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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Due to the increasing complexity of electromagnetic signals, there exists a significant challenge for recognizing radar emitter signals. In this paper, a hybrid recognition approach is presented that classifies radar emitter signals by exploiting the different separability of samples. The proposed approach comprises two steps, namely the primary signal recognition and the advanced signal recognition. In the former step, a novel rough

Radar emitter recognition is a critical function in radar electronic support systems for determining the type of radar emitter [

The recent proliferation and complexity of electromagnetic signals encountered in modern environments greatly complicates the recognition of radar emitter signals [

Classifiers can be categorized into linear classifiers and nonlinear classifiers. A linear classifier can classify linear separable samples, but cannot classify linearly inseparable samples efficiently. A nonlinear classifier can classify linearly inseparable samples; nevertheless it usually has a more complex structure than a linear classifier and the computational complexity of the nonlinear classifier will be increased when processing linearly separable samples. In practice, the radar emitter signals consist of both linearly separable samples and linearly inseparable samples, which makes classification challenging, so in an ideal case, linearly separable samples should are classified by linear classifiers, while only these linearly inseparable samples are classified by the nonlinear classifier. However in the traditional recognition approach, only one classifier is used; thus, it is difficult to classify all radar emitter signal samples.

In this paper, a hybrid recognition method based on the rough

The rest of the paper is organized as follows. In Section 2, a novel radar emitter recognition model is proposed. In Section 3, the primary recognition is introduced. In Section 4, the advanced recognition is introduced. In Section 5, the computational complexity of this approach is analyzed. The performance of the proposed approach is analyzed in Section 6, and conclusions are given in Section 7.

A combination of multiple classifiers is a powerful solution for difficult pattern recognition problems. Thinking about the structure, a combined classifier can be divided into serial and concurrent. A serial combined classifier usually has a simple structure and is easy to establish. In serial combined classifiers, the latter classifier makes the samples rejected by the former its training samples. Thus in designing it, the key is choosing the complementary classifiers and determining the rejected samples.

In this section, a hybrid radar emitter recognition approach that consists of a rough

In the rough

Training samples are clustered first. At the edge of the cluster, there is an empty area between the borderline and the midcourt line of the two cluster centers. We name this area as the uncertain area. In clustering, there is no sample in the uncertain area. When the clustering is completed, these clusters will be used as the minimum distance classifier. When unknown samples are classified, samples are distributed into the nearest cluster. However linearly inseparable samples are usually far from cluster centers and out of the cluster probably,

After sorting and feature extraction, radar emitter signals are described by pulses describing words. Radar emitter recognitions are based on these pulses describing words. The process of the hybrid radar emitter recognition approach is shown in

Based on the pulses describing words, we can obtain an information sheet of radar emitter signals. By using rough sets theory, the classification rules are extracted. These classification rules are the basis of the initial centers of the rough

Based on the process of the recognition approach described above, the accuracy of the hybrid recognition is a superposition of two parts, _{total}_{primary}_{advanced}_{primary}

As mentioned above, a classifier based on the rough

The number of clusters in the algorithm must be given before clustering.

The

The

To overcome the problem of isolated points, Pawan and West proposed the rough

In rough sets theory, an information system can be expressed by a four-parameters group [_{r}_{r}_{1}, _{2},…, _{n}_{i}

Since it is not possible to differentiate the elements within the same equivalence class, one may not obtain a precise representation for a set

In the radar emitter recognition, suppose _{P}_{P}_{P}_{P}_{Q}_{Q}_{Q}_{Q}_{Q}

After discretization and attribute reduction, the classification rules are extracted. Using this approach, the initial centers are computed based on the classification rules of rough sets. The process can be described as follows:

Classification rules are obtained based on the rough sets theory.

The mean value of every class is obtained.

The clustering number equals to the number of rules and define the mean values as the initial clustering centers:
_{p}

In rough _{lower}_{upper}_{i}_{i}_{i}_{min}_{min}_{i}_{∈[1}, _{I}_{]}_{i}_{i}_{min}

In _{k}

Compute the Euler distance of every object to

Compute the minimum value _{min}

Compute distance between every object and other class center _{i}_{t}_{min}

Obtain the minimum value _{s}

_{s}

In the training process of the rough _{ro}_{un}_{ro}_{x}_{un}_{x}_{un}_{x}_{ro}

In a cluster, the area beyond uncertain boundary (_{x}_{un}_{x}_{un}

In addition, the accuracy of primary recognition is relevant with the radii of clusters. Rough

As shown in _{r}

The relevance vector machine (RVM), a sparse Bayesian modeling approach, is proposed by Tipping [

In classification, the output function ^{−}^{z}

Suppose _{n}

Seeking the maximum posterior probability estimation is equivalent to seeking the mode point of the Gaussian function, namely, _{MP}

Due to:
_{n}_{n}

Suppose _{ωMP}^{−1}(_{MP}^{T}^{T}^{−1}. The logarithm of the approximate marginal likelihood function is given by:
^{−1}Φ^{T}

A fast marginal likelihood maximisation for sparse Bayesian models is proposed in reference [

It is showed that _{i}

The proposed marginal likelihood maximization algorithm is as follows:

Initialize with a single basis vector _{i}

Compute Σ and μ (which are scalars initially), along with initial values of sm and qm for all M bases _{m}.

Select a candidate basis vector _{i}

Compute

If _{i} > 0, _{i} < ∞, re-estimate _{i}.

If _{i} > 0, _{i} = ∞, add _{i}_{i}.

If _{i} ≤ 0, _{i} < ∞, delete _{i}_{i} = ∞.

Recompute and update Σ, _{m}_{m}_{m}_{m}^{T}_{m}-φ_{m}^{T}^{T}_{m}_{m}_{m}^{T}_{m}^{T}^{T}

If converged, terminate the iteration, otherwise go to 3.

The fast marginal likelihood maximisation for sparse Bayesian models is stated in details in [

The computational complexity of the approach proposed in this paper consists of two parts, namely the computational complexity of the primary recognition and the computational complexity of the advanced recognition.

In the training of the primary recognition, samples are clustered using rough

The RVM is used as the advanced recognition in our approach. The computational complexity of RVM has nothing with the dimension of samples, but is related with the number of samples. The computational complexity of RVM training is discussed with respect to the complexity of the quadratic programming. RVM training has a computational complexity less than ^{3}), where

In conclusion, the computational complexity of our hybrid recognition is ^{3}). In general, ^{3}). In actual practice,

The validity and efficiency of the proposed approach is proved by simulations. In the first simulation, radar emitter signals are recognized. The pulse describing words of the radar emitter signal include a radio frequency (RF), a pulse repetition frequency (PRF), antenna rotation rate (ARR) and a pulse width (PW). The type of radar emitter is the recognition result. Two hundred and seventy groups of data are generated on above original radar information for training. And the recognition accurate is calculated averaged over 200 random generations of the data set.

Another simulation is adopted to test the generalization of the hybrid recognition with the Iris data set. The Iris data set contains 150 patterns belonging to three classes. There are 50 exemples for each class and each input is a four-dimensional real vector [

An information sheet of radar emitter signals is built, which is shown as

Training and test samples are random generations of the data set shown in

After that, the dependent extent of radar type to each attribute is computed using _{D}_{D}_{D}

As shown in

In recognition of unknown samples, some important parameters are computed in the simulation. The accuracy, error and reject rate of the primary recognition are 86%, 2.5%, 11.5%, respectively. The accuracy of advanced recognition is 93.1%. Thus, the estimate of accuracy can be computed as: _{total}

The proposed method is compared with the RBF-SVM, the probabilistic SVM radar recognition approach studied by Lin

As shown in

In the first part, all 150 of the samples are used for training and testing. In this simulation, the training accuracy of the hybrid recognition is tested. In addition, the accuracy of recognition and computational complexity of the hybrid recognition is compared with those of SVM and RVM. The results are as shown in

From

In the second part, 60 random samples from Iris are used to train classifiers and other 90 samples are used for test to test the generalization. The accuracy of recognition and computational complexity of the hybrid recognition is compared with those of SVM and RVM. The results are as shown in

The recognition accuracy of the proposed approach is 96.67%, which is higher than those of other approaches. It is indicated that the hybrid recognition has not only a high training accuracy but also a good generalization.

In addition, let's compare the training computational complexities of SVM, RVM and the proposed approach. The computational complexity of SVM is ^{3}). The computational complexity of RVM is ^{3}). The computational complexity of the proposed approach is ^{3}), where ^{3}). In our approach, training samples are clustered in the primary recognition, and only the rough samples are used to train the RVM in the advanced recognition. More specifically, there are 71 training samples for the RVM in the advanced recognition, ^{3}). Similarly, when 60 samples are used as training samples, all of these samples are used to train SVM and RVM, while 36 training samples are picked up for the RVM in the advanced recognition of the hybrid recognition, ^{3}), while the computational complexity of the proposed approach is ^{3}). From the comparison above, we can know that the computational complexity of the hybrid recognition is obviously lower than those of RVM and SVM.

Theoretically, lower computational complexity leads to less computational time. The actual calculation time for each algorithm is tested and the result is shown in

In this paper, a hybrid recognition method has been proposed to recognize radar emitter signals. The hybrid classifier consists of a rough

A linear classifier based on the rough set and the rough

The hybrid recognition approach in this paper is suitable for the classification of the radar emitter signal containing both linearly separable and linearly inseparable samples. However, for the situations where only linearly separable or linearly inseparable samples are included, the effectiveness of the hybrid approach will be not significant. We admit that our hybrid recognition approach is based on the fact that these linearly inseparable samples which reduce the accuracy of clustering are mostly at the edges of clusters. From

This work was supported by a grant from National Natural Science Foundation of China (grant number: 61102084).

Regions of the rough

Flow chart of the hybrid radar emitter recognition approach proposed in this paper. First of all, samples are recognized by the primary recognition, which can classify linearly separable samples and pick up those linearly inseparable samples to be classified in the advanced recognition using relevance vector machine.

The radius of a cluster in rough

Information of known radar emitter signals.

1 | 8,799 | 1,500 | 0.1 | 1 |

2 | 8,847 | 750 | 0.5 | 1 |

3 | 8,755 | 620 | 0.5 | 2 |

4 | 8,890 | 580 | 0.5 | 2 |

5 | 8,875 | 585 | 0.5 | 2 |

6 | 8,804 | 750 | 0.1 | 1 |

7 | 8,850 | 1,500 | 0.5 | 1 |

8 | 9,460 | 1,300 | 0.25 | 3 |

9 | 9,436 | 1,600 | 0.15 | 3 |

Continuous values are changed into discrete information by using the equivalent width method.

1 | 1 | 3 | 1 | 1 |

2 | 2 | 2 | 3 | 1 |

3 | 1 | 2 | 3 | 2 |

4 | 2 | 1 | 3 | 2 |

5 | 2 | 1 | 3 | 2 |

6 | 2 | 2 | 1 | 1 |

7 | 2 | 3 | 3 | 1 |

8 | 3 | 3 | 2 | 3 |

9 | 3 | 3 | 1 | 3 |

Classification rules are extracted based on rough sets theory. These rules are the basis of the choice of the initial centers in rough

1 | - | 1 | 2 |

2 | 1 | 2 | 2 |

3 | 2 | 2 | 1 |

4 | 1 | 3 | 1 |

5 | 2 | 3 | 1 |

6 | 3 | 3 | 3 |

Centers, rough boundary radiuses and uncertain boundary radiuses of clusters.

_{ro} |
_{un} | ||
---|---|---|---|

1 | (8882.5, 582.5) | 63 | 142 |

2 | (8,755, 620) | 70 | 128 |

3 | (8,827, 750) | 56 | 119 |

4 | (8,799, 1,500) | 37 | 41 |

5 | (8,850, 1,500) | 34 | 45 |

6 | (9,448, 1,450) | 398 | 607 |

Training accuracy, training accuracy and recognition accuracy of radar emitter recognition approaches are compared.

RBF-SVM | 99.5% | 3.1 | 94.0% |

PSVM | 99.0% | 3.4 | 93.5% |

RVM | 99.0% | 4.6 | 94.0% |

Method in this paper | 99.5% | 2.1 | 96.5% |

In the first part of experiment 2, the recognition accuracy of Iris data set and computational complexity are compared among three approaches.

SVM | 98.00% | 150 | ^{3}) |
0.9 |

RVM | 98.67% | 150 | ^{3}) |
1.2 |

Hybrid recognition | 99.33% | 71 | ^{3}) |
0.6 |

In the second part of experiment 2, the recognition accuracy of Iris data set and computational complexity are compared among three approaches.

SVM | 93.33% | 60 | ^{3}) |
0.13 |

RVM | 94.44% | 60 | ^{3}) |
0.14 |

Hybrid recognition | 96.67% | 36 | ^{3}) |
0.04 |