- Research Article
- Open Access

# Fully Adaptive Clutter Suppression for Airborne Multichannel Phase Array Radar Using a Single A/D Converter

- Dan Madurasinghe
^{1}Email author and - AndrewP Shaw
^{1}

**2010**:209761

https://doi.org/10.1155/2010/209761

© D. Madurasinghe and A. P. Shaw. 2010

**Received:**2 March 2010**Accepted:**10 August 2010**Published:**17 August 2010

## Abstract

This study considers an airborne multichannel phase array radar consisting of an analog phase shifter on each channel, where the sum channel (output) is digitised using a single A/D converter. Generally for such a configuration, the array weights are predetermined for each transmit/receive direction and are nonadaptive to the clutter. In order to achieve any adaptivity to the environment, the convention is to split the array into at least two subgroups and implement two analogs to digital converters. A single A/D-based software solution (numerically stable, robust) is proposed to achieve the full sidelobe adaptation to clutter. The proposed algorithm avoids these engineering complications involved in implementing multiple A/Ds for radar applications while maintaining the same desired performance. As a large number of airborne radar platforms already exist worldwide, the possible applications of this proposed fully adaptive upgrade as a software solution can be huge.

## Keywords

- Data Stream
- Switching Time
- Processing Gain
- Steering Vector
- Coherent Pulse

## 1. Introduction

The objective of an adaptive array is to combine the elemental outputs, appropriately weighted so as to generate an output that is interference free. To achieve this we need to have observations from a sufficient number of channels of the array that we can use to calculate the adapted weights [1–3]. If a "traditional" analog beamformer is employed, then it is not usually possible to observe the individual channels. If multiple beamforming manifolds are used, it is possible to compute an adaptation in beamspace, but in most cases only a small number of beams are produced severely restricting the number of interfering sources that can be accommodated. In practice this is further complicated because "real" arrays, especially with near-field scatterers, do not have uniform elements.

There are a number of engineering advantages to employing an analog beamformer, particularly related to the number of digitisers employed and the consequential simplification in all those processes associated with digitisers (maintaining alignment, power consumption/cooling, and data management), but if low sidelobe performance is required, this is offset by the increased difficulty in calibration of the array, especially for active arrays, where effective impedance of path depends upon the frequency, power on/off, and phase status of adjacent elements. Current capabilities are such as to favour the use of analog beamforming to produce a small number of beams, typically a single sum, also known as a "sigma" beam, and additionally a number of difference beams, also known as "delta" beams, and then either (a) sacrifice low sidelobe performance; (b) require complex calibration; or (c) attempt to mitigate the sidelobes with limited adaptive processing, such as "sigma-delta" processing [4] or other forms of reduced-dimension adaptive processing.

This study considers a phased array wherein we can adjust the amplitude and phase of each element, but where we can only observe the output of a single "sum" channel, and introduces an algorithm on this channel to adaptively null any residual sidelobe clutter. The method described in this paper transmits pulses in each beam direction. Firstly coherent burst of pulses are received using an initial set of antenna weights. Then, after allowing for a switching delay, a second burst of pulses are received using a set of weights that are linearly independent, whilst satisfying certain requirements. The new algorithm developed in this paper uses the properties of the data stream to adaptively null the ground clutter with degrees of freedom. The procedure we have developed is tested using both simulated data and data from the MCARM system [5], suitably processed to represent a single "sum" beam, including the delay caused by the switching of the antenna weights. The results obtained are then compared with the fully adaptive solution available via mutlichannel data with the same number of degrees of freedom.

This paper is organised as follows. In Section 2, we formulate the standard multichannel problem and consider multichannel observation-based signal processing gains (full STAP, beamspace STAP, etc.) to provide a baseline for comparison. Section 3 formulates the proposed software solution using a single observation channel and derives the signal processing gain. Section 4 examines the theoretical performances and compares the algorithms using Monte Carlo simulation. Finally Section 5 uses MCARM data to validate the results.

## 2. Formulation

### 2.1. General Formulation

*N*elements, which transmits and receives a burst of coherent pulses. The measured

*N*1 signal vector due to the coherent pulse and range ring, which is also referred to as the fast time scale, can be expressed as

**w**represents the received weights vectors which are chosen to satisfy . The simplest beamforming choice is the uniform weights given by , and here we have ignored transmit pattern effect. The above data stream is then passed through a Fast Fourier Transform (FFT) processor to obtain the output for each Doppler bin of interest. In the presence of clutter the performance is reduced severely.

### 2.2. Adaptive Solutions (STAP)

In order to achieve full adaptivity to the clutter, generally the radar system has to undergo a multiple-A/D (hardware) upgrade where a number of sampled data streams are made available. However, for practical implementation, typically one would apply some of the degrees of freedom nonadaptively via Pre Doppler STAP, Post Doppler STAP, or Beamspace STAP, in order to simplify the computations and inversion of the covariance matrix. This will not lower the performance significantly of the system providing the number of adaptive degrees of freedom sufficient to null the number of interference signals present in the system due to clutter-related arrivals, and the results are well documented in the literature[1, 2].

where is the number of range cells used for averaging. It should be noted that is equivalent to full STAP solution requiring an A/D for each channel, which allows us to use adaptive degrees of freedom.

## 3. Multi-Transmit Receive STAP (MTR-STAP)

### 3.1. Proposed Software Solution (MTR-STAP)

where , with . The vector can be considered as the secondary receivers spatial component of the steering vector of size which is synchronised to the same coherent clock as the first transmission. This is equivalent to the original spatial steering vector, but, it is a function of the angle of arrival, the Doppler frequency of interest, the switching delay, and the pulse repetition interval, related to the target or clutter patch of interest.

Just as we avoid the spatial ambiguity by restricting our array spacing to half-wavelength, we can avoid this ambiguity by restricting the switching delay to less than one PRI (= ), because, in order to avoid Doppler ambiguities, we already have the restriction of possible Doppler frequencies to ). In any case, if one ever needs to resolve this ambiguity, the next possible value of the switching time is ( ), for some . A procedure is developed later to estimate the switching time delay very accurately subject to the above ambiguity.

### 3.2. Properties of the Two Data Streams

where is the receive patterns ratio with the property , is a combined weights matrix of size , represents a independent random entries, and is the matrix of zero entries.

### 3.3. Space-Time Stacking

### 3.4. Choice of Receiver Patterns

where are (weights) easily obtainable by equating the coefficients of the above product which is of order polynomial in . These are the weights for the second receiver. Large value of for the pattern ratio forces us to switch off too many elements at the first receiver.

## 4. Theoretical Performance Prediction

### 4.1. Comparison of Performances

In order to predict the performance of the MTR-STAP algorithm with the nonadaptive single A/D-based-FFT solution, as well as potential multichannel upgrades, we would like to establish a theoretical space-time clutter covariance matrix for each case using the parameters similar to MCARM system. Consider a 22-channel half wavelength equispaced airborne array with PRF = 1984 Hz,
,
m/sec,
, and
The estimation of the clutter covariance matrix was carried out using two methods. The continuous model described in [7] and another straightforward discrete method is to first determine a value for
(*≈*
) as the desired clutter degree of freedom. The discrete method considers a series of angles of arrivals to represent each Doppler bin of interest by using the equation (the ridge)
=
. This equation provides us with a series of clutter angles for
generally close to the figure
. This procedure creates nonuniform patches on the ground, and hence a series of power levels are associated with each patch, say
(
which follow values proportionate to the patch size
. Finally the covariance matrix is estimated by summing
terms, where
represents the appropriate manifold. In both approaches, we compute the rank of the covariance matrix to confirm the degrees of freedom.

### 4.2. Sensitivity to Switching Time Errors

### 4.3. Optimisation with Respect to Switching Time

and refers to the absolute value of a complex number (see the appendix for the proof). Simulation study has shown that the formula in (36) always produces a 99.9% accurate estimate of the switching time for all look directions which excludes broadside. This result is tested using MCARM data.

## 5. Analysis of MCARM Data

### 5.1. Selection of Pattern Ratios

The US Air Force Research Laboratory, Rome Research Site collected a large amount of multichannel airborne radar measurement (MCARM) data [5]. The size of the MCARM array's calibrated matrix ( ) is 22 129, where 129 is the number of possible beamforming angles available in azimuth. Other important MCARM parameters are as follows: transmit frequency = 1240 MHz, the number of coherent pulses = 128, pulse repetition frequency = 1984 Hz ( sec.), and number of cells = 680 (0.8 sec pulses).

### 5.2. Switching Time Estimation

Clutter center estimate for several MCARM data sets and the corresponding optimal switching time estimates.

Data set number | (estimated clutter center (Hz)) | (estimated switching time (seconds)) |
---|---|---|

Rd50150 | 0 | 0.8350 |

Rd50151 | 0 | 0.9890 |

Rd50152 | 310 | 0.9337 |

Rd50153 | 341 | 1.0735 |

Rd50154 | 325 | 0.9627 |

Rd50155 | 372 | 1.1052 |

Rd50575 | −108 | 0.8404 |

### 5.3. Signal Processing Gain

## 6. Concluding Remarks

The most important observation is that the MTR inverts a matrix of size
, but it does not mean it's adaptive degrees of freedom is
The simulation has confirmed that it is limited to
. At this stage this can only be verified using extensive simulation. Another observation based on simulation data as well as MCARM data is that the order of pattern ratio is best to be around half the total number of sensors in the array. In our theoretical simulation, even though we use 128
128 matrix inversions for both MTR and beamspace solutions, we always validated this using covariance matrix of rank *≈* 60 via both continuous and discrete clutter models. As soon as the rank of the covariance matrix increases beyond 64, the MTR with 128
128 matrix solution begins to fail, and one has to increase the length of the pulse train accordingly. This also explains why MTR processing gain is marginally inferior when it comes to MCARM data. The reduced STAP solution is able to apply 128 adaptive degrees of freedom, while the MTR is able to apply up to 64, with the same size matrix inversion. It is also important to notice the nonzero clutter centers where the clutter notch occurs in Figures 9(a) and 9(b). The solution presented in this study is much more robust than the multichannel multiple A/D solution when no jammers are encountered. This procedure can avoid all the complications involved in synchronising a number of A/D converters to achieve good results. This is not really a new STAP algorithm; rather, it provides a way to apply many standard STAP algorithms by constructing multichannel data out of a single A/D converter.

Furthermore, it also makes it much easier to calibrate the array with only a single A/D. The simulation study has shown that the optimal configuration would be to make equal to around half the number of sensors in the array. The major drawback in the software approach is that we need twice as many pulses to maintain the same performance or else a 3 dB loss occurs in the Doppler resolution. It is also possible to extend the algorithm to null sidelobe jammers as well. This analysis is beyond the scope of this paper.

## Declarations

### Acknowledgments

The authors would like to thank the Defence Science and Technology Organisation (DSTO), Australia, for sponsoring this work. Comments by Dr. Leigh Powis of DSTO and the valuable suggestions by the reviewers are highly appreciated.

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.