INTRODUCTION
Radar emitter recognition is an important part of radar system. Recognizing
radar emitter correctly plays an important role in modern war. After selection
and feature extraction, how to analyze the style of radar emitter signal for
superior decisionmaking institution is the main assignment of radar emitter
signal recognition (Zhang et al., 2009). Traditional
methods contain feature parameter matching (Zhang et
al., 2008), character in pulse analysis, data fusion (Guan
et al., 2005) and artificial intelligence analysis (Kou
and Wang, 2007). Due to the deterioration of electromagnetic environment
and noise, radar receivers receive signals with great pollution and interference.
The range of some parameter is changed, because of the impact of noise. There
are more working modes in modern radar. Correspondingly, there are more combinations
of radar signal parameters. It is more difficult to recognize the type of radar
emitter, because of electromagnetic environment deterioration, jamming technique
and new type radar. Traditional recognition can not be competent for the job
(Zhang et al., 2009). So the research about this
point has been the emphases and exploring the new radar emitter recognition
method has the theory and applying meaning.
Back Propagation (BP) neural network is a popular method for classification.
BP algorithm is one of the most widely used algorithms at present, but BP algorithm
can not be applied in depth to neural network due to its limitation and many
disadvantages such as slowness of convergence speed, imperfectness of traditional
algorithm, possibility of network paralysis and etc. Especially, BP algorithm
is easily trapped into local minimum (Feng et al.,
2000). To overcome the problem of local minimum, a new algorithm named Single
Parameter Dynamic Search (SPDS) algorithm is proposed by some researchers (Wang
and Fang, 1997). The SPDS algorithm based on the idea of circulating coordinate
in turns is an algorithm of multilayered feedforward neural network, which only
permits one of all parameters in the network to change during each epoch of
searching for parameters so that guarantees to carry out the exact onedimensional
search. In this study, a method of radar emitter recognition is proposed, which
adopts the BP neural network based on SPDS algorithm. The availability is proved
by simulation.
BP NEURAL NETWORK
At present, BP neural network is the most useful neural network in many fields
(Li et al., 2010). There are two parts are in
BP neural network: positivegoing information transition and erroneous oppositegoing
transition.

Fig. 1: 
Structure of BP neural network. Where {X_{1} , X_{2}
,....., X_{N} } is in the input layer.{Z_{1} , Z_{2}
, ......, Z_{N} } is in the hidden layer and {Y_{1 }, Y_{2}
, ......, Y_{N}} is in the output layer 
In the process of positivegoing transition, the input information is transited
through the input layer, hidden layer to the output layer (Alsaade,
2010). The states of neurons at each layer only affect that of the next
layer’s. If no anticipated output is obtained at the output layer, the
deviation value of the output layer is thus calculated and transited in the
reverse direction, returning the deviation signal through the original passage
in the network, then revise the weight values of neurons at each layer until
the expected target is reached (QiangZhu, 2006). The
structure of BP neural network is shown in Fig. 1.
The algorithm of BP neural network is as follows: first, the calculation is
made through the input layer of the network to the output layer; second, revision
and adjustment is made on the connectional weight values and threshold values,
namely, make calculation and revision through the output layer to the input
layer, then revise weight values connected to the output layer according to
the deviations of the output layer until all the requirements are fulfilled
(Yang, 2010). The flowchart of BP neural network algorithm
is shown in Fig. 2. As shown in the Fig. 2,
the algorithmic process of BP neural network is dynamic. The entry of one step
is allowed only at the fulfillment of last step, or second analysis is required
to find the deviation before entering another step.
SPDS ALGORITHM
Derivation of neural network based on SPDS algorithm: Following calculation steps of SPDS algorithm are to be introduced for application in threelayered neural network.
Let I be the number of input layer units, H be the number of hidden layer units,
O be the number of output layer units, K be the number of pattern, the vector
P_{k,i}^{(1)} be the output of kth pattern in ith input neuron,
r_{k,i}^{(1)} be the sum of input from kth pattern in ith hidden
neuron and threshold of ith hidden neuron, P_{k,i}^{(2)} be
the output of kth pattern in ith hidden neuron, r_{k,i}^{(2)}
be the sum of intput from kth pattern in ith output neuron and threshold of
ith output neuron, y_{k,i} be the output of kth pattern in ith output
neuron, w_{j,i}^{(1)} be the weight connecting ith input neuron
to jth hidden neuron, h_{i}^{(1)} be the threshold of ith hidden
neuron, w_{j,i}^{(2)} be the weight connecting ith hidden neuron
to jth output neuron, h_{i}^{(2)} be the threshold of ith output
neuron, T_{k,i} be the teaching signal of kth pattern in ith output
neuron.

Fig. 2: 
Flowchart of the algorithm of BP network 
Aimed at 4 different kinds of parameters as above, the 4 corresponding objective
functions used in onedimensional search are to be introduced in following section.
The error function can be represented as:
Then the activation function is given by:
The flowchart of SPDS algorithm is shown as Fig. 3.
As shown in Fig. 3, the SPDS algorithm consists of 4 steps as follow:
• 
Step 1: Adjustment of threshold in output layer 
For l≤i≤O, adjust h_{i}^{(2)}, since h_{i}^{(2)}
is the unique parameter permitted to change, consider the functions:
Let item (r_{k,i}^{(2)}–h_{i}^{(2)}) in Eq. 5 be the constant R_{x} with the only relevance to k, item h_{i}^{(2)} in Eq. 5 be variable x, namely:
Compute x_{0} that satisfies f_{1}(x_{0}) = minf_{1}(x) , x∈R, then x_{0 }is the updated h_{i}^{(2)}, meanwhile, adjust r_{k,i}^{(2)} and y_{k,i} according to the x_{0}, where 1≤k≤K.
• 
Step 2: Adjustment of weight connecting hidden layer
to output layer 
For l≤i≤O, 1≤j≤H, adjust w_{i,j}^{(2)}, since w_{i,j}^{(2)}
is the unique parameter permitted to change, consider the function:

Fig. 3: 
Flowchart of SPDS algorithm 
By similar procedure with step 1, Eq. 9 would then be:
Compute x_{0} that satisfies f_{2}(x_{0}) = minf_{2} (x), x∈R, then x_{0 }is the updated w_{i,j}^{(2)}, meanwhile, adjust r_{k,i}^{(2)} and y_{k,i} according to the x_{o} ,where 1≤k≤K.
• 
Step 3: Adjustment of threshold in hidden layer 
For 1≤i≤H, adjust h_{i}^{(1)}, since h_{i}^{(1)}
is the unique parameter permitted to change, consider the functions:

Fig. 4: 
Radar emitter recognition based on SPDS algorithm 
By similar procedure with step 2, Eq. (14) would be:
Compute x_{0} that satisfies f_{3} (x_{0}) = minf_{3 }(x), x∈R, then x_{0 }is the updated h_{i}^{(1)}, meanwhile, adjust r_{k,j}^{(2)}, y_{k,j}, r_{k,i}^{(1)} and P_{k,i}^{(2)}_{,} according to the x_{o}, where 1≤j≤O, 1≤k≤K.
• 
Step 4: Adjustment of weight connecting input layer
to hidden layer 
For 1≤m≤I, 1≤n≤H, adjust w_{n,m}^{(1)}, since w_{n,m}^{(1)}
is the unique parameter permitted to change, consider the functions:
By similar procedure with step 3, Eq. (19) would then be:
Compute x_{0} that satisfies f_{3}(x_{0}) = minf_{3}(x), x°R, then x_{0 }is the updated w_{n,m}^{(1)}, meanwhile, adjust r_{k,n}^{(1)}, y_{k,j}, r_{k,j}^{(2)} and P_{k,n}^{(2)} according to the x_{0}, where 1≤j≤O, 1≤k≤K.
The objective error functions f_{1}(x), f_{2}(x), f_{3}(x) and f_{4}(x) as above are onedimensional functions with infiniteorder derivative. On this basis first order derivative and second order derivative of error functions are necessary to be derived, which contributes to using the Newton iteration method to improve the convergent speed of training network furthermore. As initial value point is located nearby extremum point, which satisfies the condition of using Newton iteration method, Newton iteration method can be applied to onedimensional search. Newton iteration formula is given by:
The model of SPDS neural network: After the electronic reconnaissance system achieves to intercept radar signal, the corresponding radar parameters can be measured by frequency measurement receiver and directionfinding receiver. These parameters such as Radio Frequency (RF), Direction of Arrival (DOA) of pulse signal, Time of Arrival (TOA) of pulse signal, Pulse Width (PW), Pulse Amplitude (PA) and etc compose Pulse Description Words (PDW). Then the architecture of neural network can be established by PDW. The process of radar emitter recognition based on SPDS neural network is described by Fig. 4.
ANALYSIS OF COMPUTERIZED SIMULATION RESULTS
In this study, data sets of 3 different types of radar signal from reference
(Guan et al., 2005) are used in building the
radar emitter initialized information table as shown in Table
1.
After imperfect feature parameters of radar signal as above are reduced according
to availability of data, the attribute of antenna rotate rate is evidently unnecessary.
Table 1: 
Initialized parameter of radar signal 

Table 2: 
Data index scope of input vector 

Correspondingly, output vector T = (0 1; 1 0; 1 1) 
Thus PDW= (RF, PP, PRF, PW), where RF denotes Radio Frequency, PP denotes
Peak Power, PRF denotes Pulse Repetition Frequency, PW denotes Pulse Width.
Extraction of pattern data and establishment of evaluating index: Extraction of training pattern data: 200 groups of random PDW data limited scope are extracted from each type of radar signal and the total groups of data are 600.
Assume input vector P = PDW, data index scope of each type is required as Table 2.
Extraction of testing pattern data: Testing pattern is extracted by adding Gaussian white noise on the basis of training pattern. The evaluating indexes consist of 3 parts as following:
• 
Recognition rate of testing set 1, testing set 2 and testing
set 3 in presence of Gaussian white noise 
RESULTS AND DISCUSSION
In order to speed up convergent procedure by improving the training way, LM
algorithm and One Step Secant algorithm in MATLAB neural network toolbox are
necessary to be applied to BP neural network. Implement recognition for the
same pattern by using traditional BP algorithm, LM algorithm, One Step Secant
algorithm and SPDS algorithm that is proposed in this paper and the average
recognition rate is shown in Table 3.
As shown in Table 3, in the same training, SPDS algorithm needs less iterations to achieve a higher recognition rate and the output mean square error of SPDS is less than other methods. The computerized running results of SPDS algorithm is shown in Table 4.
Table 3: 
Recognition rate of radar emitter based on different algorithms 

Table 4: 
The quantization analysis of computerized running results
of SPDS algorithm 

As shown in Table 4, the iteration number affects recognition rates and training error sharply. As shown in Table 4, when the iteration number is close to 300, the high recognition rate is obtained. The recognition rate is even close to 100% under the condition of enough iterations and uncomplicated data. Compared with the result processed by BP algorithm to the same pattern, SPDS algorithm has higher recognition rate and faster convergent speed significantly. SPDS algorithm can overcomes the problems of local minimum and long training time, which are the giant limits of BP algorithm. The SPDS neural network is robust to the noise. In a word, compared with BP algorithm, SPDS algorithm can obtain higher recognition rate by less computational complexity in the condition of uncomplicated data and noise.
CONCLUSIONS
SPDS algorithm positively improves BP algorithm and it would not be trapped into local minimum. Meanwhile, computational complexity of SPDS algorithm is significantly less than the gradient descent algorithm. In general, radar emitter signals can be exactly recognized by the SPDS neural network.
By comparing the testing result, it is found that the radar emitter signal can be recognized more accurately with the SPDS neural network and the learning speed is improved greatly. The recognition rate is close to 100% under the condition of enough training times. In addition, neural network based on SPDS algorithm is more robust than neural network based on BP algorithm. Compared with BP algorithm, SPDS algorithm can obtain higher recognition rate by less computational complexity in the condition of uncomplicated data and noise.