Abstract

Linear sparse antenna arrays have been widely studied in array processing literature. They belong to the general class of non-uniform linear arrays (NULAs). Sparse arrays need fewer sensor elements than uniform linear arrays (ULAs) to realize a given aperture. Alternately, for a given number of sensors, sparse arrays provide larger apertures and higher degrees of freedom than full arrays (ability to detect more source signals through direction-of-arrival (DOA) estimation). Another advantage of sparse arrays is that they are less affected by mutual coupling compared to ULAs. Different types of linear sparse arrays have been studied in the past. While minimum redundancy arrays (MRAs) and minimum hole arrays (MHAs) existed for more than five decades, other sparse arrays such as nested arrays, co-prime arrays and super-nested arrays have been introduced in the past decade. Subsequent to the introduction of co-prime and nested arrays in the past decade, many modifications, improvements and alternate sensor array configurations have been presented in the literature in the past five years (2015–2020). The use of sparse arrays in future communication systems is promising as they operate with little or no degradation in performance compared to ULAs. In this chapter, various linear sparse arrays have been compared with respect to parameters such as the aperture provided for a given number of sensors, ability to provide large hole-free co-arrays, higher degrees of freedom (DOFs), sharp angular resolutions and susceptibility to mutual coupling. The chapter concludes with a few recommendations and possible future research directions.

Highlights

  • Array processing research has flourished and raked-in much attention in the past five to six decades

  • While the difference coarray approach is well suited for the Direction of Arrival (DOA) estimation of circular sources, many non-circular source signals exist in practice

  • One of the prominent designs for sparse arrays that are suitable for non-circular sources is the nested array with displaced subarray (NADiS) as it provides closed-form expressions (CFE) for element positions, virtual apertures, and DOFs

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Summary

Introduction

Array processing research has flourished and raked-in much attention in the past five to six decades. Sensor arrays find application in diverse fields such as radar (radio detection and ranging), space exploration, sonar (sound navigation and ranging), seismology, chemical sensing, medical imaging, wireless communications, navigation, source localization etc. Akaike information criteria (AIC) test and/or minimum description length (MDL) test and their variants are generally used to estimate the number of sources beforehand These methods are susceptible to failure when the signals are coherent [15]. In a passive array signal processing system, the array of sensors just listens to the environment, as in passive sonar, radio astronomy and wireless communication. An antenna array can serve two purposes It can help (i) determine the directions from which source signals impinge the receiver (direction of arrival (DOA) estimation), and (ii) in focusing the radiation pattern towards certain directions based on the knowledge of desired and undesired signal directions (beamforming). DOA estimation assumes prominence in 5G as DOA-based beamforming is one of the main requirements for smart antennas [20]

Motivation for sparse arrays
Contribution of this chapter
Introduction to sparse arrays
Sparse array notations
Difference set and the difference co-array
The weight function
Minimum redundancy arrays (MRAs)
Minimum hole arrays (MHAs)
Co-prime arrays
Nested array or the two-level nested array
Super-nested arrays
Yang’s improved nested array
Huang’s nested array
Triply primed array
Array factors of some well-known sparse arrays
MRAs with the same number of sensors and aperture might have different sensitivities
Sparse arrays with special properties
Sparse arrays for active sensing
Sparse arrays for DOA estimation of non-circular sources
Array motion
Sensor failures in ULAs
Sparse multiple input multiple output (MIMO) radar arrays
Future scope
Conclusion

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