The Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using Binary Ink Stamp Optimization

Recei ed Augus 12, 2021, accep ed Augus 26, 2021, da e o publica ion Augus 31, 2021, da e o cu en e sion Sep embe 10, 2021. Digi al Objec Iden i ie 10.1109/ACCESS.2021.3109522 The Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using Bina y Ink S amp Op imiza ion JAROSLAV ZECHMEISTER , (G adua e S uden Membe , IEEE), JAROSLAV LACIK , (Membe , IEEE), AND PETR KADLEC , (Membe , IEEE) Depa men o Radio Elec onics, Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o Technology, 616 00 B no, Czech Republic Co esponding au ho s: Ja osla Zechmeis e (ja osla [email p o ec ed]) and Ja osla Lacik ([email p o ec ed]) This wo k was suppo ed in pa by he In e nal G an Agency o B no Uni e si y o Technology unde P ojec FEKT-S-20-6526, and in pa by Czech Science Founda ion unde G an 19-06049S. ABSTRACT In his pape , linea ly and ci cula ly pola ized single-laye Subs a e In eg a ed Wa eg- uide (SIW) ho n an ennas wi h nea ly equal hal powe beamwid hs in p incipal planes o he 24 GHz ISM band a e designed. The uniqueness o he solu ion lies in he applica ion o a pixela ed s uc u e o he design o hese SIW ho n an ennas. Fo he design, a no el heu is ic algo i hm called Bina y Ink S amp Op imiza ion is p oposed. A i s , he abili y o he p oposed algo i hm is p o ed o e i een benchma k unc ions and compa ed wi h he esul s o six s a e-o - he-a op imiza ion algo i hms. Then, he no el algo i hm is exploi ed o he design o he pixela ed pa o he an ennas. The an ennas a e manu ac u ed using low-cos 3D p in ing echnology. The expe imen al esul s p o e ha he linea ly pola ized an enna has a e lec ion coe icien below −18 dB in he whole 24 GHz ISM band. A he cen e equency o his band, he an enna gain is 14.2 dBi, and he le el o side lobes is below −15 dB in E and H-planes. In addi ion, E and H-plane hal powe beamwid hs a e 26.5◦and 25◦, espec i ely. The ci cula ly pola ized an enna adia es a igh -hand ci cula ly pola ized (RHCP) wa e, he e lec ion coe icien , and axial a io a e below −12 dB and 3 dB in he whole 24 GHz ISM band, espec i ely. A he cen e equency o his band, he an enna gain is 8.9 dBi and he le el o side lobes is below −7.4 dB in bo h p incipal planes. Fu he , he hal powe beamwid hs in p incipal planes a e 30.6◦and 33.4◦, espec i ely. INDEX TERMS Subs a e in eg a ed wa eguide (SIW), SIW ho n an enna, pixela ed an enna, disc e e e olu iona y algo i hm, bina y op imiza ion. I. INTRODUCTION Ho n an ennas a e widely used in wi eless applica ions due o hei simple s uc u e, high gain and e iciency, and wide bandwid h. Howe e , since hey a e based on con en ional wa eguides, ho n an ennas su e om la ge olume and weigh , and high ab ica ion cos s. P omising al e na i es a e Subs a e In eg a ed Wa eguide (SIW) ho n an ennas. They a e elec ically simila o con en ional ho n an ennas based on he ec angula wa eguide. Howe e , hey can be easily in eg a ed wi h plana ci cui s and can be ab ica ed by a low- cos p in ci cui boa d p ocess. Un o una ely, SIW ho n an ennas ha e na ow bandwid h, high le els o side and back adia ion lobes, and p ima ily The associa e edi o coo dina ing he e iew o his manusc ip and app o ing i o publica ion was Ladislau Ma eko i s . unequal adia ion pa e ns in he E and H-plane. Se e al echniques can be exploi ed o he pe o mance enhance- men o SIW ho n an ennas. A highe gain and na owe beamwid h can be achie ed by adding a dielec ic load in on o he an enna ape u e [1]. Fu he , a highe gain can also be achie ed by adjus ing he shape o he dielec ic load, o by pe o a ing he load [2], [3]. P in ed me al pa allel pla es [4] o pe iodical ansi ions [5] on op and bo om o he load a e also easible app oaches o he gain enhancemen o SIW ho n an ennas. Al hough hese app oaches imp o e he adia ion p ope ies o SIW ho n an ennas, hese an ennas s ill p o ide unequal hal powe beamwid hs (HPBW) in E and H-plane. SIW ho n an ennas wi h almos equal E and H-plane beamwid hs we e p esen ed in [6] and [7]. Howe e , he di e ence be ween bo h beamwid hs is s ill mo e han 30%. Ho n an ennas based on SIW echnology wi h equal 122216 This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/ VOLUME 9, 2021 J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO beamwid hs in E and H-plane we e p esen ed in [8] and [9]. Un o una ely, hese s uc u es a e mul i-laye ed, he e o e he main bene i s o single-laye ed SIW ho n an ennas, such as ease o manu ac u ing and a low p o ile, a e de alued. Ci cula pola iza ion (CP) p o ides se e al ad an ages compa ed o linea pola iza ion. CP an ennas a e an impo - an echnology o sa elli e and mobile communica ions, na iga ion sys ems, e c. The main ad an age o CP lies in i s immuni y o mul i-pa h in e e ences and pola iza- ion misma ch [10]. CP SIW ho n an ennas a e mainly composed o wo o mo e an enna elemen s o ob ain o hog- onal modes [11]–[14]. In [15] an inhomogeneous pola - ize is placed in on o he an enna ape u e o achie e CP. An an ipodal ape ed s uc u e is p esen ed in [16]. I desc ibes an e ec i e app oach o designing a CP SIW ho n an enna. The goal o his pape is o desc ibe he design o lin- ea ly and ci cula ly pola ized single-laye SIW ho n an en- nas wi h equal HPBW in main o hogonal adia ion planes. A pixela ed app oach is applied o achie e desi ed pe o - mance. Pixela ed s uc u es p o ide high a iabili y o he inal shape [17]–[19]. In gene al, he pixeliza ion design ech- nique equi es no a p io i de ined an enna empla e. The e- o e, his app oach may lead o uncon en ional solu ions o load shapes. Howe e , wi h an inc easing numbe o pixels, he complexi y o he op imiza ion p oblem g ows exponen- ially. The e o e, an e icien op imiza ion p ocedu e has o be adop ed. Pixela ed pa e ns a e exploi ed in an enna appli- ca ions mos ly o inc ease bandwid h o dec ease an enna dimensions. The Gene ic Algo i hm (GA) is used in he majo i y o a ailable s udies as an op imiza ion ool. The GA upda es a bina y ec o using selec ion, c osso e , and mu a- ion p ocedu es. Du ing he op imiza ion p ocess, each bi has equal signi icance. Howe e , in eal-wo ld applica ions o bina y pa e ns, some pixels can ha e a bigge in luence on he s uc u e p ope ies. Due o his ac , we p opose an e o- lu iona y op imiza ion algo i hm named Bina y Ink S amp Op imiza ion, e lec ing he signi icance o he bi s du ing he op imiza ion p ocess. Tha is he key bene i compa ed o he es o he algo i hms in e ms o bina y pa e n op imiza ion. II. BINARY INK STAMP OPTIMIZATION A. ALGORITHM DESCRIPTION Bina y Ink S amp Op imiza ion (BISO) is a heu is ic op i- miza ion algo i hm o bina y p oblems. BISO is inspi ed by s amps wi h di e en ink sa u a ion. A se o s amps co esponds o a se o so a bes indi iduals. Thei ink sa u a ion is de e mined by hei i ness alues. The nex gene a ion is de e mined based on a p obabili y ma ix, which can be imagined as an imp in o all s amps o e each o he . A da ke posi ions, he e is a highe p obabili y o gene a ing ‘‘1’’. On he con a y, ‘‘0’’ will be gene a ed mo e o en a b igh e posi ions. Gene al s eps o BISO a e depic ed in he low cha in Fig. 1. The ollowing pa ame e s a e se a he s a o he op imiza ion un: FIGURE 1. Flow cha o he bina y ink s amp op imiza ion algo i hm. •Npop – numbe o indi iduals in each i e a ion, •Neli – numbe o selec ed eli is indi iduals, •Ni e – maximal numbe o i e a ions, •p obMin – he minimal p obabili y o gene a ing ‘‘1’’ in he nex i e a ion, •p obMinRST – he minimal p obabili y o gene a ing ‘‘1’’ in he nex i e a ion when he algo i hm ge s s uck in local ex eme, • s Coe – c i e ia o ese ing he popula ion, •sigCoe – he s eepness o he sigmoid unc ion. A he s a , an ini ial popula ion is andomly gene a ed as a bina y ma ix o size Npop ×Ndim, whe e Ndim is he numbe o op imized a iables. Rows in his ma ix co espond o he indi iduals o he i s popula ion. A e he i ness e alua ion, indi iduals a e so ed acco ding o hei alue. A se o indi iduals wi h a be e ank in he o de ed se a e selec ed. A his poin , Hamming dis ances be ween hese eli e indi iduals a e de e mined and compa ed wi h Ndim × s Coe . This pa is designed o a oid he algo i hm being s uck in a local minimum. The dec easing VOLUME 9, 2021 122217 J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO TABLE 1. Resul s o benchma k unc ions. Hamming dis ance be ween mul iple indi iduals indica es ha he sub- egion o he domain space has been exhaus i ely explo ed and he algo i hm eaches he local minimum. In he nex s ep, he p obabili y ec o is de e mined. The ec o is de ined as a weigh ed sum o componen s acco ding o he bes indi iduals: p obVec (i) =1 Neli Neli X k=1([1 −w(k)],i Eli e(k,i)=1 w(k),i Eli e(k,i)=0(1) whe e iis he index o he a iable, Eli e is he ma ix o he eli e indi iduals, kis he index o he indi idual in Eli e and wdeno es he weigh o an indi idual acco ding o: w(k)=0.5−p obMin 1+exp h−1 meanE (k)−sigCoe ×meanEi(2) whe e meanE is he mean i ness alue o cu en eli e indi- iduals and deno es he i ness alue. The ange o he sigmoid unc ion (2) is om p obMin (speci ied by use ) o 0.5 – p obMin. These wo alues de e mine he minimum 122218 VOLUME 9, 2021 J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO TABLE 2. Pa ame e s o con en ional SIW ho n an enna. and maximum p obabili y o gene a ing ‘‘1’’. The p obMin pa ame e has a signi ican in luence on he con e gence a e o he algo i hm. Fo high alues o he pa ame e (p obMin >0.1), he con e gence a e is low, and achie ing an op i- mum equi es a high numbe o i e a ions. Howe e , o low alues o he pa ame e , he algo i hm is s ongly descend- ing owa d he nea es minimum. Fo his pu pose, we ha e implemen ed he so-called ‘‘ ese ’’ ou ine. I he Hamming dis ance be ween he eli e indi iduals o one popula ion is below Ndim × s Coe , he alue o he pa ame e p obMin is se o p obMinRST. In he case ha he alue o p obMinRST is 0.5, he nex popula ion is gene a ed andomly. The new popula ion is gene a ed acco ding o he ollowing equa ion in e e y i e a ion: newPop(j,i)=(1,i and ≤p obVec (i) 0,i and >p obVec (i) j∈{1,2,...,Npop}(3) B. BENCHMARK RESULTS The p oposed algo i hm is es ed on 15 benchma k unc ions wi h bina y a iables. De ini ions o he benchma k unc ions a e summa ized in Appendix. Mos o he benchma k unc- ions ( 1- 13) a e adop ed om [20]. The selec ed benchma k unc ions can be di ided in o wo ca ego ies - unimodal ( 1- 7) and mul imodal ( 8- 13) unc ions. Ano he wo es p oblems ( b1, b2) we e p oposed as bina y es unc ions which beha e like he eal op imiza ion o ou an enna design. We ha e es ed he BISO algo i hm on hese unc- ions and compa ed i wi h six op imiza ion algo i hms, Bina y Pa icle Swa m Op imiza ion (BPSO) [21], Gene ic Algo i hm (GA) [22], Bina y Co a iance Ma ix Adap a- ion E olu ion S a egy (BCMAES) [23], Bina y Ba Algo- i hm (BBA) [20], Bina y D agon ly Algo i hm (BDA) [24] and Mul i-Ve se Op imiza ion (MVO) [25]. The ob ained alues o benchma k unc ions wi h ou di e en dimen- sions Ndim ={30,120, 300, 900} a e shown in Table 1. Please no e ha he alues a e a e aged o e 100 independen op imiza ion uns. Values in pa en heses deno e he s anda d de ia ion o he esul s. The unimodal unc ions a e use ul in e ms o examining he con e gence a e o op imiza ion algo i hms. The mul imodal unc ions benchma k he abili y o algo i hms o a oid local minimums. BISO p o ides a good capabili y in sol ing unimodal as well as mul imodal p oblems and ou pe o ms he o he algo i hms in mos cases. In gene al, BISO is a sui able al e na i e o op imizing bina y p oblems, especially o hose wi h a high numbe o a iables. FIGURE 2. Simpli ied model o con en ional SIW ho n an enna, ins ead o ias, e ical solid walls a e used. FIGURE 3. No malized simula ed adia ion pa e ns o simpli ied SIW ho n an enna a 24 GHz. HPBW is indica ed by e ical dashed lines. III. DESIGN OF ANTENNAS We exploi he p oposed BISO algo i hm o designing lin- ea ly and ci cula ly pola ized SIW ho n an ennas wi h nea ly equal beamwid hs. To ca y ou ou goal, we exploi a SIW ho n an enna designed o maximal di ec i i y depic ed in Fig. 2 and de ined by he pa ame e s in Table 2. The no malized adia ion pa e ns o he simpli ied SIW ho n an enna a e shown in Fig 3. The E and H-plane beamwid hs o he con en ional an enna a e 138.6◦and 25.6◦, espec- i ely. The con en ional an enna p o ides a gain o 8.2 dBi (please no e ha he losses o he subs a e we e no consid- e ed in his case). The pe o mance enhancemen o such an an enna is achie ed by ex ending he an enna ape u e and i s pixeliza ion. This s ep depends on he an enna pola iza- ion. The e o e, i will be desc ibed in he ollowing sec ions indi idually. The pa ame e s o he BISO algo i hm du ing he op imiza ion we e se as shown in Table 3. Bo h an ennas a e designed o a subs a e wi h a hickness o 3.3 mm and a ela i e pe mi i i y o 2.75. The subs a e is made o an XT co-polyes e 3D p in ed ilamen om Colo abb [26]. The ela i e pe mi i i y o his ma e ial is published in [27]. VOLUME 9, 2021 122219 J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO TABLE 3. Pa ame e s se ing o BISO algo i hm du ing an enna op imiza ion. FIGURE 4. Simpli ied model o he p oposed linea ly pola ized pixela ed SIW ho n an enna. The elec omagne ic simula ions we e pe o med by CST S udio Sui e, whe eas he p ocess o op imiza ion was con olled by an in-house MATLAB code. Fo he sake o he speed o he design p ocess, a simpli ied model o he SIW ho n an enna wi h e ical solid walls was exploi ed. A. LINEARLY POLARIZED ANTENNA The linea ly pola ized (LP) an enna is designed o achie e equal HPBW in he E and H-plane o he adia ion pa e n wi h emphasis on SLL educ ion. The an enna is axially sym- me ical as shown in Fig. 4. The pixeliza ion is applied o e a g id in e sec ed wi h he body o he an enna. Cells assigned FIGURE 5. Op imized bina y pa e n o he linea ly pola ized an enna. FIGURE 6. Op imized linea ly pola ized an enna wi h SIW s uc u e and coaxial-SIW ansi ion. wi h ‘‘1’’ a e illed by a subs a e ma e ial and cells wi h ‘‘0’’ a e illed by ai . The pixel g id geome y is con olled using pa ame e s lc1-lc6, which a e in ege mul iples o he side leng h o he pixels and he e o e e e o he numbe o pixels in he columns. Bi s o he op imized pa e n which a e ou side he g id become so-called dummy pixels because hese posi ions a e de ined as illed by he subs a e ma e ial and co e ed by a me al laye . A e a ew ials, we obse ed ha he shape o he g id can be oughly app oxima ed wi h a pa abolic shape, he e o e some o he pixels a e alloca ed o de e mine he pa ame e s lc1-lc7. This app oach helps o educe he numbe o a iables ( hese pixels a e highligh ed wi h blue colo in Fig. 5). The a iable lc7 is used o de e mine he leng h o he edge me alliza ion. The o al numbe o pixels o he op imized pa e n is 6×28. The i ness unc ion is speci ied as ollows: =q S112+ HPBW2+ SLL2+ G2(4) 122220 VOLUME 9, 2021 J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO TABLE 4. Pa ame e s o he p oposed linea ly pola ized an enna. FIGURE 7. No malized E- ield dis ibu ion o he linea ly pola ized an enna a 24.125 GHz in a) H-plane and b) E-plane. whe e pa ame e s S11, HPBW, SLL, and Ga e de ined by he ollowing equa ions: S11 =(S11/15 +1,i S11 ≥ −15 0,i S11 <−15 (5) HPBW =1HPBW 10 (6) SLL =     1,i SLL <8 −SLL/12 +5/3,i 8 ≤SLL ≤20 0,i SLL >20 (7) FIGURE 8. Manu ac u ed p o o ype o he linea ly pola ized an enna. FIGURE 9. Measu ed and simula ed e lec ion coe icien o he linea ly pola ized an enna. and G=     1,i G<8 −G/12 +5/3,i 8 ≤G≤15 0,i G>15 (8) whe e S11 is he e lec ion coe icien a 24 GHz in dB, 1HPBW is he di e ence be ween HPBW in he E and H-plane, SLL is he side lobe le el a 24 GHz, and Gis he gain in he main di ec ion a 24 GHz, espec i ely. The op imized pixela ed pa e n is shown in Fig. 5. The simpli ied model is ans o med o he SIW s uc u e and he coaxial-SIW ansi ion is added (see Fig. 6). Dimensions o he op imized model a e lis ed in Table 4. No e ha he coaxial eed p obe leng h in he subs a e lin is 1.8 mm. Values in pa en heses a e he ound op imal leng hs o lc1-lc7. The E- ield dis ibu ions a he cen e equency o he 24 GHz ISM band a e shown in Fig. 7. Ob iously, he E- ield is ocused by he pixela ed pa . The dielec ic pa o he p oposed an enna is made o an XT co-polyes e om Colo abb [26] using a used deposi ion VOLUME 9, 2021 122221 J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO TABLE 5. Compa ison o he linea ly pola ized an enna wi h s a e-o - he-a wo ks. FIGURE 10. No malized measu ed and simula ed adia ion pa e ns o he linea ly pola ized an enna a 24.125 GHz a) E-plane and b) H-plane. Measu ed HPBW is indica ed by e ical dashed lines. modeling 3D p in e P usa i3 MK3S wi h a 0.25 mm nozzle. The subs a e is ully p in ed wi hou any pos -p ocessing s eps, such as d illing, g inding, e c. The me al laye is made o coppe oil and i s op imized shape is cu . The e ical walls o he SIW s uc u e a e c ea ed by a coppe wi e o diame e 0.8 mm. The indi idual ias a e solde ed o he op and bo om side o he an enna and he SMA connec o is solde ed. The manu ac u ed LP an enna (see Fig. 8) was measu ed in an anechoic chambe o expe imen ally e i y i s pe - o mance. The compa ison o he measu ed and simula ed e lec ion coe icien o e he equency band 22-26 GHz is shown in Fig. 9. The measu ed e lec ion coe icien o he p oposed an enna is below -18 dB in he whole 24 GHz ISM band. The measu ed adia ion pa e ns (see Fig. 10) show good ag eemen wi h he simula ed ones. A small disc ep- ancy be ween he measu ed and simula ed esul s is caused by he inaccu acy o he ab ica ion echnology, and u he by he ac ha losses o he subs a e we e no conside ed du ing he design p ocess o he an enna. The measu ed gain o he an enna is 14.2 dBi a he cen al equency o he 24 GHz ISM band, he SLL is below -15 dB, E and H-plane beamwid hs a e 26.5◦and 25◦, espec i ely. The nea ly equal TABLE 6. Pa ame e s o he op imized ci cula ly pola ized an enna. HPBW in he E and H-plane is achie ed o he single-laye con igu a ion o he an enna. In his scope, he p oposed an enna ou pe o ms he s a e-o - he-a wo ks (see Table 5). Please no e ha he SMA connec o s used o he an ennas eeding a e a ed up o 26.5 GHz which is su icien conside - ing he ac ha he an ennas a e designed o he 24 GHz ISM band. The measu ed −10 dB S11 bandwid hs (BW) canno 122222 VOLUME 9, 2021 J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO FIGURE 11. Simpli ied model o he p oposed ci cula ly pola ized SIW ho n an enna. be conside ed alid, because hey a e beyond he connec o s ope a ing ange. Consequen ly, he p esen ed alues o -10 dB S11 BW a e acco ding o he simula ed da a. B. CIRCULARLY POLARIZED ANTENNA The app oach o gene a e he dielec ic pa o he CP an enna is simila o he LP one. The pixela ed g id o he CP an enna is also axially symme ical. Howe e , he op and bo om me al laye s a e an ipodal (see Fig. 11). We we e inspi ed by he con igu a ion p esen ed in [16] whe e he abili y o an ipodal s uc u e gene a ing CP is p esen ed. The pixel g id geome y is also con olled using pa ame e s lc1-lc6, which e e o he numbe o pixels in he columns, plus addi ional pa ame e s lc7-lc13 ha de e mine he es o FIGURE 12. Op imized bina y pa e n o he ci cula ly pola ized an enna. FIGURE 13. Op imized ci cula ly pola ized an enna wi h SIW s uc u e and coaxial-SIW ansi ion. he adjus ed pa o he me al laye . Pixels alloca ed o de e - mining pa ame e s lc1-lc13 a e highligh ed wi h blue colo in Fig. 12. The o al numbe o pixels o he op imized pa e n is 6×28. The i ness unc ion is speci ied as ollows: =q S112+ HPBW2+ AR2+ G2(9) whe e S11 and HPBW a e de ined as (5) and (6), espec i ely. The i ness pa ame e o axial a io AR is de ined as: AR =     1,i AR >10 −AR/7−3/7,i 3 ≤AR ≤10 0,i AR <3 (10) VOLUME 9, 2021 122223 J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO FIGURE 14. No malized E- ield dis ibu ion o he ci cula ly pola ized an enna a 24.125 GHz in a) xy plane and b) yz plane. FIGURE 15. Manu ac u ed p o o ype o he ci cula ly pola ized an enna. whe e AR is he axial a io in he main di ec ion a 24 GHz. The desi ed alue o gain is se as 13 dBi and Gis de ined as: G=     1,i G<8 −G/5+13/5,i 8 ≤G≤13 0,i G>13 (11) whe e Gis gain in he main di ec ion a 24 GHz. FIGURE 16. Measu ed and simula ed e lec ion coe icien o he ci cula ly pola ized an enna. FIGURE 17. Measu ed and simula ed axial a io o he ci cula ly pola ized an enna. The op imized pa e n is shown in Fig. 12. and he dimen- sions o he p oposed CP an enna a e lis ed in Table 6. Val- ues in pa en heses deno e he ound op imal leng hs o he pa ame e s lc1-lc13. The simpli ied model o he CP an enna is also ans o med o he SIW s uc u e and he coaxial-SIW ansi ion is added (see Fig. 13). The leng h o he eeding coaxial p obe in he subs a e lin is 1.8 mm. The E- ield dis ibu ion o he p oposed CP an enna is shown in Fig. 14. The CP an enna p o ides a less uni o m E- ield a he ape u e compa ed o he LP an enna. The an enna is manu ac u ed in he same way as o he LP an enna p esen ed in he p e ious sec ion. The ab ica ed sample o he an enna is shown in Fig. 15. The measu ed and simula ed e lec ion coe icien o e he equency band 22-26 GHz is shown in Fig. 16. I emains below -12 dB o he whole 24 GHz ISM band. The measu ed and simula ed axial a io (see Fig. 17) is below 3 dB o e he ope a ing band. The measu ed adia ion pa e ns (see Fig. 18) in he 122224 VOLUME 9, 2021