Beamforming

The following sections are included:

• Dedication
• Preface
• Acknowledgments
• Contents
• List of Notations

The following sections are included:

• Introduction
• Pulsed Doppler radar: System and signal models
• Conventional beamforming
• Low-rank beamforming algorithms
  • Eigenvalue-decomposition-based algorithms
  • Krylov subspace-based algorithms
  • Joint iterative optimization (JIO)-based algorithms
  • Joint interpolation, decimation and filtering (JIDF)-based algorithms
• Sparsity-aware beamforming algorithms
• Knowledge-aided beamforming algorithms
• Simulations
• Concluding remarks
• References

Look-down airborne radars illuminate significant amounts of ground clutter, which due to the radar platform motion has a geometrically defined angle-Doppler characteristic. Space-time adaptive processing (STAP) is often employed at the receiver array to capitalise on the clutter angle-Doppler relationship and to detect targets, but there are significant problems with this approach in real-world scenarios, such as clutter non-homogeneity, which severely degrade STAP performance. In this chapter, the use of transmit beamforming is explored to alleviate some of these issues. The focus of the chapter will be the non-homogeneity of STAP training data caused by the forward-looking radar platform. In particular, the signal model for this scenario is developed and it is shown that there exist circumstances where transmit beamforming can significantly increase performance, particularly in range-ambiguous scenarios. Robust beamforming under uncertainties about the geometry will also be explored.

Synthetic aperture radar (SAR) has all weather capabilities, which gives it an advantage over optical instruments for remote sensing during the night or cloudy weather. SAR also has the ability to detect targets hidden below foliage. An effectively long aperture, which would otherwise be impractical to build, is created due to SAR's method of moving along a flight path during data collection. This allows the creation of higher resolution images when compared to real aperture radar (RAR), where the radar system is stationary during data collection. Therefore, SAR has been used in many remote sensing applications including geographic mapping, ocean surveillance and ground moving target indication (GMTI), to name but a few. However, with conventional SAR data collection using a single transmitter and receiver beam there is a trade-off between resolution and the dimensions of the imaged area, in particular between cross-range resolution and the swath-width. In order to overcome this contradiction and to provide greater flexibility in meeting specific application requirements, different transmitter and receiver configurations have been proposed in the literature using multiple beamformers. The use of these systems allow the employment of additional beamforming algorithms such that ambiguity, jammer and clutter suppression can be achieved…

Arrayed multiple-input multiple-output (MIMO) radar [1,2] offers enhanced resolution and improved estimation accuracy compared to conventional radar. Consequently, significant research attention has been drawn to the field of MIMO radar. An arrayed MIMO radar is a radar system which employs two antenna arrays: one to transmit and one to receive. For each of these arrays, the antenna elements are distributed in three-dimensional real space about a common reference point. This chapter is concerned with the task of exploiting the arrays' geometries (antenna locations) in both the transmitter and receiver in order to detect, resolve and estimate the various parameters of multiple radar targets. Thus, amongst various conventional and nonconventional MIMO radar approaches presented in this chapter, an alternative representation of the arrayed MIMO radar system — namely, its equivalent virtual SIMO (single-input-multiple-output) configuration — is employed, allowing direct exploitation and analysis of the full MIMO system geometry. In particular, while the virtual array concept is heavily focused on the employment of specific algorithms (most commonly relying on the use of a bank of matched filters at the front end of the receiver) and assumes the absence of relative path delays or Doppler frequency, the formulation presented in this chapter makes no such assumptions about any specific processing applied at the receiver. Furthermore, the spatiotemporal receiver architecture presented in this chapter exploits the superior performance of a unique and fresh subspace-based Doppler, delay and direction of arrival (DOA) estimation system.

In this chapter different types of ship wake waves are described, as well as environment and synthetic aperture radar (SAR) parameters that allow the observation of certain wakes in SAR imagery. A number of common wake wave detection algorithms for 2D SAR imagery are studied. Then examples of SAR systems using two or more SAR beamformers for ocean applications are presented. In particular, the use of two SAR beamformers for the formation of interferograms is given.

Ocean towed arrays find applications in a variety of areas such as defence, oil and gas exploration and geological and marine life studies. The elements/ sensors of the towed arrays are usually hydrophones that receive acoustic energy which characterise the feature or environment being monitored. This acoustic energy may be generated by the feature under study itself (such as a marine animal) or be a reflected signal emitted by an acoustic source (such as a sparker or boomer). The major challenge in towed array processing is the receiver positional uncertainties resulting from the array's flexible structure in combination with the ship's turning maneuvers or water currents. These uncertainties can cause a significant reduction in the performance of the receiver array of hydrophones. Initially, in this chapter, we briefly explore and classify prevalent towed array signal processing techniques developed to address these uncertainties and efficiently perform tracking, channel estimation and reception/beamforming. Then, two specific techniques, namely subspace pilot calibration and H^∞-based robustification, are presented, evaluated and compared using both “synthetic” and real data.

In this chapter, an array auto-calibration approach is described which is capable of estimating geometrical (array shape), gain and phase uncertainties associated with an array of sensors. As opposed to other data-based array calibration techniques in the literature, no transmitting sources are required (either pilot sources or sources of opportunity). Instead, elements in the array operate as transceivers which are utilised to auto-calibrate the array. Hence, unlike in the case of pilot calibration approaches, all elements are at unknown locations. Under this scenario, the distance of the transmitting elements from the array is small compared to the aperture of the Rx-array formed by the remaining elements. Hence, the standard plane wave propagation assumption used in array processing is no longer valid and a spherical wave propagation model should be considered. Monte-Carlo simulations are used to analyse the performance of the approach.

A ubiquitous task with array signal processing and wireless communications is interference cancellation. This can be achieved by using a beamformer which places nulls in the interference directions while maintaining relatively high gain in the direction of the desired signal. However, when pointing errors occur, the performance of the traditional Wiener–Hopf beamformer (or Capon beamformer) may deteriorate significantly. In this chapter, a robust array processor is presented which not only reduces the effect of pointing errors but also offers asymptotically complete interference cancellation. Prior to the beamforming, a linear subspace can easily be found using the knowledge of the nominal manifold vector. Then it is shown that the manifold vector corresponding to the desired signal can be obtained by using this linear subspace and the signal subspace together. To eliminate much of the pointing error effects, the vector space projections (VSP) method is utilised to find a new manifold vector. Furthermore, we can obtain the power of the desired signal in a single-step computation. By using the estimated manifold vector and power of the desired signal, we can excise the effects due to the desired signal to form the desired-signalabsent covariance matrix. Then a weight vector orthogonal to the interference subspace can be constructed. Simulation results demonstrate the superior performance of this interference cancellation beamformer relative to other existing methods.

The following section is included:

• Index