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```8 XIAN, Y. Y. : 'New proof of higher dimensional Hadamard matrices',
J. Syst. Sci. & Math. Sci., 1987, 7, pp. 346-349
9 XIAN, Y. Y.: 'On the classification of 2 4 Hadamard matrices', ibid.,
1987, 7, pp. 40-^6
10 XIAN, Y. Y.: 'The operations and applications about higher dimensional matrices', J. Chengdu Inst. Radio Eng., 1987, 16, pp.
191-199
11 XIAN, Y. Y.: 'On the numeration of 5-dimensional Hadamard
matrices of order 2', J. Beijing Univ. Posts & Telecommun., 1987, 4
(2) If / = k + y/k for k > 1, then the equation group has no
root. In fact, taking the product of the first 4/c ? 1 equations
we have
4k-1 / 4k
n 111
J=I
bitbh,
Appendix: Proof of theorem 2:
1 < ��
Definition: Let B = (B^) be a two-dimensional matrix with
elements 0, 1. If the equation W(Bn � Bn, ...,Bin@ Bjn) = \n
holds for any i # 7 , where W(.) means the weight of the 0-1
vector and � means mod-2 sum, then the matrix B is called
an H 0 -matrix.
By this definition, theorem 2 is equivalent to the following
theorem:
Theorem 2': If k > 1, then there exists no H 0 -matrix with the
form
Bn=
l
"?
T1
b3
...
bx
T
b2
v�i
i.e.
...,bt4t_lb,l
14.*-1
Because 6, = 0 or 1, the length of every term bhbiv
. � - A 1 + A2 +2, ???,&,玙,+4*-i is at least 4/c - 1, so
...,
b
b b
h i 2,
???>bitk_lbil
+ 1
b i 2 + 2, ? ? ? , * > m - l + 4 k - i = 0
4k l
i.e. (/c ? <Jk) ~ = 0. This is in contradiction with k > 1.
(3) If / = k + y/k for k > 1, then the equation group 2 has no
root.
In fact, if blt b2,..., fe4k is a root of equation group 2, letting
i-b2
l-by
(i)
...
...
i1-
[l-b2
For the proof of theorem 2', we begin with two lemmas:
Lemma 1: Let Bo be the above matrix, p = W(bt, . . . , 6 4k );
then p = k + I, W(bxbit b2 bj+ x , . . . , 6 4k 6 ; + 4 k _ t ) = /,; > 2.
Proof: By the identical equations
then Bo is a cyclic H 0 -matrix with lt = k ? y/k; this is in
According to the above three steps, we now know that the
equation group 2 has no root.
W(at + by, ..., an + bn) = W(au ..., an) + W(bu ..., bn)
-2W(albl,...,anbn)
and
TWO-CHANNEL SYSTEM DEMONSTRATION
OF DIFFERENTIAL FREQUENCY-DEVIATION
MULTIPLEXING
We have
W(by, ..., bn)+W(bj, bj+y, ...,
Indexing terms: Optical communications, Optical multi/
demultiplexers, Multiplexing
bj+tk_y)-
-2W(blbj,...,bAkb4k.1+j)
= 2k
i.e. 2p = 2k + 21.
If the above Bo is existent, then by lemma 1 we know the
following equation group has a root:
A two-channel lightwave system using differential frequencydeviation multiplexing (DFDM) is presented. Both 90 Mbit/s
channels are differentially detected using a fibre interferometer. The performance is independent of the absolute optical
frequencies and received state of polarisation. Interchannel
interference results in a 1 dB penalty for channel separations
of 700 MHz.
bxb2 + b2b3 + ... + bAtkbl =
(2)
b2bl
b4k = k
However, in the following lemma we prove that this equation
group has no root, i.e. theorem 2' holds:
Lemma 2: If k > 1 then the above equation group has no root.
Proof: This is determined in three steps:
(1) If the root is existent then / = k � Jk. In fact, if we add the
first 4/c ? 1 equations in the equation group 1 together, we
have
bl(b2 + b3 + ... + 64t) + b2(b3 + 64 + ... + 6X)
+ ... + bAk{b, + b2 + ... + b^J
= (4/c - 1)/
By this equation we obtain (k + l)(k + I - 1) = (4/c - 1)/, i.e.
(k-l)3
1278
= k,l =
k眣/k.
A new multiplexing technique, called differential frequencydeviation multiplexing (DFDM), has recently been proposed. 1
In DFDM, information is transmitted as the relative optical
frequency, or frequency deviation fd, between light pulses
transmitted at successive time intervals. A fibre interferometer
is used to superimpose light from the two time intervals, and
the frequency difference is generated by a photodiode. Multiplexing is accomplished by assigning a unique fd to each
channel. The microwave response bandwidth of each receiver
can then be subdivided into independent narrowband channels. A desired channel can be received by detecting the microwave power through a bandpass filter centred on the
appropriate frequency deviation.
DFDM has several significant advantages over alternative
multiplexing techniques. First, information is contained
entirely within the relative frequency between two successive
bit periods. Wavelength stabilisation is not required and
pattern-dependent heating effects, which plague conventional
coherent freuqency-shift-keyed (FSK) systems,2 are not a
problem. Secondly, a DFDM receiver operates independently
of the state of optical polarisation at the input to the interferometer. Finally, the electronic components at each transmitter
ELECTRONICS LETTERS 19th November 1987 Vol. 23
No. 24
and receiver operate at speeds equal to the single-channel data
rates. High-speed switching required for time-division multiplexing (TDM), or microwave modulators required for subcarrier multiplexing (SCM),3 are avoided.
In this letter we present the results of an experiment in
which two channels with data rates of 90 Mbit/s per channel
are multiplexed using DFDM. A schematic diagram of the
experimental system is shown in Fig. 1. Two single-frequency
CH,
modulating the current into the short cavity, whereas for the
three-contact laser, fd up to at least 70 GHz can be obtained.
The output from the parallel-resonant receiver is shown in
Fig. 2, where LDX and LD2 are modulated with/d equal to 20
iiD
data in
10
15
frequency, GHz
Fig. 2 Output spectrum from parallel-resonant receiver and following
amplifier with both channels operating
L D t and LD 2 are modulated with/,,= 1-3 and 2 0 G H z , respectively. Thermal noise floor, obtained by blocking both beams, is
shown by lower curve
Fig. 1 Experimental two-channel DFDM system
Outputs of two frequency-modulated C 3 lasers are combined in a
3 dB fibre coupler. Output from interferometer is coupled either to
a parallel-resonant receiver or to a high-speed PIN. Desired
channel is selected using a bandpass filter (BPF) and detected using
a Schottky-diode detector (DET). The DET is followed by three
DC-coupled amplifiers (A3) and a postdetection filter (PDF). Each
laser is isolated from reflections using two isolators, for a total
isolation of 60 dB
cleaved-coupled-cavity (C3) lasers (LDt and LD2) are combined in a 3 dB fibre coupler. The fibre interferometer consists
of two 3dB fibre couplers and has a delay time equal to
111ns, corresponding to a bit rate of 90 Mbit/s per channel.
By adjusting the polarisation compensator (PC) within the
interferometer such that the birefringence is equal in each arm,
the polarisation states of the recombined optical signals are
matched for any state of polarisation at the input to the interferometer. One of the output arms of the interferometer is
coupled to a parallel-resonant PINFET receiver.4 This receiver uses a small inductance between the FET gate and ground
to form a response resonance centred on 3-5 GHz. The lowfrequency components of the received photocurrent are
shorted to ground. The response resonance is sufficiently
broad that reasonable sensitivity is obtained from 1-5 to
6 GHz. A separate high-speed PIN followed by a DC-coupled,
7 GHz-bandwidth amplifier (A2) provides a frequencyindependent response for test purposes. The test channel is
defined by the bandpass filter (BPF) which has a centre frequency of 20GHz and a 3dB bandwidth of 500MHz. Microwave power through this filter is detected using a low-barrier
Schottky diode square-law detector and FET preamplifier.
Pseudorandom data from two pattern generators are differentially encoded and used to frequency-modulate the lasers.
Variable attenuators are used to adjust the magnitude of the
current transitions to obtain the desired frequency deviations.
The received decoded data from the test channel are compared to the transmitted data to obtain the error probability.
LD t is a three-contact, two-cavity C3 laser that offers a
considerable improvement in FM response characteristics
over the conventional two-contact C3 laser LD2. The twocontact laser can be modulated with fd up to 2-5 GHz by
ELECTRONICS LETTERS 19th November 1987
Vol. 23
and 1-3 GHz, respectively. Low-frequency components,
including the / = 0 distributions from each channel, are
shorted to ground by the inductor used to generate the receiver resonance. The upper trace shows the f=fd distributions
from each channel. The lower trace, obtained by blocking
both optical signals, is the thermal noise level from the receiver
and amplifier. Although the average photocurrents received
for each channel are equal, the microwave power contained in
the distribution centred on fd = 20GHz is slightly higher.
This is due to the frequency-dependent resonant response of
Fig. 3 shows the error probability Pe of the filtered and
detected test channel (fd = 20GHz) as a function of the
SNR
EEH
Fig. 3 Error probability Pe against signal/noise ratio (SNR) at output
of bandpass filter
LD 2 is blocked for trace (a). For traces (b) and (c), LD 2 is modulated such that the channel separations, or differences in frequency
deviation, are 750 and 550 MHz, respectively
No. 24
1279
signal/noise ratio (SNR) measured at the output of the
bandpass filter (BPF). For the case where the signal from LD2
is blocked, an SNR of 12 dB, measured using a power meter at
the output of the BPF, is sufficient for Pe= 10"9. This is
obtained for an average received photocurrent of 7-5 fiA. The
12 dB SNR at the BPF output corresponds to a 20 dB SNR at
the output of the postdetection filter. Fig. 3 also shows the
effect of interchannel interference (ICI) when LD2 is modulated with fd= 1-25 and 1-45 GHz. This corresponds to
channel separations of 750 and 550 MHz, for which the SNR
required at the output of the BPF is increased by 1-3 and
3 0 dB, respectively. ICI is a significant limitation in this type
of system. If interchannel separations must be 750 MHz to
reduce the interference penalty to ldB, then the number of
DFDM channels that can be located within reasonable receiver bandwidths is small. A significant reduction of the laser
linewidth would result in a reduction of the minimum channel
separation.
In summary, a two-channel system that uses different
frequency-deviation multiplexing (DFDM) has been evaluated, demonstrating the advantages and limitations of this
technique. We have shown how multiplexing can be accomplished without optical frequency stabilisation or active polarisation control, without using time-division or subcarrier
multiplexing, and using simple electronics at the transmitters
We thank A. R. Chraplyvy and R. W. Tkach for several
helpful discussions. The C3 lasers were processed from wafers
grown by D. P. Wilt.
T. E. DARCIE
C. A. BURRUS
A. H. GNAUCK
B. L. KASPER
J. R. TALMAN
letter we show that this is indeed the case, but the transistor
continues to behave as an amplifying device with essentially
unchanged current gain as the base-emitter junction is driven
into reverse bias. In these circumstances, both emitter and
collector behave as minority carrier extracting junctions which
reduce the carrier concentrations in the base. The thermal
generation of minority carriers within the base region is then
seen to be equivalent to an offsetting base current bias.
Experiment: The bipolar transistor is of the lateral array type
described previously1 (Fig. 1). It consists of an array of circular 'loophole' diodes2~4 made of n-type annular regions in a
29th September 1987
;base
n-type
AT&T Bell Laboratories
Crawford Hill Laboratory
Holmdel, NJ 07733, USA
111100
/
References
1
2
DARCIE, T. E.: 'Differential frequency-deviation multiplexing for
lightwave networks', J. Lightwave TechnoL, to be published
JEROMIN, L. L., REIFFEN, B., and CHAN, v. w. s.: 'Minimum shift
keying for frequency modulation of semiconductor lasers'. OFC
conf. proc, 1985, p. 24
3 DARCIE, T. E.: 'Subcarrier multiplexing for multiple-access lightwave networks', J. Lightwave TechnoL, 1987, LT-5, pp. 1103-1110
4
DARCIE, T. E., KASPER, B. L., TALMAN, J. R., a n d BURRUS, C. A. I 'ReS-
onant PIN-FET receivers for lightwave subcarrier systems', ibid.,
1987, to be published
NEAR-AMBIENT-TEMPERATURE BIPOLAR
TELLURIDE
p-type CMT
7
sapphire
7
fi28/il
Fig. 1 Schematic diagram of transistor, showing plan view and side
elevation through centre of structure
From Reference 1
p-type substrate. The central diode is chosen to be the emitter,
with the nearest neighbour ring of diodes connected together
and designated as the first collector (C^ and the next ring
designated the second collector (C2). The junction diameters
are 10 /mi and the diodes are on a pitch of 15/mi. The CMT
composition is 30% mole CdTe with a detector cutoff wavelength of 4-3 /mi at 263 K. The electron diffusion length in the
base region is 15 /mi.
Common-emitter current/voltage characteristics are shown
in Fig. 2 for C1 alone connected. Although the collector is not
a continuous boundary, as would be the ideal case, the probability of emitted carriers escaping to the outer p-region is
relatively low. It can seen that the characteristic for zero base
base current
10uA
Indexing terms: Semiconductor devices and materials, Transistors, Photodiodes
We describe an npn cadmium mercury telluride transistor
made from a close-packed array of lateral collection diodes.
At 263 K and a collector current of 1 mA the hfe was ~ 20. A
reverse base-emitter bias is required to turn off the collector
current, owing to thermal generation of electrons in the base.
Introduction: Ashley et al.1 recently described the use of an
array of lateral collection photodiodes to demonstrate bipolar
transistor action at low temperatures in the ternary alloy
cadmium mercury telluride (CMT). At higher temperatures
the properties of the transistor may be expected to be dominated by high base minority carrier generation rates, resulting
in significant collector current at zero base current. In this
1280
0-1
02
03
0-4
collector-emitter voltage Vce
05
[128721
Fig. 2 Experimentally observed common-emitter transistor characteristics at 263 K for collector Clt with 10nA increments in base current
ELECTRONICS LETTERS 19th November 1987 Vol. 23 No. 24
```
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