Adaptive Control Algorithm for the ESPAR Antenna
Introduction
The application of advanced adaptive techniques has contributed to the development
of high-performance receiving antennas with the capability of automatically eliminating
surrounding interference. Conventionally, it has been thought that only digital
technology could provide these advantages.
ATR has proposed electronically steerable passive array radiator (ESPAR) antennas
as a means of reviving analog adaptive beamforming, which provides a dramatically
simplified architecture that results in significantly lower power dissipation
and fabrication cost than are common with digital beamforming antennas.
Recently, the concept of the Wireless Ad-hoc Community Network (WACNet) has shown
much promise. Such a network can be considered as a means of linking portable
user terminals that meet temporarily in locations where connection to a network
infrastructure is difficult.
The advantages of ESPAR antennas became the core technology to implement the WACNet.
One example of effective application of the adaptive ESPAR
antenna to a WACNet is the Contiguous Communication Network on Ubiquitous
Transmission (CoCoNut)3.
The concept is based on the physical proximity of nodes; therefore, nodes that
periodically move along assigned routes - such as bus services and mail-gathering
services - are suitable for enlarging the area of the community. They also reduce
the traffic required for information exchange. This can be effective for distributing
teaching materials, gathering questionnaires, and accommodating group learning
within a community.
ESPAR Antenna Formulation
Figs. 2 and 3
depict an (M+1)- element ESPAR antenna in which M=6. The 0-th element is an active
radiator located at the center of a circular ground plane. The remaining elements
are passive radiators symmetrically surrounding the active radiator. These elements
are loaded with varactors having reactances of xi(i=1,...,M). Fig.
2 shows a signal of interest (SOI) by its angle of direction of arrival (DOA)
and co-channel interferences from user terminals. Moreover, depending upon the
application, receiver noise and man-made interference may also be present.
The essence of the beamforming functionality of the ESPAR antenna is a complex
weighting in each branch of the array w=[w0,...,wM] and adaptive optimization
of the weights via adjustable reactances x=[x1,...,xM]. The weight current vector
w does not have independent components, but is the unconventional wuc. Its nonlinear
dependence on reactance vector x had not been studied previously. The model is
considered and evaluated numerically rather than through utilization of an analytical
method.
Objective Function
The error e(n) = y(n)-d(n) is defined as the difference between the actual response
of the ESPAR antenna y(n) and the desired response d(n) (training signal). In
adaptive beamforming, as a performance measure, one generally uses the mean squared
error (MSE) of the output waveform y(n) relative to the desired waveform d(n)
and exploits their mutual correlation: MSE(y,d)=J(w). This objective function
is quadratic (convex) with respect to w and its derivative is a linear function
of w, thus requiring the linear filtering Wiener theory for the optimization problem.
With the ESPAR antenna, the objective function J(x) is a non-convex function with
respect to reactance vector x. Thus, we must resort to the nonlinear filtering
theory, which has not been thoroughly studied and applied to adaptive beamforming.
This is the basic difficulty. Furthermore, in general, the error performance surface
of the iterative procedure may have local minima in addition to a global minimum,
and more than one global minimum may exist. There are some other difficulties
not stated in this article.
The Stochastic Approximation Method
The stochastic gradient-based adaptation is used recursively. Starting from an
initial (arbitrary) value for the reactance vector x, it improves with the increased
number of iterations
k(k=1,...,K) on the error-performance surface without the surface itself being
known. Actually, the system can be simulated or observed, and sample values J(x),
at various settings for x can be noted and used to determine the optimal solution.
We rediscovered the optimization problem of the ESPAR antenna into the frame of
the old and widely known method of stochastic approximation (SA) for obtaining
or approximating the best value of the parameter xk1.
Thus, some improvements were considered to the optimization problem of the ESPAR
antenna. We have proposed new learning rate schedules through variable control
step parameters and reactance step parameters, allowing for a faster rate of convergence
and considerably reducing the symbols required in the training sequence and the
level of gradient noise.
Adaptive Beamforming
Fig. 4 depicts the gain pattern for
the specified angles of DOA of the communication environment and specified input
signal-to-noise ratio (SNR).
Conclusion
Using the stochastic approximation theory, we have proposed a new method of optimum
adaptive control of the ESPAR antenna. This method was shown to be effective in
suppressing interference and background noise. The algorithm can be easily transformed
into a blind algorithm (without a training signal) through exploitation of the
spectral correlations of signals.
Reference
