# ADAPTIVE SIGNAL PROCESSING

### INTRODUCTION

The adaptive signal Processing refers to a class of signal processing is the techniques used to process returns of an antenna array radar system. It enhances the ability of radars to detect targets that might otherwise be obscured by clutter or jamming. The output of STAP is a linear combination or weighted sum of the input signal samples .The “adaptive” in STAP refers to the fact that STAP weights are computed to reflect the actual noise, clutter and jamming environment in which the radar finds itself. The “space” in STAP refers to the fact that STAP the STAP weights (applied to the signal samples at each of the elements of the antenna array) at one instant of time define an antenna pattern in space. If there are jammers in the field of view, STAP will adapt the radar antenna pattern by placing nulls in the directions those jammers thus rejecting jammer power. The “time” in STAP refers to the fact that the STAP weights applied to the signal samples at one antenna element over the entire dwell define a system impulse response and hence a system frequency response. STAP is a multi-dimensional adaptive signal processing technique over spatial and temporal samples. In this approach, the input data collected from several antenna sensors has a cubic form. Depending on how this input data cube is processed,

STAP is classified into Higher Order Post-Doppler (HOPD), Element Space Pre-Doppler, Element Space Post-Doppler, Beam Space Pre-Doppler, and Beam Space Post-Doppler. STAP consists of three major computation steps. First, a set of rules called the training strategy is used to select data which will be processed in the subsequent computation. The second step is weight computation. It requires solving a set of linear equations. This is the most computationally intensive step. Finally, thres holding operation is performed after applying the computed weights. In HOPD processing, Doppler processing (FFT computations) is followed by solving least square problems (QR decompositions).

### INTRODUCTION TO RADAR

Radar is an electromagnetic system for the detection and location of objects. RADAR is nothing but Radio Detection And Ranging. It operates by transmitting a particular type of waveform and detects the nature of the echo signal. An elementary form of radar consists of a transmitting antenna emitting electromagnetic radiation generated by an oscillator of some sort, a receiving antenna, and an energy detecting device or receiver .A portion of the transmitted signal is intercepted by a reflecting object (target) and is reradiated in all directions. It is the energy reradiated in the back direction that is of prime interest to the radar. The receiving antenna collects the returned energy and delivers it to a receiver, where it is processed to detect the presence of the target and to extract its location and relative velocity.

### RADAR BLOCK DIAGRAM

A basic block diagram of radar is given in the . The transmitter may be an oscillator such as magnetron, which is pulsed by the modulator to generate a repetitive train of pulses. The waveform generated by the transmitter travels via a transmission line to the antenna where it is radiated into space. A single antenna is generally used for both transmitting and receiving. The receiver must be protected from damage caused by the high power of the transmitter. This is the function of the duplexer. The duplexer also serves to channel the returned echo signals to the receiver and not to the transmitter. The receiver is usually of the superhetrodyne type. The first stage might be a low noise RF amplifier. The mixer and local oscillator convert the RF signal to an intermediate frequency. After maximizing the signal to noise ratio in the IF amplifier the pulse modulation is extracted by the second detector and amplified by the video amplifier to level where it can be properly displayed, usually on a cathode ray tube .

### CLUTTER AND JAMMING

Clutter may be defined as any unwanted radar echoes. ts name is descriptive that such echoes can clutter the radar output and make difficult the detection of wanted targets. Examples of unwanted echoes, or clutter, in Radar designed to detect aircraft include the reflections from land, sea, rain, birds, and chaff. Unwanted echoes might also be obtained from clear turbulence and other atmospheric effects, as well as from ionized media such as the aurora and meteor trails. Clutter is generally distributed in spatial extent, in that it is usually much larger in physical size than the radar resolution cell. There are also point clutter echoes such as towers, poles, and similar objects. The echo from a single bird is also an example of point clutter. When clutter echoes are thus determine the range performance. In such circumstances, the optimum radar waveform and receiver design can be quite different than when receiver noise alone is the dominant effect.

Radar echoes from land, sea, rain, birds, and other such objects are not always un desired. Reflection from storm clouds, for e.g.: , can be a bother to a Radar that must see air craft, but storm clouds are what the Radar meteorologist wants to see in order to measure rainfall rate over a large area. The backscatter echoes from land can degrade the performance of many types of Radar; but it is the target of interest for a ground ampping Radar, for remote sensing of the earth resources, and for most synthetic aperture Radars. Thus the same object might be the desired target in one application, and the undesired clutter echo in another.

Echoes from the land or the sea are known as surface clutter and echoes from rain or other atmospheric phenomena are known as volume clutter. Because of its distributed nature the measure of the backscattering echo from such clutter is generally given in terms of a Radar-cross-section density rather than the Radar cross section as for conventional targets.

Radar jammers are devices that make targets invisible to the radars, which are tracking by the use of any of the jamming techniques. Radar Jammer work by mixing a portion of the radar signal with background clutter, then reflecting it back to the tracking radar with a special antenna.

### ANTENNA ARRAYS

An array antenna consists of a number of individual radiating elements suitably spaced with respect to one another. The relative amplitude and phase of signals applied to each of the elements are controlled to obtain the desired radiation pattern from the combined action of all the elements. Two common geometrical forms of array antennas of interest in radar are the linear array and the planar array. A linear array consists of elements arranged in a straight line in one dimension. A planar array is a two dimensional configuration of elements arranged to lie in plane.

### ADAPTIVE ANTENNAS

An adaptive antenna is a primitive form of the space-time adaptive system.

An adaptive antenna senses the received signals incident across its aperture and adjusts the phase and amplitude of the aperture illumination to achieve some desired performance, such as maximizing the received signal to noise ratio. The noise may be either internal receiver noise or external noise as from jammers. Clutter echoes or interference from other electromagnetic radiations can also be minimized by adaptive antennas. Adaptive antenna techniques can automatically compensate for mechanical or electrical errors in an antenna by sensing the errors and applying corrective signals and can compensate for failed elements random effects and blockage of the aperture form nearby structures. Much of the interest in adaptive antennas has been to reduce the effects of noise jamming in the antenna sidelobes. The ideal adaptive antenna acts automatically to adjust itself as a matched filter by reducing the side lobes in the direction the unwanted signals. Adaptive antennas require some a priori knowledge of desired signal such as its direction, waveform, or statistical properties.

### SPACE-TIME ADAPTIVE PROCESSING

The above illustrates how STAP is able to pick out a weak target signal obscured by clutter. The left hand panel shows simulated input data, prior to STAP processing consisting of a target signal at 150 Hz plus clutter. The right hand panel shows those same data after STAP processing. STAP refers to an extension of adaptive antenna signal processing methods that operate on a set of radar returns gathered from multiple elements of an antenna array over a specified time interval. Because the signal returns are composed of range, pulse, and antenna-element samples, a three-dimensional (3-D) cube naturally represents STAP data. Typical STAP data cube processing requirements range from 10- 100 giga floating-point operations per second (Gflops). In most STAP implementations, there are three phases of computations, one for each dimension of the data cube (i.e., range, pulse, and Channel). To reduce computational latency, the processing at each phase must be distributed over multiple computer networks using a single program multiple data (SPMD) approach. Additionally, prior to each processing phase, the data set must be partitioned in a fashion that attempts to equally distribute the computational load over the available CNs. Because each of the three phases process a different dimension of the data cube, the data must be redistributed to form contiguous vectors of the next dimension prior to the next processing phase.

Space-Time Adaptive Processing (STAP) is an important but computationally demanding technique for mitigating clutter as seen by airborne radar. High computational requirements coupled with need for future growth and expansion have led to a major investigation of the suitability of massively parallel processors for this application domain. Delivered processing power on key STAP kernel computations is of primary importance because of the real-time nature of radar processing systems. Processing power per unit size, power and weight is also important due to the form factor constraints of the airborne platform. Since algorithm requirements for STAP systems are under continuous development, scalability of processing power both in terms of machine size and problem size is of key interest. These issues have led to an increased interest in SIMD architectures as possible candidates for a STAP processor. This paper presents a performance analysis of a key STAP processing kernel on a commercially available SIMD parallel architecture called the MeshSP. The approach used in the analysis was to derive a parameterized model for estimating latencies of computation and communication in terms of problem and machine size. By exercising the model against various radar systems and processor configurations, we can not only determine a configuration, which meets real-time requirements, but also analyze the scalability of the configuration for future changes in algorithm requirements.

Space-Time Adaptive Processing (STAP) is a signal processing technique used to suppress the effects of co-channel interference, ISI, and jammers in wireless communications systems. From the implementation of STAP algorithms, greater capacity gains and communication quality can be realized. The fundamental principle in all STAP algorithms involves the usage of multiple receive antennas on the receiving platform. Spacing the antennas apart by at least half the wavelength of the desired signal provides space diversity, which helps mitigate the effects of fading. Furthermore, the incoming signals on each antenna element are adaptively weighted using a variety of algorithms in order to steer the antenna gain towards the desired signals while nulling the signals from unwanted noise and interference. 1 below shows the baseline setup for most STAP implementations. STAP algorithms will typically begin with the configuration below in 1 and add extensions such as tapped delay lines behind each antenna receiver or different antenna array topologies

Space-time adaptive processing (STAP) for clutter mitigation in narrowband radar systems has developed rapidly over the last decade. However, new technology has enabled the production of higher bandwidth radar and high-bandwidth applications, such as high range resolution (HRR) ground moving target indication (GMTI), creating a demand for STAP algorithms that perform without the narrowband assumption. We perform wideband STAP by breaking up the radar signal into sub bands, and using well tested narrowband STAP algorithms independently in each sub band. These sub bands can then be recombined to reconstruct the wideband, high-resolution signal. This extra stage of processing makes the formulation of the STAP problem slightly more subtle. Wideband output signal-to-interference-plus-noise ratio (SINR) and range side lobe levels are affected not only by sub band SINR and side lobe levels, but also by the sub band-to-sub band variation in signal amplitude and phase. In this paper we consider three causes of variation in the sub band STAP weight response: the sub band adaptive weight normalization, target Doppler dispersion, and variation due to estimating the sample covariance matrix (SCM) independently in each sub band. We derive the SINR-optimal sub band STAP normalization, interpolate FFT Doppler filters to correct for Doppler dispersion, and employ diagonal loading and multiple constraints to stabilize variation in the STAP weight response due to covariance estimation. We show that the application of these techniques, for the system under study, results in close to optimal output SINR as well as low range side lobes without a significant increase in computational complexity.

### STAP PROCESSING

Space-Time Adaptive Processing 1 in the airborne plat-form compensates for two simultaneous effects: the presence of clutter (unwanted signal reflected from land or sea) which is spread in the frequency (Doppler) domain due to motion of the platform, and the presence of a jammer, which is localized in azimuth angle and distributed over all Doppler frequencies. STAP refers to the extension of adaptive antenna techniques to processors that simultaneously combine the signals received on multiple elements of an antenna array (the spatial domain) and from multiple pulse repetition periods (the temporal domain) of a coherent processing interval (CPI). This processing technique not only provides detection in combined clutter and jamming environments, but also improves detection of small and low-velocity targets and adds system robustness in the presence of errors. The process of electronically steering the radar receiver in different directions is called beam forming. Beam forming algorithms involve the application of weights to samples in a signal processing system. Weight application is computed as a dot product between weight vectors and sample vectors, where the vectors span the radar input channels (elements). In a non-adaptive beam forming algorithm the weights are fixed. In an adaptive beam forming algorithm, the weights are computed from the input training data and the beam steering vectors.

### STAP ALGORITHMS

The optimal adaptive weight vector w for a given steering vector s is related to the interference covariance matrix R through the relationship Rw=s. Covariance matrix R is estimated R=X H X, where training set matrix X is a subset of the input data. For reasons of numerical stability, instead of explicitly forming R, we compute the Cholesky decomposition of R directly from X via QR decomposition 2 . Specifically, we compute A=QX, where A is upper-triangular. Since Q is an orthogonal, unitary matrix, Q H Q=I, where I is the identity matrix. Therefore, R=X H X is equivalent to R=A H A. Since A is triangular, w is easily computed from the following two back solve operations: A H y=s and Aw=y. The beam forming operation is a matrix vector multiply Z=Yw where Y is the input data and Z is the output data in that beam. Fully adaptive STAP, where a separate adaptive weight is applied to all pulses as well as all channels, requires the solution to a system of linear equations of size MN, where N isthe number of array elements and M is the number of pulses per CPI. For typical radar systems, the product MN may vary from several hundreds to tens of thousands. For a variety of reasons, not the least of which is the computational power required for fully adaptive STAP, partially adaptive STAP is a more attractive candidate for implementation in an actual system. In a partially adaptive STAP algorithm, the prohibitively large problem of a fully adaptive STAP algorithm is bro-ken down into a number of independent, smaller and more manageable adaptive problems while achieving near-optimum performance.

The first step in the partially adaptive algorithm is non-adaptive filtering to reduce the dimensionality of the problem. The weight vector is computed by solving a sample matrix inversion (SMI) problem as described above with the final, reduced-dimension data. The initial, non-adaptive filtering can be either a transformation into frequency domain (FFT over pulses in each channel or element) or beam space (non-adaptive beam forming in each pulse). If desired, both space and time transformations can be performed, or non-adaptive filtering can be eliminated altogether. The non-adaptive filtering determines the domain (frequency or time, element or beam) in which adaptive weight computation occurs. Once the input data are transformed, a separate adaptive SMI problem is solved in each Doppler bin or pulse repetition interval (PRI), across either elements or beams, depending on the domain of the adaptation. Therefore, there is a natural, inherent parallelism in partially adaptive STAP algorithms, which will form the first step in parallelizing the STAP problem domain. The STAP kernel used in this analysis is adaptive in the frequency domain, and is therefore called a Higher-Order Post-Doppler (HOPD) algorithm. The input to the kernel is a 3-D data cube consisting of sample data (range gates) from some number of radar channels, for some number of Doppler bins. The range gates are divided into range segments. The sample matrix, or training set, is formed for each Doppler bin and range segment by selecting a subset of the range gates from all channels for that Doppler bin and the two adjacent Doppler bins. The 2-D data from the three Doppler bins are concatenated to form a the 2-D matrix used for SMI. The algorithm to upper triangularize the sample matrix is based on Householder transformations. Performance of the adaptive beam forming algorithm varies with the size of each training set matrix. Performance is particularly sensitive to the number of columns (degrees of freedom) as well as the ratio of columns to rows in the matrix (sample ratio). Therefore, these parameters, as well as radar-specific parameters, will be used to define the scalability of the algorithm mapping. Two algorithm approaches to STAP will be analyzed in this paper. They are interference covariance matrix estimation and direct data domain processing.

### INTERFERENCE COVARIANCE MATRIX ESTIMATION

### APPROACH

Interference covariance matrix estimation is the well-known classical approach to STAP implementation. Research using this approach has been around since the 70's. The approach begins by utilizing the initial antenna structure in 1 and adding tapped delay lines after each receiver.

As observed in the above , each of the taped delay signals is adaptively weighted as before according to the designer's processing algorithm that minimizes interference and noise while preserving or enhancing the desired signal. The final output signal is the sum of all the weighted taps. For a system of N antenna elements and M taps per element, a total of NxM signals are received and weighted. Thus, the input signal has the form:

Where denotes transpose and is the multiple of the time the sample is taken. The received voltages on the taps are the sum of the desired signal in the direction of interest plus noise. Hence,

Where L (k) is the contribution on each tap from the desired signal in the “look direction” and N(k) is the noise contribution on each tap. Again, because of the NxM signal taps, L(k) & N(k) have the form:

### APPLICATIONS

Future airborne and space-based sensor systems will operate in difficult environments where the detection of small, highly-maneuverable targets against a strong clutter background, and in the presence of jamming, is required for effective battle space surveillance. Increases in power-aperture alone are not adequate to detect advanced threats under hostile conditions. Advances in radar signal processing are required to achieve the order-of-magnitude sensitivity improvements required for future sensor systems. Researchers in the Sensors Directorate are investigating ways to improve the current capabilities of space-time adaptive processing (STAP) for new applications such as Sensor Craft, Targets Under Trees, and space-based radar programs. A target in an airborne surveillance scenario competes with ground clutter and white noise jamming in multiple dimensions as depicted in 1. In the Azimuth projection, a target competes with main beam clutter and white noise jamming at a discrete angle. One dimensional adaptive beam forming allows for mitigation of the jamming energy, however, it will also affect the target signal along with the main beam clutter. A projection of the target signal on the Doppler projection axis indicates target competition not only with jamming energy across the entire Doppler spectrum, but also strong Side lobe clutter energy. However, it is apparent in 1 that the target is separable from clutter and jamming in the two-dimensional angle-Doppler domain. STAP is a two-dimensional filtering technique that allows for the simultaneous mitigation of both airborne radar clutter and white noise jamming. STAP uses the multiple spatial channels in a phased-array antenna and the multiple coherent pulses transmitted and received by the radar to form an adaptive weight vector that is applied to the received radar spatial and temporal samples. This technique preserves target signal-to-noise ratio, thus improving the performance of subsequent detection stages. In order to calculate an adaptive STAP weight vector, the statistics of the interference environment are determined by forming a covariance matrix. The matrix is typically not known apriori and must be estimated from training or secondary space-time radar samples. This estimation process assumes the secondary data samples are independent and identically distributed (IID). However, recorded mono static radar data, proven very non-homogeneous, is non-stationary and, thus, violates the IID assumption. These facts are exacerbated when a bistatic radar system is employed. Further research is required to overcome the issues of training the STAP weight vector and the computational cost in forming a covariance matrix and adaptive weight vector. When using STAP, the increase in the number of elements and the number of transmitted pulses on new sensor systems comes with an exponential computational increase. Current power, weight, and size constraints make the real-time implementation of full degrees-off reedom STAP techniques on airborne/space borne platforms impractical. The secondary data cells used in a STAP processor to estimate the interference covariance matrix are typically very non-homogeneous, exhibit spectral dispersion and a non-state, and cannot be arbitrarily selected in a symmetrical window around the test cell as is often done for mono static applications. Bistatic clutter violates many of the basic assumptions from which STAP algorithms were historically designed. New methods must select secondary data cells in a more intelligent manner based upon knowledge of the bi static geometry, underlying terrain features, and statistical characteristics of the clutter. Sensor Craft and unmanned air vehicle applications require the use of nonconventional antenna apertures for their multi-mission intelligence, surveillance, and reconnaissance functions. This includes complex, doubly-curved conformal arrays and appliqué apertures. Conventional STAP processing approaches assume a linear or planar array with uniform element spacing. STAP approaches for these complex antenna surfaces are under development and offer the ability to simultaneously achieve low minimum discernable velocity and high sub clutter visibility. The integration of conventional numeric signal processing approaches, such as STAP, with non-conventional symbolic processing approaches, such as artificial intelligence and expert systems, offers the potential for assessing the interference environment and dynamically changing various parameters within the radar system. This includes the waveform parameters in order to achieve transmit adaptivity. It also includes the processing functions performed in the radar receiver and signal processor such as pulse compression, adaptive filtering, constant false alarm rate detection, and tracking. Directorate research to improve STAP's current capabilities demonstrates order of magnitude performance improvements using novel approaches.

### CONCLUTION

It appears that choosing between these two algorithms for STAP systems is highly problem dependent. On one hand, statistical methods (covariance estimation) greatly outperform non-statistical methods (D 3 ) when the interference environment is known to be homogeneous. However, if the interference scenario ever becomes heterogeneous, statistical methods will fail. In addition, the computational burden of statistical STAP algorithms makes real-time adaptive processing difficult or even impossible in highly transient environments. This lends non-statistical methods such as D 3 as the algorithm of choice with inferior homogeneous performance as a trade off. Solutions to this problem may lie in the development of algorithms that combine previous statistical and non statistical algorithms.

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