Analog-Domain Suppression of Strong Interference Using Hybrid Antenna Array
<p>Illustration of the proposed scheme for suppressing strong interference signals based on a uniform linear array with the antenna spacing denoted by <span class="html-italic">d</span>. The array is divided into <span class="html-italic">M</span> subarrays, each having <span class="html-italic">N</span> antennas.</p> "> Figure 2
<p><span class="html-italic">Left</span>: The value of the objective function given in (<a href="#FD8-sensors-22-02417" class="html-disp-formula">8</a>) under the iterative solution given in (<a href="#FD14-sensors-22-02417" class="html-disp-formula">14</a>), where <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mi>θ</mi> </msub> <mo>=</mo> <msup> <mn>0.1</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Θ</mi> <mi mathvariant="normal">j</mi> </msub> <mo>=</mo> <mrow> <mo>{</mo> <msup> <mn>30.5</mn> <mo>∘</mo> </msup> <mo>,</mo> <msup> <mn>60.9</mn> <mo>∘</mo> </msup> <mo>,</mo> <mo>−</mo> <msup> <mn>50.3</mn> <mo>∘</mo> </msup> <mo>}</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>=</mo> <mn>800</mn> </mrow> </semantics></math> is the total number of iterations. <span class="html-italic">Right</span>: Features of the obtained beam in the spatial passband. Three trials are performed with <math display="inline"><semantics> <msub> <mi mathvariant="bold">w</mi> <mn>0</mn> </msub> </semantics></math> randomly and independently generated for each trial.</p> "> Figure 3
<p>Illustrating the beams steered by the beamformers obtained in <a href="#sensors-22-02417-f002" class="html-fig">Figure 2</a>.</p> "> Figure 4
<p>The impact of the initialization on the convergence performance, where the left axis observes the beam flatness and the right one observes the converging value of the objective function in (<a href="#FD8-sensors-22-02417" class="html-disp-formula">8</a>).</p> "> Figure 5
<p>The amplitude response of the beams steered by the analog subarray, where subfigures (<b>a</b>–<b>c</b>) are obtained using <math display="inline"><semantics> <msubsup> <mi mathvariant="bold">w</mi> <mn mathvariant="bold">0</mn> <mo>*</mo> </msubsup> </semantics></math> given in (<a href="#FD25-sensors-22-02417" class="html-disp-formula">25</a>), and subfigures (<b>d</b>–<b>f</b>) correspond to <math display="inline"><semantics> <msub> <mi mathvariant="bold">w</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math> with randomly generated phases. The left, middle, and right columns are for <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, 16, and 24, respectively.</p> "> Figure 6
<p>MSE of the AoA estimates versus INR (=<math display="inline"><semantics> <mrow> <msubsup> <mi>σ</mi> <mrow> <mi mathvariant="normal">i</mi> </mrow> <mn>2</mn> </msubsup> <mo>/</mo> <msubsup> <mi>σ</mi> <mrow> <mi mathvariant="normal">n</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </semantics></math>, where <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. The curves with circle, square, and triangle markers are for <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, 16, and 24, respectively.</p> "> Figure 7
<p>CDF of interference power after subarray beamforming, where <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>. The curves with circle, square, and triangle markers are for <math display="inline"><semantics> <mrow> <msubsup> <mi>σ</mi> <mrow> <mi mathvariant="normal">i</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mo>−</mo> <mn>10</mn> </mrow> </semantics></math> dB, <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </semantics></math> dB, and 8 dB, respectively.</p> "> Figure 8
<p>(<b>Upper</b>) CDF of the sum of the absolute AoA estimation errors of multiple signals, where <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msubsup> <mi>σ</mi> <mrow> <mi mathvariant="normal">i</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> dB; (<b>lower</b>) illustrating the jamming suppression ability achieved using different sets of AoA estimates, where square, plus, and triangular markers denote H-ESPRIT, the first stage of the proposed method, and the second stage, respectively.</p> "> Figure 9
<p>Illustration of the amplitude responses of AINB beams designed by Algorithm 1, where <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>σ</mi> <mrow> <mi mathvariant="normal">i</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and the angles set in <a href="#sensors-22-02417-f002" class="html-fig">Figure 2</a> are used. The upper figure plots the AoA estimation errors over <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math> independent trials, where plus, triangle, and square markers are for <math display="inline"><semantics> <mrow> <msup> <mn>30.5</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mn>60.9</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>50.3</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, respectively. Note that the second inset from the left in the lower sub-figure is the copy of <a href="#sensors-22-02417-f009" class="html-fig">Figure 9</a> with the <span class="html-italic">y</span>-axis limited to <math display="inline"><semantics> <mrow> <mo>[</mo> <mo>−</mo> <mn>40</mn> <mo>,</mo> <mtext> </mtext> <mn>0</mn> <mo>]</mo> </mrow> </semantics></math> dB. It is provided to highlight the spatial amplitude response in the region of non-interference directions.</p> "> Figure 10
<p>Convergence curves of performing Algorithm 1, where <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>σ</mi> <mrow> <mi mathvariant="normal">i</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> dB, and sub-figures (<b>a</b>,<b>b</b>) are for the AINB designs in <a href="#sensors-22-02417-f007" class="html-fig">Figure 7</a> and <a href="#sensors-22-02417-f009" class="html-fig">Figure 9</a>, respectively. Among all the independent trials performed for the figures, 10 trials are randomly selected with their convergence curves presented here.</p> "> Figure 11
<p>Illustrating the impact of the quantization bit of phase shifters in subarrays on interference suppression.</p> ">
Abstract
:1. Introduction
- We develop an efficient solver for designing the phase-only AINB under the framework of majorization–minimization (MM). In particular, we design the objective function in such a way that we are able to simplify it substantially based on the newly unveiled relation between the spatial responses in the interference directions and the spatial passband. Thanks to the simplification of the objective function, we then propose a low-complexity method of constructing the majorization function, where we manage to remove the need of computationally intensive eigenvalue decomposition (EVD) required in the conventional construction. We further derive an iterative solver for the AINB design, where a closed-form solution with low complexity is achieved in each iteration. In addition, the impact of the initial solution to the proposed solver is investigated, based on which a high-quality initialization for the solver is established;
- We develop a two-stage angle of arrival (AoA) estimation method based on the conventional ESPRIT (estimation of signal parameters via invariance techniques). A major innovation of the method is the design of subarray beamforming in the two stages. In particular, an omnidirectionally flat beam is produced at each subarray in the first stage, while in the second stage the beam is created towards each of the AoA estimates obtained previously. To the best of our knowledge, it has not been investigated in the literature to use specially optimized flat beams for improving the AoA estimation performance of ESPRIT in hybrid antenna arrays.
- We provide extensive simulation results to validate the effectiveness of the proposed designs. As for the AINB, we cannot find similar designs in the literature. Thus, we comprehensively evaluate and observe numerous performance metrics, including spatial responses, interference suppression capability, and convergence curves for designing AINBs over tens of thousands of independent trials. As for the AoA estimation method, we employ the state-of-the-art [25] as a benchmark for the reasons to be explained at the beginning of Section 5. Due to the proposed use of deliberately optimized flat beams, the AoA estimation performance is substantially improved over the prior art [25]. Moreover, thanks to the high accuracy of the proposed AoA estimation method, the proposed AINB design can efficiently steer deep nulls towards interference signals.
2. Problem Formulation
3. AINB Design
3.1. Simplifying Beamformer Design Problem
3.2. MM-Based Iterative Solver for Problem (8)
3.3. Initializing
3.4. Speeding up Convergence
Algorithm 1 MM-based Analog Beamformer Design. |
|
4. Estimation of Interference AoAs
Algorithm 2 An Accurate Two-Stage AoA Estimation Method. |
|
5. Simulation Results
6. Conclusions and Future Works
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Wu, K.; Zhang, J.A.; Huang, X.; Guo, Y.J.; Nguyen, D.N.; Kekirigoda, A.; Hui, K.-P. Analog-Domain Suppression of Strong Interference Using Hybrid Antenna Array. Sensors 2022, 22, 2417. https://doi.org/10.3390/s22062417
Wu K, Zhang JA, Huang X, Guo YJ, Nguyen DN, Kekirigoda A, Hui K-P. Analog-Domain Suppression of Strong Interference Using Hybrid Antenna Array. Sensors. 2022; 22(6):2417. https://doi.org/10.3390/s22062417
Chicago/Turabian StyleWu, Kai, J. Andrew Zhang, Xiaojing Huang, Y. Jay Guo, Diep N. Nguyen, Asanka Kekirigoda, and Kin-Ping Hui. 2022. "Analog-Domain Suppression of Strong Interference Using Hybrid Antenna Array" Sensors 22, no. 6: 2417. https://doi.org/10.3390/s22062417