Takeshi OHNO , Koichi OGAWA , Toshihiro TERAOKA , and Jiro HIROKAWA†††, Regular Members
SUMMARY A slot pair array using a post-wall waveguide is a promising candidate for a Fixed Wireless Access (FWA) sector antenna to be used in a base station. This array is formed by a traveling wave antenna, and therefore its main beam direction varies with frequency. To overcome this difficulty, we propose a new structure that comprises of a cosecant array and an addi-tional Talor array. T his structure can fix the main beam in a constant direction whilst maintaining a cosecant radiation pat-tern. We conducted an investigation based on an array factor, and the validity of the method was confirmed by experiment. key words: FWA, main beam direction, traveling wave, cosecant radiation pattern, Talor radiation pattern
1. Introduction
Recently there has been a growing demand for millime-ter wave wireless communication systems. Fixed Wire-less Access (FWA) is an Internet access protocol that uses millimeter wave wireless communication to com-municate between a base station and multiple home stations. A cosecant radiation pattern is required for the FWA base station antenna in order to provide the same power to all home stations [1].
A slot pair array using a post-wall waveguide is a promising candidate for the FWA base station an-tenna [2], [3]. The structure of a slot pair array using a wall waveguide is shown in Fig. 1. The post-wall waveguide is constructed by forming two lines of via-holes aligned periodically in a straight line on a di-electric substrate in which the top and bottom of the substrate are metallized with a thin copper layer. A rectangular opening is constructed on the bottom sur-face of the substrate as a feed aperture, and an elec-tromagnetic source is applied to the aperture from an ordinary waveguide. The guided wave travels through
Manuscript received June 1, 2002. Manuscript revised September 4, 2002.
†The authors are with Devices Development
Cen-ter, Matsushita Electric Industrial Corporation Limited, Kadoma-shi, 571-8501 Japan.
††The author is with System Solutions Company,
Matsushita Communication Industrial Corporation Lim-ited, Yokohama-shi, 223-8639 Japan.
†††The author is with the Department of Electric &
Elec-tronic Engineering, Tokyo Institute of Technology, Tokyo, 152-8552 Japan.
a) E-mail: [email protected]
Fig. 1 Structure of the slot pair array using a post-wall waveguide.
the substrate between the two lines of via-holes [1]. Slot pairs are formed on the upper surface, which are ar-ranged so that the resultant return loss caused by the reflection of the waves from each slot is minimized [3]. The antenna is a simple structure, and is therefore less expensive than the metal waveguide counterpart. The array has a cosecant radiation pattern if we choose a suitable excitation coefficient, but its main beam direc-tion varies with frequency because of the traveling wave feed structure. To overcome this difficulty, we have pro-posed a new structure that can fix the direction of the main beam whilst maintaining the cosecant radiation pattern [4]. The effectiveness of this structure has been confirmed by a theoretical investigation.
In this paper, a slot pair array that has an in-variant main beam direction with a cosecant radiation pattern created by using a post-wall waveguide is pre-sented. In Sect. 2, the mechanism for the variation in the main beam direction is explained. Two types of phase delay are shown to be main factors causing the variation in the main beam direction. In Sect. 3, a new structure is proposed. This structure consists of a cose-cant array and an additional Talor array [5]. In Sect. 4, the effectiveness of the structure is investigated using a calculation based on an array factor. We divide this calculation into two steps. In the first step, we assume that the elements are point sources and the slot effects are not included in the calculation. In the second step, we assume that the elements are slot pairs and the slot effects are rigorously included. Finally, in Sect. 5, the validity of the method is confirmed by an experiment.
Fig. 2 Measured radiation pattern of the slot pair array using a post-wall waveguide.
Table 1 Measured results.
Fig. 3 Permissible range of the cosecant radiation pattern.
2. Tilt Mechanismof the Main Beam
In Fig. 2 we show the measured radiation pattern when the cosecant array is designed using 16 slot pairs at 25.48 GHz, and the results are summarized in Table 1. In the table, σ is the ratio of the cumulative elevation angle, in which the measured radiation pattern exists between certain upper and lower limits, to the whole angle of interest. These two limits can be primarily derived from an outage consideration in a particular radio zone, and they depend on the particular system requirements. In this paper, an upper limit of 6 dB larger and a lower limit of 3 dB smaller than the ideal cosecant curve were chosen, as shown in Fig. 3. The reason for the smaller value of the lower limit is that a smaller signal level due to the gain degradation of the antenna has a greater effect on the system communi-cation link. Using these limits we calculated σ over an angular range from 2◦ to 60◦. In the case where σ ex-ceeded 70%, we regarded the radiation pattern as being a cosecant one. Following this criterion, the measured
Fig. 4 Cross sectional view of the waveguide.
radiation patterns in Fig. 2 show good cosecant char-acteristics because σ(fL) = 78%, σ(fD) = 76% and
σ(fH) = 79% in Table 1.
It was found that the main beam direction varies with frequency due to the traveling wave structure. The main beam direction varies by about 4◦ over 400-MHz of bandwidth. As a result, the gain at 2◦, which is the direction to the area edge of the radio zone, is reduced by 3 dB by changing the main beam direction.
Figure 4 shows a cross sectional view of a wave-guide. In this figure, Φd is the phase delay of the wave
traveling between the elements, S21 is the phase de-lay of the wave traveling under the slot, and S31 is the phase delay of the wave traveling through the slot. It can be considered that there are two major factors leading to the variation in the main beam direction, as follows [3]:
1) The phase delay effected by the distance between the slot pairs (Φd) varies with frequency.
2) The phase delay effected by the slot pairs ( S21and
S31) varies with frequency.
As the frequency rises, these two types of the phase delay both increase. Because of the traveling wave structure, the phase delay is accumulated to reduce the excitation phase to a great extent at the slots further away from the feed point. This leads to the main beam tilting towards the direction of the traveling wave, but when the frequency falls, the main beam moves to the opposite direction.
3. Proposal for a New Structure
We propose the new structure shown in Fig. 5 to main-tain the main beam in a constant direction. In this fig-ure, ∆θt, which is depicted by the curved arrow, is the
variation in the main beam direction of a Talor array with frequency, and ∆θcis that of a cosecant array. ∆θ
is defined as the variation in the main beam direction of the whole array. The Talor array has a narrow main beam width and a low side lobe. The Talor array is ar-ranged so that the wave travels in the opposite direction to the cosecant array. Because the main beam of each array moves in the opposite direction with changing fre-quency, the combined direction of the main beam of the
Fig. 5 New structure using a Talor and cosecant array combination.
whole array in principle remains constant. However, to prevent the cosecant radiation pattern from collapsing due to the Talor array, the maximum excitation ampli-tude of each element of the cosecant array (Ac) needs to
be sufficiently larger than that of the Talor array (At).
In such a situation, the effect of ∆θt on ∆θ is much
smaller than that of ∆θc. Thus, in order to allow ∆θ
to be nearly equal to zero, ∆θtmust be larger than ∆θc.
This structure permits the cosecant radiation pattern to be invariant over a wide frequency range.
4. Investigation Based on an Array Factor 4.1 Calculation with Regard to Point Sources To investigate the behavior of the new structure, an investigation was conducted based on an array factor. Because it was assumed that the elements could be re-garded as point sources, the phase delay effected by the slot was not included as a cause of the variation in the main beam direction with frequency. The array factor
AF (θ) was calculated by AF (θ) = N n=1 AD(n)ejφD(n)ejβ0(n−1)d sin θ · ej(n−1)∆φd(n) (1)
where AD(n) and ΦD(n) are the excitation amplitude
and the excitation phase respectively at the design fre-quency (fD) (usually the center frequency). β0 is the
phase velocity in free space, and d is the distance be-tween the elements. ∆Φd is the variation in Φd with
frequency, expressed as ∆φd(n) = 1 λgD − 1 λg · 2πd (2)
where λgD and λg respectively are the wavelength in
the waveguide at the design frequency and at the fre-quency of the calculation. Figure 6 shows the radia-tion patterns of the Talor and cosecant arrays used in the calculation, which were designed using 16 elements. The radiation pattern of the whole array was calculated by combining these two arrays. This can be expressed as
(a) Talor radiation pattern (∆θt= 1.6◦).
(b) Cosecant radiation pattern (∆θc= 0.8◦).
Fig. 6 Radiation patterns used for the calculation of the combined radiation pattern with regard to point sources.
AF (θ)= Nt n=1 ADt(n)ejφDt(n)ejβ{(−n+1)dt−dm/2} sin θ ·ej(−n+1)∆φdt(n)+ Nc n=1 ADc(n)ejφDc(n) ·ejβ{(n+1)dc+dm/2} sin θej(n−1)∆φdc(n) (3)
where the suffixes t and c are associated with the Talor and the cosecant array respectively. dmis the distance
between the first element of the Talor array and that of the cosecant array. ∆θ can be obtained by calculating the difference in the main beam direction of the whole array (θw) at the higher (fH) and lower (fL) frequencies
of the FWA system by using the following equation; ∆θ =|θw|f =fH− θw|f =fL| (4)
where fH= 25.69 GHz and fL = 25.27 GHz.
For design purposes, the quantitative relation-ship between the variation in the main beam direction with frequency and the excitation amplitude should be known. Figure 7 shows the calculated results of ∆θ as a function of Ac/At with ∆θt/∆θc as parameters. In
the calculation, Ac/Atis adjusted for any ∆θt/∆θc to
obtain the minimum ∆θ.
Figure 8 shows the calculated radiation patterns of the whole array when Ac/At= 0 dB and ∆θt/∆θc= 1.
Fig. 7 Relationship between the excitation amplitude ratio of both arrays and the variation in the main beam direction of the whole array with regard to point sources.
Fig. 8 Calculated radiation pattern of the whole array with regard to point sources. (Ac/At= 0 dB, ∆θt/∆θc= 1)
Fig. 9 Calculated radiation pattern of the whole array with regard to point sources. (Ac/At= 13 dB, ∆θt/∆θc= 2)
vary with frequency, but that the cosecant radiation pattern collapses so that σ(fL) = 56%, σ(fD) = 36%
and σ(fH) = 62% respectively. This result proves that
Acneeds to be sufficiently larger than At. Ac/Atneeds
to be more than 10 dB to maintain a well-formed cose-cant radiation pattern. For example, Fig. 7 shows that when ∆θt/∆θc = 2, the optimum value for Ac/At is
found to be 13 dB. Figure 9 shows the calculated ra-diation patterns in this situation. The main beam di-rection does not vary with frequency and maintains an excellent cosecant radiation pattern because σ exceeds
In the second step of our investigation, we calculated the radiation pattern when the slot pair effects were taken into account. The calculation procedure is dif-ferent from that in Sect. 4.1, since the frequency de-pendence of the phase delay effected by the slot was rigorously considered (factor 2 in Sect. 2).
As mentioned in the previous section, ∆θtneeds to
be larger than ∆θc. The problem is how to make ∆θt
larger. From the array design viewpoint, it would be convenient if a simple method for calculating the main beam direction could be used to estimate ∆θt
approx-imately without calculating the structural parameters of the antenna [6]. To obtain an approximate value of ∆θt, the main beam direction can be calculated as
fol-lows. The main beam direction of the Talor array θt
can be expressed as sin θt=−
φ(n) β0· (n − 1) · d
(5) and the excitation phase can be expressed as
φ(n) = φ(n− 1) − S31(n− 1) + S21(n− 1) + φd(n) + S31(n) + 2π
= −(n − 1)(βgd + Save− 2π) (6)
where Save is the average of the phase delay effected by the slot. The last term 2π corresponds to the spa-tial distance of a wavelength between two slot pairs. This term is needed in order that the slot pairs do not overlap. Save is obtained by solving the recurrence formula, because there is no rapid change in the array for any n. Save can be expressed as
Save = n { S31(n)− S31(n− 1) + S21(n− 1)} n− 1 ≈ n S21(n− 1) n− 1 (7) Hence, θtbecomes θt= sin−1 λ0 λg +λ0 Save 2πd − λ0 d (8) where λ0is the wavelength in free space and λg is the
wavelength in the waveguide. ∆θt can be obtained by
calculating the difference in θt at the higher and lower
Fig. 10 Calculated phase delay effected by the slots.
Fig. 11 Calculated main beam direction as a function of the phase delay effected by the slots.
∆θt=|θt|f =fH− θt|f =fL| (9)
It can be deduced from the first term in Eq. (8) that a variation in λg (∆λg) needs to be small to make ∆θt
larger. To make ∆λg small, we take the approach that
the dielectric constant of the substrate can be consid-ered to be large. Figure 10 shows the calculated results of Save as a function of frequency with the dielectric constant as a parameter. Figure 11 shows the calcu-lated results of the main beam direction of the Talor array, θt, as a function of Save. It is found from Fig. 10
that the variation in Save (∆ Save) changes little when we change the dielectric constant. By contrast, Fig. 11 shows that ∆θt varies rapidly as the dielectric
constant becomes larger. The Talor array is designed using a substrate with a dielectric constant of 6 and a thickness of 1.6 mm. In this situation, ∆θt = 6.6◦,
as indicated in Fig. 11. The cosecant array is designed using a substrate with a dielectric constant of 2.2 and a thickness of 3.2 mm.
By using these substrates, the structural param-eters for each slot pair can be calculated using the method of moments to meet the ideal excitation co-efficient for the cosecant and Talor patterns at a center frequency of 25.48 GHz [7], [8]. To obtain ∆θ we need to calculate the excitation coefficient at the lower and higher frequencies of 25.27 and 25.69 GHz. At these two frequencies, slot pair effects are rigorously taken into consideration in the following expressions.
(a) Talor radiation pattern (∆θt= 6.9◦).
(b) Cosecant radiation pattern (∆θc= 3.1◦).
Fig. 12 Radiation patterns used for the calculation of the combined radiation pattern including slot effects.
The excitation coefficient at the n-th element can be expressed as
A(n) = 1− ρ(n − 1)
ρ(n− 1) ρ(n)A(n− 1) (10)
φ(n) = φ(n−1)− S31(n−1)+ S21(n−1)
−βg{z(n)−z(n−1)}+ S31(n)+2π (11)
where ρ(n) is the coupling coefficient of the n-th slot pair [3] and z(n) is the location of the n-th slot pair. The radiation pattern can be calculated from these ex-citation coefficients.
The radiation patterns are shown in Fig. 12. These were found to be ∆θt = 6.9◦ for the Talor array and
∆θc = 3.1◦ for the cosecant array. It was also found
that the side lobe level in the Talor radiation pattern was less than−30 dB.
To investigate the properties of the whole array, both arrays can be combined to form a new structure. Figure 13 shows the relationship between Ac/At and
∆θ. It is found that the behavior is similar to that shown in Fig. 7, and that the minimum variation in the main beam direction is obtained when Ac/At= 12 dB.
The calculated radiation pattern of the whole array for this situation is shown in Fig. 14. The calculated radi-ation pattern of the whole array maintains a cosecant radiation pattern in the frequency range of 420 MHz, where σ(fL) = 74%, σ(fD) = 79% and σ(fH) = 72%.
Fig. 13 Calculated relationship between the excitation ampli-tude ratio of both slot pair arrays and the variation in the main beam direction of the whole array including slot effects.
Fig. 14 Calculated radiation pattern of the whole array includ-ing slot effects. (Ac/At= 12 dB, ∆θt/∆θc= 2.2)
5. Experimental Results
The effectiveness of the new structure has been con-firmed by an experiment designed to verify the validity of the calculation described in the previous section. Op-timum values for Ac/At of 12 dB and for ∆θt/∆θc of
2.2 are obtained from the calculation. Table 2 shows the structural parameters of the arrays to realize the de-sired characteristics. For experimental purposes, Ac/At
is derived by setting up a power divider and an attenua-tor between both arrays to divide the feed power. The power divider is a hybrid divider that can divide an input signal into two output signals with equal ampli-tude and which are in phase. The power to be divided is decided using the following equation.
x = 10 log n {Ac(n)}2 n {At(n)}2 + 20 logAc At [dB] (12)
where At(n) is the excitation amplitude at the n-th
element of the Talor array and Ac(n) is that of the
cosecant array, while x is the value of the attenuator. ∆θt/∆θc is given as the difference in the dielectric
con-stant of the substrate, as mentioned in Sect. 4.2. Fig-ure 15 shows the experimental set up. In Fig. 15, all of
Fig. 15 Experimental set up.
Fig. 16 Measured Talor radiation pattern.
the parts shown that make up the feed circuit, such as the attenuator, the divider and the waveguide adapter, are coaxial based components that are available com-mercially. They are connected via short lengths of coax-ial line. Although the experiment was carried out using coaxial components, an integrated feed network con-structed using a post-wall waveguide with smaller in-herent loss is feasible [2], and this is left for further studies.
Figure 16 shows the measured Talor radiation pat-tern when ∆θt = 7.9◦. Figure 17 shows the measured
relationship between Ac/Atand ∆θ. It was found that
the behavior is similar to that seen in Fig. 7 and Fig. 13, and that the minimum variation in the main beam di-rection of ∆θ = 0.9◦is obtained when Ac/At= 14.8 dB.
The measured radiation pattern of the whole ar-ray in these circumstances is shown in Fig. 18. The measured radiation pattern maintains a cosecant radi-ation pattern in the frequency range required for the
Fig. 17 Measured relationship between the excitation ampli-tude ratio of both slot pair arrays and the variation in the main beam direction of the whole array.
Fig. 18 Measured radiation pattern of the whole array. (Ac/At= 14.8 dB, ∆θt/∆θc= 2.1)
FWA system, because σ(fL) = 71%, σ(fD) = 71% and
σ(fH) = 73%. The variation in the gain of the whole
array with frequency at 2◦from the broadside direction was 1.3 dB, as compared with that of the cosecant array alone, which was 3.34 dB, as shown in Table 1.
6. Conclusion
A slot pair array having an invariant main beam direc-tion with a cosecant radiadirec-tion pattern using a post-wall waveguide has been proposed and investigated exper-imentally. This structure consists of a cosecant array and an additional Talor array. The optimum ratio of the excitation amplitudes of the two arrays is equal to 14 dB, and the variation of the main beam direction with frequency is equal to 2. From the experimental re-sults, the variation in the main beam direction of this structure with frequency was measured to be 0.9◦ com-pared with 3.8◦ using only a cosecant array, demon-strating the effectiveness of the proposed antenna for a FWA base station.
Acknowledgment
The authors would like to thank Dr. M. Ando, professor of the Tokyo Institute of Technology, for his encourage-ment and support.
pp.625–630, May 1998.
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[4] T. Ohno, K. Ogawa, T. Teraoka, and J. Hirokawa, “A pro-posal and inspection for invariant main beam direction of a slot pair array with cosecant radiation pattern using a post-wall waveguide,” The 4th Topical Symposium on Millimeter Waves Technical Digest, pp.171–174, March 2002.
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Takeshi Ohno was born in Gifu, Japan, on February 23, 1976. He received B.S. and M.S. degrees from the Nagoya Institute of Technology in 1998 and 2000, respectively. In 2000, he joined Matsu-shita Electric Industrial Co., Ltd., Osaka, Japan, where he has been engaged in re-search and development on millimeter-wave antenna.
Osaka, in 1981, where he was engaged in research and development work on a 50-GHz millimeter-wave integrated circuit and a 12/24-50-GHz very small aperture terminal (VSAT) satellite communication system. He is currently a research group leader of Mobile Communication RF-Devices. His research interests include diversity antennas for mobile communication systems and other related areas of radio propagation. He received the OHM Technology Award from the Promotion Foundation for Electrical Science and Engineering in 1990. He also received the TELECOM System Technology Award from the Telecommunications Advancement Foundation (TAF) in 2001. He is a member of the IEEE. He is listed in Who’s Who in the World.
Toshihiro Teraoka was born on March 7, 1970. He received the B.S. and M.S. degrees in electrical engineer-ing from Kyoto University in 1993 and 1995, respectively. He joined Matsu-shita Electric Industrial Co., Ltd., Osaka, Japan in 1995. He was transferred to Matsushita Communication Industrial Co., Ltd., Yokohama, Japan in 2001. He has been engaged in research and devel-opment on antennas and millimeter-wave circuitry.
Jiro Hirokawa was born in T okyo, Japan, on May 8, 1965. He received the B.S., M.S. and D.E. degrees in electri-cal and electronic engineering from Tokyo Institute of Technology, Tokyo, Japan in 1988, 1990 and 1994, respectively. He was a Research Associate from 1990 to 1996, and is currently an Associate Professor at Tokyo Institute of Technology. From 1994 to 1995, he was with the antenna group of Chalmers University of Technol-ogy, Gothenburg, Sweden, as a Postdoctoral Researcher, on leave from Tokyo Institute of Technology. His research area has been the analysis of slotted waveguide array antennas. He received the Young Engineer Award from IEICE Japan in 1996.
