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The
introduction of digital wideband communications and
advancements in digital processing techniques in early 1960s
created a large gap in analog communication research.
However, many current applications can benefit from analog
communications and processing. To bridge this gap, many
fundamental issues have to be addressed, including the
development of analog memories, transmitters which can
generate wideband carriers and receivers with low
complexity. We found that nonlinear dynamics, especially
chaos, provide a way to generate wideband analog random
signals. Over the last project period, our goal was to
address these problems and to develop functional prototypes
of non-coherent analog and digital wideband communication
schemes.
1. Mathematical
Foundation for Wideband Communications based on Nonlinear
Dynamics
Design of multi-scroll attractors for analog
transmitter
A systematic threshold control approach is used for the
design of multi-scroll chaotic attractors which demonstrate
complex dynamics. Our objective was to develop an attractor
design scheme, using which one can generate chaotic
sequences with specific properties. The controlled jerk system can generate
various limit cycles and multi-scroll chaotic attractors by
tuning the corresponding thresholds.
Using this technique, multi-scroll attractors are generated
from a general jerk circuit and Chua’s circuit with sine
nonlinearity. Circuit implementations of these attractors
demonstrate the capability of such systems to generate
versatile dynamics.
Ergodic theory
for a low complexity demodulator design
One of the major breakthroughs in our
research was the discovery of the linear ergodic property
behind nonlinear dynamical systems. We proved that the mean
of the chaotic signals generated by the Renyi map and the
Tent map has a monotone relationship with their bifurcating
parameters. By using this discovery, we have developed a
non-coherent communication scheme¾ergodic
chaotic parameter modulation scheme (ECPM) - which has very
low receiver complexity and superior multipath performance
while maintaining comparable performance as the conventional
schemes.
Nonlinear signal processing for chaos
When chaotic signals are used, we have found
that it can lower the Cramer Rao lower bound of system
identifications. However, conventional techniques such as
the extended Kalman filter display aperiodic behavior
leading to a poor estimation performance. Based on the
measure theoretic approach, we have developed a new
nonlinear filter without using any approximation of the
nonlinear model. The new filter demonstrates a better mean
square error performance for highly nonlinear systems. This
new filter is further extended to a discrete state-space
model based on the Viterbi algorithm for parameter
estimation in Markov chains.
Delayed recurrent inhibitory loop as analog
memory
Within a purely analog system, an analog
memory is necessary for data storage. In this project, we
designed content addressable memories based on the human
brain concept. By incorporating biological features (such as
the firing procedure, the absolute refractory period and
inhibitory rebound spike) to the integrate and fire
neuron model, we showed that it is capable of generating
a large number of asymptotically stable periodic solutions
with predictable patterns of oscillations. This improvement
is expected to have great potential applications in analog
memory. And this network architecture provides another
prototype of hybrid process for analog and digital
information.
2.
System Design of the Proposed Communication Systems
Chaos-based
digital communication
Quadrature
amplitude modulation (QAM) scheme was used to increase the
data rate of digital ECPM. Bit error rate performance of
non-coherent 16QAM-ECPM is analyzed and show that it has
similar performance as conventional coherent wideband
communication schemes. We have developed a new multipath
compensations scheme for QAM-ECPM. It requires only one
symbol for estimating the effect of channel, thus saves
precious bandwidth. We are currently working on 32 and 64
QAM-ECPM schemes.
Chaos-based
analog communication
By following
the philosophy of digital spread spectrum techniques, we
developed analog direct sequence spread spectrum using
continuous pseudo random signals. After a thorough analysis,
we found that it is difficult to synchronize the analog
pseudo-random spreading signal at the receiver side. Based
on the ergodic properties mentioned in Section 1, we
developed two noncoherent analog wideband communication
schemes: analog ergodic chaotic masking (ECM) and analog
ECPM. A multipath compensation scheme for analog wideband
communication, which can be implemented with a simple notch
filter, was another key achievement. Based on the
stochastic delay differential equations, we have developed
another analog communication scheme–delay time modulation
(DTM). However, it was found that the output of differential
delay equations is not truly wideband
– its bandwidth is less than 100 kHz which is not
sufficient for wideband communications. Therefore, it is
determined that the prototype would be developed based on
analog ECM and ECPM, as will be discussed in more detail in
Section 3.
3. Prototyping
Prototype of
chaos-based software radio
Development of
the prototypes for digital ECPM was completed in three
stages. Baseband design was carried on the FPGA. Practical
implementation uses 105 logic elements and can achieve a
maximum speed of 185 Mbps. Total IO power consumption is
260.07 mW, which is comparable to the standard
correlation-based demodulator. To compare the performance,
we analyze the data rate performance of this scheme with
direct sequence spread spectrum scheme which uses 20MHz
bandwidth and found that both of them have 1 M bps (bits per
second) data rateHH. We
worked with Neocific Inc. to integrate our design to develop
the prototype of world’s first chaos-based software defined
radio. Since the modulation schemes are implemented in
software opposed to the hardware implementation in
conventional systems, it allows easy reconfiguration. As
shown in Fig.1, the software radio mainly consists of
transceiver at radio frequencies (RF), synchronization
module, ECPM-based modulator/demodulator at baseband and the
medium access control (MAC). The MAC and network layer of
the software module are based on the IEEE 802.16e (WiMAX)
standard. It can provide up to 70Mb/s of data rate.
Functional prototype of ECPM-WiMAX is shown in Fig. 2.
Fig. 1. Schematic of the chaos based software
radio
Fig. 2. Prototype of our software radio.
Prototype of
analog wideband transceiver
Based on our
study detailed in section 2, we are working on the prototype
of two analog non-coherent wideband communication schemes.
First, the ECM communication schemes are designed and
analyzed using the circuit simulator software, Electronics
Workbench. The properties of the chaos generator are
fine-tuned by adjusting resistor and capacitor values.
Using off-the-shelf components, a hardware prototype of ECM
was developed on the breadboard. It is also found that the
prototype has a power consumption of 675 mW while the
existing digital wideband transceivers have higher power
ratings (SSRx 868 mW, STEL-200 1760 mW). Currently we are
building this circuit on chip using the multi-scroll
attractor developed (c.f. section 6.2.1) which will not only
reduce the cost but also improve the noise performance. Our
students are working on the circuit implementation of analog
ECPM schemes on the breadboard. It will be completed by the
end of the current project period.
Fig. 3. Hardware for ECM transceiver
4.
Wireless Sensor Network for Analog Information
Wireless sensor network (WSN) has been studied intensely in
recent years. Its performance is affected by many factors
such as communication link quality, sensor quality, fusion
rules, etc. But most of the existing works only study the
case of binary-hypothesis, where each sensor assesses the
presence or absence of a phenomenon of interest (POI). But
as for the role of communication link quality, in these
earlier studies, the transmission from sensors to the fusion
centre is usually assumed to be error free. This assumption
is reasonable when the transmission link quality is good and
error correction technique is employed. However, due to
power and bandwidth constraints, this assumption may not be
always valid for WSN.
In our work, we study the performance of wireless sensor
network where the observed data are in the analog format.
The sensed data are contaminated by the sensor noise, before
converting to digital bits by quantization. The digital bits
are transmitted through noisy wireless communication
channel, which suffer from additive white Gaussian noise (AWGN)
and multipath fading. In fusing the sensed information from
individual sensors, certain fusion rules are employed to
recover the original data. In this work, we analyze the
fusion performance of WSN in non-ideal communication
environments. We assume a WSN model where i) observation of
each sensor is independent, and ii) the complex coding with
side information is not used. Three fusion rules: least
squares error (LSE), Bayesian minimum square error (BMSE),
and likelihood ratio test (LRT) methods are considered in
our analysis. The distortion level, which reflects the mean
squared difference between the original and estimated data,
is adopted as a criterion to evaluate the system
performance. According to our analysis and simulation
results, we can see that the growth of sensor noise level
increases the distortion almost linearly. Also adding more
sensors does not always improve the performance for BMSE
approach. In most cases Bayesian MSE achieves the best
performance, followed by LSE and LRT. We also find that
after sensor's transmission power increases to certain
level, it will not affect the system performance any more.
It indicates that it is unnecessary to consume too much
sensor power to keep channel SNR high, as after certain
level the SNR doesn't affect the system performance too
much. The distortion level is then mainly dominated by the
sensor noise.
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