Single element antenna

In this section ‘Single element antenna’, the complete analysis of the 2 × 2 MIMO antenna is studied and before this, the evolution of the single element antenna offering wider impedance bandwidth is developed. Figure 1 shows the isometric view as well as the front view of the antenna. Figure 1(a) which is the isometric view consists of an FR4 substrate with dimension L × W mm² and thickness h = 1.60 mm. The radiating patch is printed on one plane and ground on the opposite plane of the substrate as observed in Fig. 1(b). The radiating patch which is connected to the microstrip feed line is attached to the 50 Ω SMA connector.

Fig. 1. (a) Isometric view of proposed multiband antenna (b) Front view.

Figures 2(a) and 2(b) shows the evolution of the proposed antenna in two iterations and Fig. 2(c) compares the S ₁₁ result of both the antennas. Figure 2(a) consists of a polygon patch with 12-sides and a rectangular ground. The equivalent circle of radius R forming the polygon is calculated by following equations [Reference Sharma, Awasthi and Singh27]

(1)$$R_{5.8\,{\rm mm}} = \displaystyle{F \over {\sqrt {( {1 + ( {2h/F\pi \varepsilon_{\rm r}} ) [ {\ln \{ {\pi F/2h} \} + 1.7726} ] } ) } }}$$

(2)$$F = \displaystyle{{8.791 \times {10}^9} \over {6.65 \times {10}^9\sqrt {\varepsilon _{\rm r}} }}$$

Fig. 2. (a) Antenna #1: Without ground slot (b) Antenna #2: With ground slot (c) S ₁₁ (Antenna #1 & Antenna #2). Parametric Study of (d) R (e) L₁.

The effective radius of the patch antenna is given by

(3)$$a_{\rm e} = a\sqrt {1 + \displaystyle{{2h} \over {\pi R[ {\ln ( {R/2 \times h} ) + 1.7726} ] }}} $$

Also, the area of the polygon is given by

(4)$$Area_{Polygom} = 3S^2\left({2 + \sqrt 3 } \right)\;{\rm m}{\rm m}^2$$

Antenna #1 shown in Fig. 2(a) provided the impedance bandwidth of 4.53–11.52 GHz. It can be observed that for the bandwidth between 7.02–8.32 GHz, the matching of impedance is very poor. However, to improve the deteriorated bandwidth, the modification of Antenna #1 is subjected by etching a semi-elliptical slot in the ground which not only improves the impedance bandwidth but also provides two resonant frequencies at 6.88 GHz (S ₁₁ = −25.02 dB) and 11.52 GHz (S ₁₁ = −28.31 dB).

The optimized impedance bandwidth which is obtained from Antenna #2 is dependent on two key parameters, one equivalent circle radius R and the slot length L ₁ mm in the ground The two extreme values of R = 3.90 and 7.90 mm show that the antenna achieves wider impedance bandwidth but filters partial band from 7.52–9.51 GHz for R = 3.90 mm. The value of R corresponding to 7.90 mm observes a very high mismatch of impedance but, for R = 5.90 mm, the objective of the proposed work is achieved with a highly matched impedance bandwidth of 5.08–12.12 GHz. Similarly, another key parameter that contributes to the design of Antenna #2 is involved in the matching of impedance, thereby resulting in wider bandwidth. The semi-elliptical etched slot in the ground denoted by L ₁ (major radius of the ellipse) with the value of 3.00 mm achieves an impedance bandwidth of 4.50–11.52 GHz and with the value of 9.00 mm the bandwidth is 6.51–10.10 GHz. In the former case, L ₁ = 3.00 mm, in comparison to L ₁ = 6.00 mm which is an optimized value with a bandwidth 5.08–12.12 GHz do achieve the objective but, the proposed work is extended to MIMO configuration with two band notched filters. Due to this, better matching of impedance is required which is fulfilled by L ₁ = 6.00 mm.

MIMO configuration

The single-element antenna discussed in Figs 1 and 2 is an example of a single-input-single-output (SISO) communication system. This system when placed in a real-time communication system does suffer from drawbacks such as multiple-path fading and thus directly affects the working bandwidth of the antenna. Accordingly, Shannon–Hartley has given the advantage of using more than 1 radiating element which is called a multiple-input-multiple-output (MIMO) system and is defined as the maximum rate at which the signal containing the information is radiated over the wireless communication channel with the defined bandwidth of interest in the presence of noise.

However, in a real-time scenario (measurement in an anechoic chamber), the level of noise is 0 dB. The Channel Capacity (CC) for SISO is given by

(5)$$C_{C1 \times 1} = B_{1 \times 1}\log _2( {1 + {\rm SNR}} ) $$

where C_{C 1×1} is Channel Capacity (b/s/Hz), B _1×1 is the operating bandwidth. In the absence of noise, C_{C 1×1} = B _1×1 which means completed bandwidth is utilized in the ideal case, but in a real scenario, the noise does exist, and also there will be multiple reflected signals received by the receiver. Figure 3 shows 1 × 1, 2 × 2, and m × n (m = n) MIMO configurations. It can be observed that, in the SISO system, the receiver will encounter multiple path fading effects, but in MIMO configuration, the receiver antennas will receive the signals all the time, and hence the modulated transmitted signal is preserved at the receiver. Also, equation (5) for channel capacity in absence of noise suggests that the bandwidth is multiple of several antenna elements present in a MIMO system. This concludes that MIMO configuration outclasses the SISO technology in comparison with mitigating the effects of signal interference noise ratio and thereby, preserving the operational bandwidth.

Fig. 3. Different MIMO Configuration.

TCM analysis implementation on 2 × 2 MIMO configuration

The set of independent current vectors are analyzed by TCM theory which corresponds to different modes which naturally occur within the structure. By applying infinite number of modes, it can be easily calculated the closer resonances which are supported within the structure itself. As an antenna designer, the current patterns which naturally exist in the structure is valuable which helps in utilization of characteristic modes more attractive for antenna design, helping in obtaining physical insights into antenna radiation. Moreover, the quantative analysis of the characteristics angle (CA) and eigenvalues do dependent on the size or shape of the structure and, thus TCM analysis offers important role in designing the antenna for different wireless applications.

Figure 4 shows the configuration of the proposed 2 × 2 MIMO antenna configuration. The purpose behind the conversion of the single radiating antenna to a 2-port MIMO configuration is already discussed in section ‘MIMO configuration’ where the channel capacity of the MIMO antenna is increased without comprising the operational bandwidth. Figure 4(a) shows the front and ground view of the antenna. The front view of the antenna is printed on an FR-4 substrate with two identical 12-side polygon patches and a common shared ground which is printed on the opposite plane of the substrate.

Fig. 4. Proposed 2-Port Design with Parameters; (a) Single Notch; (b) Dual Notch and (c) Isometric View.

As observed from Fig. 4(a), the radiating patch is etched by a rectangular slot which acts as the band-stop filter for interfering WLAN band (5.150–5 GHz). Also, the common-shared ground is etched by two semi-elliptical slots placed behind the microstrip feedline for better matching of the impedance. The isolation between the two radiating patches is taken care of by a T-shaped stub attached symmetrically to the ground. Figure 4(b) shows the etched U-type slot in the microstrip feed-line which mitigates downlink-uplink satellite (DUS) interference (7.25–8.30 GHz). The isometric view is represented in Fig. 4(c) with a different color legend showing various sections of the antenna. FR-4 substrate which is low cost and commercially available is used which also easily integrates with MMIC circuits. Two opposite planes of the substrate are used to print the isolated patch and shared common ground.

Recent time has seen the evolution of wireless technology in both narrow as well as wideband applications. These wireless applications have a wide range of implementations ranging from mobile phones to modern wireless communication say ships, aircraft, etc. The challenges encountered in designing these antennas have fuelled the advancement in the field of the antenna due to reasons such as the need for antennas with smaller physical size, lower weight, and cost, multi-wideband bandwidths, the capability of reconfigurable, etc. Therefore, the breakthrough in designing these antennas has emerged in the form of the TCMs [Reference Addepalli, Babu, Beno, Potti, Nageshwara, Sundari and Devana28–Reference Babu, Aldhaheri, Sai, Perli, Addepalli, Pasumarthi, Kumar and Devana30] which gives freedom to analyze the physics behind the key attributes including bandwidth polarization and distribution of surface current density (SCD) on a patch of antenna and ground. The theory behind TCM is older than 50 years which was proposed by Garbacz in 1965. This theory correlates the surface current distribution on PEC bodies (perfect electric conductor) which is decomposed to several modal currents and each of these radiates the respective characteristic modal pattern. The key parameters which are evaluated by characteristic mode analysis include modal significance, CA, and eigen current. The impedance matrix associated with Eigen current is given by

(6)$$Z = R + jX$$

(7)$$R = \displaystyle{{Z + Z^\ast } \over 2}$$

(8)$$X = \displaystyle{{Z-Z^\ast } \over 2}$$

where Z is the total complex impedance, R and X are the real and imaginary parts of the impedance.

The weighted Eigen equation is given by

(9)$$ZJ_n = e_nWJ_n$$

where J_n is the eigenvector, e_n is the eigenvalue and the W is chosen matrix. The generalized

form of eigenvalue equation can be written as

(10)$$XJ_n = \lambda _nRJ_n$$

The above Equation can also be derived by using Poynting's theorem [Reference Chen and Wang1] achieving the same result. The characteristic field is defined as the far-field due to modal currents and is given by

(11)$$\left\langle {J_m^\ast , \;\;Z\cdot J_n} \right\rangle = ( {1 + j\lambda_n} ) \delta _{mn}$$

(12)$$ = \mathop{{\int \!\!\int}\mkern-17mu \bigcirc}\nolimits_s {( {E_m \times H_n^\ast } ) dS + j\omega \int \! \int \!\int_v {( {\mu H_m\cdot H_n^\ast{-}\varepsilon E_m\cdot E_n^\ast } ) dv} } $$

By interchanging m and n

(13)$$( {1-j\lambda_m} ) \delta _{nm} = \mathop{{\int \!\!\int}\mkern-17mu \bigcirc}\nolimits_s {( E_n^\ast{\times} H_m) ds-j\omega \mathop{{\int \!\!\int}\mkern-17mu \bigcirc}\nolimits_s {( \mu H_m^\ast{-}\varepsilon E_n^\ast{\cdot} E_m) dv} } $$

It is known that

(14)$$\lambda _n\delta _{mn} = \lambda _m\delta _{nm}$$

(15)$$2\delta _{nm} = \mathop{{\int \!\!\int}\mkern-17mu \bigcirc}\nolimits_s {( {E_m \times H_n^\ast{ + } \;E_n^\ast H_m} ) dS} $$

In far-field, the characteristics field is given by

(16)$$E = \eta H \times \hat{k}$$

were $\hat{k}$ is the unit vector.

The characteristic current, δ _mn in terms of electric field € and magnetic field (H) is given as

(17)$$\displaystyle{1 \over \eta }\;\mathop{{\int \!\!\int}\mkern-17mu \bigcirc}\nolimits_s {E_m\cdot E_n^\ast \;dS = \delta _{nm}} $$

(18)$$\eta \;\mathop{{\int \!\!\int}\mkern-17mu \bigcirc}\nolimits_s {H_m\cdot H_n^\ast \;dS = \delta _{nm}} $$

This shows the characteristic field from the orthogonal set (in far-field). It can also be concluded that both, polarization and magnitudes of characteristics fields are orthogonal to one another.

The Eigen-value λ _n, between electric and magnetic field concerning m and n coefficients, is given by

(19)$$\mathop{{\int \!\!\int}\mkern-17mu \bigcirc}\nolimits_s {E_n \times H_n^\ast \;dS = \mathop{{\int \!\!\int}\mkern-17mu \bigcirc}\nolimits_s {E_n^\ast{\times} H_m\;dS} } $$

Also,

(20)$$\omega\int \! \int \!\int_v {( \mu H_m\cdot H_n^\ast{-}\varepsilon E_m\cdot E_n^\ast ) dV = \lambda _{n\;}\delta _{mn}} $$

For m = n in equation (20), a few important conclusions are derived which are given below

1. (1) The magnitudes of the eigenvalues are directly proportional to the total stored energy field

2. (2) For λ_n = 0, it indicates that the energy stored (electric and magnetic) are equal and hence, the resonance condition is achieved

3. (3) For λ_n > 0, the stored magnetic field is more dominant than the stored electric field and hence, is known as inductive modes

4. (4) For λ_n < 0, the stored electric field is more dominant than the stored magnetic field and hence, these modes are known as capacitive modes

The expansion of the induced currents and far-field due to the external source for characteristics modes are completely set of orthogonal modes. The characteristic current for a PEC body (patch/ground) is represented as

(21)$$J = \mathop \sum \limits_n a_nJ_n$$

The far-field electric and magnetic field produced by the external source due to induced current is given by

(22)\begin{align} E = & \mathop \sum \limits_n a_nE_n, \;\;H = \mathop \sum \limits_n a_nH_n\; \\ &( {{\rm an\ is\ the\ complex\ weighted\ coefficient}} ) \end{align}

Substituting equation (21) in $\lceil{L( J ) } \rceil _{\tan } = E_{\tan }^r ( r ) , \;\;r\epsilon S$

(23)$$\mathop \sum \limits_n a_nZ( {J_n} ) = E_{\tan }^i ( r ) $$

Inner-product of equation (23) gives

(24)$$\mathop \sum \limits_n a_n\left\langle {ZJ_n, \;\;J_m} \right\rangle = \left\langle {E_{\tan }^i ( r ) , \;\;J_m} \right\rangle $$

were J_m is the characteristic current and Z is the impedance matrix. For m = n, and applying the property of orthogonality for the characteristic current in the above equation, the following equation (25) is evolved which is given by

(25)$$a_n( {1 + j\lambda_n} ) = \left\langle {E_{\tan }^i ( r ) , \;\;J_n} \right\rangle $$

(26)$$a_n = \displaystyle{{\left\langle {E_{\tan }^i \;( r ) , \;\;J_n} \right\rangle } \over {1 + j\lambda _n}}$$

here $\left\langle {E_{\tan }^i \;( r ) , \;\;J_n} \right\rangle$ is the modal excited coefficient and hence, modal significance (MS) is given by

(27)$$MS = \left\vert {\displaystyle{1 \over {1 + j\lambda_n}}} \right\vert $$

The key point to be noted irrespective of modal significance is that it provides the ease of measuring the bandwidth and thus half-power bandwidth $\left({\left({1/\sqrt 2 } \right) = 0.707} \right)$ is given by

(28)$$BW = \displaystyle{{\,f_H-f_L} \over {\,f_{res}}}$$

were f_H, f_L and f _ees are the resonance and at f _res, MS is given by

(29)$${\rm MS}( {\,f_{{\rm res}}} ) = 1$$

(30)$$MS( {\,f_H = f_L} ) = \left\vert {\displaystyle{1 \over {1 + j\lambda_n}}} \right\vert = \displaystyle{1 \over {\sqrt 2 }} = 0.707$$

This concludes that for MS > 1/$\sqrt 2$ corresponds to significant modes and MS < 1/$\sqrt 2$ is the non-significant mode.

Also, when different modes are applied to PEC, there will be constant phase lag between real current Jn and also the equal-phase for $E_n^{\tan } ( S )$. The constant phase lag (α_n) between the two is given by 1

(31)$$\alpha _n = 180^\circ{-}\tan ^{{-}1}\lambda _n$$

This indicates that the phase lag is directly calculated from the eigen value and for α _n = 180° indicates resonance otherwise the modes are said to be internal or cavity resonance for α _n = 90° or 270°. Thus for α _n = 180° the modes are resonance modes, 90° < α _n < 180°, the modes are inductive and for 180° < α _n < 270°, the modes are capacitive.

The 2-port MIMO antenna configuration is developed by using the TCM shown in Fig. 5. In the proposed 2-port MIMO configuration, ten modes are subjected which can be observed in Figs 5(a) and 5(c) including two interfering filters (WLAN and DUS). The $MS \gt \left({1/\sqrt 2 } \right)$ for mode 1, mode 3, mode 5, mode 6, and mode10 which are the significant modes. Therefore, these five modes are responsible for the wider impedance bandwidth. Also, it can be observed that the resonance values of a frequency corresponding to 3.54 GHz (mode 1), 3.68 GHz (mode 3), 5.20 GHz (mode 5), 6.32 GHz (mode 6), and 8.20 GHz (mode 10). Figure 5(b) shows the two modes (mode 7 and mode 9) exclusively play a vital role in notching the two interfering bands. The CA is represented in Figs 5(c) and 5(d) for the dual notched band 2-port MIMO antenna. It can be noted that α_n = 180° at 3.54, 3.68, 5.20, 6.32 and 8.20 GHz corresponds to resonance modes. In mode 7 and mode 9, the CA values correspond to 168° (5.52 GHz) & 150° (8.10 GHz) are the inductive modes.

Fig. 5. Characteristics mode analysis (a) MS for dual notched band MIMO antenna (b) MS for two notched bands (c) CA for dual notched band MIMO antenna (d) CA for two notched bands.

Figures 6(a)–6(e) shows the distribution of surface current which is initiated for mode 1 (3.54 GHz), mode 5 (5.20 GHz), mode 10 (8.20 GHz), mode 9 (5.60 GHz), and mode 7 (8.10 GHz). The significant modes shown in Figs 6(a)–6(c) offer an even distribution of surface current and hence the MIMO antenna radiates the signal efficiently with good Omni-directional and di-pole patterns in both the planes. In the case of Figs 6(d) and 6(e), the current vectors cancel with each other and hence there is no radiation. Table 1 gives the parameter values of the MIMO configuration shown in Fig. 4.

Fig. 6. Proposed Design: (a), (b), and (c) are Surface Current Distribution with 3D-Radiation Patterns; (d) & (e) are only Surface Current Distribution at Notched Bands. (a) 3.54 GHz (mode 1) (b) 5.20 GHz (mode 5) (c) 8.20 GHz (mode 10) (d) 5.60 GHz (mode 9-Notched) (e) 8.10 GHz (mode 7-Notched).

Table 1. Proposed design parameters with values

Evolution of the 2-port MIMO antenna, input impedance, and time domain analysis

The evolution of the proposed 2 × 2 MIMO antenna is shown in Fig. 7 with a comparison of reflection as well as transmission coefficient results. Figure 7(a) which is designed as Antenna #A is formed by placing two polygon patches adjacent to each other and commonly shared

Fig. 7. Evolution of the proposed antenna (a) Antenna #A (b) Antenna #B (c) Antenna #c (d) Antenna #4 (e) S ₁₁/S ₂₂ result (f) S ₁₂/S ₂₁.

rectangular ground. This offers the operating bandwidth of 4.02–10.92 GHz as shown in Fig. 7(e). Also, from Fig. 7(f), it can be seen that the isolation between the two ports is very poor. To improve the impedance bandwidth and to achieve higher isolation, Antenna #B is reported which has two modifications, one semi-elliptical slot in the ground to improve the bandwidth and the other, the T-shaped stub attached to the ground plane. The S ₁₁/S ₂₂ −10 dB bandwidth corresponds to

3.03–12.38 GHz with two resonances at 4.38 GHz (S ₁₁ = −42.31 dB) and 11.52 GHz (S ₁₁ = −27.61 dB). The isolation of Antenna #B is also improved with S ₁₂/S ₂₁ being more than 15 dB. The impedance bandwidth generated by Antenna #B also occupies other wireless communication applications such as WLAN and DUS. These two bands impact as interference and have to be mitigated. Band stop filters which are the solution to the above two said interference are added to Antenna #B in the form of an etched C-type slot on the radiating patch (Antenna #C) and a U-shaped slot in the microstrip feed-line (Antenna #D). Antenna #C shown in Fig. 7(c) occupies the operational bandwidth of 3.00–11.18 GHz with filtered WLAN interference (5.02–5.89 GHz). Similarly, the final version of the required MIMO configuration is achieved by Antenna #D which filters WLAN and DUS interfering bands. On the other hand, the MIMO configuration

Also shows the isolation of more than 15 dB with maximum isolation of −35, −50 and −34.8 dB is noted at 5.32, 8.10 and 11.22 GHz respectively.

The effect of the parameters shown in Table 1 is the optimized parameters. However, when their values are changed, they do affect the operating bandwidth which indicates the change in the value of overall impedance. In this proposed study, key parameters affecting the notched bandwidth are investigated. The quarter-wavelength for both the notched bands are calculated from equations (32) and (33) given below.

(32)$$L_{IB} = \displaystyle{k \over {2f_{\rm r}\sqrt {\varepsilon _{eff.}} }}$$

where L _IB is the length of the interfering band in mm, f _r is the center frequency of the corresponding notched band, k is the speed of light which is 3 × 10⁸ m/s, and ɛ _reff. is calculated by

(33)$$\varepsilon _{eff.} = \displaystyle{{\varepsilon _{\rm r} + 1} \over 2} + \displaystyle{{\varepsilon _{\rm r}-1} \over 2}\sqrt {\displaystyle{{1 + 12h} \over {W_{\rm f}}}} $$

These equations suggest that the total length of the stub is dependent on the center notched frequency, effective permittivity, the height of the substrate, and the width of the microstrip (W _f). However, the electrical parameter such as effective permittivity, the height of the substrate, and with of the microstrip are static values. So. By changing the L _IB, the center notched frequency will also change. For the WLAN interfering band, the total overall length of the stub id L _IB = S _L2 + 2(S _L3 + S _L1). Thereby, changing the value of S _L3 and S _L1 will also change the shifting of the notched frequency corresponding to WLAN interference. Figures 8(a) and 8(b) shows the change of S _L1 from 2.25 to 2.75 mm which records the shifting of the band from the lower to higher frequency side. However, for S _L1 = 2.50 mm the intended WLAN interference is mitigated. Also, the parameter associated with WLAN notched filter slot, S _L3, is varied between 1.50 to 2.00 mm. For S _L3 = 1.75 mm, which is an optimized value that ensures the removal of the WLAN interfering band. Similarly, the position of the WLAN slot with distance P mm is changed from 5.00 to 5.50 mm observing a very negligible change in the position of the WLAN notched bandwidth. However, for P = 5.25 mm, the optimized result is obtained for the WLAN interfering band. The thickness of the rectangular slot S _LW, however, has a large impact on the WLAN notched bandwidth as shown in Fig. 8(d). So for S _LW = 0.60 and 0.90 mm, the notched bandwidth widens and more frequencies are included which is extended beyond WLAN. For S _LW = 0.30 mm, the exact WLAN notched band is achieved. Figures 8(e) and 8(f) shows the effect of change in length S _L4 on reflection as well as on transmission coefficient. The total physical length corresponding to DUS interfering band is L _IF = S _L5 + 2S _L4. For the value of S _L4 = 5.25 mm, the intended DUS notched band is achieved while for the other two values of S _L4 = 5.00 and 5.50 mm, the out of required notched band is filtered, and also, during the optimization process, the WLAN band is not affected which concludes that the two interfering band are independent to each other. Figure 8(g) shows the parametric variation of the gap G between the radiating patch and the ground. For G = 1.50 mm, the antenna offers bandwidth of 2.74–2.92 GHz, 5.11–8.71 GHz and 10.08–12.00 GHz. The gap G = 1.70 mm offers an impedance bandwidth of 2.76–3.09 GHz, 4.26–8.64 GHz and 11.12–12.0 GHz. However, for the above-said values, the required bandwidth is not obtained. On the other hand, for higher values of G = 2.10 & 2.30 mm, the partial bandwidth is achieved. For G = 1.90 mm, which is an optimized value provides operational bandwidth useful for both UWB and X-band applications.

Fig. 8. Proposed 2-Element Design Parametric Study; (a) S _L1; (b) S _L3; (c) P and (d) S _LW; (e) S _L4 for S ₁₁ and (f) S _L4 for S ₂₁ (g) G.

To have more insight into the working of the proposed 2-port MIMO antenna, SCD distribution on patch and ground is studied which is shown in Fig. 9. Figures 9(a) and 9(c) shows the SCDD for the three selected frequencies 4.00, 6.60 and 11.20 GHz. The simulation is carried out by giving input at Port 1 and the other Port 2 is terminated in characteristics impedance of 50 Ω. In all three cases, it can be seen that the SCDD is concentrated evenly on the patch other than the feed-line. This shows that all the input signals are radiated efficiently. However, the feed-line is not the part of the radiation which is used only as a transmission line between the input port and the transmitting antenna. Interestingly, the isolation element which is in the form of a T-shaped stub and attached to the ground plays important role in providing higher isolation. This is due to the concentration of current flow from the ground behind the antenna where input is given towards the T-shaped stub (shown by arrow). This phenomenon is observed in all three frequencies centered at 4.00, 6.60 and 11.20 GHz respectively. This justifies the addition of a T-shaped stub in achieving higher isolation and also there is almost nil interference in Antenna #2. However, for 6.60 GHz, there is slight interference in Antenna #2 from Antenna #1 which is due to the isolation value of −15 dB. Figures 9(d) and 9(e) shows the SCDD for the two center-notched frequencies 5.60 and 8.10 GHz. The C-type rectangular stub is used as a filter for the WLAN interfering band, all the SCD is accumulated around the slot which indicates the mismatch of impedance. Similar observations are noted for the DUS center notched frequency 8.10 GHz with all the SCD being on the U-type slot etched in the microstrip line. It is worth noting that the T-shaped stub which is used to achieve isolation between the two radiating elements has no role to play during the two filtering bands (WLAN and DUS). Figure 10 shows the plot of impedance and time response of the proposed 2 × 2 MIMO antenna with group delay & impulse response. Figures 10(a) and 10(b) shows the real and imaginary impedance for single and dual-notched bands.

Fig. 9. Proposed Design Surface Current Distribution; (a) 4.0 GHz; (b) 6.6 GHz; (c) 11.2 GHz; (d) 5.6 GHz (Notched Band) and (e) 8.1 GHz (Notched Band).

Fig. 10. Proposed Design Time Response Analysis; (a) Input Impedance & Group Delay (Single Notch) and (b) Input Impedance & Group Delay (Dual Notch) (c) Input Impulse (d) Received signal in two orientations.

Figure 10(a) shows the real impedance value almost follows the 50 Ω and imaginary impedance to 0 Ω. However, at the WLAN notched band, there is a high mismatch of the impedance due to the introduction of a band-stop filter in the form of an etched C-shaped slot on the radiating patch. At, this band, the maximum real value of impedance corresponds to 300 Ω at 5.68 GHz and two values of imaginary impedance at 148/−148 at 5.56/5.82 GHz. Similarly, Fig. 10(b) shows the real and imaginary impedance plot for the additional DUS band which was achieved by etching an inverted U-type slot on the microstrip feed-line. For the real value of impedance at notched bands, the maximum values are 225 and 300 Ω at 5.44 and 8.32 GHz. Also, there is a large deviation observed for imaginary impedance at these two notched bands. Figure 10 also examines the time response of the antenna as it becomes necessary due to the wideband bandwidth. Group delay is generally used to characterize the two antennas, one transmitter, and the other receiver. Group delay is used to measure the delay of the signal and the distortion in phase. Thus, the group delay is defined as the derivation of the phase-response and is given by

(34)$$\tau = {-}\displaystyle{{d\varphi ( \omega ) } \over {d\omega }}$$

The Group Delay, in the ideal case, is expected to be a constant value with no variations but, the change of ±1 ns is acceptable which preserves the shape of the received pulse without distortion. Figures 10(a) and 10(b) shows the plot of Group Delay for single and dual notched band MIMO antenna. In both, cases, the operating bandwidth of interest to preserve the values of Group Delay is between ±1 ns except in the notched bands (WLAN and DUS). Figure 10(c) represents the input impulse which is from the family of Gaussian is fed to the transmitter and observed the shape of the pulse at the receiver with ensuring far-field region. Figure 10(d) shows the received pulse in two orientations, one face-to-face and side-to-side. The receiver when placed in face-to-face orientation receives a more faithful signal than in side-to-side orientations. It can be also observed that the ringing effects are noted in received pulses which might be due to the reasons for undesired energy stored or multiple reflections. This ringing affected is more prominent in the SISO system and much improved in MIMO technology. The correlation coefficient between the transmitter-receiver signifies the similarity between the two is given by

(35)$$\rho = \max _\tau \left[{\displaystyle{{\mathop \smallint \nolimits S_{Tx\;}( t ) S_{Rx}( {t-\tau } ) dt} \over {\sqrt {S_{Tx}^2 \;( t ) dt} \sqrt {S_{Rx}^2 } \;( t ) dt}}} \right]$$

here S _Tx (t) is the transmitted signal and S _Rx (t) is the received signal with τ being the delay of the received signal. The transmitted and received pulses are matched when the fidelity factor is 1. The correlation coefficient corresponds to 0.88 and 0.82 for face-to-face and side-to-side orientation.

Comparison of proposed work with present-state-of-the-art

Table 2 shows the comparison of the proposed MIMO antenna with earlier published work. The compact MIMO antenna is fabricated on a commercially available FR4 substrate which is very easy to integrate with other PCB circuits such as filters, amplifiers, etc. The proposed antenna also offers good isolation and outclasses other reported work in terms of diversity performance parameters. The proposed MIMO antenna is suitable for multiple wireless applications in UWB and X-Band.

Table 2. Comparison of proposed work with other published articles

P, Proposed; ■, Connected Ground; □, Isolated Ground; NC, Not Calculated