Spatial diversity configuration

The scattering parameters of spatial configuration with variations in inter-element spacing are presented in Fig. 4. It is observed that the reflection coefficient and isolation improved with an increase in inter-element spacing from 0 to 2 mm.

Fig. 4.

Scattering parameters of spatial diversity configuration with variations in inter-element spacing.

The MIMO antenna prototypes are presented in Fig. 5. Due to the limitation of available facilities, measurements up to only 40 GHz can be carried out. The variations of scattering parameters with respect to the frequency obtained from HFSS and experimental measurement are illustrated in Fig. 6. The discrepancies between the simulated and experimental results are due to fabrication and soldering errors. Due to the identical antenna elements, this MIMO antenna configuration is a symmetrical network. This symmetry in network leads to equal input impedance at both excitation ports of this MIMO antenna configuration. This impedance equivalence leads to equivalence in reflection coefficient, i.e. S ₁₁ = S ₂₂. The couplings or isolation plots are identical, i.e. S ₂₁ = S ₁₂ because the two-port network is passive and hence reciprocal. Figure 6 demonstrates that both elements have an operating bandwidth (for VSWR ≤ 2) of 4.4–51.5 GHz (~11:1). In addition to this, isolation (S ₂₁ or S ₁₂) ≥15 dB at maximum operating frequencies in the operating band is observed. This isolation fulfills the requirement of MIMO applications.

Fig. 5.

MIMO antenna prototypes. (a) Spatial diversity. (b) Pattern diversity.

Fig. 6.

Scattering parameters of spatial diversity antenna configuration. (a) Simulated. (b) Measured.

Figure 7 presents that bidirectional and omnidirectional patterns in E-plane and H-plane are achieved at frequencies <10 GHz for both elements. Similarly for frequencies >10 GHz, the patterns acquired distorted omnidirectional nature due to excitation of higher order modes.

Fig. 7.

Radiation patterns of spatial diversity antenna configuration. (a) 5.5 GHz. (b) 15 GHz. (c) 25 GHz. (d) 35 GHz.

Pattern diversity configuration

Figure 8 displays the effect of diagonal strip on the pattern diversity configuration performance. It is observed that the reflection coefficient is unaffected, whereas the inter-element isolation is improved with the introduction of diagonal strip between the elements.

Fig. 8.

Scattering parameters of pattern diversity configuration with and without diagonal strip.

Since the antenna elements are identical, equal input impedance is observed for both ports leading to equal reflection coefficients (S ₁₁ = S ₂₂) and isolation values (S ₁₂ = S ₂₁). Figure 9 illustrates that each element has an operating bandwidth of 3.8–51.5 GHz (~13:1). Except at the frequency of 5 GHz (S ₂₁ = S ₁₂ = 11 dB), the inter-port isolation≥15dB is achieved. The isolation is increasing with frequency. A maximum isolation of 43 dB is achieved. These values of inter-port isolation present a very low level after considering the extreme bandwidth and miniaturized antenna dimensions.

Fig. 9.

Scattering parameters of pattern diversity antenna configuration. (a) Simulated. (b) Measured.

Figures 10 and 11 present the radiation patterns of both elements at some frequency points in both planes. It is observed that the patterns are bidirectional and omnidirectional for frequencies <10 GHz. For higher frequencies, distorted omnidirectional patterns are observed in both planes. The patterns of element 2 are found to be orthogonal to those of element 1 at lower frequencies. In case of higher frequencies, due to the distorted omnidirectional nature, the 90^o phase shift in patterns is not easily recognizable.

Fig. 10.

Radiation patterns of pattern diversity antenna configuration for Port 1. (a) 6 GHz. (b) 17 GHz. (c) 25 GHz. (d) 35 GHz.

Fig. 11.

Radiation patterns of pattern diversity antenna configuration for Port 2. (a) 6 GHz. (b) 17 GHz. (c) 25 GHz. (d) 35 GHz.

Envelope correlation coefficient (ECC):

It is calculated by using the scattering parameter values through the standard equation (1)[Reference Blanch, Romeu and Corbella36]:

(1)$$\rho _e = \displaystyle{{{\vert {S_{11}^{\rm \ast } S_{12} + S_{21}^{\rm \ast } S_{22}} \vert }^2} \over {\lpar {1-\lpar {{\vert {S_{11}} \vert }^2 + {\vert {S_{21}} \vert }^2} \rpar } \rpar \lpar {1-\lpar {{\vert {S_{22}} \vert }^2 + {\vert {S_{12}} \vert }^2} \rpar } \rpar }}.$$

An ECC of 0.5 or −6 dB is the maximum limit for any diversity antenna [Reference Najam, Duroc and Tedjini37]. Figure 12 presents the ECC values for both diversity configurations. For spatial diversity configuration, ECC ≤ −30 dB is observed across a frequency spectrum of 4–24 GHz. Thereafter, ECC ≤ −40 dB is observed at higher frequencies. In case of pattern diversity configuration, −20 ≤ ECC ≤ −30 dB is achieved between 4 and 12 GHz. After 12 GHz, ECC ≤ −40 dB is observed for every frequency in the operating band.

Fig. 12.

Envelope correlation coefficient for two MIMO configurations.

Diversity gain (DG):

It quantifies the diversity effect on the received signal in a multichannel wireless environment. It can be calculated by replacing time-averaged SNR with cumulative distribution function (CDF) in the difference equation given in [Reference Taga38]. The normally used CDF is 1 or 10% [Reference Flaviis, Jofre, Romeu and Grau39, Reference Kildal and Rosengren40]. It is calculated from the above calculated ECC values by using the following relation:

(2)$${\rm DG} = 10\sqrt {1-{\vert {\rho_e} \vert }^2} .$$

The calculated values of DG are shown in Fig. 13. It is observed that an almost constant DG is obtained across the entire operating band for each configuration.

Fig. 13.

Diversity gain variations with frequency for two MIMO antenna configurations.

Capacity loss, $C_{{\bf loss}}$

It quantifies the estimated maximum transmission rate in a communication channel in case of rich multipath environment for reliable transmission. For a MIMO antenna, the maximum value accepted in a MIMO antenna is 0.4 b/s/Hz. It is calculated in b/s/Hz by using correlation matrix (3) [Reference Tripathi, Mohan and Yadav41].

(3)$$C_{{\rm loss}} = -\log _2\lpar {\psi^R} \rpar \comma \;$$

where ψ ^R = correlation matrix of the receiving antenna and is expressed mathematically as

(4)$$\psi ^R = \left[{\matrix{ {\rho_{11}} & {\rho_{12}} \cr {\rho_{21}} & {\rho_{22}} \cr } } \right]\comma \;$$

(5)$$\rho _{ii} = 1-\lpar {{\vert {S_{ii}} \vert }^2 + {\vert {S_{ij}} \vert }^2} \rpar \comma \;$$

(6)$$\rho _{ij} = -\lpar {S_{ii}^{\rm \ast } S_{ij} + S_{\,ji}^{\rm \ast } S_{ij}} \rpar \comma \;$$

i, j = 1 or 2.

Figure 14 demonstrates that the capacity loss is <0.4 b/s/Hz for each configuration.

Fig. 14.

Channel capacity loss for two MIMO configurations.