Electronics and Communications in Japan, Part 1, Vol. 90, No. 1, 2007 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J87-B, No. 10, October 2004, pp. 1771 1783 Element-Localized Doppler STAP (Space Time Adaptive Processing) for Clutter Suppression in Automotive Forward-Looking RADAR Takayuki Inaba Information Technology R&D Center, Mitsubishi Electric Corporation, Kamakura, 247-8501 Japan SUMMARY Key words: automotive radar; STAP; MSN filter. In forward-looking radars such as automotive radars, it is necessary to suppress the reflected undesirable signal (clutter) from such objects as the ground surface (especially hills), guard rails, and buildings, in order to detect moving targets ahead. When using a pulse-doppler filter (PDF), which is the conventional method for clutter suppression, separation is difficult when the velocity of the target relative to the clutter is small. In this paper, as a high performance clutter suppression method for such low-velocity targets, we propose element-localized Doppler space time adaptive processing (ELD-STAP), which includes a PDF in the preprocessing, and which uses an array antenna. In the proposed ELD-STAP, only the PDF output corresponding to the Doppler frequency breadth of the clutter, predicted from the speed of the vehicle on which it is mounted, is selected for applying STAP, and hence the dimension of the data vector, which is the greatest difficulty in the application of STAP, can be reduced. By reducing the dimension of the data vector, not only the computation load, but also the number of cells that must be referenced to estimate the clutter correlation matrix (called secondary cells), can be reduced. Computer simulation reveals that the proposed ELD-STAP yields an improvement factor better than that provided by the combination of PDF and multibeam forming (MBF). 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 90(1): 77 89, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20221 1. Introduction As part of an intelligent transport system (ITS), research and development efforts are being made for a collision prevention technology using a millimeter-wave-band automotive radar as the sensor. By detecting danger early with an automotive radar so as to control the vehicle safely, it is hoped that collisions can be avoided or damage can be reduced. Hence, an automotive radar must measure the distance and angle of the vehicles and accurately predict their motion. However, in order to limit false detection and accurately detect the target, the challenge is to suppress interference from the radars of opposing traffic and unnecessary reflections of the signals transmitted by the user s own radar (clutter), from such things as the road surface (especially hills), guard rails, construction signs, and buildings. Recently, some automotive radars have appeared, but they are intended to be used only under good conditions, such as on trunk highways [1]. To enable their use on regular roads, further improvements in interference suppression and clutter suppression are desirable. In particular, when the vehicle ahead has slowed and is stopping, as in traffic congestion, the difference in Doppler frequency between the clutter and the reflected signal from the vehicle ahead becomes small, and effective detection of the vehicle ahead is possible only by providing clutter suppression with high resolution. 77 2006 Wiley Periodicals, Inc.
We have proposed a new method of interference suppression signal processing that suppresses the interference from the opposing traffic by using an array antenna as the automotive radar [2]. This method suppresses the interference when the interference and the desired signal are in the main beam direction, and in addition, it allows angular measurement of the desired signal with few snapshots. However, in this method, high-performance suppression of interferences is made possible by stopping transmission from the vehicle s own radar in order to get reception data containing only the interference. The clutter which is the object of suppression in this paper, is received only as the unnecessary signal when a radar signal is transmitted, and thus the method proposed in Ref. 2 cannot be applied to it. Also, clutter has different physical characteristics: for example, the interference from the opposing traffic does not have a wide range of angles of incidence, but since the clutter has many reflection points, its angle of incidence has a wide range of variation, and hence a different countermeasure is required. In this paper, we discuss a clutter suppression method to improve the detection performance for slowly moving targets. In the field of clutter suppression, the processing in time series called the pulse-doppler filter (PDF) is well known and is commonly utilized in applications such as aircraft radar [3 5]. The baseband signal received by the radar is a superposition of signals having a Doppler frequency dependent on the relative velocity of each of the reflection points. PDF is a method that forms a Doppler filter bank by applying the fast Fourier transform (FFT) to a data sample in the transmitted pulse series at each delay time (range samplings). By eliminating the aforementioned PDF output filter for the relative velocity of the clutter reflector deduced from the vehicle s own speed, it is possible to eliminate clutter reflected from stationary objects. However, in order to improve the frequency resolution, the number of pulses transmitted must be increased and the response time for target detection and the like will be increased. In order to search a wide coverage angle and also improve the response time, there is a tendency to use phased array antennas in automotive radar [1]. In a radar equipped with an array antenna, simultaneous multibeam forming (MBF) is possible by digitally processing in the baseband. Beam formation consists of applying the Fourier transform in the array element direction, and MBF directed in even intervals is accomplished by the FFT. However, to make the beam width narrower and improve the angular resolution, an antenna with a large aperture would be necessary. To address these issues, in a radar equipped with an array antenna, space time adaptive processing (STAP) has been proposed as a two-dimensional clutter suppression filter to provide a resolution exceeding the Doppler frequency resolution and the beam width [6], and it is being actively investigated as a method of moving target detection for side-looking radars used for airborne early warning [7 15]. However, there has not yet been any discussion of the application of STAP to automotive radars. Therefore, in this paper we discuss the application of STAP to automotive forward-looking radars. In applying STAP, deciding how to reduce the dimension of the data vector (= number of array elements number of pulses) is the greatest challenge. Reduction of the dimension of the data vector is an important issue not only for reducing the computational load, but also for maintaining the core performance of the STAP. Namely, while the STAP weights consist of the inverse matrix of the clutter correlation matrix, the accuracy of estimation of this correlation matrix is dependent on the number of referenced cells (called secondary cells; the clutter must be homogeneous over this region). Therefore, as the dimension of the data vector increases, the number of required secondary cells increases, and inhomogeneity of clutter among those secondary cells becomes an issue. In this paper, we propose element-localized Doppler space time adaptive processing (ELD-STAP), which, in order to reduce the dimension of the data vector, includes a PDF as preprocessing, and, assuming that the speed of the radar mounted platform (namely, the own vehicle) is a known quantity, utilizes the filter number in the PDF filter bank that includes the clutter. In STAP according to the proposed method, the dimension of the data vector can be reduced to as low as the product of the number of filters that include the clutter and the number of array elements. Pulse-Doppler radar and STAP signal processing are explained in Section 2. After an explanation of the characteristics of clutter in an automotive forward-looking radar, an ELD-STAP method is proposed in Section 3. A comparative evaluation of the proposed ELD-STAP and other conventional methods is made by computer simulation in Section 4. The conclusion of this paper is presented in Section 5. 2. Pulse-Doppler Radar and STAP Signal Processing A pulse-doppler radar is a radar that transmits a continuous signal in pulses, switching between transmission and reception, and reception is performed with a fixed delay time with respect to the transmitted pulse, where the received signal in the series of each pulse is expressed as a sampling signal having the same phase as the transmitted pulse. Generally, each pulse undergoes spectrum spreading within the pulse, but in this paper, the inverse process (called pulse compression in the radar field) is omitted for brevity, and the transmitted and received pulses are as- 78
sumed to be short pulses (pulse width T P ) corresponding to the required range resolution. The interval between the transmitted pulses is called the pulse repetition interval (PRI, T PRI ). It is assumed that the target object can be treated as coherent over M transmitted pulses, and this time period is called the coherent processing interval (CPI, T CPI ). Namely, The timing diagram of a pulse radar is shown in Fig. 1(a). Pulse radars are, in general, categorized according to the length of the PRI, and when the PRI is long, allowing the range corresponding to the maximum subscript K (= ct PRI /2 = ckt P /2) to be longer than the supposed maximum detection range R max, there is no ambiguity in the range and the radar is called a low-pulse repetition frequency (Low-PRF) radar. Conversely, when the PRI (= 1/PRF) is short and the PRF is larger than the supposed maximum Doppler frequency of the target, f d,max, there is no ambiguity in the Doppler frequency (relative velocity), and such a radar is called a high-pulse repetition frequency (High-PRF) radar. However, in an automotive radar, the required maximum detection range is shorter than in airborne radars, and the relative target velocity is relatively small; thus, it has no ambiguity in either the range or the velocity. The detailed specifications of automotive radars are explained in Sections 3 and 4. The reception data set measured by a pulse radar equipped with an array antenna is a set of three-dimensional data consisting of three variables, namely, the range (k), element (n), and pulse (m), as shown in Fig. 2. The reception (1) data vector, with the antenna element series as the vector element, is x(k, m) C N (k = 1,..., K; m = 1,..., M) N is the number of elements in the array antenna. The data vectors in the same range cell k are considered to be reflected signals from reflectors at the same range. Also, examining the data samples in the pulse sequence along a constant range cell k, a coherent sinusoidal signal with a Doppler frequency that is dependent on the relative velocity of the reflectors occurring at that range is observed. Further, in general, the incident wave is considered to be a plane wave, and hence on examining the samples along the element, a sine wave signal with a frequency that is dependent on the direction of arrival is observed. We next explain the STAP signal processing that uses the three-dimensional reception data shown in Fig. 2. As shown in Fig. 1(b), the data vector of a certain range cell k is examined. This examined cell is called the primary cell (or test cell). The reception data matrix at the range cell k, X(k) C N M, is expressed as follows: where the elements of this data matrix X(k) are rearranged to define a one-dimensional data vector, X ~ (k) C NM 1, as follows: Here T denotes the transpose of a matrix. (2) (3) Fig. 1. Schematic diagram of radar pulse timing. 79
(6) Here J is the number of main eigenvalues (the number of clutter eigenvalues). Also, the approximation on the right holds when the clutter power (the main eigenvalue) is sufficiently larger than the noise power (the noise eigenvalue). Finally, the inner product of the measured data vector in the primary cell (that with a possibility of containing the target) and the aforementioned weight gives the filter output: Fig. 2. Data cubic of pulse radar reception signals. In order to obtain the weight of the STAP filter corresponding to the one-dimensionalized data vector, the correlation matrix R c is estimated from the data vectors before and after the primary cell, X ~ c(τ): where H denotes the complex conjugate transpose, * denotes an averaging operation over several range cells before and after the primary cell, each called a secondary cell: k k τ < k, k < τ k + k [see Fig. 1(b)]. The subscript c indicates that these secondary cells contain clutter, but not the target. In general, in pulse compression radars, to reduce the adverse effect of the target s range side lobe on STAP performance, several cells before and after the primary cell are eliminated as guard cells, but the discussion of the guard cell is omitted here for brevity. In this paper, the clutter in the secondary cell is assumed to be homogeneous. Namely, it is assumed that: these secondary cells do not contain other targets but only have clutter and internal noise; the time variation of the clutter is sufficiently small during the target s coherent processing interval (T CPI ); and the clutter power has the same probability density distribution and is independent in each secondary cell. Hence, from the inverse matrix of the clutter correlation matrix R c and the desired wave s space-time steering vector s, the STAP weight is obtained [6, 7] as where R c 1 is calculated by performing an eigen-expansion of R c and using its main eigenvalue λ j and eigenvector e j and the eigenvalue of the noise σ [1, 7, 8]: (4) (5) Thus, a two-dimensional maximum signal-to-noise ratio (MSN) filter called STAP is implemented [7]. In radars, since the purpose is to obtain the range cell that contains the target, the processing expressed by Eqs. (3) to (7) is performed on each range cell k, treating it as the primary cell, and target detection is performed by threshold value processing of the amplitude of the output y(k), which is a signal in the range cell series. In applying STAP, the number of secondary cells to use is an important issue. When using twice the dimension of the data vector X ~ (= NM) as the number of secondary cells, at 50% probability, the loss compared to the optimal filter has been shown to be 3 db or less by Reed, Mallett, Brennan, and others (RMB rule) [9]. Also in the cases where the clutter is a superposition of reflected signals from many reflection points, exceeding the data vector dimension in number, when the displaced phase center antenna (DPCA) condition is satisfied, namely, in a side-looking linear array, if the antenna element spacing d satisfies d = n T PRI, Brennan s group reported that the number of clutter eigenvalues J can be expressed as [10, 11] where n is the velocity of the platform. Thus, the challenge in applying STAP is that the dimension of the data vector becomes NM, and hence the computational load in calculating the inverse matrix of the correlation matrix is large. For example, as described later, if M is about 64 pulses and the element number N is 9 elements, for each primary cell the calculations of Eqs. (3) to (7) must be performed in real time on a 576-dimensional data vector, which would be a large computational load. In addition, as mentioned, if the dimension of the data vector is large, the number of secondary cells required for estimating the correlation matrix is also large. For example, if we take the required number of secondary cells to be the aforementioned 2NM, it would be 1152 cells. Even if the width of one cell (range resolution) is sufficiently small, (7) (8) 80
about 37 cm (T P = 5 ns), the region of the secondary cells would be 426 m, which is larger than the maximum detection range required of automotive radars, and hence the application of STAP would be unrealistic. Also, it must be homogeneous among the secondary cells, and thus it would be unrealistic in that regard as well. As a countermeasure, a method of detecting inhomogeneity by using the asymptotic formula of the inverse matrix of the correlation matrix and trying to reduce its influence has been proposed [12]. On the other hand, the data space to apply STAP for a range cell k could be selected, as shown in Fig. 3, from: the angle pulse space obtained by applying MBF based on the measured data (element pulse data); the element Doppler space obtained by applying the PDF; or the angle Doppler space obtained by applying both. By performing these conversions in the preprocessing for STAP, if the clutter is localized in the STAP for that space, the dimension itself can be reduced. For example, in Ref. 13, a method called joint domain localized STAP (JDL-STAP) is proposed, in which, to reduce the dimension of the STAP, the FFT (namely, PDF + MBF) is taken in the pulse and element series during preprocessing in order to convert to the angle Doppler space, and then, in that space, STAP processing divided into multiple local areas is performed. In JDL-STAP, for the desired angle Doppler frequency, the local area surrounding it is made into a data vector to separately calculate the correlation matrix [13, 14]. However, to avoid degradation of STAP performance in this space, the array s mutual interference and interelement variation in the amplitude and phase must be small. Also, only nondirectional linear arrays can be used. However, due to the difference between these assumptions and real-life arrays, orthogonality among the multibeams by FFT cannot be maintained, and the problem arises that a target in the element-pulse space is not localized at one point in the beam space [14, 15]. Also, it has been pointed out that there are constraints, such as the directional pattern can be restricted, or the window below the side lobe cannot be used [15]. On the other hand, the above-mentioned interelement variation in the amplitude and phase does not exist in the PDF, which is the FFT in the pulse series, and the use of only the linear array, that is, the limitation of using only evenly spaced sampling, is not considered to be an operational constraint. 3. The Proposed Element-Localized Doppler STAP Method 3.1. Characteristics of clutter in automotive forward-looking radar The status of the moving vehicle assumed in this paper is shown in Fig. 4. The vehicle ahead is the target and the wave reflected from it is the desired wave. Vehicles in the opposing traffic are also transmitting radar waves, which are incident on the radar of the vehicle under consideration as interference waves. The waves transmitted from the own vehicle s radar and reflected back from the road surface or the guard rail on the side toward the emitting radar to form a signal constitute clutter. In a pulse radar, the road surface and guard rails in the same range cell as the target will constitute the problem. In the constant range cell, the angle Doppler distribution of the clutter and the interference wave would have the characteristics shown in Fig. 5. The interference wave s incident angle range is narrow and its frequency is broadly distributed within the band. In general, clutter can come from any angular direction, and its Doppler frequency has a maximum in the frontal direction (0 direction) and minima on both sides, and the frequency value is dependent on the speed of the vehicle under consideration. The Doppler frequency in the frontal direction is (9) In the azimuthal angle (φ) direction, it is (10) Fig. 3. Relationship between data spaces. where n and λ are the self speed and the wavelength, respectively. Combined PDF and MBF processing, which is the method currently in common use for suppressing clutter, forms a filter bank having a lattice-shaped gain in the angle Doppler space shown in Fig. 5. On the other hand, as shown in Eqs. (3) to (7), STAP is an MSN filter based on two-dimensional data, and hence the detection performance 81
Fig. 4. Schematic diagram of vehicle location. for a target in the vicinity of the clutter spectrum, as shown in Fig. 5, is expected to improve. The STAP processing can be applied to cases where the clutter and the interference coexist, as shown in Fig. 5, but in this paper it will be explained as a clutter suppression method omitting the interference, for brevity. First, in an automotive millimeter-wave radar, taking the transmission frequency to be f = 76.5 GHz and the self speed to be n = 50 km/h, the Doppler frequency of the ground surface clutter would be 7.083 khz. Assuming the azimuth angle coverage to be ±30 (approximately ±10 in the currently available radars, with further widening in prospect [1]), the Doppler frequency at both ends of the coverage would be 6.134 khz. The difference between the frontal and edge frequencies would be 949 Hz. On the other hand, taking the maximum relative velocity to be approximately ±180 km/h, the PRF of the transmitted wave to be 50 khz (PRI = 20 µs), and the velocity resolution to be 5 Fig. 5. Clutter and interference spectrum in Doppler-azimuth angle. km/h, the pulse number M (the PDF number, i.e., the number of points in FFT in the pulse series) would be 64 and the CPI would be 1.280 ms (the reciprocals of the filter bandwidths in the PDF). Combining the above, the bandwidth of each filter in the PDF would be 781 Hz, and the road surface clutter at the self speed (Doppler frequency breadth 949 Hz) would be contained in 2 filters among the PDF bank, or depending on the relation between the central frequency of the clutter and each filter in the PDF bank, it would be contained in 3 filters. This shows that among the 64 filters in the PDF bank, other than the aforementioned 2 or 3 filters containing the clutter, the remaining 61 or 62 filters are clutter free. Thus, in an automotive millimeterwave radar parameter, the clutter spectrum is localized in the Doppler space. On the other hand, as mentioned above, the clutter can come from any angular series, and thus it is not necessarily localized in the angle space. 3.2. The proposed element-localized Doppler STAP method As explained in the previous section, in an automotive forward-looking millimeter-wave radar, the clutter spectrum is localized. Therefore, we propose the elementlocalized Doppler STAP (ELD-STAP) method, in which PDF preprocessing is performed, and in the PDF bank, based on the self speed and coverage range, a few filters are selected to perform STAP processing on their output. Namely, we apply STAP processing to the output from the selected filters, but perform the regular MBF processing on the other filter outputs. Thus, by selecting the filter that contains the clutter based on the self speed, with information obtained in advance, the challenge in applying STAP, namely, reduction of the dimension of the data vector, can be met. The signal processing schematic for the proposed ELD-STAP is shown in Fig. 6. The explanation of this processing follows. 82
Doppler frequency given by Eq. (9) to be f d0 and the required maximum coverage angle to be ±φ 0 : (18) Fig. 6. Schematic diagram of proposed automotive forward-looking space-time adaptive processing. (1) The pulse-doppler filter (PDF) The steering vector s t ( f ~ d) for the PDF and the steering vector s s (φ) for the MBF are expressed as We select the filter number m that satisfies the formula above as the filter for STAP. Let the selected filter numbers be m = 1, 2,..., M (m = L, L + 1,..., L + M 1), and let these be the input for STAP processing. Here M is the number of filters selected, and L is the first one among them in the sequence. We rearrange the output data vector of the selected filter into a one-dimensional data vector, as in Eq. (3): (19) (11) where the array antenna is assumed to be a uniform linear array in which the antenna element spacing is equi-interval. The normalized Doppler frequency f ~ d and space frequency α are expressed as PDF processing is implemented by multiplying the steering vector of formula (11) by the measured data vector X(k) C N M of the primary cell (range cell k): where the asterisk denotes the complex conjugate. A filter bank can be created by the FFT if the steering series for the PDF is taken to be equally spaced, as follows: The output from filter number m in the PDF bank is expressed as (2) Pulse-Doppler filter selection (Doppler selection) (12) (13) (14) (15) (16) (17) Next, we separate the PDF bank into the filters for STAP processing and the filters for MBF. Namely, take the (3) STAP processing We let the data vector in the secondary cells before and after the primary cell be Y ~ c(τ), and we estimate the correlation matrix by the following averaging operation: Next, the STAP weight in the element-localized Doppler space is obtained from the inverse matrix of the clutter s correlation matrix R c and the element-localized Doppler space steering vector s eld (φ) as where, letting the s eld (φ) is (20) (21) (22) (23) Finally, we take the inner product of the data vector of the primary cell (that with the possibility of containing the target) and the aforementioned weight in order to obtain the filter output: (24) 83
We apply Eqs. (15) to (24) to all range cells k, treating each as a primary cell, to obtain the STAP output data sample in the range series. We perform threshold value processing on this STAP output data sample with improved S/C (signal-to-clutter ratio) for target detection. (4) Multibeam forming (MBF) In the PDF bank, the filters other than those that satisfy Eq. (18) do not contain clutter, but only internal receiver noise. We apply the regular MBF to the output from these filters. Letting the filter number be m, we have The above formula gives the output of beam forming in the φ(n) direction on filter number m. With the beam formation expressed by Eq. (25), as before, we apply processing to the data samples of all range cells k, and perform threshold value processing on these range series data samples for the target detection. If we use the following, which is equally spaced in terms of sin(φ), as the space steering vector Eq. (25) can be evaluated by the FFT, as in the case of the PDF. 4. Computer Simulation (25) (26) In this section, we evaluate the effect of the proposed ELD-STAP by a computer simulation, using the following example of a set of automotive radar parameters: Frequency: 76.5 GHz PRI: 20 µs [PRF: 50 khz, Doppler field of view ±25 khz (maximum relative velocity ±176 km/h)] Number of pulses in the pulse-doppler filter: 64 [CPI: 1.28 ms, Doppler frequency resolution 781 Hz (relative velocity resolution approximately 5 km/h)] Transmitting and receiving antenna beam: nondirectional Number of transmitting antenna: 1 Number of receiving array antenna elements N: 9 Receiving array antenna element spacing: 0.9 λ (linear array) Receiving synthesis beam width: approximately 6 Azimuth angle coverage: ±30 S/N: after synthesizing 9 elements, there are four levels: 0, 10, 20, and 30 db Number of clutter reflection points at each range cell: N c (= 61 or 5) reflection points equally spaced in the ±30 range Amplitude of each of the above reflected waves: Assuming the target amplitude to be 1, a Gaussian distribution with a standard deviation of σ c, with all reflection points independent Phase of each of the above reflected waves: a uniform distribution from 0 to 2π, with all reflection waves independent. As explained in Section 2, we assumed that the clutter is homogeneous in each range cell and that the amplitude and phase of each reflected wave have the aforementioned identical distribution and are independent. In this computer simulation, since the purpose is to verify the basic characteristics, we assumed that there is no Doppler frequency broadening at the reflection points of the clutter. 4.1. Verification of qualitative effects of ELD-STAP When the vehicle ahead is about to stop in situations such as traffic congestion, the difference between the relative velocity of the vehicle ahead and the road surface clutter becomes small, making it difficult for conventional automotive radars to detect the target, and thus creating a challenge for collision avoidance. For example, consider the case in which the own speed is 50 km/h and the target speed is 5 km/h (angle 0 ). The angle Doppler distribution of the signal and clutter in that situation is shown in Fig. 7 (for a frequency resolution of 250 Hz). As mentioned above, the clutter is assumed to be from N c = 61 reflection points Fig. 7. Pulse-Doppler and multibeam forming response of the target (5, 10.63 khz). 84
equally distributed in the range of ±30, and to have an amplitude with a Gaussian distribution and phase with a uniform distribution. In Fig. 7, the area with strong signal power is shown in white. The difference in speed between the road surface clutter and the target is only 5 km/h (708 Hz), and in addition, the signal power of the target (0 direction, Doppler frequency 6.375 khz) is smaller than that of the clutter (Doppler frequency 7.083 khz in the 0 direction), and it can be inferred from Fig. 7 that the target detection is difficult. On the other hand, the PDF for 64 pulses (frequency resolution 781 Hz) would give a resolution of having 64 sections on the vertical axis in Fig. 7, so that detecting the target by selecting the PDF that gives the maximum signal power is likely to be difficult. With 64 pulses, the target would be in filter number m = 40. At this point, determined by the PDF output filter selection according to Eq. (18), three filters m = 1, 2, and 3 are selected, corresponding to m = 39, 40, and 41, respectively. Namely, the target is contained in m = 2, the clutter s 0 direction is distributed in m = 3, and the ±30 direction is distributed in m = 1. By selecting 3 filters from among the 64 in the PDF bank, the dimension of the element-localized Doppler data for processing of STAP has been reduced to 27 (= 9 3). Next, the result of verifying the number of the clutters reflection points N c and the number of eigenvalues in the element-localized Doppler space is shown in Fig. 8. Even when the number of the clutter reflection points N c exceeds the number of antenna elements (N c = 61), the number of eigenvalues in the element-localized Doppler space is approximately 12 to 13, similar to the sum of the number of elements in the array N (= 9) and the number of selected PDF filters L (= 3) [7] (Sec. 3.2), [10] (Sec. 5.3). The results of applying PDF + MBF processing [Fig. 9(a)] and STAP processing [Fig. 9(b)] to the aforementioned three PDF filters (m = 1 to 3) are shown in Fig. 9. In Fig. 8. Relationship between number of the clutter and the eigenvalue in localized Doppler data. Fig. 9. An example of angular response for PDF and STAP (target velocity = 45 km/h, angle = 0 ). the plots, the horizontal axis is the angle which is used in the steering vector. The dotted line represents the PDF filter with m = 1, the solid line represents m = 2 (the number of the PDF filter containing the target), and the dashed line represents m = 3. With PDF + MBF, since the clutter is distributed in the angle direction in any of the PDF filters, the expected beam pattern cannot be obtained. Also, even in the PDF filter containing the target (solid line m = 2), the 0 direction is not the maximum, and an effective target detection would be difficult. On the other hand, with STAP, when steering in the direction of PDF filter number m = 2, which contains the target according to Eqs. (22) and (23), there is a peak at 0, and a desirable beam pattern can be obtained. This suggests extremely high target detection performance of STAP processing. There is a requirement that the clutter be distributed homogeneously among the secondary cells for estimation of the STAP weight. However, on regular roads, it seems unrealistic to assume that this region is longer than 10 m. Therefore, assuming the distance resolution to be 37 cm (5 85
ns), we let the number of secondary cells L be 27 (NM ), so that the distance is 10 m or less. Next, keeping the statistical properties of the clutter and the noise the same, the results of five trials for different data are shown in Fig. 10. Only m = 2, which contains the target, is shown in Fig. 10. Examining the five trials, it can be seen that in STAP, the maximum gain consistently occurs in the target direction. We next check the amount of calculation required. Letting the dimension of the data vector be a and the number of the secondary cells be b, the number of multiplication or addition operations in the calculation of the correlation matrix would be 4a 2 b and that in the eigen-analysis for obtaining the inverse matrix would be 140a 3 + 110a 2. In the element-pulse space, a = 9 64, letting b = a ( N M), the number of arithmetic operations may be as high as 2.75 10 10. On the other hand, in JDL-STAP, as a localized area in the angle Doppler frequency space, let a = 9 (3 3), b = a, and further, as in the proposed method, if the PDF output is limited to 3, since the number of individual STAP weights is 27 (= N 3), the number of arithmetic operations is reduced as low as 2.86 10 6. Finally, in the proposed method, a = 27 (= N 3), and thus, letting b = a, the number of arithmetic operations is 2.83 10 6, similar to JDL-STAP. 4.2. Evaluation based on the improvement factor Here the proposed ELD-STAP, JLD-STAP, and PDF + MBF are compared using the improvement factor (IF). The IF is the ratio of the output S/C and the input S/C, defined by the following formula (IF is also the ratio of the signal gain and the clutter gain): (27) Here S is the data vector of the signal (in reality, S + C + N), and R c is the correlation matrix of the clutter (in reality, C + N). In the aforementioned three methods, the input S/C was taken to be the S/C in the element-localized Doppler space after M = 3 (m = 1, 2, 3) is selected in the PDF bank (i.e., the input S/C is the same). The output S/C is in all cases that obtained when using the filter containing the target (m = 2) and a steering vector with a steering angle of 0 (in the target direction). In JDL-STAP, the beam directivity was set at 0, ±7.5, ±15, ±22.5, and ±30 ; and the nine filters in the angle Doppler space consisting of the three beams of 0 and ±7.5 with the aforementioned M = 3 were taken as the data vector. Also, in both ELD-STAP and JDL-STAP, the number of secondary cells was set as 27. Below, with mutual interference in the array antenna assumed to be negligible, as in Ref. 16, the relation between the number of clutter reflection points and IF, and the relation between the input noise level and IF, are evaluated in the cases with and without error due to variations of ±10% in amplitude and of ±10 in phase between the elements. 4.2.1. Dependence on the number of clutter reflection points and the amplitude Fig. 10. Results of angular response for PDF and STAP (PDF No. = target containing cell). Five trials. The dependence of IF on the number of clutter reflection points and the amplitude was evaluated. First, for a number of the clutter reflection points N c, two conditions were used, namely, 61 points (1 interval), where multiple reflection points exist in a beam, and 5 points (10 interval), where there is 1 or less in a beam. Also, for the standard deviation σ c of the amplitude of each clutter reflection point, four values were tried, namely, 2, 1, 0.5, and 0.25 in the case of 61 points; and 20, 10, 5, and 2.5 in the case of 5 points. The S/N after beamforming with the 9 elements was set to 30 db (20.46 db for 1 element). The results, that is, 86
the mean and standard deviation of the IF (in db) in 50 trials under identical conditions, are shown in Table 1(a). From Table 1(a), the following features can be observed as a result of the computer experiment. (1) As an overall trend, the ELD-STAP gave the best IF value among the three methods evaluated. (Compared to the PDF + MBF, which is a combination of fixed filters, under the conditions set in this paper, the results were as much as 20 to 40 db better.) (2) For N c = 5 (1 clutter reflection point within a beam width), the ELD-STAP and the JDL-STAP showed similar IF value, but while the former had no dependence on the clutter amplitude σ c, the latter was dependent on σ c (as σ c increases, IF increases as well). (3) For N c = 61 (multiple clutter reflection points within a beam width), the IF was somewhat lower than for N c = 5 in both ELD-STAP and JDL-STAP. (4) When there are amplitude and phase errors for each element, ELD-STAP did not show a performance degradation compared to the absence of errors, but with JDL-STAP, for N c = 61, IF was significantly lowered. These characteristics concerning IF are considered to be dependent on the filter gain in each method and the clutter spectrum spread. In ELD-STAP and JDL-STAP, which estimate the weight adaptively, the filter gain is related to 1 the C/N (clutter-to-noise ratio) in weight estimation, and input clutter spectrum spreading and target signal broadening depending on 2 the method of conversion to the data space to which STAP is applied. In the case of item 1, if the clutter amplitude σ c was small, the C/N in weight estimation would be small, and hence there would be a tendency to increase the estimation error, resulting in a degradation of IF. As the cause of 2, we reason as follows. In ELD- STAP preprocessing, the FFT (unitary matrix) is performed only in the time (range) series to select the output filter. Due to the orthogonality of the FFT, only one steering vector (target velocity) is contained in one output filter. Therefore, no error would result from selecting only the filters corresponding to the clutter frequency obtained from the prior information (own speed). On the other hand, the FFT in the time (range) series is the same in the JDL-STAP, but in the element series, beam forming and selection, which are not orthogonal, are performed. A combination of these causes is considered to be reflected in the results of computer experiment (1) to (4). In particular, even when there are amplitude and phase errors for each element, if the direction of arrival is different, in ELD-STAP, which uses the element space, the column vectors in the direction matrix of the incident wave are independent, and hence the correlation matrix is of full rank. That is, a clutter eigenspace (i.e., STAP weight) including these errors is obtained, and thus Table 1. Results of improvement factor evaluations 87
the measured clutter is likewise suppressed with influence from the same amplitude and phase errors in the examined range cell. On the other hand, in JDL-STAP, the reason is considered to be as follows: if there are errors in the amplitude and phase for each element, they would be compounded with the cause of 2, and the estimation error for the clutter space would become larger. 4.2.2. Dependence on the input noise level The dependence of IF on the input noise level was evaluated. The noise level was set the same in the reference (secondary) cell and the test (primary) cell. The noise level was set to three levels so that if the examined cell contained the target, the S/N after beamforming with 9 elements would be 0, 10, and 20 db. We set N c = 61 and σ c = 1. The result is shown in Table 1(b). The following features can be observed as a result of the computer experiment. (1) In both ELD-STAP and JDL-STAP, there is a dependence on the input noise level, and as the noise increases, the IF decreases. (2) In ELD-STAP, even with S/N as low as 0, an IF 10 db larger than with PDF + MBF was obtained. The cause of item (1) is considered to be the C/N in weight estimation. Also, in PDF + MBF, which is a combination of fixed filters, IF, which is a ratio of the input and the output of S/C [S + C + N)/(C + N)], does not have an input noise level dependence. 5. Conclusions In automotive millimeter-wave radars, it is hoped that slow-moving target detection performance can be improved by suppressing unnecessary waves such as ground surface reflection (clutter). In this paper, as a high-performance clutter suppression method for covering even slow-moving targets, which are difficult to separate by the pulse-doppler filter (PDF) conventionally used for clutter suppression, we proposed the element-localized Doppler space time adaptive processing (ELD-STAP) method, which includes a PDF in the preprocessing and uses an array antenna. In the proposed ELD-STAP method, reduction in the dimension of the data vector is implemented by applying STAP in the element-doppler space, where only the PDF output filter corresponding to the Doppler frequency of the clutter predicted from the own speed is selected. By reduction in the dimension, the computation load and the number of required reference cells (secondary cells) are reduced, and hence the requirement of homogeneity in the range series for the clutter is lessened. We used a computer simulation to perform a comparative verification of the qualitative effect of a method combining PDF and MBF (multi-beam forming), which is widely used in fields such as defense radar, and the ELD- STAP method. Further, we made a statistical evaluation of the improvement factor (IF), which is the ratio of the input and output S/C (signal to clutter ratio), and confirmed that a 20 to 40 db improvement (when S/N = 30 db after beamforming) over the combination of PDF and MBF can be expected. We also confirmed that when there are amplitude and phase errors for each element, the JDL-STAP (joint domain localized) method which has been proposed similarly for reducing the dimension is greatly affected and the IF is lowered, whereas in the ELD-STAP method the performance is not degraded. In a real road environment, electric poles, road signs, etc. are present, and thus the clutter distribution among the secondary cells is not expected to be homogeneous. In such an inhomogeneous environment, the estimation precision of the clutter eigenspace is degraded, which causes the IF to be lower, and consequently the target detection performance and the false alarm performance are degraded [12]. Hereafter, it will be necessary to perform evaluations using real field data, and to improve the algorithm in order to make it more robust in an inhomogeneous environment. In this paper, the assumed application is an automotive forward-looking radar, but in, for example, a side-looking L-PRF radar with a PRF of several khz (maximum detection distance = several dozen km) on a marine vessel in situations such as traveling at about 20 30 km/h, the Doppler frequency of the sea surface reflection clutter is localized in a particular Doppler filter, and therefore the ELD-STAP method is applicable. REFERENCES 1. Otsuki T, Tanokura Y. Electronic eyes start to blink in cars, camera and mm-wave radar. The goal is standard equipment in all cars. Nikkei Electronics, 2003.8.4, p 57 68. (in Japanese) 2. Inaba T, Araki K. A study on automotive radar signal processing for angle estimation in interferences. Trans IEICE 2004;J87-B:199 212. (in Japanese) 3. Skolnik MI. Radar handbook. McGraw Hill; 1970. 4. Barton DK. Modern radar systems analysis. Artech House; 1988. 5. Natherson FE. Radar design principle. McGraw Hill; 1969. 6. Bernnan LE, Reed IS. Theory of adaptive radar. IEEE Trans Aerosp Electron Syst 1973;9:237 252. 7. Klemm R. Space-time adaptive processing principles and applications. IEE Press; 1998. 88
8. Melvin WL. Eigenbased modeling of nonhomogeneous airborne radar environment. IEEE 1998 National Radar Conference, p 171 176, Dallas, TX. 9. Reed IS, Mallett JD, Brennan LE. Rapid convergence in adaptive arrays. IEEE Trans Aerosp Electron Syst 1974;10:853 863. 10. Brennan LE, Shaudaher FM. Subclutter visibility demonstration. Tech Rep RL-TR-92-21, Adaptive Sensors Incorporated, 1992. 11. Ward J. Space-time adaptive processing for airborne radar. Tech Rep 1015, Lincoln Laboratory, MIT, 1994. 12. Melvin WL, Wicks MC. Improving practical spacetime adaptive radar. IEEE 1997 National Radar Conference, p 48 53, Syracuse, NY. 13. Wnag H, Cai L. On adaptive spatial-temporal processing for airborne surveillance radar systems. IEEE Aerosp Electron Syst 1994;30:660 669. 14. Adve RS, Wicks MC. Joint domain localized processing using measured spatial steering vectors. IEEE 1998 National Radar Conference, p 165 170, Dallas, TX. 15. Adve RS, Hale TB, Wicks MC. Practical joint domain localized adaptive processing in homogenous and nonhomogeneous environments. Part 1: Homogeneous enviornment. IEE Proc Radar Sonar Navig 2000;147:57 65. 16. Inaba T, Yanagisawa M, Araki K. Two step angle measurement method for automotive radar. Trans IEICE 2003;J86-B:1652 1658. (in Japanese) AUTHOR Takayuki Inaba (member) received his B.S. and M.S. degrees in physics from Tokyo Institute of Technology in 1981 and 1983 and joined the Kamakura Works of Mitsubishi Electric Corporation. He is now affiliated with the Information Technology R&D Center. He holds a D.Eng. degree. His research interests include radar signal processing, superconducting magnetic sensor signal processing, and adaptive array signal processing. 89