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CHAPTER 1
APPLICATION FIELDS AND FUNDAMENTAL MERITS OF COMPLEX-VALUED NEURAL NETWORKS
AKIRA HIROSE
The University of Tokyo, Tokyo, Japan
This chapter presents historical and latest advances in applications of complex-valued neural networks (CVNNs) first. Then it also shows one of the most important merits of CVNNs, namely, the suitability for adaptive processing of coherent signals.
1.1 INTRODUCTION
This chapter presents historical and latest advances in applications of complex-valued neural networks (CVNNs) first. Then it also shows one of the most important merits of CVNNs, namely, the suitability for adaptive processing of coherent signals.
CVNNs are effective and powerful in particular to deal with wave phenomena such as electromagnetic and sonic waves, as well as to process wave-related information. Regarding the history of CVNNs, we can trace back to the middle of the 20th century. The first introduction of phase information in computation was made by Eiichi Goto in 1954 in his invention of ”Parametron” [17, 18, 61]. He utilized the phase of a high-frequency carrier to represent binary or multivalued information. However, the computational principle employed there was ”logic” of Turing type, or von Neumann type, based on symbol processing, so that he could not make further extensive use of the phase. In the present CVNN researches, contrarily, the researchers extend the world of computation to pattern processing fields based on a novel use of the structure of complex-amplitude (phase and amplitude) information.
We notice that the above feature is significantly important when we give thought to the fact that various modern technologies centered on electronics orient toward coherent systems and devices rather than something incoherent. The feature will lead to future general probability statistics, stochastic methods, and statistical learning and self-organization framework in coherent signal processing and information analysis. The fundamental idea is applicable also to hypercomplex processing based on quaternion, octonion, and Clifford algebraic networks.
Some parts of the following contents of this chapter were published in detail in the Journal of Society of Instrument and Control Engineers [29], the Frontiers in Electrical and Electronic Engineering in China [28], and IEEE Transactions in Neural Networks and Learning Systems [35].
1.2 APPLICATIONS OF COMPLEX-VALUED NEURAL NETWORKS
Complex-valued neural networks (CVNNs) have become widely used in various fields. The basic ideas and fundamental principles have been published in several books in recent years [27, 22, 26, 41, 53, 2]. The following subsections present major application fields.
1.2.1 Antenna Design
The most notable feature of CVNNs is the compatibility with wave phenomena and wave information related to, for example, electromagnetic wave, lightwave, electron wave, and sonic wave [28]. Application fields include adaptive design of antennas such as patch antennas for microwave and millimeter wave. Many researches have been reported on how to determine patch-antenna shape and sub-element arrangement, as well as on the switching patterns of the sub-elements [46, 10, 47]. A designer assigns desired frequency-domain characteristics of complex amplitude, or simply amplitude, such as transmission characteristics, return loss, and radiation patterns. A CVNN mostly realizes a more suitable design than a real-valued network does even when he/she presents only simple amplitude. The reason lies in the elemental dynamics consisting of phase rotation (or time delay × carrier frequency) and amplitude increase or decrease, based on which dynamics the CVNN learning or self-organization works. As a result, the generalization characteristics (error magnitude at nonlearning points in supervised learning) and the classification manner often become quite different from those of real-valued neural networks [28, 35]. The feature plays the most important role also in other applications referred to below.
1.2.2 Estimation of Direction of Arrival and Beamforming
The estimation of direction of arrival (DoA) of electromagnetic wave using CVNNs has also been investigated for decades [67, 6]. A similar application field is the beamforming. When a signal has a narrow band, we can simply employ Huygens’ principle. However, in an ultra-wideband (UWB) system, where the wavelength is distributed over a wide range, we cannot assume a single wavelength, resulting in unavailability of Huygens’ principle. To overcome this difficulty, an adaptive method based on a CVNN has been proposed [60] where a unit module consists of a tapped-delay-line (TDL) network.
1.2.3 Radar Imaging
CVNNs are widely applied in coherent electromagnetic-wave signal processing. An area is adaptive processing of interferometric synthetic aperture radar (InSAR) images captured by satellite or airplane to observe land surface [59, 65]. There they aim at solving one of the most serious problems in InSAR imaging that there exist many rotational points (singular points) in the observed data so that the height cannot be determined in a straightforward way.
Ground penetrating radar (GPR) is another field [21, 66, 43, 44, 49, 34]. GPR systems usually suffer from serious clutter (scattering and reflection from non-target objects). Land surface as well as stones and clods generate such heavy clutter that we cannot observe what are underground if we pay attention only to the intensity. Complex-amplitude texture often provides us with highly informative features that can be processed adaptively in such a manner that we do in our early vision.
1.2.4 Acoustic Signal Processing and Ultrasonic Imaging
Another important application field is sonic and ultrasonic processing. Pioneering works were done into various directions [69, 58]. The problem of singular points exists also in ultrasonic imaging. They appear as speckles. A technique similar to that used in InSAR imaging was successfully applied to ultrasonic imaging [51].
1.2.5 Communications Signal Proce...
