Properties of Spherical Lens Antennas for High Altitude Platform Communications

HAPs may exploit millimetre-wave spectrum by supporting multi-cell architectures. The overall data capacity is governed by the properties of the antennas which serve the cells. Optimum coverage is expected when each antenna radiation pattern is tailored to its respective cell, but this leads to a bulky payload. In contrast, this paper shows how a payload based on multi-beam spherical lenses, which have wide-scan properties but also offer circular beams, can give comparable performance while offering a much more compact payload. Models for spherical lens radiation patterns are presented which include the effect of the primary feed beamwidth. This allows a comparison of aperture diameter, sidelobe level, and the resulting co-channel interference, from which may be estimated the performance and relative mass of different antenna payload types. INTRODUCTION. This paper concerns communications from High Altitude Platforms (HAPs), which may be based on either aircraft or balloons, and stationed in the stratosphere at altitudes of around 17-22 km [1], [2]. This geometry will allow for line-ofsight links which are required for effective exploitation of the high bandwidths available at mm-wave frequencies. Multi-cell architectures will allow for spectrum re-use and will require a multi-beam HAP payload [4] possibly using a group of spot-beam antennas. The level of carrier-to-interference ratio (CIR) is a consequence of the spatial overlap of the antenna radiation patterns. The ITU have allocated the 47/48 GHz band [6] for usage by HAPs worldwide, and the 27/31 GHz band has also been allocated to about 40 countries [7]. At these frequencies it is difficult and expensive to produce electronically reconfigurable antennas based on phased-array principles and digital beam forming (DBF). For example, DBF presents challenges associated with: the close spacing of radiating elements, the requirement for a large number of elements, the need to minimise sidelobe levels, the cost and complexity of RF active circuits, and the problem of scanning loss. The latter point is particularly detrimental for HAPs communications because links to users at low elevation angles, where scanning loss for a horizontal planar array are worst, experience also the longest free space and atmospheric losses. Nevertheless a number of programmes are developing DBF antennas for Ka band e.g. [8] which reports on a 16-element module, and the Japanese HAPs programme [9] have reported a similar prototype for 28 GHz while conceding that horn antennas stabilised by mechanical gimbals are a more pragmatic solution for 48 GHz. The more conservative solution for the HAP antenna payload is a group of aperture antennas, where each antenna serves a single quasi-stationary cell. This approach has been studied in some depth [4], [5], [10] where the important relationship between the radiation patterns and the CIR levels on the ground has been quantified for various channel re-use schemes. Ultimately, the economic viability of a HAP cellular network may be determined by the extent to which it can maximise the re-use of spectrum. This paper explores the properties of multi-beam antennas based on spherical lenses, since these can yield a much more compact HAP antenna payload compared to the use of single-beam aperture antennas. An estimate of payload mass compared to CIR coverage levels is introduced. DEDICATED BEAMS FOR THE HAP ANTENNA PAYLOAD. It is worth listing the pros and cons of using dedicated beams, i.e. one antenna per cell. Advantages include: • • • • • each antenna pattern can be tailored to the shape required by each cell. asymmetric beams yield equal size, circular cells, which aids tessellation of cells and maximises coverage [11]. low sidelobe levels are feasible e.g. -40 dB relative to peak gain. Disadvantages include: A bulky, massive payload, which requires mechanical stabilisation. A non-reconfigurable network. These disadvantages can to some extent be overcome with multiple-beam antennas which allow for the payload mass and volume to be reduced, but at the expense of eroding the advantages associated with dedicated beams because it becomes more difficult to tailor each beam to each cell. Multi-beam aperture antennas typically use a cluster of primary feeds to illuminate a secondary aperture which might be a prime-focus reflector or lens, but the angular range of scanning is limited. For a HAP payload a wide conical scan is needed e.g. 150° for users at elevation angles as low as 15°. The following sections explore the potential to use multiple-beam, wide-scanning antennas based on spherical lenses, and quantify the CIR values which could be expected. PROPERTIES OF SPHERICAL LENS ANTENNAS. In the context of HAPs communications, the very useful property of antennas using spherical lenses is their ability to form multiple beams over a wide range of angles without inducing any scanning loss. A number of spherical lens variants are well know, and some are briefly reviewed below. A classic type of spherical lens is the Luneburg lens [12], which focuses an incident plane wave at a point on the lens surface. The spherical geometry allows for multiple beams to be produced from multiple feeds [14], and it is this property which is attractive for a HAP payload. The Luneburg lens requires a radial variation of dielectric constant: 2 2       − = R r r ε (1) where r is radius within the lens, and R is the outer radius. Thus the dielectric constant varies from 1 at the lens edge to 2 at the centre and there is no reflection loss due to abrupt transitions. This leads to a very good aperture efficiency, but it somewhat problematic to manufacture. In practice such a lens is often fabricated from a set of concentric shells and this inevitably degrades the efficiency: a useful treatise is given by [15]. However, for limited bandwidth applications a two-shell design can give almost equivalent performance [16]. A single shell spherical lens has no single focus, but exhibits a paraxial focus when a small proportion of the lens is illuminated. The paraxial focus may lie inside or outside the lens outer radius. A low dielectric spherical lens can give good performance e.g. [17] reports on a Teflon lens (εr = 2.08) for wide-scanning automotive radar at 77 GHz and is of course much more simple to manufacture than a multi-shell lens. Using the Luneburg lens aperture distribution given by [12], where the primary feed pattern is also taken into account, the far field radiation pattern can be computed. The geometry is illustrated in Fig. 1 for a generalised lens where the focus may lie inside or outside the lens radius a. However, for the remainder of the analysis we will assume a conventional Luneburg lens where f = a.