UROS Report

1. Dispersion Tolerant Flexible Bandwidth Multi-subcarrier Modulation
UROS Report | September 2014 | Author: Itrat Rahman | Supervisor: Dr Robert Killey | University College London
Introduction: The motivation of the research is to
investigate a new fibre-dispersion tolerant multi-subcarrier
modulation scheme that consists of variable bandwidth
subcarrier positioned at the peaks of dispersive fibre
transfer function. The investigation is carried out using
MATLAB simulation. First some related modulation schemes
and fibre dispersion are briefly described, then the
modulation scheme is overviewed and finally results of the
simulation are discussed.
Multicarrier modulation techniques: Orthogonal Frequency
Division Multiplexing (OFDM) is a multicarrier modulation
scheme where the available bandwidth is divided into
multiple narrowband sub-channels positioned at equidistant
frequencies. It is based on overlapping sinc(f) methods,
assuming that each subcarrier is made rectangular by pulse
shaping. Orthogonally of the subcarrier is maintained as
each subcarrier is positioned at the nulls of sinc functions of
other subcarriers, and owing to this mutual orthogonally,
each subcarrier signal can recovered by simple mathematical
correlation technique. To combat ISI a guard interval known
as cyclic prefix is added which is a copy of last part of symbol
prepended to the transmitted symbol. As long as the cyclic
extension is sufficiently larger than multipath delay spread
of the channel, ISI is completely removed. However due to
cyclic prefix, OFDM is a spectrally inefficient modulation
scheme, and also the high sidelobes of OFDM symbols lead
to significant power leakage to adjacent bands.
In contrast, Filtered Multitone (FMT) modulation scheme,
based on filter bank technique achieves high spectral
containment. Here spectral partitioning is done by non-
overlapping sinc(f) methods. The uniform synthesis bank
consists of M branch filters, which are frequency shifted
versions of lowpass prototype filter and each carry out signal
processing on separate symbol. Cyclic prefix is not required
to maintain subcarrier orthogonally, this increases the
throughput. However, the time domain responses of the
filter may overlap several symbol periods so per subchannel
equalisation is necessary to remove the remaining ISI. [1] &
[2] describe the efficient realisation of FMT using M
polyphase components of filter and FFT, so that filtering is
performed at a rate of 1/T instead of M/T, where T is the
symbol period.
Dispersive-fibre transfer function: Fibre dispersion adds
nonlinearity in fibre transfer function. [4] & [5] gives analysis
of dispersive fibre transfer function, the latter in microwave
optical system. For this research linear propagation is
assumed and adiabatic chirp is neglected, these assumptions
reduce the fibre transfer function to a simple cosine
function: x(f)=cos(β2ω2
z) | β2=-λ2
D/2πc, where ω is
frequency in radian, z is the distance of the link, D is the
dispersion parameter, and c is the speed of light.
Figure 1 Parameters used in the transfer function: D=16.2 ps/nm km;
λ=1532nm; z=100km
Figure 1 shows the dispersive fibre transfer function which
contains a series of decreasing bandwidth windows. Signal
suffers maximum attenuation and phase distortion at
frequencies corresponding to troughs of the plot.
Figure 2 Spectrum of sinusoid & spectrum of dispersed electrical signal
The dispersion affect is simulated in MATLAB with a
function. Initially the function is verified and tested with
sinusoids. An example is given in fig 2; the first trough of the
fig 1 is at 6.281GHz, so a sinusoid of 6.281GHz is added to an
optical carrier and then made to suffer dispersion through
the simulation function, then it underwent square law
optical detection. The plot on the right shows the expected
result; the sinusoid has been completely supressed, only the
sidelobe is appearing.
Modulation scheme: It is evident that standalone without
any compensation techniques either OFDM or FMT
modulated subcarriers would suffer dispersion if the
bandwidth of a subchannel spans across one of the troughs;
the probability of this increases further at higher frequency
since size of window decreases with frequency, hence this
also limits the bandwidth of subcarriers and number of
subcarriers used in modulation. Complex compensation
techniques are required to compensate for the dispersion
which proves to be both compromising and expensive.

2. The novel modulation technique under investigation is
implemented by putting variable bandwidth subcarriers that fit
the different sized windows of the dispersive fibre transfer
function and do not span across a trough. The operations in
MATLAB simulation are carried out in the following
chronological order: 1) four QPSK channels of different
bandwidth are created separately and shaped by Bessel filter of
8GHz and then filtered out by brick wall filter 2) the channels
are frequency-shifted by appropriate amounts and added
together with an optical carrier such that they are positioned at
the peaks of the dispersive fibre transfer function and fit the
different sized windows, this forms the symbol 3) the
subcarriers from a DSB spectrum suffer dispersion and then
undergo square-law optical detection 4) the subchannels are
separately filtered out using brick wall filters and are frequency
downshifted to the zero of the spectrum 5) the constellation of
QPSK subchannels are plotted and investigated.
Results of simulation: Results of two useful simulations are
shown. The parameters for 1st
simulation: λ=1532nm, z=100km,
D=4.5 ps/nm km, symbol period Ts=15.626ps, symbol-rate of
subcarrier 1 & 2 & 3 & 4 = 16 & 32 & 64 & 128 respectively
(symbol-rate has an inverse relationship with bandwidth, so
bandwidth of a subcarrier is half to that of the previous one),
optical carrier amplitude=10. Figure 3 gives a sense about how
the subcarriers are positioned.
Figure 3 Different bandwidth subcarriers fitting the different sized
windows
Figure 4 Constellation plots of four subchannels
The constellation plots of the four subchannels clearly
correspond to that of a QPSK signal with four distinct phases
with very little dispersion. Dispersion is lesser in the 1st
subchannel but it remains same with the other three channels,
this is because bandwidth of the first subchannel is relatively
much smaller than the 3dB bandwidth of its window.
Figure 5 Effects of dispersion after putting the subcarriers at the troughs
of dispersive fibre transfer function
Figure 5 gives the constellation plots of the subchannels when
they are positioned at the troughs of the dispersive fibre
transfer function instead of the peaks of the windows. The plots
clearly show the signal suffered so much phase distortion that
QPSK modulation format of each subchannel is completely
unrecognisable.
Parameters for 2nd
simulation: same parameters as in
simulation 1, except D=16.2 ps/nm km (typical dispersion
parameter of fibre), symbol-rate of subcarrier 1 & 2 & 3 & 4 =
32 & 64 & 128 & 128 respectively (last two rates are same since
the difference between the windows is very small). Results are
very similar to that of 1st
simulation with very little dispersion,
except that the constellation plots show a slight increasing
trend of dispersion with index number of subchannel.
Simulations carried out on the same parameter settings, varying
only the optical carrier amplitude show that dispersion
decreases with increase in amplitude, and there is minimum
threshold amplitude which can support QPSK modulation
before phase distortion completely impairs it.
Conclusion: The results of the MATLAB simulation are
promising. This modulation technique could provide a good
multi-subcarrier scheme for fibre network without having to
use complex expensive compensation techniques. The next
stage of the research would be to design the optical transmitter
and receiver of the modulation and run simulation in hardware
description language like Verilog. The transmitter and receiver
designs are almost close to completion using the HDL coder of
MATLAB.
References:
[1] Santosh V Jadhav (2005), Filtered Multitone Modulation
and Equalization Techniques, Ph.D., Indian Institute of
Technology, Bombay, India
[2] IBM Zurich Research Laboratory (2000), Filtered Multitone
Modulation, IBM Europe
[3] OFDM: Concepts for Future Communication Systems (Signals
and Communication Technology). 2011 Edition. Springer.
[4] Wedding, B., "Analysis of fibre transfer function and
determination of receiver frequency response for dispersion
supported transmission," Electronics Letters, vol.30, no.1,
pp.58, 59, 6 Jan 1994
[5] Ramos, F.; Marti, J., "Frequency transfer function of
dispersive and nonlinear single-mode optical fibres in
microwave optical systems," Photonics Technology Letters,
IEEE, vol.12, no.5, pp.549, 551, May 2000