Subarray Selection for Adaptive Array Signal Processing in GNSS Applications

X. Wang, E. Aboutanios, M. Trinkle

Abstract:	Radio Frequency Interference is a significant threat to the successful operation of Global Navigation Satellite Systems (GNSS) receivers. Thus adaptive antenna arrays have been proposed to mitigate strong interference and multipath in GNSS applications. However, the high cost of a large array, in terms of both hardware and computational load, makes adaptive array processing a luxury for civilian GNSS receivers. Moreover, under some array configurations, the satellite signal may also be heavily impacted when the interference is suppressed by the adaptive array processing methods such as the maximum signal-to-interference ratio algorithm. But if the satellite signal is made spatially orthogonal to the interference with respect to a specific array configuration, the adaptive antenna array can cancel the interference completely without affecting the satellite signal. This shows the utility of array reconfiguration for improving performance. In order to achieve the above two objectives, namely reducing the high cost and preserving the satellite signal while suppressing the interference, a subarray selection strategy is proposed in this paper. Only K front-ends are required in the receiver for implementing this strategy and we choose K from N antennas that are then switched on and connected to the available front-ends. Then the corresponding beamforming weight vector is developed based on the selected subarray to obtain the interference suppression adaptively. The Spatial Correlation Coefficient (SCC) is introduced in this paper to characterize the effect of array configuration on the signal processing performance. The SCC represents the spatial separation between the desired signal and the interference. A smaller SCC implies that the two signals are more orthogonal with respect to the operating array spatially and the adaptive array processing algorithm behaves better. The effective carrier to noise density ratio (C/N0), which is calculated after de-spreading with the locally generated C/A code, is adopted as a metric to measure the performance. The closed formulas derived in this paper demonstrate an inverse relationship between the effective C/N0 and the SCC value. Interestingly, we find that the SCC value can be larger for an array with more antennas than one with a smaller number of antennas if the signal and interference are more orthogonal with respect to the latter under some scenarios. In such cases, the large array exhibits little performance gain over the small array, while incurring significantly higher hardware and computational cost. The trade-off curve between the effective C/N0 and the computational cost is used to express the compromise resulting from the subarray selection. The optimum array configuration is found by solving a SCC minimization problem which is usually NP-hard. In order to circumvent an exhaustive search of a large antenna array, we adopt an iterative reweighted l1-norm regularization method to select the optimum subarray. However, as we seek a binary entry solution with a value of 1 (0) denoting selected (not selected) antenna, the conventional algorithm may become stuck at a local infeasible minimizer solution. Therefore, we propose a modified method that uses a randomly generated weight vector to re-initialise the algorithm should this happen. The proposed algorithm converges fast and returns either a global optimum, or suboptimum that is closest to the global minimizer, feasible solution in any scenario. In this paper we implement the proposed subarray selection strategy in a real GPS experiment where an 8-antenna circular array was used to collect the data. To test the antenna selection strategy, only the data received from the selected K (K<8) antennas are processed. In this way we can see the performance of subarrays with different numbers of selected antennas by changing the value K. After determining the arrival directions of the satellite and interference signals we proceed to consider two scenarios. In the first scenario, the interference is incident on the array from a horizontal direction that is well separated from the satellite signal in space. For the second scenario, we inject interference into the collected clean data in order to simulate the case where the interference is close to the satellite signal. The interference to noise ratio is 20dB in both scenarios. Experimental results lead to a number of observations: firstly the SCC is indeed a convenient parameter to characterize the impact of array configuration on the adaptive array processing performance; secondly a comparison of the effective C/N0 of the optimum and worst K-antenna subarrays under the same scenario confirms the utility of array reconfiguration for performance improvement; thirdly, the trade-off curve shows that the optimum 4-antenna subarray can reduce both the hardware and software cost dramatically with negligible performance loss; and finally, the modified iterative reweighted l1-norm regularization is an effective and efficient method of solving subarray selection problems. In summary, the subarray selection strategy proposed in this paper is successfully verified by real GPS experiments. Although antenna selection has been applied in the area of array beampattern synthesis and MIMO communication for several years, there is little research work combining adaptive array processing and subarray selection together. Both the theoretical and experimental results prove that a large antenna array is not necessary for all scenarios and a subarray can preserve the performance when optimally configured. Since only K front-ends are required in the GPS receiver, both the hardware and computational costs are greatly decreased. The antenna array configuration is implemented adaptively using switches. The proposed subarray selection strategy can achieve better performance than the conventional array processing scheme which develops adaptive beamforming algorithms based on the fixed array configuration.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	2776 - 2785
Cite this article:	Wang, X., Aboutanios, E., Trinkle, M., "Subarray Selection for Adaptive Array Signal Processing in GNSS Applications," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 2776-2785.
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