Signal Processing of Automobile Millimeter Wave Radar Base on BP Neural Network

Transcription

1 AIML 06 International Conference, 3-5 June 006, Sharm El Sheikh, Egypt Signal Processing of Automobile Millimeter Wave Radar Base on BP Neural Network Xinglin Zheng ), Yang Liu ), Yingsheng Zeng 3) ))3) Institute of Mechatronics and Automation, National University of Defense Technology Changsha, 40073, China Abstract In this paper BP neural network is used for signal processing of automobile millimeter wave radar instead of FFT(Fast Fourier Transform). Simulation results show that BP neural network is superior to FFT. FFT has the drawback such as large computation and frequency spectrum leakage. The BP neural network has three layers(one input layer, one hidden layer, one output layer).the network is trained by using ideal value in the off-line situation. Then inputting the sampling value of signal, the frequency of signal can be got from output in the online situation. Compared with conventional FFT, significant performance improvement has been achieved. Keywords : BP neuron network, FFT, millimeter wave radar.. Introduction In recent years, the automobile production and sales quantity increase significantly along with the development of the economy. So the traffic accident is also more and more multifarious than before. In this situation, the safety of the automobile becomes more important than before. Then many kinds of automobile radars appear gradually, some of them are ultrasonic wave, laser and millimeter wave. Compared with the other ways, millimeter wave radar has stable performance of detecting and excellent ability of adapting the environment. Especially, along with the high frequency device and MMIC (microwave monolithic integrated circuit) appearance and application, millimeter wave radar will be the first choice for automobile radar. There are two (main kinds of) important methods for signal processing, FFT (Fast Fourier Transform) and non-fft. The theory of FFT is mature, it is the most popular method for signal processing in common. But in this paper, BP neural network is used to replace FFT. Simulation results indicate that the proposed method is feasible, and is better than FFT. The remainder of the paper is organized as follows: Section () focuses on the theory of FFT and BP neural network. Section (3) proposes an improved method to solve signal processing for automobile millimetre radar and illustrates the experimental results. Section (4) gives the results and comments. Section (5) is the conclusion.. Theory The principle of distance measuring of millimeter wave radar is that backward wave and sending wave mix, then the beat frequency is obtained. The beat frequency contains distance information. The distance of a goal can be obtained by detecting the beat frequency. As it was mentioned earlier, FFT is the most popular method for signal processing, because it is realized easily, and it has high reliability. However, the drawback of FFT is outstanding. First, computational complexity is large. Second, frequency spectrum leakage exists in FFT []. A typical BP neural network is made of input layer, hidden layer and output layer, but the hidden layer can own one layer or more layers []. BP neural network has its own unique algorithm backpropagation algorithm. The learning process of backpropagation algorithm can be described as this, the first step is to propagate the input signal forward through the network, the second step is to propagate the error signal backward through the network. Finally, the weights and biases are updated [3]. Though the learning process of backpropagation is clear, the drawbacks of backpropagation is obvious. Two of these is local minimum value and slow learning rate. So some improvement must be done for backpropagation. Usually two approaches are applied to improve backpropagation algorithm. The first approach is heuristic modifications of 36

2 AIML 06 International Conference, 3-5 June 006, Sharm El Sheikh, Egypt backpropagation. In this improved method momentum or variable learning rate is used. The second approach is to use numerical optimisation techniques. Levenberg-Marquardt algorithm is one of these. It is a modification to Gauss-Newton s method. The BP neural network can be designed following FFT. When inputting the sampling value of a certain frequency, the corresponding neuron inputs,others input 0. According to this principle, the ideal samples are used to train the BP neural network in the off-line situation. Then the sampling values of signal are inputted in the on-line situation, the frequency of signal can be obtained from the output. 3. Design Network As discussed above, FFT is often used for signal processing, but the drawback of FFT makes us try to find better methods for signal processing. The relation between the sampling value of beat frequency signal of radar and the frequency of signal is non-linear. BP neural network does well in dealing with non-linear problems. So the proposed method is based on BP neural network. 3. Choice of Network Architecture and Parameter Robert Hecht Nielson once pointed out that a BP neural network of three layers could be used to approximate almost any non-linear function if there are enough neurons in the hidden layer [4]. So BP neural network of one hidden layer is usually used except a few quite complex problems. In this paper, one hidden layer is used to constitute a three-layer BP neural network. The number of neurons in the input layer is chosen on the problem being dealt, so does the number of neurons in the output layer. As discussed former, the BP neural network is designed following FFT. It s well known that the output of FFT is symmetrical, so if the number of neurons in the input layer is N, then the number of neurons in the output layer is N /. In order to compare with FFT, the number of sampling N is chosen to be 6, though N can be chosen at will. So input layer has 6 neurons, and output layer has 8 neurons. Suppose that the sampling frequency of signal is fs = 600Hz. According to Shannon sampling theorem, the highest frequency of signal which will be processed should be less than fs /= 800Hz. Because the number of neurons of output layer is 8, the frequency should be divided into 8 segments from the lowest to the highest. The corresponding relation between the input and the output is like table. According to table, a set of band-pass filters can be constructed based on BP neural network. When the frequency of input signal is in a certain range, the output value of the corresponding output neuron is close to, the others are close to 0. So it s easy to know which range the frequency of input signal is belong to according to the output value. It is supposed that the center frequency of any frequency range is n* fs / N ( n is integer between 0 and 7), then the center frequency can be used to substitute the other frequency in this range. The division in table is better than others, because in the same value of N, the difference(50 Hz ) between the center frequency and the other frequency in any frequency range is the least one. Table relation between input and output Frequency( Hz ) output 0~ ~ ~ ~ ~ ~ ~ ~ It s so important to choose the number of neurons in the hidden layer. Whether the number is right or not decides that BP neural network is success or failure. If the number of neurons in the hidden layer is egregious small, the learning process may be not convergent. The larger the number of neurons in the hidden layer is, the stronger the mapping ability of network is. But the learning time is quite long, the ability of fault-tolerant also brings down. There are not uniform theory guide on how to choose the best number of neuron in the hidden layer so far. In practical application, a small number is usually chosen by former experience, then change the number larger step by step. Finally, a right number of neuron in the hidden layer is decided by training. In this paper, we first chose 5 neurons in the hidden layer. After training, the final and right number is. 3. Choice of Samples The beat frequency signal of radar is sinusoidal signal. So we first sample the sinusoidal signal, the sampling values of sinusoidal signal are regarded as input samples. Then, the corresponding output samples can be got according to table. The amount of samples plays an important role on output performance of network. If there are too many samples, the training time will become so long, and learning process even will be not convergent. If there are too few samples, it can not attain excellent results. So the amount of samples must be appropriate. Usually, two rules can be used on choosing the sample [5]. First, not only all patterns should be included, but also each pattern has almost equal amount of sample. Second, adding a little noise into samples, it can improve anti-noise 37

3 AIML 06 International Conference, 3-5 June 006, Sharm El Sheikh, Egypt capability to do so. According to the rules, every 0 Hz from 0 Hz to 800 Hz we choose a set of samples of sinusoidal signal without noise, in all 80 groups, then every 0 Hz from 0 Hz to 800 Hz we choose a set of samples sinusoidal signal with white noise, in all 80 groups. So we finally choose 60 groups samples. 3.3 Training of Network Neural network toolbox of Matlab makes backpropagation very easy to be implemented. The rate of convergence of traditional backpropagation is quite slow, and it can not satisfy practical problems. Neuron network toolbox of Matlab offers many improved backpropagation algorithms, the rate of convergence of these algorithms becomes faster than before, the training time remarkably decreases. One of these algorithms is from hidden layer to output layer, b is the bias of hidden layer, b is the bias of output layer, P is the input vector. Combining the two equations, such equation can be got, a = f ( W f ( W P+ b ) + b ) 3.3 This is the equation of a three-layer BP neural network between input P and output a. The four parameters( W, W, b, b ) of network are got by training. We choose tansig function as transfer function f, purelin function as transfer function f. Then according to equation 3.3, we get the frequency of signal by inputting the samples of signal. Figure - to figure -5 show the output of BP neuron network. In these figures, symbol + expresses frequency spectrum of signal without noise using BP neural network, symbol of square expresses frequency spectrum of signal with white noise using BP neural network, symbol * expresses frequency spectrum of signal without noise using FFT. 4. Results and comments In order to test anti-noise capability of network, we respectively choose sinusoidal signal without noise and sinusoidal signal with white noise as input of network. The frequency spectrum got by using FFT is added to the figures to compare BP network to FFT. The sampling frequency of figure - to figure -5 all is 600 Hz, the frequency of processed signal is 455 Hz, 475 Hz, 495 Hz, 55 Hz and 535 Hz respectively. By analysing the five figures, such conclusions are got: Figure training error curve Levenberg-Marquardt algorithm. It combines steepest descent method and Gauss-Newton method, and the training time is short. So we choose this method in this paper. Figure is the training error curve of this method. 3.4 Output of Network There are two such equations in the earlier part, a = f ( W P+ b ) 3. a = f ( W a + b ) 3. In the two equations, a is the output of hidden layer, a is the output of output layer, f is the transform function of hidden layer, f is the transform function of output layer, W is the weight from input layer to hidden layer, W is the weight Figure - 38

4 AIML 06 International Conference, 3-5 June 006, Sharm El Sheikh, Egypt Figure - Figure -5 Figure output result comparing () When using BP neural network, the output is right whether the input is signal with noise or signal without noise, though there is a little deviation from ideal value. () When the frequency of input signal is close to center frequency, FFT and BP neural network can detect the frequency exactly(figure -3). When the frequency of input signal is far from center frequency, especially close to critical frequency, BP neural network can still detect the frequency, but FFT can not(figure - and figure -5). Figure Conclusion In a word, this method can detect the frequency of signal correctly, and has a certain extent anti-noise ability. And the performance of this method is better than that of FFT. Furthermore, computational complexity of BP neural network remarkable reduces when compared with FFT. Because training network is done in the off-line situation, we use equation3.3 to compute frequency of signal in the on-line situation. In on-line computation, there is no circulation and iteration. When applied in automobile millimeter wave radar, train network in the off-line situation, get the parameters of network. Then we input sampling values of signal in the on-line situation, compute the frequency of signal. So BP neural network is suitable for automobile millimeter wave radar in theory, and it is better than FFT. Figure -4 The proposed method is not only applied in automobile radar, but also applied in many other fields. 39

5 AIML 06 International Conference, 3-5 June 006, Sharm El Sheikh, Egypt 6. References [] Sanjit K.Mitra. Digital Signal Processing: A Computer-Based Approach,Second Edition. Electronics Industry Press, ~649. [] Gao Jun. Principle of Neural Network and Simulation Example. China Machine Press, ~54. [3] Dong Changhong. Matlab Neural Network and Application. International Defence Industry Press, ~0. [4] Zhang Liming. Model of Neural Network and Application. Shanghai: Fudan University Press,995. [5] Guo Haitao, Zhang Dianlun, Ma Guofang. Some Problems to Be Considered in Using BP Algorithm. Journal of Jiamusi University. 000,: 363~365. [6] [Martin T.Hagan, Howard B.Demuth, Mark Beale. Neural Network Design. China Machine Press, ~7-30. [7] Simon Hayhin. NEURAL NETWORK A Comprehensive Foundation, Second Edition. Tsinghua University Press, 00. 6~48. [8] Ju Junzhang, Zhuo Rong. Convenient Realization of BP Networks on MATLAB. Journal of Xinjiang Petroleum Institute. 999,:4~46. [9] Wang C J, Wu C H. Neural Networks for Target Detection[J]. Proceeding of the IEEE, 990:863~866 40