Radar Pulse Compression for Point Target and Distributed Target Using Neural Network

Transcription

1 JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 23, (2007) Radar Pulse Compression for Point Target and Distributed Target Using Neural Network FUN-BIN DUH AND CHIA-FENG JUANG * Department of Electronic Engineering Feng Chia University Taichung, 407 Taiwan * Department of Electrical Engineering National Chung Hsing University Taichung, 402 Taiwan An important study of the responses to the point target and the distributed target of the radar echoes processed by a neural network pulse compression (NNPC) algorithm is presented in this paper. For whatever the purpose of a radar system, both of the point target and distributed target echoes are received simultaneously. It is always necessary and helpful to discriminate them clearly while detecting the desired target, which will reduce the influence for each other in pulse compression processing. However, in most of the pulse compression algorithms, it is only considered the radar purpose to process one type of the targets but neglect the other. This will make either the presence of a point target s range sidelobes masking and corrupting the observation of the weak distributed target nearby or a distributed target with extended range interfering with the detection of the neighboring point target. By completely considering the interactions of a point target with a distributed target, we acquire all the possible data occurred in the procedure. Using these valid data, we can train the backpropagation (BP) network to construct it as a well performance of NNPC. To compare with the traditional algorithms such as direct autocorrelation filter (ACF), least squares (LS) inverse filter, and linear programming (LP) filter based on 3-element Barker code (B3 code), the proposed NNPC provides the requirements of high signal-to-sidelobe ratio, low integrated sidelobe level (ISL), and high target discrimination ratio. Simulation results show that this NNPC algorithm has significant advantages in targets discrimination ability, range resolution ability, and noise rejection performance while processing the interaction of point target with distributed target, which are superior to the traditional algorithms. Keywords: barker code, distributed target, least squares inverse filter, linear programming filter, neural network, pulse compression, point target, sidelobe. INTRODUCTION In spite of the different purposes of radar systems, there exist two types of target received from radar echoes, the point target and the distributed target. The former is the echo occupying a space much smaller than the radar resolution cell, and the latter is composed of a number of scatters, in which the target extent is more than the radar resolution cell []. Usually one type of radar target echo is regarded as the desired target in a radar system, while the other is considered as clutter. For example, a given point target echo such as the airplane is considered to be the desired target in an air traffic control (ATC) radar or a military radar, but it is regarded as clutter or interference for a weather Received November 30, 2004; revised May 5, 2005; accepted June 8, Communicated by Liang-Gee Chen. 83

2 84 FUN-BIN DUH AND CHIA-FENG JUANG radar. On the contrary, for the meteorological application of the weather radar, the distributed target echo such as cloud, precipitation, thunderstorm etc. is observed as the desired target, but the point target echo should be rejected to avoid an observation barrier. A precise block of a radar system is shown in Fig., which also shows the environments encountered. Environments Radar System Noise Duplexer Receiver Signal processor Data processor Display Antenna Transmitter Fig.. A precise block of a radar system. One of the main purposes of waveform design for pulse compression in a pulse radar system is to solve the dilemma between the range resolution and the pulse length. That is we would transmit a long pulse to have large power and long-range detection, but it will decrease the range resolution. However, while decreasing transmitting pulse length to increase range resolution, it will decrease the detection range. Pulse compression allows a radar system to transmit a long coded pulse length and compresses the received pulse to a relatively narrow pulse using a matched filter by special code processing. This will result in an increased detection performance associated with a long pulse while still maintaining the fine range resolution as a short pulse in a radar system. Therefore, pulse compression processing is one of the most important factors in determining the performances of a high-resolution and/or high detection radar. There are two basic waveform designs suitable for pulse compression: frequencycoded and phase-coded waveforms. The former includes linear frequency modulation (LFM) and nonlinear frequency modulation (NLFM) waveforms. The latter includes binary phase-coded and polyphase-coded waveforms. The phase-coded waveforms differ from the frequency modulation waveforms in that the pulse is subdivided into a number of equal duration subpulses. Each subpulse has a particular phase which is selected in accordance with a given code sequence. Both of the waveforms are designed to bunch up the received signal by the pulse compression processing. That is the amplitude of pulse is increased and the width is decreased. The performance comparison between the basic waveforms described above is given in [, 2]. Compared with the LFM signals, the phase codes have received less at-

3 PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET 85 tention for radar applications. Owing to the continuity of the phase variations in LFM, the LFM may provide better results than biphase codes in which the phase variations are sharp. But the Barker-based binary phase codes have better range resolution than the FM waveforms at the price of higher loss and higher sidelobes [3, 4]. In this paper, we consider only phased-coded waveforms for easy in implementation. The simplest type of phase code waveform is the binary phase code. One family of binary phase codes that can produce compressed waveforms with constant sidelobe levels equal to unity is the Barker code. The special features of the Barker codes are () their sidelobe structures contain the minimum energy that is theoretically possible, (2) this energy is uniformly distributed among the sidelobes [5], and (3) it can be easily implemented in digital form. These features are helpful to the general requirements of pulse compression. Pulse compression algorithms with well performances have been proposed for applications in military and aviation systems, in which the desired target is the point target, but they had not been used for the distributed target until the early 970 s. Based on the 7-bit Barker phase-coded, Fetter [6] demonstrated the use of pulse compression to enhance the radar weather performance. Also based on binary phased-coded pulse compression, Gray and Farley [7] explored incoherent scatter measurements. Ackroyd and Ghani [8] have developed an optimum mismatched filter for the 3-element Barker (B3) code sidelobe suppression in the least-square (LS) sense, and Steven Zoraster has utilized linear programming (LP) techniques to determine the optimal filter weights for minimizing the peak range sidelobes of the Barker code [9]. Basically, these two algorithms are based on the point target. In 998, Mudukutore et al. [4] tried to use the LS pulse compression algorithm for the distributed target in weather radar application. But all of these algorithms could not simultaneously deal with both the point target and distributed target. Due to lack of examining both types of target in developing pulse compression algorithms, the developed algorithms so far are easy to cause the interferences each other between the point target and the distributed target. Therefore, to avoid the interferences between these two types of target, a well performance pulse compression should be required to provide with the ability of processing both the point target and the distributed target. In this study, we use neural network backpropagation (BP) [0] to perform the processing of pulse compression with a B3 code of the sequence {,,,,,,,,,,,, }. The algorithm combines the Barker code with neural network to constitute the neural network pulse compression (NNPC). In LS, LP, and autocorrelation filter (ACF) [] algorithms, only the point target is considered to develop the pulse compression algorithm. However, we collect all the possible data sets occurred in the interaction process of a point target and a distributed target as the training data sets of NNPC. This will lead the NNPC, while the BP being well trained off line to deal with the radar echoes, to be a well performance of pulse compression. As a result, both the abilities of the point targets and distributed target detection and discrimination are increased in the radar system. The rest of this paper is organized as follows. Section 2 gives the problem statements. In section 3, we introduce the structure of NNPC used to process the pulse compression in radar system. In section 4, we present the performances of pulse compression for NNPC. Discussion and conclusion are made in sections 5 and 6, respectively.

4 86 FUN-BIN DUH AND CHIA-FENG JUANG 2. PROBLEM FORMUATION Pulse compression is a practical implementation of a matched filter in a radar signal processing. A filter is matched to an input signal and has a maximum output if the signal is complex conjugate of the time inverse of the filter s response to a unit impulse. When there is no Doppler shift present in the received signal u(t), the matched filter response is given by the convolution of the signal and the conjugate impulse response u * ( t) of the matched filter: * () χ(,0) t = u( λ) u ( t λ) dλ which results in an autocorrelation function of the transmitted signal with the received signal []. To apply the simplest type of phase code, the biphase code, we subdivide the transmitted pulse of duration T into N subpulses of duration τ = T/N. Hence, the modulation function of a signal with the biphase code consisting of N continuous rectangular pulses of equal amplitude can be written as N t nτ jθn u() t = rect e, θn = 0orπ Nτ n= 0 τ N t nτ +, θn = 0 = xrect n, xn = Nτ τ, θ = π n= 0 = u * () t (2) where the signal is normalized with the square root of the total signal duration, {x n } the code sequences with the values of + s and s, and the rectangular function rect( ) is defined as /2 t /2, rect() t = (3) 0 otherwise. Substitution of u(t) in autocorrelation function and considering u * (t) with a time delay t, we obtain n * χ( t t,0) = u( λ) u ( t t + λ) dλ N N λ mτ λ nτ t + t = xnxm rect rect dλ. Nτ τ τ n= 0 m= 0 (4) In this paper, the autocorrelation function can be obtained by calculating the values of the function at t t = kτ; i.e., the biphase waveform is sampled once per element at the inverse bandwidth sampling intervals, τ then the value of the integral is zero unless k = m n, so that the double sum in Eq. (4) reduces to a single sum [2]. Letting m = k + n, we obtain

5 N + N N N 2 N 3 N 0 N N N 2 2 N 2 N N N N 2 N N N N N PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET 87 N k χ( kτ,0) = xnxn+ k. (5) N n= 0 Eq. (5) is the direct autocorrelation function (ACF). For pulse compression processing, the most important effect for ACF is to achieve a high signal-to-sidelobe ratio under all possible practical environments encountered, such as induced noise interference, possible Doppler shift effect, and two close targets. The signal-to-sidelobe ratio of ACF is highly related to the code used, including code words and code length. Presently, the Barker code is more efficient than the others; however, the longest length of the Barker code is 3 elements, and without oversampling the greatest sidelobe reduction is 22.3 db [], which may not be sufficient for the desired radar applications. For the convenient, we rewrite Eq. (5) as y N k k xixi+ k N i= =, k = N +,, N. (6) Eq. (6) can be separated to two parts as follows: y N k = x x, k = N +,,, 0 (7) k i i+ k N i= N k y = x x, k =, 2,, N. (8) k i+ k i N i= When expanding Eqs. (7) and (8), we can obtain a matrix form, y x y x x x y x x x x 0 x y x x x x x x y = N 0 x x x x. y 0 0 x x x x x y x x y x (9) The vector in the right-hand side of Eq. (9) is the replica of the transmitted code. Alternatively they are the weightings for the received signal sequence. That is, we can express the above equation as y = (/N)XW, where matrix X is formed by the shifting of the input sequence {x i } and W is a weighting vector. Observing the matrix X, it defines 2N patterns, and the proper code word is in the Nth pattern. However, we must consider an additional null sequence, {0}, meaning no input signal exists. Subsequently there are 2N different sequences that may be encountered in the input of a pulse com-

6 88 FUN-BIN DUH AND CHIA-FENG JUANG pression network. Except that the output of proper code word sequence is, the others are expected to be 0. Thus the problem in acquiring the output sequence with high signal-to- sidelobe ratio and low ISL of pulse compression can be considered as a mapping of the received input sequences: y k = f(input sequences). (0) As the analysis described above, there exists a nonlinear mapping relationship between the received input sequence and the desired output. With the performance of being very suitable for nonlinear mapping, the neural network algorithm, BP, is proposed to compress the coded pulse while received. The received sequence of a point target with biphase code, which occupies a space much smaller than the radar resolution cell, can be exactly described as the above X matrix. But the received input sequence of the distributed target could be modeled as follows, because its echoes disperse more than the radar resolution cell [4, 3]. Based on the dispersed behavior of a distributed target, the subpulses are reflected one by one. Each subpulse in the transmit pulse defines a range bin. When the first subpulse disperses a range cell to arrive at the second range cell in a distributed target, the second subpulse arrives at the first range cell. Both echoes of the subpulse are reflected at the same time. For the next subpulse duration, when the first subpulse disperses from the second range cell to the third, the second subpulse moves from the first range cell to the second and the third subpulse arrives at the first range cell. Besides, the echoes of these subpulses are reflected simultaneously, and so forth. The dispersing behavior does not terminate until all subpulses pass through the distributed target area. Given that the time spacing between samples T s is equal to the subpulse duration τ. At sample-time index i, the sample of the time sequence received from the distributed target echoes can be represented as x i (m, n), m =,, n bins, and n =,, n p, where n bins is the number of range bins, and n p the number of subpulses. According to the echoes of the distributed target, the output of each sample instant exists all the subpulse echoes. The evolution of the dispersed echoes with step type and rectangular type at sample-time index i is shown in Figs. 2 (a) and (b). At any sample-time index i and the first rangesampling instant, the first subpulse echo encounters the first range bin x i (, ) contributing to the first sampled echo y(i, ). At the next range-sampling instant, the first subpulse echo now encounters the second range bin x i (2, ) and the second subpulse echo encounters the first range bin x i (, 2). Both range bins are combined to yield echo sample y(i, 2), and so forth. The output range cell can be mathematically described as y(, i j) = x ( m, n). () m+ n = j i For step-dispersed echo with B3 code as shown in Fig. 2 (a), the number of range bins n bins is 26, and the sequence of the output cells from y(i, 26) to y(i, ) is {5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 2,, 0,, 2,, 0,, 0, }. In practical application, we may normalize the amplitudes of the received input sequence to {,,,,,,,,,,,,,,.8,.6,.4,.2, 0,.2,.4,.2, 0,.2, 0,.2} by the gain control at receiver for avoiding saturation. Similarly, for the rectangular-dispersed echo with B3 code as shown in Fig. 2 (b),

7 PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET 89 Output Range Cell y(i,26)=5 + y(i,25)=5 + y(i,24)=5 + y(i,23)=5 + y(i,22)=5 + y(i,2)=5 + y(i,20)=5 + y(i,9)=5 + y(i,8)= y(i,7)=5 + y(i,6)=5 + y(i,5)= y(i,4)=5 n y(i,3)=5 + y(i,2)=4 + y(i,)=3 + y(i,0)=2 + y(i,9)= y(i,8)=0 + y(i,7)= y(i,6)=2 + y(i,5)= + y(i,4)=0 + y(i,3)= + y(i,2)=0 + y(i,)= m (a) The sequence of the 3-element Barker code for a 26-element step-dispersed echo is: {5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 2,, 0,, 2,, 0,, 0, }. Fig. 2. The evolution of dispersed target for a step dispersed echo and a rectangular-dispersed echo at sample-time index i. the sequence of the output cells from y(i, 27) to y(i, ) is {, 2, 3, 4, 5, 4, 3, 4, 5, 4, 5, 4, 5, 5, 5, 4, 3, 2,, 0,, 2,, 0,, 0, } and is normalized in amplitude to be {.2,.4,.6,.8,,.8,.6,.8,,.8,,.8,,,,.8,.6,.4,.2, 0,.2,.4,.2, 0,.2, 0,.2}. 3. PULSE COMPRESSION USING A NEURAL NETWORK In the following, we shall introduce the structure of the backpropagation (BP) neural network and how it is used to process the pulse compression in the modern radar system. 3. The Use of Backpropagation (BP) Neural Network to Process the Pulse Compression (NNPC) in a Radar System The block diagram of the digital pulse compression system using NNPC is shown in Fig. 3. The 3-element Barker code sequences generated by the Barker code generator are sent to RF modulator and transmitter, not the NNPC where the pulse compression is

8 90 FUN-BIN DUH AND CHIA-FENG JUANG Output Range Cell + y(i,27)= + y(i,26)=2 + y(i,25)=3 + y(i,24)=4 + y(i,23)=5 - + y(i,22)= y(i,2)= y(i,20)= y(i,9)= y(i,8)= y(i,7)= y(i,6)= y(i,5)= y(i,4)= y(i,3)= y(i,2)=4 n y(i,)= y(i,0)= y(i,9)= y(i,8)= y(i,7)= y(i,6)= y(i,5)= y(i,4)=0 - + y(i,3)= - + y(i,2)=0 + y(i,)= m (b) The sequence of the 3-element Barker code for a 5-element rectangular-dispersed echo is {, 2, 3, 4, 5, 4, 3, 4, 5, 4, 5, 4, 5, 5, 5, 4, 3, 2,, 0,, 2,, 0,, 0, }. Fig. 2. (Cont d) The evolution of dispersed target for a step dispersed echo and a rectangulardispersed echo at sample-time index i. System Timing I_channel I_det A/D Barker code Generator NNPC (BP) To RF Modulator and Transmitter Square Received IF Signal Subpulse Filter LO 90 o 2 Q 2 I + Detector Q_det Q_channel A/D NNPC (BP) Square Fig. 3. The block diagram of the digital pulse compression system using NNPC.

9 PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET 9 executed. The IF signals received are passed through a bandpass filter matched to the subpulse width and are demodulated by two detections, I_det and Q_det, with a localoscillator (LO) signal at the same IF frequency, and then the in-phase (I) and quadrature (Q) channel echo signals are detected respectively. These echo signals are converted to digital form by analog-to-digital (A/D) converters under the system timing control which also clocks the Barker code to be transmitted. The digital form of the echo signals consists of the Barker code and interfering noise. The NNPCs, which are implemented by the trained BP, carry out the pulse compression based on the received sequence. Once the echo sequence is matched with the transmitted Barker code, the output of each BP will be + with one subpulse duration. When the signal-to-sidelobe ratio of the NNPC output is very high, the false alarm of the detector is reduced, and eventually the detection ability of the radar system is enhanced. 3.2 Backpropagation (BP) Neural Network for Pulse Compression A multilayer feedforward neural network with the backpropagation (BP) learning algorithm [0] can be used for pulse compression to improve the performance of the pulse radar detection ability. The network has n input units, three hidden units, and one output unit, the structure of which for the 3-element Barker code is shown in Fig. 4. The output unit is a classifier, which has a value of if the code is used in received and presented as a whole in the input layer. The learning used here is the backpropagation with bias training. The sigmoid function is used as activation function of the neurons in the hidden and output layers. A bias unit always with a constant value of b is connected to all neurons directly in the hidden and the output layers to achieve a better classification. [2] a = Fs ( z z [2] [2] ) = w + w a [2] [] a [2] [] w + b a [2] [] 2 2 [2] w [2] w 2 [2] w 3 [] a [] [] w [] w 2 w 3 [] a 2 [] a3 = Fs ( z [] [] [] w 3 w 32 w 33 [] 3 ) [] [] [0] [] z3 = w3 a + w23a [] [0] + + w a + b 33 3 [0] 2 [0] a [0] a 3 ' x z ' x 2 z z ' x 3 Fig. 4. Structure of backpropagation neural network for 3-element barker code.

10 92 FUN-BIN DUH AND CHIA-FENG JUANG The neural network to be considered consists of L layer, where L = 3, starting from the layer 0 to the layer 2. The number of neurons in the hth layer is denoted by N h. Hence, the input layer is N 0 = n = 3, the hidden layer N is set to 50, and the output layer is N 2 =. Here, the sigmoid function is used and given by F s (z) = /( + e -z ). (2) Before using this network, it should be trained by presenting a training data set repeatedly to the input layer. Here, in the 3-element Barker code application, the training data set is just the time-shifted sequences with the magnitude + or of the code word. The desired output is when the whole code word is received, and 0, otherwise [4]. The output error of an input code pattern k is defined as ( d [2] 2 ek = ak a k ) (3) 2 d where a k represents the desired output and a [2] k is the obtained output at the output layer of an input code pattern k. Parameter learning is based on backpropagation learning algorithm with momentum term. 3.3 The Interaction Procedure of a Point Target and a Distributed Target The BP is repeatedly trained off-line with the training set. The training set is composed of the complete data extracted from the interaction procedures of a point echo and a rectangular distributed echo. We first set a point target apart from a distributed target by one subpulse distance. Then a radar echo sequence with a point target and a 3-element rectangular distributed target is received as shown in Table. This can represent all cases that a point echo and a distributed echo are without any interacting. In this case, the received sequence is the point target code sequence and the distributed target code sequence individually with zero(s) between these two targets. Meanwhile, we can set the desired outputs of the training sequence for the neural network to be zeros except the subpulse duration at the point target code and the subpulse durations between the rectangular distributed target codes being completely received. For more convenient to discriminate the point target and the distributed target, we set the output to be while a point target code sequence is received and the outputs to be 0.5 while the rectangular distributed target code sequence are received. Then the distributed target closes the point target by one subpulse duration. In this case, the point target echo and a distributed target echo are connected without any distance. This is the beginning of interactions. Obviously, while the distributed target is closing to the point target by one subpulse duration again, the combination output of a point target echo and a distributed target echo z at time index 3 is p(i, 3) + y(i, ) and the corresponding desired output for neural network training is, and so forth. When the interaction procedure goes the 5th step, we have completely received a point target code echo and a distributed target code echo simultaneously. In this situation, the desired output we set for neural network training is.5 to benefit for discriminating a point target and a distributed target, that is d =.5 at time index 3. At the 6th step, we start to

11 PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET 93 move the point target inside the distributed target subpulse by subpulse. When at the 28 step, the point target leaves the distributed target as shown in Table 2. Repeat above operations until the point target echo leaves the distributed target by one subpulse. Totally, there are 53 sequences acquired from this interaction procedure. Table. A point target echo and a distributed target echo exist at sample-time index I. Time Index p p(i,0) p(i,02) p(i,03) p(i,04) p(i,05) p(i,06) p(i,07) p(i,08) p(i,09) p(i,0) p(i,) y z p(i,0) p(i,02) p(i,03) p(i,04) p(i,05) p(i,06) p(i,07) p(i,08) p(i,09) p(i,0) p(i,) d p(i,2) p(i,3) y(i,0) y(i,02) y(i,03) y(i,04) y(i,05) y(i,06) y(i,07) y(i,08) y(i,09) p(i,2) p(i,3) 0.0 y(i,0) y(i,02) y(i,03) y(i,04) y(i,05) y(i,06) y(i,07) y(i,08) y(i,09) y(i,0) y(i,) y(i,2) y(i,3) y(i,4) y(i,5) y(i,6) y(i,7) y(i,8) y(i,9) y(i,20) y(i,2) y(i,0) y(i,) y(i,2) y(i,3) y(i,4) y(i,5) y(i,6) y(i,7) y(i,8) y(i,9) y(i,20) y(i,2) y(i,22) y(i,23) y(i,23) y(i,25) y(i,26) y(i,27) y(i,28) y(i,29) y(i,30) y(i,3) y(i,32) y(i,33) y(i,22) y(i,23) y(i,23) y(i,25) y(i,26) y(i,27) y(i,28) y(i,29) y(i,30) y(i,3) y(i,32) y(i,33) y(i,34) y(i,35) y(i,36) y(i,37) y(i,34) y(i,35) y(i,36) y(i,37) p: point target echo sequence, B3; y: distributed target echo sequence; z: the combination outputs of a point target echo and a distributed target echo z = p + y; d: the desired outputs for neural network training set. Time Index Table 2. The 28th interaction step of a point target and distributed target p p(i,0) p(i,2) y y(i,0) y(i,02) y(i,3) y(i,4) y(i,25) z y(i,0) y(i,02) y(i,3) p(i,0) + y(i,4) p(i,2) + y(i,25) d y(i,27) y(i,36) y(i,37) y(i,27) y(i,36) y(i,37)

12 94 FUN-BIN DUH AND CHIA-FENG JUANG 3.4 Training Neural Network as Pulse Compression The neural network, BP, is trained by a data set before being used as pulse compression function, NNPC. The training data set is extracted from the interaction behavior stated as above. From observing these interaction procedures, it is clear that all the different situations occurred between a point target and a distributed target are completely considered. The interaction procedure is started by separating the point target from the distributed target by one subpulse, then the point target is made one subpulse step forward to the distributed target, and terminated by separating a distributed target from a point target by one subpulse. Totally, 53 difference sequences are generated as B3 is used. The longest sequence among these difference sequences has 64 patterns and therefore we can totally obtain 3,392 patterns with some same patterns. To reduce the numbers of training patterns, we discard the same patterns and keep all possible different patterns, so that we can finally obtained only,90 patterns. In these training sequences, we set four different outputs for different situations. First, the desired output of the BP, d, is for the point target when the proper Barker code just presenting in the input. Second, the desired output is set to 0.5 for durations of the distributed target received. Third, when the point target and the distributed target are received simultaneously, the desired output is set to.5. Finally, the output is 0, otherwise. These settings lead the desired outputs of BP not only to easily isolate the point target and distributed target but also to have equal distances when the point target and the distributed target are received simultaneously. The BP was constructed something like [4, 5] and trained to stop by the convergence criterion of the maximum output error being less than for,90 time-shifted sequences of the 3-element Barker code. The output error of the input code pattern k, corresponding to the desired output and the training output is defined as Eq. (6). 4. SIMULATION RESULTS AND PERFORMANCE EVALUATIONS This section illustrates the performances of the proposed NNPC by comparing it with direct autocorrelation filter (ACF), least squares (LS) inverse filter, and linear programming (LP) filter based on 3-element Barker code. To evaluate the effect of the proposed NNPC algorithm to pulse compression, while compared with these traditional algorithms, we used the discrimination rate, signal-to-sidelobe ratio and ISL as the performance evaluation in the following subsections. Before using the NNPC algorithm, we should train the BP by entering a training set to its input layer. 4. Ability to Discriminate Point Target and Distributed Target To know all the features about the target from the radar echo is very difficult. However, it is one of the important demands of modern radars. Before accomplishing this object, the first step is to discriminate the target from received echoes which include point target and distributed target. In addition to the discriminate point target and distributed target, it is necessary to discriminate the sidelobes, which is the by-product of pulse compression, from these two kinds of targets. Hence, we define the discrimination rate ρ d to specify the ability after the pulse compression processing as

13 PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET 95 P D ρd ( db) = 20log Dmax S min max (4) where P is the amplitude of the point target, D max is the maximum amplitude of the distributed target, D min is the minimum amplitude of the distributed target, and S max is the maximum amplitude of the sidelobe. We construct a testing sequence as shown in Table 3, in which a point target locates on the middle of a distributed target to examine this ability. The comparison results of the discrimination performance of the NNPC, ACF, LS, and LP algorithms are shown in Fig. 5 when B3 is used, and the discrimination rate is 57.32dB, 4.83dB, 7.dB, and 6.09dB, respectively. Table 3. A sequence for testing the discrimination ability of the algorithms for point target and distributed target. Time Index p p(i,0) p(i,02) p(i,03) p(i,04) p(i,05) y y(i,0) y(i,02) y(i,03) y(i,04) y(i,05) y(i,06) y(i,07) y(i,08) y(i,09) y(i,0) y(i,) z y(i,0) y(i,02) y(i,03) y(i,04) y(i,05) y(i,06) y(i,0) p(i,02) p(i,03) p(i,04) p(i,05) +y(i,07) +y(i,08) +y(i,09) +y(i,0) +y(i,) d p(i,06) p(i,07) p(i,08) p(i,09) p(i,0) p(i,) p(i,2) p(i,3) y(i,2) y(i,3) y(i,4) y(i,5) y(i,6) y(i,7) y(i,8) y(i,9) y(i,20) y(i,2) y(i,22) y(i,23) p(i,06) p(i,07) p(i,08) p(i,04) p(i,05) p(i,06) p(i,07) p(i,08) y(i,20) +y(i,2) +y(i,3) +y(i,4) +y(i,0) +y(i,) +y(i,2) +y(i,3) +y(i,4) y(i,2) y(i,22) y(i,23) y(i,24) y(i,25) y(i,26) y(i,27) y(i,28) y(i,29) y(i,30) y(i,3) y(i,32) y(i,33) y(i,34) y(i,35) y(i,24) y(i,25) y(i,26) y(i,27) y(i,28) y(i,29) y(i,30) y(i,3) y(i,32) y(i,33) y(i,34) y(i,35) y(i,36) y(i,37) y(i,36) y(i,37) Range Resolution Performance The range resolution performance is the examination of the ability to discriminate between two targets solely by measurement of their ranges in a radar system. To resolve these two types of target in range, the basic criterion is that the targets must be discriminated by at least the range equivalent of the width of the processed echo pulse. Obviously when a point target is discriminated from a distributed target, it is significant in any applications to clearly discriminate them to avoid disturbance and mixing up each other [2, 3, 5].

14 96 FUN-BIN DUH AND CHIA-FENG JUANG Fig. 5. The discrimination performance comparison results of the ACF, LS, LP, and NNPC algorithms for 3-element Barker code. To compare the range resolution ability between NNPC, ACF, LS, and LP algorithms, the targets discriminated from one subpulse delay-apart each other are simulated, and the signal-to-sidelobe ratio and ISL from the outputs of these algorithms are examined, respectively. For this performance examination, two test patterns are generated. That is, the point target is before and after the distributed target by one subpulse, respectively. A test sequence generated by a point target before a distributed target is shown in Table 4. The other test sequence generated by a point target after a distributed target is something like this pattern. The comparison results of the range resolution performance of the NNPC, ACF, LS, and LP algorithms are shown in Fig. 6 when the B3 is used. The performance comparisons in Fig. 6 on signal-to-sidelobe ratio (SNR) [3, 5] and integrated sidelobe level (ISL) [2, 4, 3, 5] defined as follows are shown in Table 5. (a) Simulation results of test sequence generated by a point target before a distributed target. Fig. 6. The comparison results of range resolution performance of the NNPC, ACF, LS, and LP algorithms.

15 PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET 97 (b) Simulation results of test sequence generated by a point target after a distributed target. Fig. 6. (Cont d) The comparison results of range resolution performance of the NNPC, ACF, LS, and LP algorithms. Table 4. A test sequence of point target before a distributed target. Time Index p p(i,0) p(i,02) p(i,03) p(i,04) p(i,05) p(i,06) p(i,07) p(i,08) p(i,09) p(i,0) p(i,) y y(i,0) y(i,02) y(i,03) y(i,04) y(i,05) y(i,06) y(i,07) y(i,08) y(i,09) z p(i,0) p(i,02) p(i,03) p(i,04) p(i,05) p(i,06) p(i,07) p(i,08) p(i,09) p(i,0) p(i,) +y(i,0) +y(i,02) +y(i,03) +y(i,04) +y(i,05) +y(i,06) +y(i,07) +y(i,08) +y(i,09) d p(i,2) p(i,3) y(i,0) y(i,) y(i,2) y(i,3) y(i,4) y(i,5) y(i,6) y(i,7) y(i,8) y(i,9) y(i,20) y(i,2) p(i,2) p(i,3) +y(i,0) +y(i,) y(i,2) y(i,3) y(i,4) y(i,5) y(i,6) y(i,7) y(i,8) y(i,9) y(i,20) y(i,2) y(i,22) y(i,23) y(i,24) y(i,25) y(i,26) y(i,27) y(i,28) y(i,29) y(i,30) y(i,3) y(i,32) y(i,33) y(i,34) y(i,22) y(i,23) y(i,24) y(i,25) y(i,26) y(i,27) y(i,28) y(i,29) y(i,30) y(i,3) y(i,32) y(i,33) y(i, y(i,35) y(i,36) y(i,35 y(i,36)

16 98 FUN-BIN DUH AND CHIA-FENG JUANG Table 5. The performance comparisons of range resolution on signal-to-sidelobe ratio (SNR) and ISL (db). Algori. Point target before distributed target Point target after distributed target Perform. NNPC ACF LS LP NNPC ACF LS LP SNR ISL mainlobe power SNR = 0 log, maximum sidelobe power power integrated over sidelobes ISL = 0 log. mainlobe power 4.3 Noise Robustness Any signal other than the target echoes in the radar receivers is considered as noise. Noise is a random signal, which interferes with target echoes. The noise added in the signal is passed through the mixing and amplification processes in radar receiver before reaching the pulse compression process. If the noise is large enough, it can mask completely the true target echoes so that the performance to examine the noise rejection ability of the pulse compression cannot be neglected [3, 5]. The input signals used to evaluate the noise robustness are generated by a 3-element Barker code, and both of them are perturbed by additive white Gaussian noise with noise strength, σ n = 0.3, 0.5, and 0.7. Two kinds of target are considered in this paper, therefore we examine the signal to the maximum sidelobe ratio and ISL performances for the point target and distributed target, respectively. Carefully inspecting the distributed target responses for ACF, LS, and LP algorithms, we can find that the distributed target is extended in range about a distributed target length after pulse compression. This extended range indeed affects the detection for nearby target, but unlike the sidelobe being dispersed around the target, it directly joins the true distributed target and can be looked as a fake part of a distributed target. Hence when evaluating the signal to the maximum sidelobe ratio, we would calculate the intensity of the distributed target, including the fake part to represent the signal of the distributed target. The noise performance comparison result of the NNPC, ACF, LS, and LP algorithms with noise strength of 0.3 for 3-element Barker code is shown in Fig. 7, and the performance comparisons on signal-to-sidelobe ratio and ISL with noise strength, σ n = 0.3, 0.5, and 0.7 are shown in Table 6. Table 6. The performance comparisons of noise robustness on signal-to-sidelobe ratio and ISL. Signal-to-sidelobe ratio (in db) ISL (in db) Perform. (Point target, distributed target) (Point target, distributed target) Algo. σ n = 0.3 σ n = 0.5 σ n = 0.7 σ n = 0.3 σ n = 0.5 σ n = 0.7 NNPC (24.8, 42.8) (22.4, 40.4) (6.6, 30.9) (28.9, 33.) (0.3, 2.8) (2.3, 4.6) ACF (5.5,28.4) (5.5, 28.4) (3.4, 26.4) ( 7.4, 5.6) ( 0.2, 2.9) ( 2.6, 0.9) LS (5.5, 26.3) (5.5,26.4) (4.4, 26.) ( 5.5, 5.3) ( 9.4,.7) ( 2.2, 0.5) LP (6., 30.7) (6., 30.8) (3.8, 26.7) ( 6.9, 5.7) ( 0.2, 2.2) ( 2.8, 0.)

17 PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET 99 Fig. 7. The comparison results of noise robustness performance of the NNPC, ACF, LS, and LP algorithms with the noise intensity σ n = DISCUSSION From the results of the performance examinations on the ability to discriminate the target and distributed target in section 4, NNPC algorithm has higher discrimination rate than other algorithms. This means that NNPC is more effective to discriminate the point target, distributed target, and sidelobes, which leads the NNPC algorithm to be a better pulse compression processor than other algorithms. Fig. 5 shows that if a point target and a distributed target are to be effectively discriminated, they must have a larger distance. However, this will make the distributed target and the surrounding sidelobes hard to be isolated. Thus it makes the surrounding sidelobes to smear the distributed target. On the contrary, when the distributed target has a larger distance from the sidelobes, it will cause the point target and the distributed target in short distance and lead them to interfere with each other. Thus it makes a dilemma between them. To solve this dilemma, the surrounding sidelobes should be smaller and the fluctuation of the distributed target should be slight. Besides, when the distance between the point target and distributed target is equal to that between the distributed target and the sidelobes, it is helpful to discriminate them. As the NNPC can be trained to have the output with equal distances among the point target, the distributed target, and the null target, this benefits NNPC to have more effective range to discriminate them. In addition, a well-trained NNPC also provides low surrounding sidelobes and slight fluctuations in the distributed target. All of these contribute NNPC to have better discrimination ability than other algorithms. Because the range resolution is related to the ability to distinguish two closed targets, high range resolution radar, therefore, should be applied to avoid incidents in any applications. To examine the influence of a point target and a distributed target on range resolution each other, two sequences that a point target locates before and after a distributed target by one subpulse are generated. These are the closest situations for the discriminated point target and distributed target. From the simulation results, Fig. 6 shows that the ACF, LS, and LP algorithms extend the distributed target in time index from 28 to 39, which is about a distributed target length. This drawback will smear the target just near

18 200 FUN-BIN DUH AND CHIA-FENG JUANG to the distributed target. The NNPC algorithm is without the extension and with low surrounding sidelobes. Table 5 shows that the NNPC algorithm has signal-to-sidelobe value of db, while the other algorithms about 20 db for the point target before the distributed target situation. On the other hand, the NNPC algorithm has signal-to-sidelobe value up to db, while the other algorithms about 25 db for the point target after the distributed target situation. 6. CONCLUSION A backpropagation neural network approach to radar pulse compression is proposed in this paper to discriminate the point target and the distributed target simultaneously existed in radar echoes signal. This algorithm is called neural network pulse compression, NNPC. The detail interaction procedures of the point and the distributed target are illustrated completely, and thus generate the training patterns for the neural network. The success, based on the ease-implementing 3-element Barker code, is due to the NNPC being well trained by a data set extracted from the complete interactions of a point target and a distributed target, which, thereafter, can clearly discriminate the point echo and the distributed target. While compared with traditional algorithms, NNPC has achieved higher range resolution and noise rejection ability. Moreover, it is worthy to point out that the conventional algorithms have an extension of the distributed target in range about a distributed target length. This is harmful to range resolution. These examining results lead NNPC to be very suitable not only for air traffic radar but also for the weather radar applications as both require high signal-to-sidelobe ratio and low ISL. Obviously with the NNPC, the radar can further provide a better performance in target recognition applications. REFERENCES. D. K. Barton and S. A. Leonov, Radar Technology Encyclopedia, Artech House, J. M. Ashe, R. L. Nevin, D. J. Murrow, H. Urkowitz, N. J. Bucci, and J. D. Nespor, Range sidelobe suppression of expanded/compressed pulses with droop, in Proceedings of the IEEE International Radar Conference, 994, pp N. J. Bucci, H. S. Owen, K. A. Woodward, and C. M. Hawes, Validation of pulse compression techniques for meteorological functions, IEEE Transactions on Geosci. Remote Sensing, Vol. 35, 997, pp A. S. Mudukutore, V. Chandrasekar, and R. J. Keeler, Pulse compression for weather radars, IEEE Transactions on Geosciences Remote Sensing, Vol. 36, 998, pp J. L. Eaves and E. K. Reedy, Principles of Modern Radar, Van Nostrand Reinhold, R. W. Fetter, Radar weather performance enhanced by pulse compression, in Preprints, the 4th ASM Conference on Radar Meteorology, 970, pp R. W. Gray and D. T. Farley, Theory of incoherent-scatter measurements using compressed pulses, Radar Sciences, Vol. 8, 973, pp

19 PULSE COMPRESSISON FOR POINT TARGET AND DISTRIBUTED TARGET M. H. Ackroyd and F. Ghani, Optimum mismatched filters for sidelobe suppression, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-9, 973, pp S. Zoraster, Minimum peak range sidelobe filters for binary phase-coded waveforms, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-6, 980, pp C. T. Lin and C. S. G. Lee, Neural Fuzzy Systems: A Neuro-Fuzzy Synergism to Intelligent Systems, Englewood Cliffs, Prentice-Hall, NJ, M. I. Skolnik, Introduction to Radar Systems, McGraw-Hill Book Co., NY, A. W. Rihaczek, Principles of High-Resolution, Peninsula Publishing, F. B. Duh, C. F. Juang, and C. T. Lin, A neural fuzzy network approach to radar pulse compression, IEEE Geoscience and Remote Sensing Letters, Vol., 2004, pp K. D. Rao and G. Sridhar, Improving performance in pulse radar detection using neural networks, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-3, 995, pp H. K. Kwan and C. K. Lee, A neural network approach to pulse radar detection, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-29, 993, pp Fun-Bin Duh ( ) received the B.S degree in Electronic Engineering and M.S. degree in Automatic Control Engineering from the Feng Chia University, Taichung, Taiwan, R.O.C., in 98 and 983, respectively, and the Ph.D. degree in the Department of Electrical and Control Engineering from the National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in Since 983, he has been with the Chungshan Institute of Science and Technology, Taiwan. He is currently a part-time assistant Professor of Electronic Engineering at Feng Chia University. His current research interests are digital signal processing, neural network, estimation theory, radar tracking system, servo control system, and VHDL digital system design. Chia-Feng Juang ( ) received the B.S. and Ph.D. degrees in Control Engineering from the National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 993 and 997, respectively. From 999 to 200, he was an Assistant Professor of the Department of Electrical Engineering at the Chung Chou Institute of Technology. In 200, he joined the National Chung Hsing University, Taichung, Taiwan, R.O.C., where he is currently an Associate Professor of Electrical Engineering. His current research interests are computational intelligence, intelligent control, computer vision, speech signal processing, and chip design.