1. Performance of Adaptive Array Antennas in Mobile Fading Environment by: Amin Al-Ka’bi, M. Bialkowski and John Homer School of Information Technology & Electrical Engineering The University of Queensland, Australia

2. Outline I. Abstract II.Introduction III. Problem formulation IV. Modeling of Mobile Fading Channel V. Results and Discussion VI. Conclusions

3. I. Abstract TTTThe performance of steered beam adaptive array antennas in mobile fading environment is presented, using simula- tion model of the mobile fading channel. TTTThe behaviour of the adaptive array antenna in terms of the output Signal-to- Interference-plus-Noise Ratio (SINR) and pointing accuracy is investigated.

4. 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.  The output SINR is affected by the signal fading due to multipath propag- ation. Moreover, the movement of the mobile unit causes frequency shift called Doppler Effect.

5. II. Introduction (cont.)  It is assumed that the array is fixed on a highly mounted base station or on a satellite system that communicates with mobile units surrounded by scatterers.  Modified Loo’s model of the mobile fading channel was found to be suitable for this case.  The performance of uniformly spaced and non-uniformly spaced steered beam adaptive arrays has been studied under the same operating conditions.

6. III. Problem Formulation. 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.

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

8. III. Problem Formulation (cont.).. Assuming that the desired narrowband signal comes from θ max : The SINR is calculated from:

9.  Loo’s model applies to frequency-non-selective terrestrial mobile radio channels, where the line-of- sight m(t) component under-goes slow-amplitude lognormally-distributed fluctuations, caused by shadowing effects. m(t) is given as: where and denote the Doppler frequency and phase of the line-of-sight component respectively, and is the lognormal process, with and are the mean and variance, of the white Gaussian process. IV. Modelling of Mobile Fading Channel

10.  The short-term fading caused by the multipath propagation, behaves like the Rice process, and it is represented by a complex-valued Gaussian random process where, IV. Modelling of Mobile Fading Channel (Cont.) Here,and represent zero-mean colored Gaussian random processes, andis the Hilbert transform of for (i=1, 2). Here, and represent zero-mean colored Gaussian random processes, and is the Hilbert transform of for (i=1, 2).  The Modified Loo’s process is given as

11. IV. Modelling of Mobile Fading Channel (Cont.).. Stochastic Model of Mobile Fading Channel (Modified Loo’s Model)

12.  The simulation model for modified Loo process approximates the behaviour of the stochastic reference model, where the three stochastic Gaussian random processes by deterministic Gaussian processes of the form  Therefore, can be written as: IV. Modelling of Mobile Fading Channel (Cont.)

13. IV. Modelling of Mobile Fading Channel (Cont.).. Simulation Model of Mobile Fading Channel that approximates the stochastic model.

14.  The simulation model for modified Loo process approximates the behaviour of the stochastic reference model, where the random processes are replaced by are replaced by  Therefore, can be written as: IV. Modelling of Mobile Fading Channel (Cont.)  The Doppler coefficients and for (i=1,2,3) can be calculated using Mean Square Error method. calculated using Mean Square Error method.

15. V. Results & Discussion  Two arrangements of 12 array elements are used: Arrangement (a): The elements are uniformly spaced by λ/2. Arrangement (a): The elements are uniformly spaced by λ/2. Arrangement (b): Non-Uniform array elements arrangement with spacings (0.85λ,0.7λ,0.5λ,0.4λ, Arrangement (b): Non-Uniform array elements arrangement with spacings (0.85λ,0.7λ,0.5λ,0.4λ, 0.25λ, 0.1λ,0.25λ,0.4λ,0.5λ,0.7λ,0.85λ) 0.25λ, 0.1λ,0.25λ,0.4λ,0.5λ,0.7λ,0.85λ)  In arrangement (b), the elements are arranged such that the elements in the middle of the array are closer to each other than the elements in the edges of the array.  It is shown that non-uniform array (arrangement (b)) has better performance than the uniformly spaced array in terms of sensitivity to pointing errors in non- fading and fading environments.

16. V. Results & Discussion (Cont.) Performance of 12-element adaptive array vs. pointing error (without fading). Performance of 12-element adaptive array vs. pointing error (without fading).

17. V. Results & Discussion (Cont.) Simulation of the received faded signal for light and heavy shadowing regions, respectively.

18. V. Results & Discussion (Cont.) Output SINR vs. SNR for uniformly and non- uniformly spaced array. Output SINR vs. SNR for uniformly and non- uniformly spaced array.

19. V. Results & Discussion (Cont.) Output SINR vs. time for light shadowing regions, with and without pointing error (uniform array). Output SINR vs. time for light shadowing regions, with and without pointing error (uniform array).

20. V. Results & Discussion (Cont.) Variance and mean of output SINR vs. pointing error for uniformly and non-uniformly spaced-array. Variance and mean of output SINR vs. pointing error for uniformly and non-uniformly spaced-array.

21. VI. Conclusions  A suitable simulation model for mobile fading channel has been suggested.  A comparison between uniformly and non-uniformly spaced array has been conducted.  It is shown that non-uniform array (arrangement (b)) has better performance than the uniformly spaced array in terms of sensitivity to pointing errors in non- fading and fading environments.  It is shown that mean output SINR of the non-uniform array is greater than that of the uniform

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