the locking range decreases rapidly with the increase of N. Assuming W

11 >We ,

the variance of the noise component at the output of the phase detector is given by

( 2 2 ) 2 u 2 = u st +uti, r (2 p )

I A 2 'i Ill . .. (20)

Note that in deriving the above relation linear operation of the loop has been assumed.

Therefore, CNR in the case when the subcarrier frequency is small compared to the locking range, is given by

(CNR) - {32 P,PLR2 x----::-OMPLL - ( 2 2) (I AK )2 u,, + u,h + P

x( w sc )

2

(J)II

. . . (21)

where, w sc is the subcarrier frequency of a particular

channel. Comparing Eq. (21) with Eq. (11) it is seen that for

low values of {3, the improvement in CNR is nothing over the ordinary detection scheme. However, as the index of modulation is increased the improvement is substantial, and this is shown in Fig. 2. Incidentally, Eq. (21) is derived on the basis of linear tracking.

56 INDIAN 1 RADIO & SPACE PHYS, FEBRUARY 2001

10

m 8 "'0 ,

~ z 6 w

~ w • . > 4 -0 0::: •• Cl. 2 ~

0::: z 0 0

It

•• . . . . . . .. . .. -2 I

0 0.05 0.1 0.15 0.2 PHASE MODULATION INDEX{/1)

Fig. 2-Simulation results showing the improvement of the carrier-to-noise ratio of the OMPLL over that of the conventional detection scheme usi ng mixing and phase-detection (A twenty­channel microwave multiplexed lightwave signal has been taken .)

Had it been otherwise, there would have been intermodulation distortions. However, it will be much less than that of the conventional case.

The CNR for OMPLL [Eq. (21)] does not depend on the intermodulation distortion unlike in the case of the demodulator proposed by the earlier works, where the optimum value of f3 depends on the shot and thermal noise level, the number and spectral form of the lMP's and the received signal level [Eq. (11)] . Simulation results with two subcarriers are shown in Figs 3 and 4. The results have been obtained using MATLAB's Simulink. In deriving Eq. (9), it has been

tacitly assumed that llf>l<n/6. To find the maximum

value of f3k , so that the phase detector works in the

linear region, we proceed as follows. When the number of channel :is ten or more, we can approximate the probability density function (PDF) of lJI s to be Gaussian with zero mean and variance

N/3 2 /2. Since we are at this moment interested in the

largest value of f/>(s) depending on f3 , we can ignore

the presence of the noise term. Therefore, the variance of¢ is given by

2

... (22)

where, S"'(w) is the spectral density of lJI 5 (t) and J,.. the highest value of the subcarrier frequency. Now

S"' ( w) can be ex pressed as

N/32 S (w)=-

"' 2!, . .. (23)

Assume a simple imperfec t integrating filter, i.e .,

1 F(s)=--

1+sT

and

2 A(KL +K,) w, = T

1+AKP 2~w, = T

~ =0.707

a=--- --+-- dw 2 1 N{32 fw111 {(1)4 (1)2 } ~ 2n 2/, o w,; w~T 2

Nf3 1 w, 1 W111 2 { ( ]2 )( ]2 =-2- S w, + 3A(KL + K,)T -;;;::

This can also be expressed as

The PDF of¢ is written as

1 j-q>2

} p(l/>) = exp - 2 ~2naJ 2ao

... (24)

... (25)

... (26)

. .. (27)

Therefore, the probability that 14>1 < n/6 is given by

tr/6 { n ) P{j¢l(n/6}=2 f p(f/>)dq>=erf j2c o 6 2a 2

~

... (28)

BJSWAS et al.: OPTO-MICROWAVE PHASE-LOCKED RECEIVER FOR SCM SIGNALS

t::f!\~~ 6 8 10 12 14 16

TIME,s

.. ~

!;IR l "0 E o· (I)

~ 1\ tl.

16. I 6 J~ J I J

10 20 30 40 50 60

FREQUENCY,rad/s

i::~~=t J 10 20 30 40 50 60

FREQUENCY,rad/s

Fig. 3-Power spectral density and the time history of the detected signal for a two tone phase modulated signal, when the conventional detection scheme is used (Simulation results are obtained with the help of the MATLAB's simulink.)

I_::~~ 30 32 34 36 38 40

TIME, s

1 ilr-l --~--,--1

--.-~----,-1---~--~

I

10 20 30 40 50

FREQUENCY,ra<t/s

t:r:::::==:;;:J 10 20 30 40 50 60

FREQUENCY ,ra<t/s

Fig. 4-Same as Fig. 3, but when OMPLL is used for the recovery of the subcarriers

57

58 INDIAN J RADIO & SPACE PHYS, FEBRUARY 2001

The dependence of P(J¢j<n/6}, i.e., probability of linear operation, on the ratio of the loop natural frequency to the subcarrier frequency is shown in Fig. 5 for two values of {3. The solid line denotes the case for {3 = 0.1 and the dotted line for {3 = 0.2. From Fig. 5 it is evident that, if the ratio of the loop natural frequency to the subc:arrier frequency is twice or

more, the linear operation is almost guaranteed, and hence there will be hardly any intermodulation error.

The optimum value of {3 as obtained by Mendes

and Tan3 is seen to be about 0.15 for

Ns = 20, P, = 1.0 m Wand Po= 0.55 m W, noise figure

= 3.8 dB, R = 1 A/W, r ==50 Q and IF bandwidth=

120 MHz. Here, the maximum value of {3 is limited

by intermodulation distortion. However, in the

proposed subcarrier demodulator, it is almost

independent of IMPs, as the IMPs can be reduced

almost to nothing by adjusting the loop parameters.

For example, by referring to Fig. 4, it is seen that the

value of {3 can be much larger than 0.2, provided

W sc /W, is greater than 2.5. Further, for a 20-channel system where each signal

has a modulation index of 0.44, the probability of

exceeding the linear region is 3x 10-1 and the

corresponding probability of loosing lock is of the

order of 10-33. This is acceptable performance of the

detector.

4 Conclusions

In this paper a simple phase-locked receiver for

demodulation of the subcarriers of SCM signal s is

presented. In the proposed system, the in ~:er­

modulation noise at the output is almost negligible

and, therefore, is capable of handling large index

SCM signals or a larger number of SCM signals.

Depending upon the extent of noise contamination

due to the local laser phase noise or other sources of

5 1.0 £::: ffi 0.8 t5 ~ 0.6 ~ 5 0.4

'"" ~ 0.2 0 ~ c..

~·· · "

1.0 2.0 3.0 NORM. LOOP NATURAL FREQUENCY

Fig. 5-Curves showing the dependence of the probability of the

phase error lying within ± n 16, i.e., probability of linear

operation of the loop, on the ratio of the loop natural frequency to the subcarrier frequency when the number of subcarrier is twenty (The solid line denotes the case for {3 = O. l and the dotted line for

{3 = 0.2.)

noise, phase modulator is to be judiciously used. Incidentally, the double loop arrangement provides a larger locking range without encroaching into the non-linear region of the frequency-voltage characters of the VCO's.

Acknowledgement Financial assistance from the Department of

Science and Technology, University Grants Commission and Department of Electronics, Govt of India, is thankfully acknowledged.

References I Dercie T E, /£££1 LT (USA), 5 (1987) I 103. 2 Olshansky R, Lanzisera V & Hill P, /£££ 1 L T (USA ), 7

( 1989) 1329. 3 Mendes F V C & Tan B T, /£££ 1 Sel Areas Commun

(USA), 8 (1990) 1285. 4 Gross R & Olshansky R, /£££1 L T(USA), 8 (1990) 406. 5 Hill P M & Olshansky R, /£££ 1 L T (USA), 10 (1992)

1656. 6 Biswas B N, Phase-Lock Theories & Application (Oxford &

rBH, New Delhi), 1989.