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In this letter we show first experimental data on the dependence of the lineshape of 1-3 /mi InGaAsP DFB lasers on the
measurement time. The lineshape is measured by using
delayed self-heterodyne set-ups5 with fibre delay lines having
different lengths (1-5 km and 27 km). The result shows that
the linewidth with the longer delay line is larger than that
measured with the shorter delay line. Furthermore, an
analysis of the data suggests that the \/f noise in the FM noise
spectrum is the principal cause of the power-independent line
broadening. The possibility of linewidth reduction using a
narrowband automatic frequency control scheme is also discussed.
dominant cause of the spectral broadening in such high-power
operation of a DFB laser. (Note that the dependence of the
linewidth on the delay-line length is even stronger in the
experiment than in the theory.)
Lineshape determined by delayed self-heterodyne method: We
assume first that the FM noise spectrum S{f) consists of the
power-dependent white noise and power-independent \/f
noise:
S(f) = C + K/f
(1)
where K and C are frequency-independent, whereas C is
inversely proportional to the output power.
The lineshape determined by a scanning Fabry-Perot interferometer with a finite measurement time xm is not affected by
the FM noise component having frequencies below l/rm,
because the finite measurement time is equivalent to a highpass filter which eliminates frequency fluctuations below l/xm.
Consequently, as shown theoretically by O'Mahony and
Henning,4 the measured lineshape depends strongly on the
measurement time only when \/f noise exists in the FM noise.
Next, we consider the delayed self-heterodyne method,
whose principle is described in Reference 5. The delay time xd
in the delayed self-heterodyne method corresponds to the
measurement time xm of a scanning Fabry-Perot interferometer. The reason is given in the following. We consider a frequency fluctuation component whose frequency is much lower
than l/xd. For such a component the phase difference between
the signal beam and the reference beam after travelling
through the delay line is small; hence the frequency component of the FM noise below l/xd is eliminated automatically
in the delayed self-heterodyne method. Therefore, similarly to
the case of a scanning Fabry-Perot interferometer, the measured IF linewidth will depend strongly on the delay-line
length only when the 1//noise exists. When it does not exist,
the linewidth increase is practically negligible in most cases.
The lineshape /(/) of the IF signal obtained by the delayed
self-heterodyne method is related to the FM noise spectrum
S(/)as
10MHz
l^U
Fig. 1 IF spectra measured by delayed self-heterodyne method
a Length of delay line = 27 km
b Length of delay line = 1-5 km
The above conclusion is particularly important in the application of such lasers to coherent communications, because it
means that the lineshape could be improved effectively by an
automatic frequency control (AFC) having a relatively narrow
bandwidth. It has generally been believed for the AFCoriented lineshape improvement techniques at microwave frequencies that an AFC circuit with a bandwidth fm reduces the
spectral density of noise sideband within ±fm of the carrier.
This statement is valid when the origin of the spectral spread
is white noise, but not valid when it is 1// noise. When the 1//
noise is predominant, an AFC in narrow bandwidth may
reduce the linewidth drastically. In heterodyne optical communications, such a reduction can also be achieved in the
receiver by an AFC scheme in the local oscillator. Experiments are now being performed and will be reported later.
Acknowledgments: We thank Dr. K. Kobayashi of OptoElectronics Research Laboratories, NEC, for supplying DFB
lasers. This work is supported by a Scientific Research grantin-aid from the Japanese Ministry of Education, Science &
Culture.
K. KIKUCHI
T. OKOSHI
3rd September 1985
Department of Electronic Engineering
University of Tokyo
Bunkyo-ku, Tokyo 113, Japan
x (1 - cos 2nf'xd) df
'X]
(2)
References
1
5
where J " denotes a Fourier transform. Derivation of this
equation will be given elsewhere. In eqn. 2 the fact that lowerfrequency components are cut off is expressed by the term
(1 — cos 2nf'xd).
3
Experimental results: The laser under test was a 1-3 fim
InGaAsP DFB laser. Lineshapes were measured by using the
delayed self-heterodyne set-ups with 1-5 km and 27 km singlemode fibre delay lines. Fig. 1 shows lineshapes of the IF signal
measured when the bias current level was six times the threshold. The FM noise spectrum of the laser was also measured,
giving K = 1-44 x 1012 Hz2.
Discussion: In Fig. 1 the linewidth (FWHM) measured with
the 27 km fibre is 21 MHz, and that with the 1-5 km fibre is
14 MHz; a remarkable change is observed in the linewidth.
We calculate here the linewidth of the IF signal using
eqns. 1 and 2. We assume temporarily that the white noise
component in the FM noise spectrum is negligible (C = 0 in
eqn. 1) because the bias current level is fairly high. Under such
an assumption, the linewidth calculated for the 27 kmfibreis
21 MHz, and that for the 1-5 km fibre is 17 MHz. These
results support the assumption that the 1//" noise is the pre1012
2
4
5
YARIV, A.: 'Quantum electronics' (J. Wiley & Sons, New York,
1975), eqn. 13.2-18
WELFORD, D., and MOORADIAN, A.: 'Output power and temperature
dependence of the linewidth of single-frequency CW (GaAl)As
diode lasers', Appl. Phys. Lett., 1982,40, pp. 865-867
KIKUCHI, K., and OKOSHI, T.: 'Measurement of spectra of and cor-
relation between FM and AM noises in GaAlAs lasers', Electron.
Lett., 1983,19, pp. 812-813
O'MAHONY, M. J., and HENNING, I. D. : 'Semiconductor laser linewidth
broadening due to 1//carrier noise', ibid., 1983,19, pp. 1000-1001
OKOSHI, T., KIKUCHI, K., and NAKAYAMA, A. : 'Novel method for high
resolution measurement of laser output spectrum', ibid., 1980, 16,
pp. 630-631
TRANSFER CHARACTERISTIC OF A LINEAR
PHASE DETECTOR FOR VARIABLE PHASE
Indexing terms: Circuit theory and design, Detector circuits
The performance of a linear phase detector for noisy signals
and variable phase is investigated. It is shown both theoretically and experimentally that in this case the range of phase
differences, which can be measured without systematic errors,
decreases.
ELECTRONICS LETTERS 24th October 1985 Vol. 21 No. 22
Introduction: It is well known that the performance of the
so-called linear (sawtooth) phase detector degrades when the
input SNR is small. 12 These detectors are essential parts of
many types of phase meters, so a systematic error of phase
measurement arises when the input SNR is poor. However, to
the author's knowledge, nothing is known about what
happens if the phase varies during the measurements. This is
of importance, for example, in phase ranging of mobile vehicles.
Operating principle: A model of the sawtooth phase detector
and its characteristic A($) for noiseless signals is shown in
Fig. 1. The positive edge of the first signal sets the RS flip-flop
and the positive edge of the second signal resets it. Then the
output of the flip-flop is averaged. In this way the output of
the detector for noiseless signals is directly proportional to the
measured phase shift.
limiter
inputs
limiter
_d_
dt — !
RS
flip-flop
d
dt
We study in detail the case when the phase varies linearly
during the measurements according to the rule
tel
T T
-—,—
(5)
This corresponds to the uniform motion of the positioned
object. Using on eqns. 3 and 5, we can compute the values of
<$*> for various <f>0 and A. The results for SNR = 10 are
presented in Fig. 2. As is readily seen, when the value of A
increases it makes the useful (linear) range of the phase detector narrower.
360*
integrator
2 7 7 <(>
ex
[77O/T1
30*
300*
60°
Fig. 1 Linear phase detector and its characteristic
330°
360*
[7707F|
Characteristic for variable phase: When the phase varies
during the time T, the result of measurements in the presence
of narrow bandwidth noise is given by
T/2
<t>* = -
(1)
Fig. 2 Mean value of(f>* against parameter (f>0
To compute the variance of </>*, 0^., we note that in the
linear (useful) part of the characteristic of the detector this
variance is approximately equal2 to o~\.
When M independent measurements are taken during time
T, the value of <J\* is then given by
-772
Here <f>(t) is the true value of the measured phase shift and n(t)
is the value of the noise. The function A(<£) is depicted in
Fig. 1. The mean of <f>* is
Measurements: The measurement system used to verify the
theoretical results is depicted in Fig. 3.
signal
generator
T/2
phase
meter
dt
-T/2
filter
T/2
ill
A[$(f) + n]p{n) dn dt
(2)
-T/2 - x
Here p(n) is the probability density function of n. For additive
Gaussian narrow bandwidth noise in one channel and moderate and large SNRs, the function p(n) is also Gaussian1-2 with
zero mean and variance a\ ~ 1/(2SNR). In this case we have,
from eqn. 2,
T/2
T/2
= Y J MWRdt + Y f
-T/2
-T/2
where the function G(<f>) is defined as
:
J
e"
(f2/2)
dt
<t> e (0, n)
(4)
(6)
2M . SNR
summer
I
noise
generator
/
variable
phase
shifter
/
impulse
generator
-output
1
voltagecontrolled
phase shifter
1 ^ L
r
integrator
Fig. 3 Block diagram of experimental system
To obtain the linearly varying phase, a voltage-controlled
phase shifter (VCPS), similar to that described in Reference 3,
was used. During the experiment the phase shift of the VCPS
had an almost linear dependence on the controlling voltage.
The phase meter worked only during the impulse from the
generator. The results are marked in Fig. 2 and they agree
well with the predictions. Some discrepancies are most probably caused by instabilities of the VCPS.
Conclusions: It has been shown that changes of the phase
during the measurements decrease the effective range of the
phase differences which can be measured without systematic
errors. This range becomes smaller if the values of a\ and/or A
increase.
2x)
[
K. HOLEJKO
J
It follows from eqn. 3 that errors of measurement arise even in
the absence of the noise if the measured phase exceeds the
0-2TC range. To avoid this effect it is necessary to equip the
detector with some kind of memory able to record 0—*2n
(27i-»0) transitions. The second term in eqn. 3 describes the
errors due to noise.
ELECTRONICS LETTERS 24th October 1985
27th August 1985
J. SIUZDAK
Vol. 21
Instytut Telekomunikacji PW
ul. Nowowiejska 15/19
00-665 Warszawa, Poland
References
1
HOLEJKO, K.: 'Phase measurements in the presence of narrowband
noise', Rozpr. Elektrotech., 1977, 23, pp. 487-506
No. 22
1013
RAAB, F. M., and WAECHTER, J. R.: 'The counting phase detector
with VLF atmospheric noise', IEEE Trans., 1977, AES-13, pp.
522-532
TAY, E. w., and MURTI, v. G. K.: 'Unity-gain frequency-independent
quadrature phase shifter', Electron. Lett., 1984, 20, pp. 431-432
Let q be the difference between quantiser levels. The probability density function (PDF) of the quantisation noise is
assumed to be uniform between — q/2 and q/2, and zero elsewhere. Since we assumed that the receiver's A/D levels are
identical to the transmitted levels, the receiver quantiser only
affects the WGN. If a 'zero level' is transmitted, the PDF of
the WGN will be modified by the quantiser to the function
shown in Fig. 2. In Fig. 2, the delta functions have the areas
a0, at, a2,... as shown and the quantisers have 2n levels (i.e.
log2 2n bits). It can be easily shown that
PERFORMANCE OF A FOURIER
TRANSFORM DATA TRANSMISSION
SYSTEM
9/2
exp (-£)*,-erf
(1)
-9/2
Indexing terms: Data transmission, Fourier transforms
Results on the performance of a Fourier transform data
transmission system in white Gaussian noise are presented
for various quantisation widths and transform sizes.
Introduction: Recently, there has been some interest in the
Fourier transform data transmission (FTDT) system,1-2 which
was first proposed by Weinstein and Ebert.3 The Fourier
transform is used in this line coding/modulation technique to
process the incoming data prior to transmission and this
allows the spectral properties of the signal to be controlled.
This leads to the following advantages:
where erf (x) is the error function and a2 is the noise power.
Similarly
k 4= n
at positive end
k =(= n — 1 at negative end (2)
and at the positive end
(a) Injection of pilot tones provides the receiver with timing
information, automatic channel equalisation ability and
immunity to channel fades and Doppler shifts.
(b) A constant tone interference in the channel can be neutralised by avoiding the use of the part of the spectrum affected.
(c) Using a variable data rate for different parts of the spectrum for optimum error performance when the channel noise
is coloured.
In addition to these, the system may be designed to detect and
remove isolated impulsive interference.4
This letter examines the error performance of the FTDT
system in the presence of white Gaussian noise (WGN).
Results comparing the error rate using different quantisation
levels and transform sizes are given.
data in transmitter
modem
channel
jantise
antiser
noise
receiver
modem
(3)
and at the negative end
a=h
erfc
(2n-
(4)
where erfc (x) = 1 — erf (x). For this analysis, it is convenient
to make the following approximations:
(a) Although the quantised noise PDF varies with the transmitted signal level, it is simpler to use only the one presented
above in the evaluation instead of averaging over the various
PDFs. This should not affect the final result significantly, as
most of the transmitted signal levels are near to and centred
around zero.
(b) The quantised noise PDF is made symmetric by equating
an to zero and setting both a n _! by eqn. 3. The effects of this
should be negligible.
data out
O"
a-
P(s)
Fig. 1 System model
Theory: Let Fig. 1 represent the system. The following
assumptions have been made:
cyq
(a) There is negligible rounding noise in the transform process,
compared to the amount of quantisation noise.
(b) The transmitted signal levels are identical to the receiver's
A/D levels.
(c) There is negligible correlation between noise samples.
5q/2 9q/2
(d) A constant power transform is used and no arithmetic
overflow occurs.
•"0
a
-nq
2»
ifl
-Aq -2q 0
*a2
On-,
Fig. 3 PDF of total received noise p(s)
The quantised noise is added to the transmitter quantisation
noise that is originally present and the PDF of the sum, p(s)
(which is a convolution of their respective PDFs), is as shown
in Fig. 3.
The N-point DFT can be represented by
2q Aq
[gisTi]
Fig. 2 PDF of quantised noise
1014
ELECTRONICS LETTERS 24th October 1985
Vol. 21
No. 22
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