Effect of Mutual Coupling on the Performance of Uniformly and Non- Uniformly spaced Adaptive Array Antennas by: Amin Al-Ka’bi, John Homer and M. Bialkowski School of Information Technology & Electrical Engineering The University of Queensland, Australia

V. Experimental Results Outline I. Abstract II. Introduction III. Signal Model IV. Simulation Results V. Experimental Results VI. Conclusions

I. Abstract We present the effect of mutual coupling on the performance of uniformly and non-uniformly spaced steered beam adaptive dipole array antennas. The behaviour of the adaptive array antennas in terms of the output Signal-to-Interference-plus-Noise Ratio (SINR) and pointing accuracy is investigated .

II. Introduction It is desirable that the output SINR exceeds a certain threshold; hence the adaptive algorithm aimed at SINR maximization is used to set the elements weights. Maximizing SINR, referred to as optimal combining in the mobile communications literature, requires the knowledge of the Direction-Of-Arrival (DOA) of the desired signal, where a DOA estimation algorithm is used to provide this information with certain inaccuracy known as pointing error.

II. Introduction (cont.) The paper is concerned with an analysis of performance of antenna arrays formed by wire dipoles, in which mutual coupling effects and elements’ radiation patterns are taken into account. A method is presented to enhance the array’s output Signal to Interference plus Noise Ratio (SINR) in presence of pointing errors, and mutual coupling. It is shown that the array’s performance is significantly enhanced, by controlling the inter-element spacings.

III. Signal Model Consider the array with N vertical dipoles separated by non-uniform distances along the y-axis . . The output signal from each element , which is assumed to be a complex random process, is multiplied by a complex weight and summed to produce the array output .

III. Signal Model (cont.) The steady state weight vector is given by:- I is the identity matrix, k is the feedback loop gain, and . .

III. Signal Model (cont.) Assuming that the desired narrowband signal comes from θmax: The SINR is calculated from: . .

III. Signal Model (cont.) The mutual coupling can be included using the coupling matrix C, where where is the element's impedance in isolation, is the impedance of the receiver at each element and is chosen as the complex conjugate of to obtain an impedance match for maximum power transfer, and Z is the mutual coupling impedance matrix given by: . . Note: for λ/2 dipole, =73+j42.5 Ω,

III. Signal Model (cont.) For the side-by-side configuration and dipole length , an element of the mutual impedance matrix is given by:- . . where and is the horizontal distance between the two dipole antennas. and are the cosine and sine integrals, respectively, and are defined as: and

III. Signal Model (cont.) When mutual coupling is considered, the signal vector is expressed as: . . The mutual coupling in the array can be compensated for by using the inverse coupling matrix . Therefore, the signal vector X can be rewritten as:

IV. Simulation Results Performance of three-element adaptive array with two interference signals and different DOA’s of the desired signal.

IV. Simulation Results (Cont.) Radiation patterns of the array with and without mutual coupling.

IV. Simulation Results The following four arrays, each including eight (0.45λ long)-dipoles, are considered. Arrangement (a) with spacing of 0.75λ, 0.5 λ, 0.35 λ, 0.3 λ, 0.35 λ, 0.5 λ, 0.75 λ (i.e. the elements in the middle of the array are closer to each other than the elements in the edges of the array). Arrangement (b) with spacing of 0.9λ, 0.5 λ, 0.25 λ, 0.2 λ, 0.25 λ, 0.5 λ, 0.9 λ (i.e. a similar spacing trend as arrangement (a) but with the elements in the middle of the array even closer to each other). Arrangement (c) with spacings of 0.2 λ , 0.4 λ , 0.7 λ , 0.9 λ , 0.7 λ , 0.4 λ , 0.2 λ (i.e. the elements in the edges of the array are closer to each other than the elements in the middle of the array). Arrangement (d) with uniform spacing of λ/2.

IV. Simulation Results (Cont.) Performance of 8-element adaptive array with different arrangements of the elements, without interference., and input SNR/element= 5dB. (a) Mutual coupling is ignored or compensated (b) With mutual coupling

IV. Simulation Results (Cont.) Performance of 8-element adaptive array with different arrangements of the elements. With 5 20dB-INR interference signals with DOA’s @ -40o, -50o, -70o ,-75o , and 60o . Input SNR/element=10dB. (a) Mutual coupling is ignored or compensated. (b) With mutual coupling.

IV. Simulation Results (Cont.) Normalized radiation patterns of 8-element adaptive array with different arrangements of the elements. With 5 20dB-INR interference signals with DOA’s @ -40o, -50o, -70o ,-75o , and 60o . Input SNR/element=10dB. (a) Mutual coupling is ignored or compensated. (b) With mutual coupling.

V. Experimental Results An experiment is carried out to prove that the array with non-uniform arrangement (b) (which provided the best performance in the simulation results), has better performance than the λ /2-uniformly spaced array. In this experiment, it is assumed that a desired signal (with input SNR/element =10dB) and four interference signals (with INR’s=20dB) are incident on the 8-element adaptive array with DOA’s of (0o, and 65o, 70o , -65o , -70o ).

V. Experimental Results Two array antennas formed by wire dipoles for operation at 2.5GHz are developed. In order to obtain the required complex weights, the antenna elements are connected to varying-length cables whose small sections are stripped of an outer conductor. Therefore, the complex weights (attenuation and phase shifting) required by the adaptation process of the adaptive array, are accomplished using fixed attenuators and cables with different lengths.

V. Experimental Results (Cont.) Photograph of uniformly spaced 8-element dipole antenna array used in the experiment with spacings of λ/2.

V. Experimental Results (Cont.) Photograph of non-uniformly spaced 8-element dipole antenna array used in the experiment with spacings of 0.9λ, 0.5λ, 0.25 λ, 0.2 λ, 0.25 λ, 0.5 λ, 0.9 λ.

V. Experimental Results The phased signals are combined using an 8:1 power combiner/divider. The dipoles length is chosen to be 0.45 λ (=54mm) in order to minimize the return loss. The measurements of individual elements showed return loss not less than 13dB. In order to obtain the required complex weights, the antenna elements are connected to varying-length cables. Therefore, the complex weights (attenuation and phase shifting) required by the adaptation process of the adaptive array, are accomplished using fixed attenuators and cables with different lengths.

V. Experimental Results (Cont.) Radiation patterns of uniformly and non-uniformly spaced 8-element adaptive array antenna (shown in Fig. 5 & 6) with mutual coupling. (a) Simulation results (b) Experimental results.

V. Experimental Results (Cont.) Performance of uniformly and non-uniformly spaced 8-element adaptive array antenna with mutual coupling.

VI. Conclusions We have presented theoretical and experimental investigations into the performances of narrowband uniformly and non-uniformly spaced steered beam adaptive dipole array antennas when they are subjected to pointing errors. In the theoretical analysis mutual coupling effects between array elements have been taken into consideration.

VI. Conclusions It has been shown that the array's tolerance to pointing errors can be enhanced by controlling the inter-element spacing. It has been found that the array gives more tolerance to pointing errors by arranging the elements of the array such that the elements in the middle of the array are closer to each other than the elements in the edges.

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