In high performance aircraft, space craft, satellite communications, long distance radio telecommunications where the size, weight, cost etc are constraint the Microstrip Antennas (MSAs) are susceptible to these communications as MSAs are light weight, low cost, easy to install and flexible. However, it has certain disadvantages like narrow bandwidth, high MC, high orthogonal radiation etc [1].Researchers have proposed various techniques to overcome these disadvantages.
MIMO antenna systems have various advantages in the wireless applications because multiple antennas are used at both the transmitter and receiver ends. These multiple antennas are employed for transmitting/receiving good signal in a multipath fading scenario. MIMO antenna system increases data rate and reliability of communication without the need of extra power and bandwidth as compared to Single-Input-Single-Output (SISO) communication systems. Apart from these advantages, it has few disadvantages also, one of which is MC.
To design compact MIMO antenna, multiple antennas are placed on a single ground plane and MC takes place between adjacent antenna elements, as energy absorbed by one antenna when other is operating. As a result, electromagnetic interaction between the antenna elements will take place which is known as MC. MC occurred due to the signal interference and near field coupling between closely spaced two radiating elements. MC between two or more microstrip elements takes place due to separation, geometry and alignment of the antenna elements.
The voltage current relationship for coupled antenna system is written as, E=ZI
![](data:image/png;base64,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)
E1, E2, E3… Em = Voltage applied to antennas 1, 2 …m.
I1, I2, I3…Im = Current flowing in antennas 1, 2…n.
Z11, Z22…Zmn= Self impedances of antennas 1, 2…n.
Zij (i ≠j) = Mutual impedance of antennas 1, 2, 3…n.
Due to the effect of MC of multiple antennas Zij (i ≠ j) are not the same. When, the Near Field Scatterer (NFS) is brought to the antenna 1, 2, 3…n, the MC matrix changes. The presence of NFS, the above matrix changes to-
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAegAAABwCAYAAADVEuOWAAAcV0lEQVR4Ae2dL6wWydLGkSuRSORKkjU4Vm5yDW6RK1bgQCJINqvAIRDrQBIUarOSrEIRJEEhSTBI5Pvld+6tb2ubrpnpme6e6fM+nbxnZnp6uqqeqq5npufPuXJSEQIFCLx69ep0/fr10/fff3+6f//+6a+//jp9+vSpoAc1FQJC4MgIfP369fT69evTb7/9drpx48bp2rVrpz/++OPIKl9a3a5cWstkWFUE3r9/f/rxxx9Pt2/fPn38+LFq3+pMCAiB4yLACfjdu3cvyJoTcpV+CIig+2E9rKQXL15cDE7OqlWEgBA4TwTevXt3+umnn06PHj06TwB2sFoEvQPoI4lkGvvOnTsnpr1UhIAQEAIPHjxQTugUBiLoTkCPKIZpLZ0tj+g56SwE2iLArBpX0yptERBBt8V32N6fPHly8RDYsAZIcSEgBJoioBzRFN6LzlcRNPci9ih7yd3D1j1lcq+Zs2NNa+/pBckWAsdHgNtfXE2PXnpyS4msxQTN03s3b948Xbly5eJp3i9fvnT3CU8QI59XfJ4/f95d/jkIhJTxc0kQnQMuslEICIFvEeAJb17FGvFVS95M4UKkJ6fxBgx4IRPZc7jNEjQJ+5dffrno7M2bN996aIcagDWd9jhR2MHkbiI1bdUNagkSApcCgRFzBjpDlHu+NoZsLjandJglaKYwMOaIhY9m8G6upmLreAcc+QjJ3FldHWnqRQgIgcuAwGh5A0IsuYX366+/nvi1KFxgTs1YThI09xYg6CMXvnbDT2U7Aha423uq28PLly/rdhj09ueff55++OGH09u3b4MW41R/+PDh9Pfff3dR+PHjx6dbt251kTWSkF5xi6/B/9mzZ7vBw6tXI7zxASFy1VpyEdKSoHEYM8JczecuNCcJmk+8lRiyR3SMdva2B0ZLZXLb4Ij39ludvaa4PH369IKgexFbKr/mNjZgT4+CfzixUfk3Ar3iFl+Dfy9//9vK/27xYCmzmUcvzLryLNPRCtjlPgQVEjQ3s5nuHKEwXTE1jz+CDUfQ8agnZL0THVcko5eeBA0x/Oc//xkdsur694pbFIege12xR0BdvXr1dPRngvjw0hFv2UZ6hQRda3qbaUMGLwHEskUQjTK9EgX2EerXnpDZVSf+TX+1zuijRFdb9ufPn7tN1dbWPY2hKYIGz9RXts1xpYUxfu/evdLDdm1vV51mt19G8VaqcNRPC9k///zz7rdmoqvAUtxati+9mCO2Hz582OwetNka3aoNCTo6wDpcsoSMCRyuSEh+GMpAWJMEpuTV0HWq/3PYt3aKivte/ooTP+PzKDmtwTLqq4VsYrRHaaG715sxFp0gUY+frHDPnXuYUXtrFy3x/9pjoz5b14MPydcXfA8OHhu/v3Q9itsWsnvF7RQGR71F5nUuOYkgDvAVF5aRL33fW9YjDmtK0AR7mrwhaH+2DYlvnR6LjNsC2LkdW2vGxB4YSpMcAZ5L4mk92/5qJlpn4KQlkh3N3ET1ab89tkt0N0x80rC6uWXOltwJFeOWvvz4BXPrP+fLXN+j1EHW2JbGFXZ6nCN7aGfYTC1zuEWyId0jEG9kc1o/wkxmCUGbffg/jYHc+LD2a5YRhzUjaD+Y04A1Qoac2WfbawzjmMi4tf2d43E8gckA21KiRENw4+c0OUX1qQ7p4Ej3sx3JJraQnd5aiepzfbeuK9HdY4ENKaamK+Mv2mdtWOZODCz5gJsnaJNt+1My8/2OtI49uRkE8AMDs7vUpiXHRbIhZmSPRNAj5OEaBG3xn46P0vjw7SPsmhO0VyK3ziAXQeeQ6VsXBchSLSzRkPBzhUSTI4yo3vcxl+jmZHN8StD0H9V72a3X1+qOXtgUYbOEoO3EgGWuTCWgJX7L9XnEOmYQ+OXKFMa59r4u8o1vMyWb8SKC9mhtX69B0KbF1PiwNkuXUf5tTtC5we/rRNBLXdi2XRQgS6VOJRr6iBJ6VO/lziW6OdkREUf1Xnbr9bW6oxdjJ0rgcwQ9d2JA/1MJCPLInfS0xqt2/zaDAB65khI0MQMu4MuSX1Tm4nZOdkrQNutjsrde2ER6r63fmkPWyi05TgTt0GLaiATk70cyEPyVFMG2NdBGCAwHyyFXt2AYJRr/4YSIiKN6D9JUolsiOyLiqN7Lbrm+RXf0YhwxfnKFej/O0ja5EwMeFvP9TRH0lE9SWUfdjmYQfNymBI0t4GI5Cxw8Zt7WKYyWyE4JmtyJbOsXHaITC69Hr/UtOaSXjiJohzSBTkBB1CQjfgSVJ2yC24LdHVq0OkJgFBm0Q+O1GOI/fOxnRVCfbU8QERFH9R4C4iZXlsomoeWu9qL6nKzadVt1Rx+wiwpkm7OZ9vglfYCTenBGLyv4NUcAtIn6tmP9kvGOPCMWv8+vs592Pj/4/awbbj620jZL5FmbNLawN32INdXb4zIVQ2nfpudS2RFBWz/kTe8vq99ruTaH9NS3lKDxFTinvIXOPg622hBh12yK2xSGpDEOYwjm9DOKBBj7t5TIuC19ntuxazC0RINvcz+fRCMijurn8C+RHSXRqH5O9tb9tXRfo4cRXM5f1PmEz3aOoMGtpFiS88SXO579uUTo26IfJO6vcv1+1pfIw4YIA29fdAVtuKyJoaWyRdCpZ7dvlxJ0GiNeg2h8+DZL16P825yg5xQUQc8h1Gd/FCC1pEdEHNXXkks/URKN6mvK3tpXTkcwMyKFQGx9q6z0+FwC8ifT6HHZSwuCXoqZCHopUsvblRL0VM+58THVfmpflH93JWgSi52h+IE/ZUhuX2Rcrq3q8gi0xJBEbn5Or6pz9XkN19X6qxU/LRvVr5PS5qicjowTw4zllnEzpbWXwdUiP1/H+mUnaOLFbMYXFPMJuPu4tivqKUxL9jFOTLbhbL5HB9ODNkcpLXNILRtrEbT5hmUN30fY7UrQtUCPjKvV/zn0IwzPwcuyUQi0Q2CEHFKLoGujGGEngq6N9KD9RQEyqDlSWwgIgc4IjJBDRNCdgwJxIwTGDrAUiRSGRXCpsRAQAgkCI+QQEXTitB6bIwRGDxy2yBCGW9DTsUJACIyQQ0TQO8TpCIGxAyxFIoVhEVxqLASEQILACDlEBJ04rcfmCIHRA4ctMoThFvR0rBAQAiPkEBH0DnE6QmDsAEuRSGFYBJcaCwEhkCAwQg5ZS9D2alticrXNCDs9xV0N4rE7igKkpVW8B1/jHcIlOvLZRb5AdRmKf5+7tT18s3vuC2CtdTha/8Rsq4/DpLbaN7vTLzCm7Y6wvUcOKbVbBF2KWIX2IwRGBTObdrEHhnyMoVeisw87NAWxU+fY0qvwIYae8nrZtUUOMes/uLOlr7lj7YMlvcbJnD5T+/fIIVP65PatJehcXzXrIux0BV0T5YH7igKkpUk9CRpZrb661RKjXN89CRNZ9iWrnC7nWNeToJFV62tVrX21Rw4ptemsCZppGAY0AcV0YvTfXEpBnWs/QmDM2bD3/hyG5kv8mf5qnNFPEXQqz7bn/ttRhCNThb2mak3XdLlW99SmKYJOZdr2WtmM4al/TJHqdoRtu+o02/2SfVvLFEHXHjP2j1W26tzj+FwO6SG3RMYagiZ3cJI6Ne5KdMi1jbCrdgUNOXOFYonb/tVkjQGRM8jXRcb5NlqfRiCHIb4jQVjBxyT6Wj6lH4sXk2HL9OTOvosctbfjoiX3DWvpHcmw+tq6W7+2nEoUtWWD+1rMTd/eS3KPf7aBGOZe+hRuJTqCRxRL1NceM6PMYORySAmuPdqWEjS+xN9wW634ydkZYVeNoLk6SR9eYVCQ0CkMGDuTrR1wkXE5IFSXR2AJhmmSm/Mp/rbkztL8P7XMDQLkpCcGRtj0lcadycpb2re2VPdUOxL+FF62L0cYOdmMPTuG/edQOGlJZxDsH08sue1heM0tc1iWjplcH6PULckhe9tSStCmL3nJ5ybLMcREbuzZcUuXEXbVCHoqeEkE3jjapkl1qSG5dpFxubaqyyMwh2EuyU351OLBCDonlcCe2m/H5JKcneTZQDGysW3kH6GU6L5UX4/71DGpbMacjTuwX0JOU/2PsM+egvZxRuxYvIClxdJSe+hrSVIuHTNL5R+13VwOOYLetQjaxiBxRK7x8bXGzgi7qgS9VEmCu3RQTBkdGTd1jPb9G4EpDC3JsYxKzqcQwFRMcMzUfmRZkrOEmpPPYDHiYb8NmlzbnnVrdF+inyWHqbZLZJNYpnCd6n+EfdjGlTNYRIX4Kz1R4Zg5gl47ZiI9R6ifyiFH0b8WQXt74LK5ePDtc+sRdlUJOjcQckmdZLrVIG9kZJxvo/VpBCIMlyQ5es75dCtBL0lyyGaAeKI/AkGX6s54gDDBEdymzsrnCHqpbCMm+jN5LPldhsIMAr+pQqwYntgNJviAdatPj58j6NIxQ3/II475sV4zP6b6t9qOckgreWv6bUHQ+IqY2VIi7KoRNPegOVtNX6gn4NJCHUFcq0TG1er/HPqJMMwlOXzsCRF8cj7dQtBRkss9UZwmUo4lye1V1upuRMnxDPooSaf2ejuXyqadH5vg5Qk79a+XMcJ6NIOQxg+J1ZKrJ0psjGKIdpFvOG7NmKE/5KEL/U/5+Kj4RznkSPq2IOgavoqwq0bQJG0CjB8Dn4DLJWhLPjWdFhlXU8Zl7yuHIT7kpAuf+ULy8wk88mnO/74fklF6Qmf7Cfr06ocnKtPBYAnNjmOJPlFy9e1ara/VneOMLMDeE6jXNTdTZfuXyk77Bi/zs9fD+o2WRmroGxX8RhzR71RhP+38U9Bp+yXyrE06e8d2qqfHgePsJAW5HhOvBzFrfvL1rK8dM97fqR6pjKNu53LI0XRdQ9DEI3HBL41NfBXFQontEXbVCBplUJakSmBjTDpAaDM3SEuMsraRcbZfy3kEUgzxJX6Mfuy3EvmUGPDtrP3ckmQVyaXeCoTiE6yv9+2svsdyi+7gaIPdJ+ylei+VjQyTY32D11qChlTTK1Prl6UluLn30NmfS4K+L+JpSh6y2B/FDxhZIXbMZuroG/lWPCZWN7Xk+Egu9X4spGPG+zvVY0rmkfalOeRIupkuawg69an1xTL1o99Xsh5hV5Wg5xTCGBsQBKStzx03tz8ybu447f8HgbUYTvl0LUH/o9X0mk+mnqiJKwbVkUtOd7A04vQJu6YdJH+Pla2Dl41Hr0dN2UfqC3wNazBhPSVGj0lN3XNjxvs71aOm7JZ9rc0hLXVK+15D0Gkftp0bw7avdBlh142g07MQgrRWiYyr1f859LMGwymfEry2n4RTs9Cf9W1LEhzFyNnqa8qt0VekO/qbzn7dSKSGbN+vyUIfxiLb+AzCtn1G2DVkH6kPs9fsZEmxbTCw+PVJuIYNJsOW6OJjwvvITp5qyO3Rx5oc0kMvL6MGQac5Bl9u9VWEXTeC9iDVXo+Mqy3nMvcnDC+zd2WbEGiPwAg5pAZBt0Aywk4E3QLtAfuMAmRAU6SyEBACOyAwQg4RQSswdkBgu8gRBtd2K9WDEBACrRAYIYeIoFt5f6LfEQJjQv1D7BKGh3CDlBACwyIwQg4RQe8QXiMExg6wFIkUhkVwqbEQEAIJAiPkEBF04rQemyMERg8ctsgQhlvQ07FCQAiMkENE0DvE6QiBsQMsRSKFYRFcaiwEhECCwAg5RASdOK3H5giB0QOHLTKE4Rb0dKwQEAIj5BAR9A5xOkJg7ABLkUhhWASXGgsBIZAgMEIOEUEnTuuxOUJg9MBhiwxhuAU9HSsEhMAIOUQEvUOcjhAYO8BSJFIYFsGlxkJACCQIjJBDRNCJ03psHjUw/Dd27du7uWXt7/2uwfyoGK6xRccIASHQH4ERcogIun9cnEYIjB1gKRIpDIvgUmMhIAQSBEbIISLoxGk9NkcIjB44bJEhDLegp2OFgBAYIYeIoHeI06MGhqa4dwgGiRQCQmAXBI6ahz0YImiPRqf1EQKjExSrxQjD1dDpQCEgBE6nIW41iqB3CFWRy3bQheF2DNWDEDhnBEbIISLomQj99ddfT7du3Tp9/vx5puXy3SMExnJr9mnZC8MW/t8HMUk9MgKKs/7e6ZVDtlhWk6CfPn164q0cbmVuLRF2V6KOowOi9kvr7927d+K1IhH0UsT6tGvl71T7Fv5PZWhbCCjO+sdArxyyxbKaBP3s2bOLi81LRdBbwI2OHSEwIt2PUi8Mj+IJ6SEExkRghBxSk6BreinCrvsVdE2jrK/IONuv5TwCwnAeI7UQAkIgRmCEHCKCjv3XbM8IgdHM+EodC8NKQKobIXCmCIyQQ0TQOwTnCIGxAyxFIoVhEVxqLASEQILACDlEBJ04rcfmCIHRA4ctMoThFvR0rBAQAiPkEBH0DnE6QmDsAEuRSGFYBJcaCwEhkCAwQg4RQSdO67E5QmD0wGGLDGG4BT0dKwSEwAg5RAS9Q5yOEBg7wFIkUhgWwaXGQkAIJAiMkENE0InTemyOEBg9cNgiQxhuQU/HCgEhMEIOEUHvEKcjBMYOsBSJFIZFcKmxEBACCQIj5JAtBM3nY/m1KBF2+lBJC7QH7DMKkKOZ8vLly11Uevz48cVn/XYRLqHDIPDhw4cq32YuNfjPP/+8+C7027dvSw+t1n6EHCKCrubu5R2NEBjLrdmn5SgYtjqDnUMduXwYX0UITCHAd5n5Jwq9S81/3LBW9xFyyBaCXovLkuMi7HQFvQS9M2gTBcjRTN+LoEmA/JMXFSEwhcBeBI1cTiC5gt+rjJBDRNBJdDD1QmIjeFi2mKIcITASWA63uRZDO3PHv+mvxZVERNCWoFId2I6OKXECccx/SFIZD4FcTFBX+9/egswUQdssTE4fjttS+O+A2LNnWZtDeuq8lqAZ/w8fPqySS3L2Rtg1vYKGjH/++eeLszoCCAMJzq3BmBoYGZe203aMwFoM+Zdr/qwdP+PzGqSY0zbql5hiEPlCvNVKwtjY4oTD66v1Ngjw/IAv5KUWeQgZUwRN/Ph/s8v9YuKzVlwR73uWtTmkp85rCBqf4VcuMKP8s9WGCLumBE3wpcmbgVH7SiQybito53R8LQztYSqfiJbiSOL008gkrtzVRlqXS3CQ9dokzGDkWJXLhwD5qCYpprEYbeeQbHkim5PXuq5WDmmp5xqCNn0g50tD0JbkcgHrk7AZv2U5QmBssa/HsTUw3EKKdlUzFxtLBsiWJOzjtgfuktEXgdakSPzkThhTK7ecyKZ9HWW7Rg5pbYsI+n8IW6JrDTj9jxAYPXDYImMrhkaK6XRiiU7ETA2CJgnzW1uwRVfQa9E77nFGivi3VVlC0HYim96SaaVTr3635pAeeoqg/4eyEXQuCKnz96PtKnvtwBkhMHoE3xYZWzGMSBHfQrp2hczVha2nZFyDoKMkjCx0sbgk/mw9JWMR9JZIOuaxESnabRS7vWKxYPFCvcUDszfWPrrfS0xNXUHTF1Ps6YmsjQmORQ560NbWrU/q/XhaMqPUyyNbc0gPPWsRtMWBjxt8v7ZE2DW/B03i9vcjCToLNhsEGEXAY+yaEhm3pq9zPWYLhhEp8gCZkSD+tURnyQ3/U2eFttRNlamEFCVhe5CN5GbH+3Xq/OAyPaf00L5xEMCfOVIkLij43wiR2LR18pHFqidQ+ovilDiy/JZDKHciy8NiHGeyrQ/0YJ2fxS3r1JterB+lbMkhvWyoRdDo6+MGn0/5fc6+CLumBM0AIIBscJDICWwjbNYJOAoBt9bAyLg5ULT/HwTWYmgJI50pYRt/st8nM59QvP/RJG37j3b/rKVXHraHmLI4szqWJFMeSkxJF9nUURho/uQwbev7i9ZNviXSqB370dPGQK4duIGTjY1cm3OUtwSXHFZgnt7yAD/zFUvzPzL4UaizNn59Kj4gW+sr1YV+8b3Fne0npvG1z4H0YSTsx4Vf53jiJO3P+u29XJtDeuq5lqCJF3IGPxu7adyYv9bYE2HXlKBRFJLGKAIJg/yn6Ki3JOSDs9TAyLjSfs65/RoMjSTwbe5HQsolFMPZ+5+6tK21W7IktnI6WNylSRXZltj8QENW2naJfBvAc28osB/ZNshzfTNmSOQ2NnJtzlHeElxSrIjBKC6op3j/054fxZOyX18TH/hySg/2+xwogr5wQfU/awk69R2KpXEzJEFPIewTtA/OqWNy+9aQS66fc65rhWFKupYUwdr7n+20bU1/pEm1NkHX1FV99UUgTbQtCHqJRT4HiqCXIFbeZi1B5ySlcXOpCBpj7KzEn+WSpEtLK3Ip1WPk9q0wNB/jb0iRbZYEt+0DN/xu2+yvXUw2cr1sH4eQuBG56VJbD/V3LAR87vHrPi5+//33/49N34Y4qlUgZIs5L8Prka5bTLcYL2vsapVD1ugSHVOLoL2P/Dp+XFMi7JpPca9RtvSYyLjSfs65vTA8Z+/LdiGwHYERckgtgt6O1r97iLATQf8bp7PdigLkbAGR4UJACBQhMEIO+eWXX07Pnz8vsqtH4wcPHpwePXr0jSgR9DeQnGfFCIPrPD0jq4XAGAiMkEP++OOP0927dw8H6O3bt0+vXr36Ri8R9DeQnGcFZ2+cxakIASEgBNYgMAJBv3///vT999+vMa/ZMV+/fj1dv3799OnTp29kiKC/geQ8K168eHG6c+fOeRovq4WAENiMQDRNu7njyh0cTU+u6Lmyz5WQoEe6ohrhzC0H/pHqXr9+feIBChUhIASEwBoEjnp/N7WFK9abN29m7/mmbVtuowcnC+AWlZCgmQ9nXnyEcv/+/dOTJ09GUPWwOn78+PFimuWwCkoxISAEDo3AUZ+QzoFm5Mh0NwTZiz+Qy8UvMpGdezDM6xsS9JcvX05Xr171bQ+7ztnQmzdvDqvfKIrhb/yuIgSEgBAoRWDE/ME9aZ7qZha2R+7jQghZyGR9roQEzYE3btw4vXv3bq6PXfcDKjfYe4C7q6EdhI8yRdUBCokQAkKgAAHdIisAq6DpJEFDzlydcll+1CJSqeeZkW5r1LNaPQkBIbAVAT0HtBXB/PGTBM0h3MTmKbMjkjTz96PcJ8/Df6xafBw97n8sTaWNEBACR0GAvMFsK9PFKnURmCVoxEGEOIB5873v9RIEvBLElT0nD0c8cajror698bAED92pCAEhIASWIKCcsQSldW0WETRdQ4xMJ0OM3333Xfal6nUqLDsKIr527drFk2+8r7v3icIyrcdrpbPh8XwmjYXAXgjw7A9PI+c+srGXTpdJ7mKCvkxGy5ZpBPTAxzQ+2isEhMB/EdAzQG0jQQTdFt9he9e01bCuk+JCoAsCyhHtYRZBt8d4WAncSog+QTesUVJcCAiBzQjYGx96BmgzlJMdiKAn4TnvnQw+nuA/6lP85+0dWS8E9kGAK2fenhE5t8dfBN0e4+ElcBXNZ/yO/tGa4YGWAULgwAjw5SuIWW959HOSCLof1kNL4ql5XrXjoRA9sTm0K6W8EChCgCe1eaWVp7Vz/7O4qDM1LkJABF0ElxrzLjyvu/G6He/H66paMSEELh8CvFbLVPZPP/108T8ZGOua0u7vZxF0f8wvhUSuqDmr5qr6ypUrFz+mwXWGfSncKyPODAHGM+OXb1wwnrlaZir7r7/+OjMkjmWuCPpY/hhaG96f1j8tGdqFUv5MEeDqmPGrq+RjBYAI+lj+kDZCQAgIASEgBC4QEEErEISAEBACQkAIHBCB/wNOTulE4/Y2YgAAAABJRU5ErkJggg==)
e1, e2…en= Change voltages.
i1, i2…in= Change currents.
zmn+zmn'= Change impedances.
The above parameters are modified due to NFS and antenna spacing. Additional impedance parameter now added to the actual impedance effectively increases the total impedance of individual antenna elements. As a result, the efficiency as well as the gain of the antenna changes because of the changes in antenna current. As the impedance changes by MC the resonant frequencies as well as the gain of the antenna are also changed. In mobile communication if the spacing of the antenna elements are < λ/2 the received signal will be affected by MC [2]. For patch antennas, dielectric constant of the substrate and also the thickness affect the MC. With higher dielectric constant and thickness, the MC is higher since more energy is coupled to the surface waves. To reduce the affect of MC, the isolation (S21) between the antenna elements needs to be maximized. Authors in the open literatures have proposed various methods [3-33] to suppress the affect of MC.
In recent years, researchers have proposed various methods such as DGS[3-8], EBG[9-10], parasitic element[11-13], microstrip resonators[14-20], EMSS[21-24], FSS[25-27], metamaterial structure [28], coupling matrix based band stop filter[29], meander line [30-31] etc. to suppress the affect of MC between two patch antennas. DGS and EBGs are not very popular techniques as they cannot protect undesirable back radiation. It is seen in the open literatures that the parasitic elements, microstrip resonators, metamaterial structures, coupling matrix based band stop filter can reduce MC between closely spaced antenna elements.
Recently, a new technique known as Frequency Selective Surface (FSS) has been introduced to suppress MC between very closely spaced antenna elements. Design of FSS is very complicated and most of the cases FSS integrated antennas are erroneous after fabrication. Other than MC, there is one more drawback of probe feed antenna design for MIMO application. This drawback is the XP radiation as some degree of orthogonally polarized fields is always associated with the radiating energy [32-33]. Researchers suggest that the XP radiation level should be ≤ -20dB for better MIMO antenna performances.
Presently, researchers have introduced EMSS for reducing the affect of MC between the antenna elements. In our design, we have explored a new EMSS structure between two rectangular patch antennas as shown in Figure-3(b).This proposed EMSS created on the substrate between antenna elements effectively exhibits anti-resonance characteristics at the designed frequency and as a result both MC and XP are suppressed. It has been observed that the proposed EMSS structure does not affect the other characteristics of the antenna like return loss, bandwidth, antenna efficiency and radiation pattern in the principal plane.