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Biologically Inspired Antenna Array Design Using Ormia Modeling1 2 3 4 Biologically inspired antenna array design 1 2 3 4 using Ormia modeling Murat Akcakaya1 , Carlos Muravchik2 and Arye Nehorai3 1 Electrical and Computer Engineering Department University of Pittsburgh Pittsburgh, PA, USA email: [email protected] 2 LEICI, Departamento Electrotecnia, Universidad Nacional de La Plata, La Plata, Argentina email: [email protected] 3 Department of Electrical and Systems Engineering Washington University in St. Louis, St. Louis, MO, USA email: [email protected] 1 This chapter is based on the dissertation work completed by Dr. Murat Akcakaya when he was in Washington University in St. Louis 2 Based on Akcakaya, M. Muravchik, C. M and Nehorai, A. (2011) ‘ Biologically inspired coupled antenna array for direction of arrival estimation’, IEEE Transactions on Signal Processing, 59 (10), 4795-4808. 3 Based on Akcakaya, M and Nehorai, A. (2010) ‘ Biologically inspired coupled antenna beampattern design’ , Bioinspiration and Biomimetics, 5 (4) , 046003. 4 The work of Dr. Arye Nehorai was funded by NSF grant CCF-0963742. 1 Abstract This chapter describes the design of a small-size antenna array having high direction of arrival (DOA) estimation accuracy and radiation performance, inspired by female Ormia ochraceas’ coupled ears. Female Ormias are able to locate male crickets' call accurately, for reproduction purposes, despite the small distance between its ears compared with the incoming wavelength. This phenomenon has been explained by the mechanical coupling between the Ormia's ears, modeled by a pair of differential equations. In this chapter, we first solve the differential equations governing the Ormia ochracea's ear response, and propose to convert the response to pre-specified radio frequencies. We consider passive and active transmitting antenna arrays. First, to obtain a passive antenna array with biologically inspired coupling (BIC), using the converted response, we implement the BIC as a multi-input multi-output filter on a uniform linear antenna array output. We derive the maximum likelihood estimates (MLEs) of source DOAs, and compute the corresponding Cramér-Rao bound (CRB) on the DOA estimation error as a performance measure. Then, to obtain an active antenna array with BIC, together with the undesired electromagnetic coupling among the array elements (due to their proximity), we apply the BIC in the antenna array factor. We assume finite-length dipoles as the antenna elements and compute the radiation intensity, and accordingly the directivity gain, half-power beamwidth (HPBW) and side lobe level (SLL) as radiation performance measures for this antenna system with BIC. For both the passive and active antenna arrays, we propose an algorithm to optimally choose the BIC for maximum localization and radiation performance. With numerical examples, we demonstrate the improvement due to the BIC. Keywords: Ormia ochracea, Biologically inspired sensing, Biomimetics, Antenna Array, Maximum likelihood Estimation, Cramér-Rao bound. 2 1 Introduction For animals, source localization through directional hearing relies on the interaural acoustic cues: interaural time differences (ITD) and interaural intensity differences (IID) of the incoming sound source (Popper & Fay 2005). The ears of large animals are acoustically isolated from each other, i.e., the organs are located on opposite sides of the head or body. For these animals the distance between the hearing organs provides relatively large ITDs between the ipsilateral and contralateral ears (the ears closest to and furthest from the sound source, respectively). Moreover, a large body or head, with a size comparable to the incoming signals wavelength (above one tenth of the wavelength (Morse & Ingard 1968)), diffracts the incoming sound and increases the IIDs between received signals. Therefore, these big interaural differences can be detected by the hearing systems of large animals such as monkeys (Brown et.al. 1978), (Houben & Gourevitch 1979); humanbeings (Masterton et.al. 1969), (Blauert 1997); cats (Huang & May 1996); horses (Heffner & Heffner 1984); and pigs (Heffner and Heffner 1989). On the other hand, small animals may sense no diffractive effect in the incoming signal, and hence have almost no IID between their two ears. Moreover, due to the closely spaced ears, the ITD drops below the level where it can be processed by the nervous systems of the animals. Therefore many small animals develop a mechanism to improve these interaural differences (Michelsen 1992). A pressure difference receiver is the most common mechanism employed by many animals in this category. In animals with pressure difference receivers, the ears are acoustically coupled to each other through internal air passages. Thus, the resulting force stimulating the eardrum is the difference between the internal and external acoustic pressures, and hence the name pressure difference receiver (Popper & Fay 2005). This structure amplifies the ITDs and IIDs and improves the directional hearing performances of many small animals 3 (Fletcher & Thwaites 1979), (Michelsen et.al. 1994), (Palmer & Pinder 1984), (Eggermont 1988), (Narins et.al. 1988), (Knudsen 1980). We focus on the hearing system of a parasitoid fly Ormia ochracea. For reproduction, a female Ormia acoustically locates a male field cricket and deposits her larvae on or near the cricket (Cade 1975). The localization occurs at night, relying on the cricket's mating call (Walker 1986), (Cade et.al. 1996). The fly is very small and its ears are very closely separated, and physically connected to each other, resulting in ITDs as small as 4 microseconds (Robert et.al. 1992), (Robert et.al. 1994). Moreover, there is a big incompatibility between the wavelength of the mating call (a relatively pure frequency peak around 5KHz, with a resulting wavelength of 7 cm) and the size of the fly's hearing organ (around 1.5 mm), resulting in negligible IIDs (Morse and Ingard 1968). It is theorized that these extremely small interaural differences can not be processed by the nervous system of the Ormia. However, confounding theory, the fly still locates the cricket very accurately, with as low as 2° of error in direction estimation (Mason et.al. 2001), (Akcakaya & Nehorai 2008). Female Ormias have a mechanical structure (referred as intertympanal bridge) that connects their two ears, and it is this structure that amplifies the interaural differences to improve the localization accuracy (Miles et.al. 1995), (Robert et.al. 1996), (Robert et.al. 1998). This mechanical coupling is unique to the female Ormia (Popper & Fay 2005, Chapter 2); even the male Ormias do not have anything similar (Robert et.al. 1994). From here on, by Ormia, we refer to the female Ormia Ochracea. In this chapter, we propose to design biologically inspired small-sized compact antenna arrays to have high direction of arrival (DOA) estimation accuracy (Akcakaya et.al. 2010), (Akcakaya et.al. 2011a), (Akcakaya et.al. 2011b) and radiation performance (Akcakaya & Nehorai 2010a), (Akcakaya & Nehorai 2010b). Our approach is inspired by the ears of the Ormia, which has a 4 remarkable localization ability despite its small size (Mason et.al. 2001), (Akcakaya & Nehorai 2008). In many civil and military applications, antenna arrays developed using the proposed approach would be valuable for sensing systems that are confined to small spaces demanding high resolution and DOA estimation accuracy from small-sized arrays (Bar-Shalom 1987), (Pavildis et.al. 2001), (Reddingt et.al. 2005), (Long 2001), (Brenner & Roessing 2008), (Nehorai & Paldi 1994), (Stoica & Sharman 1990), (Swindlehurst & Stoica 1998). 2 Biologically inspired coupled antenna array for direction of arrival (DOA) estimation Inspired by the Ormia’s coupled ears, we develop a biologically inspired small-sized coupled passive antenna array with high DOA estimation performance. We realize the inspired coupling as a multi-input multi-output filter, which we call as biologically inspired coupling (BIC) filter, and accordingly employing this filter, we obtain the desired array response. In the following, by standard antenna array we will refer to a system without the BIC. Note here that to simplify the analysis, we assume that we know the carrier frequency and the bandwidth of the incoming signal 2.1 Antenna array model We employ the following measurement model for a standard antenna array under the assumption of a narrow-band incoming signal (Stoica & Sharman 1990). Then, the complex envelope of the measured signal is ( ) = ( ) ( ) + ( ), = 1, … , [1.1] where 5 • ( ) is × 1 output vector of the array with antennas • () = [ ( ), … , ( )] is the × 1 input signal vector with as the number of the 1 sources • ( ) = [ ( ), … , ( ) ] is the array response with as the DOA of the source ℎ 1 ( ) • = [1, , … , ] for a uniform linear array −� Δ� − −1 Δ �� • = with as the distance between each antenna, and as the speed of signal �� propagationΔ in the medium, and • ( ) is the additive environment noise. Over the model described in (1.1), we build the BIC as a filtering procedure and obtain the response of the proposed biologically inspired antenna array. As described below, we compute the BIC filter by converting the frequency response of the Ormia’s ears’ to fit the desired radio frequencies. 2.2 Response of the Ormia’s coupled ears The coupled ears of the Ormia was modeled using a mechanical system composed of spring and dash-pots as shown in Figure 1.1 (Miles et.al. 1995). In this figure, the
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