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Interference suppression techniques have been intensively studied in nearly two decades due to their importance for maintaining the integrity and functionality of global navigation satellite system (GNSS). However, the interference suppression method applicable for the complex receiving environment in which there are multitype interfering signals has not been considered in most of the researches. To deal with this problem better, a cascaded multitype interferences suppression method using sparse representation and array processing is proposed. In the first stage, according to the sparsity of the narrowband and modulated wideband interference signals, a novel parallel multichannel signal interference suppression method based on matching pursuit (MP) algorithm and a design strategy for the overcomplete dictionary are proposed to mitigate the interferences with sparse features. Then, the minimum power distortionless response (MPDR) beamformer is employed in the second stage to suppress the residuary interferences (such as Gaussian noise interferences). Compared with existing algorithms, the proposed method can not only effectively suppress the interference arriving from the same direction with the desired signal and increase the Degree of Freedom (DoF) of the array antenna, but also introduce no distortion into the navigation signal. The effectiveness of the proposed method is illustrated by theoretical analysis and several simulation results.

The global navigation satellite system (GNSS) has been widely used in military and civilian applications; however, the problems caused by the vulnerability of satellite navigation signals are increasingly serious. Therefore, interference suppression techniques are necessary to ensure the reliability, accuracy, and continuity of GNSS services. According to the characteristics of the GNSS, there are two ways to improve the capability of radio frequency (RF) interference suppression [

The interference suppression techniques for GNSS receivers include time-domain processing, transform-domain processing, spatial processing, and spatial-time processing [

On the contrary, the interference suppression techniques using an antenna array can effectively suppress both narrowband and wideband interferences regardless of their time and frequency characteristics. One of the most effective space-based processing methods has been referred to as the minimum variance distortionless response (MVDR) beamformer [

In addition, with the rapid development of jamming technology and the increasingly complex electromagnetic environment, there are multiple types of interferences existing simultaneously rather than a single type of interference in the environment. Although the interference suppression methods mentioned in the prior context improve the performance of GNSS receivers, they still face the following problems when dealing with multiple types of interferences:

To solve the above problems, [

In this paper, a cascaded multitype interferences suppression method using sparse representation and array processing for GNSS receivers is proposed. Firstly, the signal sparse decomposition theory [

The signal received by the GNSS receiver is the aggregate of the satellite navigation signal, interfering signals, and the thermal noise. Without loss of generality and for the sake of simplicity, assume that they are independent of each other and there is only one GNSS signal. Considering an arbitrary antenna array with

In the coexistence of multiple types of interfering signals, we can suppress them according to their different characteristics in different dimensions. In view of that, a cascaded multitype interferences suppression method using sparse representation and array processing for GNSS is proposed, and the structure of the proposed method is as shown in Figure

Block diagram of the proposed method.

The MP algorithm was introduced to adaptively decompose signals in an overcomplete dictionary when the signal sparse decomposition theory was proposed. And with the flexibility of the redundant dictionary and the adaptability to signals, it has gained more and more attentions. MP is a kind of iterative “greedy” algorithm. At each iteration, the best matching atom that is the most similar to the residual signal is selected and regarded as one of the components of the sparse representation.

Let

In order to facilitate the analysis, only one single-tone or LFM interfering signal is considered in the formulations below. And assume that there are

According to the characters of interference signals, select a series of linear frequency modulated signals as atoms in the overcomplete dictionary, which could be expressed as

The signal to be decomposed contains only one signal that can be sparse in the overcomplete dictionary. Then (

The best matching atom is selected according to formula (

In order to further understand the nature of

Relation between

Relation between

Relation between

This periodicity of

Although signal sparse decomposition based on MP has better performance with the increase of the number of atoms in the overcomplete dictionary, the improvement of the performance for such ways is at the cost of the increase of complexity. In order to reduce the amount of computation while maintaining the accuracy, we propose a design strategy of the hierarchical adaptive overcomplete dictionary. In step

Taking the fixed frequency parameter as an example, assume that the bandwidth of the desired signal is 2 MHz, while the decomposition accuracy is 0.0001 MHz. The number of fixed frequency parameters in the overcomplete dictionary is

Decompose the received signal with 0.02 MHZ precision in 2 MHz bandwidth, and get the primary best frequency parameter

Generate new frequency parameters dictionary with 0.001 MHz precision at 0.02 MHz bandwidth centered in

Generate new frequency parameters dictionary with 0.0001 MHz precision at 0.001 MHz bandwidth centered in

The total number of fixed frequency parameters in the 3-stage overcomplete dictionary is 130. The computation of the latter is 0.65 percent of the former.

Because the GNSS receiver used in the proposed method is equipped with the array antenna, there are multichannel signals to deal with. If these signals are decomposed independently, the calculation is very great. Fortunately, array signal processing theory demonstrates that there is a potential correlation among the signals of each channel. In particular, they have the same frequency, similar amplitude, and distinct phases. Therefore, we can extend the concept of single channel signal sparse decomposition to the multichannel signal by using the correlation among the signals of each channel. The detailed implementation steps are as follows.

Divide the overcomplete dictionary into

Each

Compare the inner products of subbest matching atoms and corresponding signals, and select the global closest matching atom

According to the frequency parameters of the global best matching atom, calculate the unique phase and amplitude parameters of the signals in each channel

The conventional terminative condition of the MP algorithm is to determine whether the number of iterations or the energy of the residual signal meets the requirements. However, in complicated electromagnetic environment, since the number of signals that can be sparse representation is unknown, the number of iterations cannot be preset; and when the energy of the signals which could be sparse representation is smaller than that of the other interferences, the residual signal energy may have little difference with the original signal energy, so the existing terminative condition is not able to guarantee the effectiveness of the algorithm. Hence, a ratio principle is introduced to judge whether the ratio of inner product of the best matching atom obtained in the

Based on the conclusions above, a multichannel signal interference suppression method based on sparse decomposition is proposed. The basic steps are as follows.

Algorithm initialization: set up the overcomplete dictionary classification layer, search accuracy, and the threshold value of the termination conditions.

Generate the global overcomplete dictionary

Use parallel multichannel signal sparse decomposition method to decompose array signals.

Judge the accuracy of decomposition; if it reaches the preset accuracy, then take the next step; otherwise, regenerate global overcomplete dictionary according to the information acquired, and iterate to step 3.

Shift the phase of the best atoms 90° to get the best atoms of the corresponding

Determine whether the termination condition is met; if not, iterate to step 2; otherwise, take the next step.

Output the residual signal of each channel, which can be written as

In the second stage, by applying the spatial filtering, the beam of receiver antenna arrays is pointed towards the GNSS satellite and away from interferers to protect the GNSS signal and reject interferences. In GNSS applications, MPDR beamformer is one of the powerful approaches available to suppress interfering signals while maintaining desired signals due to its effectiveness for interference suppression without considering the structure and direction of the interfering signals. And the optimization problem for the MPDR beamformer can be expressed as

In order to verify the effectiveness of the proposed method, three simulations have been conducted. In all simulations, a linear half-wavelength space antenna array with 5 elements has been considered. A navigation signal operates on 1.023 MHz with bandwidth of 2 MHz and C/A code rate of 1.023 MHz, whose incident angle is

Interference signals characteristics.

Name | Type of interference | Center frequency (MHz) | Bandwidth (MHz) | DOA (°) | Linear modulation frequency rate | Interference to noise ratio (dB) |
---|---|---|---|---|---|---|

1 | Narrowband | 1.023 | 0 | 80 | — | 32 |

2 | Narrowband | 1.04 | 0 | 60 | — | 32 |

3 | Narrowband | 0.95 | 0 | 70 | — | 32 |

4 | LFM | 1.023 | 2 | 110 | 10^{9} | 45 |

5 | Wideband Gaussian | 1.023 | 2 | 20 | — | 45 |

6 | Wideband Gaussian | 1.023 | 2 | 100 | — | 45 |

7 | Wideband Gaussian | 1.023 | 2 | 150 | — | 45 |

8 | Wideband Gaussian | 1.023 | 2 | 40 | — | 45 |

9 | LFM | 1.023 | 2 | 80 | −10^{9} | 45 |

The parameters involved in the proposed algorithm.

Name of parameter | Value |
---|---|

Termination threshold | 8 |

Layers of overcomplete dictionary | 3 |

The decomposition accuracy of fixed frequency in the first layer (corresponding range) | 0.01 MHz ( |

The decomposition accuracy of fixed frequency in the second layer (corresponding range) | 0.001 MHz ( |

The decomposition accuracy of fixed frequency in the third layer (corresponding range) | 0.0001 MHz ( |

The decomposition accuracy of phase in the first layer (corresponding range) | 0.1 |

The decomposition accuracy of phase in the second layer (corresponding range) | 0.01 |

The decomposition accuracy of phase in the third layer (corresponding range) | 0.001 |

The decomposition accuracy of linear modulation frequency rate in the first layer (corresponding range) | |

The decomposition accuracy of linear modulation frequency rate in the second layer (corresponding range) | |

The decomposition accuracy of linear modulation frequency rate in the third layer (corresponding range) | |

Computational complexities of the proposed method and the conventional MP.

Name | Layers of overcomplete dictionary | Numbers of atoms in overcomplete dictionary | Computational complexity of one channel | Total computational complexity |
---|---|---|---|---|

Conventional MP | 1 | 8 × 10^{11} | O(8 × 10^{11}) | O(4 × 10^{12}) |

The proposed | 3 | 8.06 × 10^{4} | O(8.06 × 10^{4}) | O(4.03 × 10^{5}) |

In this simulation, to examine the performance of the parallel multichannel signal interference suppression method based on MP proposed in Section

Figures

Normalized mean square error (NMSE) of estimated signals.

Name | Interference 1 | Interference 2 | Interference 4 | The residual signal |
---|---|---|---|---|

NMSE | 0.022 | 0.025 | 0.001 | 0.001 |

Characteristic of received signals.

Relationship between terminate condition and the iteration number.

Time-domain waveform of original interfering signals.

Retrieval interference from the first best atom

Retrieval interference from the second best atom

Retrieval interference from the third best atom

The residual signals

Time-domain waveform of estimated interfering signals.

Retrieval interference from the first best atom

Retrieval interference from the second best atom

Retrieval interference from the third best atom

The residual signals

In this simulation, the proposed method is compared to the well-known space-only MPDR (S-MPDR) beamformer and three simulation scenarios are considered. In scenario 1, Interferences 3, 4, 5, and 6 are used. In other words, there is not any interfering signals with the same direction as the GNSS signal and the number of interferences is less than that of antenna elements. In scenario 2, Interferences 1, 4, 5, and 6 are adopted. It means that there is one interfering signal with the same direction as the GNSS signal. In scenario 3, Interferences 2, 3, 4, 5, and 6 are used. It implies that the number of interferences is equal to that of antenna elements.

The normalized correlation peaks after interference suppression are shown in Figures

Correlation peaks after interference suppression by S-MPDR beamformer for scenario 1.

Correlation peaks after interference suppression by the proposed method for scenario 1.

Correlation peaks after interference suppression by S-MPDR beamformer for scenario 2.

Correlation peaks after interference suppression by the proposed method for scenario 2.

Correlation peaks after interference suppression by S-MPDR beamformer for scenario 3.

Correlation peaks after interference suppression by the proposed method for scenario 3.

In this simulation, the proposed method is compared to the well-known space-time MPDR (ST-MPDR) beamformer [

The normalized correlation peaks after interference suppression by the three methods for each scenario are shown in Figures

Correlation peaks after interference suppression by ST-MPDR beamformer for scenario 1.

Correlation peaks after interference suppression by DST-MPDR beamformer for scenario 1.

Correlation peaks after interference suppression by the proposed method for scenario 1.

Correlation peaks after interference suppression by ST-MPDR beamformer for scenario 2.

Correlation peaks after interference suppression by DST-MPDR beamformer for scenario 2.

Correlation peaks after interference suppression by the proposed method for scenario 2.

Correlation peaks after interference suppression by ST-MPDR beamformer for scenario 3.

Correlation peaks after interference suppression by DST-MPDR beamformer for scenario 3.

Correlation peaks after interference suppression by the proposed method for scenario 3.

Based on the sparsity of the interfering signals and the advantage of the spatial processing, a novel cascaded multitype interferences suppression method using sparse representation and array processing is proposed and examined in this paper. Firstly, the parallel multichannel signal interference suppression method based on MP is proposed, which can save the spatial DoF of the antenna array by effectively detecting and canceling the narrowband and modulated wideband interference even when they vanish into the Gaussian interferences. Then, the MPDR beamformer is employed to suppress the residuary interferences (such as Gaussian noise interferences) by utilizing the spatial DoF of the antenna array. Numerical simulations show that the proposed method not only can suppress more interferences, but also does not affect the shape and position of the correlation peaks. Compared with the space-only MPDR beamformer, space-time MPDR beamformer, and the distortionless space-time adaptive processor, the proposed method is able to deal with multitypes interferences more effectively and can suppress the interference with the same direction as the desired signal. Therefore, the proposed method is able to effectively improve the interference suppression ability of GNSS receiver while reducing the cost of space and hardware.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work has been supported by the National Natural Science Foundation of China (no. 61371172) and the International S&T Cooperation Program of China (ISTCP) (no. 2015DFR10220) and Fundamental Research Funds for Central Universities (no. HEUCF1708).