Tài liệu Digital Signal Processing Handbook P70 pdf

Space-Time Adaptive Processing for Airborne Surveillance Radar Hong Wang Syracuse University 70.1 Main Receive Aperture and Analog Beamforming 70.2 Data to be Processed 70.3 The Processi

Hong Wang “Space-Time Adaptive Processing for Airborne Surveillance Radar.”

2000 CRC Press LLC <http://www.engnetbase.com>.

Space-Time Adaptive Processing for Airborne Surveillance Radar

Hong Wang

Syracuse University

70.1 Main Receive Aperture and Analog Beamforming 70.2 Data to be Processed

70.3 The Processing Needs and Major Issues 70.4 Temporal DOF Reduction

70.5 Adaptive Filtering with Needed and Sample-Supportable DOF and Embedded CFAR Processing

70.6 Scan-To-Scan Track-Before-Detect Processing 70.7 Real-Time Nonhomogeneity Detection and Sample Conditioning and Selection

70.8 Space or Space-Range Adaptive Pre-Suppression of Jammers 70.9 A STAP Example with a Revisit to Analog Beamforming 70.10 Summary

References

Space-Time Adaptive Processing (STAP) is a multi-dimensional filtering technique developed for minimizing the effects of various kinds of interference on target detection with a pulsed airborne surveillance radar The most common dimensions, or filtering domains, generally include the az-imuth angle, elevation angle, polarization angle, doppler frequency, etc in which the relatively weak target signal to be detected and the interference have certain differences In the following, the STAP principle will be illustrated for filtering in the joint azimuth angle (space) and doppler frequency (time) domain only

STAP has been a very active research and development area since the publication of Reed et al.’s seminal paper [1] With the recently completed Multichannel Airborne Radar Measurement project (MCARM) [2]– [5], STAP has been established as a valuable alternative to the traditional approaches, such as ultra-low sidelobe beamforming and Displaced Phase Center Antenna (DPCA) [6] Much of STAP research and development efforts have been driven by the needs to make the system affordable,

to simplify its front-hardware calibration, and to minimize the system’s performance loss in severely nonhomogeneous environments Figure70.1is a general configuration of STAP functional blocks [5,

7] whose principles will be discussed in the following sections

FIGURE 70.1: A general STAP configuration with auxiliary and main arrays.

70.1 Main Receive Aperture and Analog Beamforming

For conceptual clarity, the STAP configuration of Fig.70.1separates a possibly integrated aperture into two parts: the main aperture which is most likely shared by the radar transmitter, and an auxiliary array of spatially distributed channels for suppression of Wideband Noise Jammers (WNJ) For convenience of discussion, the main aperture is assumed to haveN ccolumns of elements, with the column spacing equal to a half wavelength and elements in each column being combined to produce a pre-designed, nonadaptive elevation beam-pattern

The size of the main aperture in terms of the system’s chosen wavelength is an important system parameter, usually determined by the system specifications of the required transmitter power-aperture product as well as azimuth resolution Typical aperture size spans from a few wavelengths for some short-range radars to over 60 wavelengths for some airborne early warning systems The analog beamforming network combines theN ccolumns of the main aperture to produceN sreceiver channels whose outputs are digitized for further processing One should note that the earliest STAP approach presented in [1], i.e., the so-called “element space” approach, is a special case of Fig.70.1when

N s = N cis chosen

The design of the analog beamformer affects

1 the system’s overall performance (especially in nonhomogeneous environments),

2 implementation cost,

3 channel calibration burden,

4 system reliability, and

5 controllability of the system’s response pattern

The design principle will be briefly discussed in Section70.9; and because of the array’s element error, column-combiner error, and column mutual-coupling effects, it is quite different from what

is available in the adaptive array literature such as [8], where already digitized, perfectly matched channels are generally assumed

Finally, it should be pointed out that the main aperture and analog beamforming network in Fig.70.1may also include nonphased-array hardware, such as the common reflector-feed as well as the hybrid reflector and phased-array feed [9] Also, subarraying such as [10] is considered as a form

of analog beamforming of Fig.70.1

70.2 Data to be Processed

Assume that the radar transmits, at each look angle, a sequence ofN t uniformly spaced, phase-coherent RF pulses as shown in Fig.70.2for its envelope only Each ofN sreceivers typically consists of

a front-end amplifier, down-converter, waveform-matched filter, and A/D converter with a sampling frequency at least equal to the signal bandwidth Consider thekth sample of radar return over the

N t pulse repetition intervals (PRI) from a single receiver, where the index “k” is commonly called

the range index or cell The total number of range cells,K0is approximately equal to the product of the PRI and signal bandwidth The coherent processing interval (CPI) is the product of the PRI and

N t; and since a fixed PRI can usually be assumed at a given look angle, CPI andN t are often used interchangeably

FIGURE 70.2: A sequence ofN t phase-coherent RF pulses (only envelope shown) transmitted at a given angle The pulse repetition frequency (PRF) is 1/T

WithN sreceiver channels, the data at thekth range cell can be expressed by a matrix X k,N s × N t, fork = 1, 2, K0 The total amount of data visually forms a “cube” shown in Fig.70.3, which is the raw data cube to be processed at a given look angle It is important to note from Fig.70.3that the term “time” is associated with the CPI for any given range cell, i.e., across the multiple PRIs, while the term “range” is used within a PRI Therefore, the meaning of the frequency corresponding

to the time is the so-called doppler frequency, describing the rate of the phase-shift progression of a return component with respect to the initial phase of the phase-coherent pulse train The doppler frequency of a return, e.g., from a moving target, depends on the target velocity and direction as well

as the airborne radar’s platform velocity and direction, etc

FIGURE 70.3: Raw data at a given look angle and the space, time, and range axes.

70.3 The Processing Needs and Major Issues

At a given look angle, the radar is to detect the existence of targets of unknown range and unknown doppler frequency in the presence of various interference In other words, one can view the processing

as a mapping from the data cube to a range-doppler plane with sufficient suppression of unwanted components in the data Like any other filtering, the interference suppression relies on the differences between wanted target components and unwanted interference components in the angle-doppler domain Figure70.4illustrates the spectral distribution of potential interference in the spatial and temporal (doppler) frequency domain before the analog beamforming network, while Fig.70.5shows

a typical range distribution of interference power As targets of interest usually have unknown doppler frequencies and unknown distances, detection needs to be carried out at sufficiently dense doppler frequencies along the look angle for each range cell within the system’s surveillance volume For each cell at which target detection is being carried out, some of surrounding cells can be used to produce an estimate of interference statistics (usually up to the second order), i.e., providing “sample support”, under the assumption that all cells involved have an identical statistical distribution Figure70.4 also shows that, in terms of their spectral differences, traditional wideband noise jammers, whether entering the system through direct path or multipath (terrain scattering/near-field scattering), require spatial nulling only; while clutter and chaff require angle-doppler coupled nulling Coherent repeater jammers (CRJ) represent a nontraditional threat of a target-like spectral feature with randomized ranges and doppler frequencies, making them more harmful to adaptive systems than to conventional nonadaptive systems [11]

Although Fig.70.5has already served to indicate that the interference is nonhomogeneous in range, i.e., its statistics vary along the range axis, recent airborne experiments have revealed that its severe-ness may have long been underestimated, especially over land [3] Figure70.6[5,7] summarizes the sources of various nonhomogeneity together with their main features As pointed out in [12], a serious problem associated with any STAP approach is its basic assumption that there is a sufficient amount of sample support for its adaptive learning, which is most often void in real environments even in the absence of any nonhomogeneity type of jammers such as CRJ Therefore, a crucial issue for the success of STAP in real environments is the development of data-efficient STAP approaches,

in conjunction with the selection of reasonably identically distributed samples before estimating interference statistics To achieve a sufficient level of the data efficiency in nonhomogeneous envi-ronments, the three most performance- and cost-effective methods are temporal degrees-of-freedom (DOF) reduction, analog beamforming to control the spatial DOF creation, and pre-suppression of WNJ as shown in Fig.70.1

Another crucial issue is the affordability of STAP-based systems As pointed out in [9], phased-arrays, especially those active ones (i.e., with the so-called T/R modules), remain very expensive despite the 30-year research and development For multichannel systems, the cost of adding more

FIGURE 70.4: Illustration of interference spectral distribution for a side-mounted aperture.

receivers and A/D converters with a sufficient quality makes the affordability even worse

Of course, more receiver channels mean more system’s available spatial DOF However, it is often the case in practice that the excessive amount of the DOF, e.g., obtained via one receiver channel for each column of a not-so-small aperture, is not necessary to the system Ironically, excessive DOF can make the control of the response pattern more difficult, even requiring significant algorithm constraints [8]; and after all, it has to be reduced to a level supportable by the available amount of reasonably identically distributed samples in real environments An effective solution, as demonstrated in a recent STAP experiment [13], is via the design of the analog beamformer that does not create unnecessary spatial DOF from the beginning — a sharp contrast to the DOF reduction/constraint applied in the spatial domain

Channel calibration is a problem issue for many STAP approaches In order to minimize perfor-mance degradation, the channels with some STAP approaches must be matched across the signal band, and steering vectors must be known to match the array Considering the fact that channels generally differ in both elevation and azimuth patterns (magnitude as well as phase) even at a fixed frequency, the calibration difficulty has been underestimated as experienced in recent STAP experiments [5]

It is still commonly wished that the so-called “element-space” approaches, i.e., the special case of

N s = N c in Fig.70.1, with an adaptive weight for each error-bearing “element” which hopefully can be modeled by a complex scalar, could solve the calibration problem at a significantly increased system-implementation cost as each element needs a digitized receiver channel Unfortunately, such

a wish can rarely materialize for a system with a practical aperture size operated in nonhomogeneous environments With a spatial DOF reduction required by these approaches to bring down the number

of adaptive weights to a sample-supportable level, the element errors are no longer directly accessible

by the adaptive weights, and thus the wishful “embedded robustness” of these element-space STAP approaches is almost gone In contrast, the MCARM experiment has demonstrated that, by mak-ing best use of what has already been excelled in antenna engineermak-ing [13], the channel calibration problem associated with STAP can be largely solved at the analog beamforming stage , which will be discussed in Section70.9

The above three issues all relate to the question: “What is the minimal spatial and temporal DOF

FIGURE 70.5: Illustration of interference-power range distribution, where1 hindicates the radar platform height

required?” To simplify the answer, it can be assumed first that clutter has no Doppler spectral spread caused by its internal motion during the CPI, i.e., its spectral width cut along the doppler frequency axis of Fig.70.4equals to zero For WNJ components of Fig.70.4, the required minimal spatial DOF is well established in array processing, and the required minimal temporal DOF is zero as no temporal processing can help suppress these components The CRJ components appear only in isolated range cells as shown in Fig.70.5, and thus they should be dealt with by sample conditioning and selection so that the system response does not suffer from their random disturbance With the STAP configuration of Fig.70.1, i.e., pre-suppression of WNJ and sample conditioning and selection for CRJ, the only interference components left are those angle-doppler coupled clutter/chaff spectra

of Fig.70.4 It is readily available from the two-dimensional filtering theory [14] that suppression of each of these angle-doppler coupled components only requires one spatial DOF and one temporal DOF of the joint domain processor! In other words, a line of infinitely many nulls can be formed with one spatial DOF and one temporal DOF on top of one angle-doppler coupled interference component under the assumption that there is no clutter internal motion over the CPI It is also understandable that, when such an assumption is not valid, one only needs to increase the temporal DOF of the processor so that the null width along the doppler axis can be correspondingly increased For conceptual clarity,N s − 1 will be called the system’s available spatial DOF and N t − 1 the system’s available temporal DOF While the former has a direct impact on the implementation cost, calibration burden, and system reliability, the latter is determined by the CPI length and PRI with little cost impact, etc Mainly due to the nonhomogeneity-caused sample support problem discussed earlier, the adaptive joint domain processor may have its spatial DOF and temporal DOF, denoted by

N psandN ptrespectively, different from the system’s availables by what is so-called DOF reduction However, the spatial DOF reduction should be avoided by establishing the system’s available spatial DOF as close to what is needed as possible from the beginning

70.4 Temporal DOF Reduction

Typically an airborne surveillance radar hasN tanywhere between 8 and 128, depending on the CPI and PRI With the processor’s temporal DOF,N pt, needed for the adjustment of the null width, normally being no more than 2∼ 4, huge DOF reduction is usually performed for the reasons of the sample support and better response-pattern control explained in Section70.3

FIGURE 70.6: Typical nonhomogeneities.

An optimized reduction could be found, givenN t,N pt, and the interference statistics which are still unknown at this stage of processing in practice [7] There are several non-optimized temporal DOF reduction methods available, such as the Doppler-domain (joint domain) localized processing (DDL/JDL) [12,15,16] and the PRI-staggered Doppler-decomposed processing (PRI-SDD) [17], which are well behaved and easy to implement The DDL/JDL principle will be discussed below The DDL/JDL consists of unwindowed/untapered DFT of (at least)N t-point long, operated on each of theN s receiver outputs The sameN pt + 1 most adjacent frequency bins of the DFTs of the

N s receiver outputs form the new data matrix at a given range cell, for detection of a target whose Doppler frequency is equal to the center bin Figure70.7shows an example forN s = 3, N t = 8, and

N pt = 2 In other words, the DDL/JDL transforms the raw data cube of N s × N t × K0into (at least)

N tsmaller data cubes, each ofN s × (N pt + 1) × K0for target detection at the center doppler bin The DDL/JDL is noticeable for the following features

1 There is no so-called signal cancellation, as the unwindowed/untapered DFT provides no desired signal components in the adjacent bins (i.e., reference “channel”) for the assumed target doppler frequency

2 The grouping ofN pt+1 most adjacent bins gives a high degree of correlation between the interference component at the center bin and those at the surrounding bins — a feature important to cancellation of any spectrum-distributed interference such as clutter The cross-spectral algorithm [18] also has this feature

3 The response pattern can be well controlled asN pt can be kept small — just enough for the needed null-width adjustment; andN pt itself easily can be adjusted to fit different clutter spectral spread due to its internal motion

4 Obviously the DDL/JDL is suitable for parallel processing

While the DDL/JDL is a typical transformation-based temporal DOF reduction method, other methods involving the use of DFTs are not necessarily transformation-based An example is the PRI-SDD [17] which applies time-domain temporal DOF reduction on each doppler component This explains why the PRI-SDD requiresN pt times more DFTs that should be tapered It also serves

FIGURE 70.7: The DDL/JDL principle for temporal DOF reduction illustrated withN s = 3, N t = 8, andN pt = 2

as an example that an algorithm classification by the existence of the DFT use may cause a conceptual confusion

70.5 Adaptive Filtering with Needed and Sample-Supportable DOF

and Embedded CFAR Processing

After the above temporal DOF reduction, the dimension of the new data cube to be processed at a given look angle for each doppler bin isN s × (N pt + 1) × K0 Consider a particular range cell at

which target detection is being performed Let x, N s (N pt + 1) × 1, be the stacked data vector of this

range cell, which is usually called the primary data vector Let y1, y2, , y k, allN s (N pt + 1) × 1

and usually called the secondary data, be the same-stacked data vectors of theK surrounding range

cells, which have been selected and/or conditioned to eliminate any significant nonhomogeneities

with respect to the interference contents of the primary data vector Let s,N s (N pt + 1) × 1, be

the target-signal component of x with the assumed angle of arrival equal to the look angle and the

assumed doppler frequency corresponding to the center doppler bin In practice, a look-up table of

the “steering vector” s for all look-angles and all doppler bins usually has to be stored in the processor,

based on updated system calibration A class of STAP systems with the steering-vector calibration-free feature has been developed, and an example from [13] will be presented in Section70.9

There are two classes of adaptive filtering algorithms: one with a separately designed constant false alarm rate (CFAR) processor, and the other with embedded CFAR processing The original sample matrix inversion algorithm (SMI) [1] belongs to the former, which is given by

η SMI = ˆwH

SMIx 2H1

>

where

ˆR = K1 XK

k=1

ykyH

The SMI performance under the Gaussian noise/interference assumption has been analyzed in detail [1], and in general it is believed that acceptable performance can be expected if the data vectors are independent and identically distributed (iid) withK, the number of the secondary, being at least

two timesN s (N pt +1) Detection performance evaluation using a SINR-like measure deserves some

care whenK is finite, even under the iid assumption [19,20]

If the output of an adaptive filter, when directly used for threshold detection, produces a probability

of false alarm independent of the unknown interference correlation matrix under a set of given conditions, the adaptive filter is said to have an embedded CFAR Under the iid Gaussian condition, two well-known algorithms with embedded CFAR are the Modified SMI [21] and Kelly’s generalized likelihood ratio detector (GLR) [22], both of which are linked to the SMI as shown in Fig.70.8 The

FIGURE 70.8: The link among the SMI, modified SMI (MSMI), and GLR whereN = (N ps +

1)(N pt + 1) × 1.

GLR has the following interesting features:

1 0< 1

K η GLR < 1, which is a necessary condition for robustness in nongaussian

interfer-ence [23]

2 Invariance with respect to scaling all data or scaling s.

3 One cannot expressη GLRasˆwHx; and with a finiteK, an objective definition of its output

SINR becomes questionable

Table70.1summarizes the modified SMI and GLR performance, based on [21,24]

It should be noted that the use of the scan-to-scan track-before-detect processor (SSTBD to be discussed in Section70.6) does not make the CFAR control any less important because the SSTBD itself is not error-free even with the assumption that almost infinite computing power would be available Moreover, the initial CFAR thresholding can actually optimize the overall performance,

in addition to a dramatic reduction of the computation load of the SSTBD processor Traditionally, filter and CFAR designs have been carried out separately, which is valid as long as the filter is not data-dependent Therefore, such a traditional practice becomes questionable for STAP, especially whenK