In this reply, we refer to comments made by a

reader on our publication “Overlapped Phased Array Antenna

for Avalanche Radar”. Authors would like to thank the reader

for reading the paper. In this paper authors provided detailed

answers to the comments made by the reade

Brennan, P

Tanha, MA

English

UCL Discovery

1Reply to comments on Overlapped Phased ArrayAntenna for Avalanche RadarMandana Ardeshir, Paul BrennanAbstract—In this reply, we refer to comments made by areader on our publication “Overlapped Phased Array Antennafor Avalanche Radar”. Authors would like to thank the readerfor reading the paper. In this paper authors provided detailedanswers to the comments made by the reader.Index Terms—Phased array, power divider, feed network.I. REPLY TO COMMENTSAuthors believe that the technical comments that the readermade on the published are not very accurate and may be mis-leading other readers.The reader commented that the authorsdid not cite all the relevant papers discussing the overlappedsubarraying techniques. However, in this work overlappingsubarraying technique is used to suppress grating lobes withoutcompromising array gain and scan angle [1]. As a resultrelevant papers which are discussing the techniques to avoidphased array grating lobes were cited in the Introductionsection and also throughout the paper. As the reader alsomentioned, the fundamentals of overlapping Subarrays havebeen discussed in several papers and books, however, the ref-erences cited by the authors in [1] are the most relevant paperswhich cover all essential materials for the proposed work.However, papers [2]–[5] suggested by the reader may be usefulto those readers who would like to expand their knowledgeon overlapping subarrays and phased array feed networks ingeneral. Authors believe that papers which are partly relevantor the papers which do not add enough information to thereader’s knowledge should not be randomly cited. For instance,the reader suggested the paper titled “Methods of constructingoptimum phased array antennas” [6]. The suggested paper is asurvey paper which discusses methods to construct flat-toppedphased array element pattern which was not at all relevant tothe focus of the proposed work. Moreover, the reader alsosuggested the paper titled “Some features of the overlappedsubarrays built up of beamforming matrices for shaping flat-topped radiation pattern” [7] which authors again do not findit relevant to the proposed work as the main focus of thepublished work [1] was to suppress phased array grating lobesutilising overlapping subarraying technique with a uniquefeeding network and not designing a phased array antenna withflat-topped radiation pattern. The reader also suggests a papertitled “Radiation pattern optimisation of Skobelev Networks”[8] which is entirely irrelevant to the work presented [1], sincein the published paper [1] by the authors the designed phasedarray structure and the proposed feed power distribution net-work is very unique to the application requirements (Imagingsnow avalanche). The suggested reference paper by the readeris a conference paper which discusses optimization methodsfor computing the coupling coefficients of directional couplersconstituting Skobelev network and sidelobe level improvementof the subarray which based on above discussions is alsoirrelevant to the work presented by the authors. Moreover,authors would not cite proceedings as the materials may nothave passed through full research cycle. The reader shouldbe careful that if the keywords of the presented work are onlyincluded in a paper, it does not necessarily mean that particularpaper is relevant and it is required to be cited.Also, the authors never mentioned throughout the publishedpaper [1] that the overlapping subarraying technique wasa novel technique and proposed by them. In the publishedpaper [1] the authors mentioned “Overlapped Subarray: In theoverlapped subarray structure, each subarray shares its outerelements with a neighbouring subarray[21].” and this sentencewas also referenced properly. The reference number (21) [9]inthe published paper [1] titled “The Use of Overlapped Subar-ray Techniques in Simultaneous Receive Beam Linear Arrays,(Defence Technical Information Center), DTIC, 1984.” thor-oughly discusses the fundamentals of overlapping subarrayingto suppress grating lobes and it is very relevant to the publishedpaper [1]. The reader must not invalidly accuse authors for notproviding a valid reference or undermining other researcherswork. As authors mentioned, the reference number [21] [9] (inthe published paper [1]) was the most relevant to the presentdwork. The restrictions of the overlapping approach have beenalso discussed to the point which was necessary based onthe opinion of the authors and IEEE transaction reviewersand associate editors who accepted [1] for publication. Thepublished paper [1] is on developing a phased array antennafor a radar system to image the snow avalanche, therefore avery unique phased array antenna is designed to accommodatethe application requirements utilising overlapping subarrayingand a unique feed network which consists of a novel Two-inTwo-out power splitter structure. The published paper [1] isnot a review/ survey/history paper on the subject of overlappedsubarray structures, therefore citing a “Overlapping subarrays”patent paper which was published in 1974 is out of the contextof the published paper [1].The reader also made inaccurate technical comments. Thefocus of this paper was to utilise overlapping sub-arraysto avoid grating lobes without compromising scan angle orarray gain. The reader commented that “the Authors pay theirattention only to additional reduction of the grating lobe level.However, the effect is achieved only at the expense of fastdrop of the array gain with beam scanning from the broadsidedirection” this statement is inaccurate. The reader shouldpay attention that how by utilising overlapping subarrayingtechnique the grating lobes can be suppressed which wasexplained in details in [1]. In the published paper [1] by2utilising overlapping subarraying technique the array elementpattern was used as a spatial ant-alias filter. Also, in ordertoeffectively suppress grating lobes wider antenna aperturewasrequired which was achieved by using overlapping subarrayingtechnique. As a result the array element width exceeded theinter-element spacing which resulted in a narrower beamwidthwhich was capable of attenuating aliased signals. The readecommented that “the grating lobe reduction is achieved at theexpense of fast drop of gain with beam scanning from thebroadside direction” which is an inaccurate statement based onabove explanations and this means that the reader denies thefact that the overlapping subarraying technique is an effectivtechnique to be used to suppress the grating lobes which isinaccurate. However, the reader in another sentence followingabove sentence mentioned that “Meanwhile there exist a fewother networks of overlapped subarrays allowing not onlysuppression of the grating lobes but also providing almost nn-dropping array gain over the whole sector of scanning as itis often required from radar systems for limited-scan appli-cations.” This sentence is in contradictory with the reader’sprevious discussion, and based on this sentence the readerthis time accepts the fact that the overlapping subarrayingtechnique is an effective technique to suppress grating lobes.Also the reader compares the published work to that onsectoral radiation pattern which is not a valid comparison andit is irrelevant. The reader also mentioned that “Moreover,the indicated chess-board network utilizes transmission linesections of identical electrical length unlike the networkusedin [1] where it is required to adjust the sections of differentlength carefully for providing correct phase match in radiatingelements, and such a situation impose additional restriction onoperating bandwidth of the array antenna developed in [1].”and compares the published work with Chess-board network(Skobelev network) which is not again a valid comparison.In the published work [1] the unique power distribution feednetwork was required to be able to apply amplitude taperingto the overlapping or sharing element to further reduce thesidelobe level. Based on the studies shown in the publishedpaper [1] the 3dB power difference was required betweenthe overlapping and non-overlapping elements to reduce thesidelobe level, therefore, the conventional Skobelev networkcannot be used for this work. As a result a power distributionfeed network using the novel Two-in Two-out splitter wasproposed in the paper to achieve the required amount of powerat each phased array element. It should be also mentioned thatelements within a subarrays in [1] are in phase by adjustingthe transmission line lengths in wavelength.II. A IM OF THE PUBLISHED PAPERThe Aim of the published paper was to develop a phasedarray antenna for an FMCW radar with a novel and uniquefeeding network and novel power divider. Authorsnever men-tioned or claimed in the published paper [1] that overlappingsubarraying technique was the contribution of the paper or aninvention by the authors and as mentioned relevant papers werecited. As mentioned the contribution of this paper was a noveltwo-in two-out power divider and a unique feeding networkFig. 1. Diamond Two-in Two-out splitterdesigned a unique and novel avalanche imaging application.The theoretical and mathematical analysis of the proposedpower divider and feeding network were thoroughly discussedthrough out the paper specifically in the Discussion section.However, it is worth repeating those analysis for the readerswho may have misunderstood or missed those sections in thepublished paper.A. Proposed Two-in Two-out power splitterThe diamond two-in two-out power splitter is composedf four parallel microstrip transmission lines in series withZ0 characteristic impedance transmission lines in diamondorientation. The diamond two-in two-out power splitter is amicrostrip power divider which has four ports and dividesquarter of the input power among its four points. Therefore,itcan also be called 6-dB power divider. The main advantage ofthe diamond two-in two-out splitter is that it has a simplestructure and resistors are not used in its structure. TheDiamond Two-in Two-out splitter Fig.1. behaviour has beenmathematically analysed based on transmission line princiles.Fig. 2. indicates the equivalent circuit model of the DiamondTwo-in Two-out power splitter. Assuming, the power splitteris fed using a single AC power supply at one of the four endswhile the other ends are terminated to 50Ω matched load.Also, for ease of analysis the Z0 characteristic impedancetransmission line is considered as two parallel 2Z0 and thejunction between the transmission lines is considered as node1.The input impedance at node1 (Z1) is defined as shown inEquation (1, 2 and 3), which is in parallel with Z0 Thus,the input impedance at the feed point can be determinedbased on transmission line fundamentals as well as reflectionand transmission coefficient, see Equation (4) Moreover, byassuming P0 and P1 is the amount of power which travelsthrough port2 and port3 respectively. The S-parameter valuescan be determined as illustrated by Equation (5), Equation(6) and Equation(7). Utilising the proposed power divider andthe designed feed network, the amplitude level of overlappinglements will 3dB less than non-overlapping elements whichimproves the phased array sidelobe level. The phased array an-tenna with unique feeding network was successfully deployedat a test site in Alps, Switzerland to image the snow avalanche.The radar image of the snow avalanche which was successfullyproduced using the developed phased array antenna is shownin Fig. 3. In the following equationsβ, ℓ, V are phase constant, length and voltage respectively.3Fig. 2. Equivalent circuit of the diamond two-in two-out power splitter (left).Equivalent circuit of the upper half of the diamond splitter (right)Fig. 3. Radar image of a large powder snow avalanche. Beside this complex,distributed target, a helicopter can be identified.Z1 = Z(2Z0 cosβℓ+ jZ sinβℓZ cosβℓ+ j2Z0 sinβℓ) (1)Z2 = Z0||Z1 =Z0Z1Z0 + Z1(2)Zin =Z2(Z2 cosβℓ+ jZ sinβℓZ cosβℓ+ jZ2 sinβℓ) (3)Γin =Zin − Z̄0Zin + Z̄0, | Tin |2= 1− | Γin |2 (4)P0 =V 2Z0, P1 =V 2Re(Z1)| Z1 |2(5)| S21 |2=| Tin |22×P0P0 + P1(6)| S31 |2= 2| Tin |22×P1P0 + P1(7)REFERENCES[1] M. A. Tanha, P. V. Brennan, M. Ash, A. Khler, and J. McElwaine, “Over-lapped phased array antenna for avalanche radar,”IEEE Transactions onAntennas and Propagation, vol. 65, no. 8, pp. 4017–4026, Aug 2017.[2] D. Petrolati, P. Angeletti, and G. Toso, “A lossless beam-forming networkfor linear arrays based on overlapped sub-arrays,”IEEE Transactions onAntennas and Propagation, vol. 62, no. 4, pp. 1769–1778, 2013.[3] T. Azar, “Overlapped subarrays: Review and update [education column],”IEEE Antennas and Propagation Magazine, vol. 55, no. 2, pp. 228–234,2013.[4] R. Mailloux, “Phased array antenna handbook, 2nd edn. artech house,”Inc., Norwood, 2005.[5] R. J. Mailloux, “Electronically scanned arrays,”Synthesis Lectures onAntennas, vol. 2, no. 1, pp. 1–82, 2007.[6] S. P. Skobelev, “Methods of constructing optimum phased-array antennasfor limited field of view,” IEEE Antennas and Propagation Magazine,vol. 40, no. 2, pp. 39–50, 1998.[7] S. P. Skobelev, “Some features of the overlapped subarrays built up ofbeam-forming matrices for shaping flat-topped radiation patterns,” IEEETransactions on Antennas and Propagation, vol. 63, no. 12, pp. 5529–5535, Dec 2015.[8] D. Petrolati, P. Angeletti, A. Morini, and G. Toso, “Radition pattern op-timization of skobelev networks,” inProceedings of the Fourth EuropeanConference on Antennas and Propagation. IEEE, 2010, pp. 1–5.[9] D. Sinnott and G. Haack, “The use of overlapped subarray techniques insimultaneous receive beam linear arrays,” ELECTRONICS RESEARCHLAB ADELAIDE (AUSTRALIA), Tech. Rep., 1984.

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