EuCAP 2006 - European Conference on Antennas & Propagation

 
Session: Session 3A05A - Smart and Signal Processing Antennas, MIMO (08e)
Type: Oral Antenna
Date: Wednesday, November 08, 2006
Time: 08:30 - 12:20
Room: Risso 8
Chair:
Co-chair:
Remarks:


Seq   Time   Title   Abs No
 
1   08:30   A Simple Pattern Correction Approach for HF Surface Wave Radar on Buoys
Bourges, A.1; Guinvarch, R.1; Uguen, B.2; Gillard, R.2
1SONDRA, FRANCE;
2IETR, FRANCE

High Frequency Surface Wave Radar (HFSWR) allows to detect boats at long distance, far beyond the horizon [1]. It works typically from 3 to 30MHz, using long wavelengths (>10m), so their antennas take up a very large room. Furthermore, they must be located near the sea surface so that the surface waves are optimally generated and received. Both conditions imply a very high complexity when deploying such systems, especially near the coast. The concept of floating antenna array is to replace conventional coastal receive unit by a sea floating array, constituted of a set of receive buoys. The problem for sea-floating antenna array is that each phase center element has a different movement, caused by waves and wind. The three linear motions are described in Figure 1. In literature, compensation methods exist: perfect methods to correct exactly the radiation pattern are considered but they are very time consuming. On sea surface, buoys know a continuous movement in three directions, so the corrections will have to be realized in real time.


Figure 1: description of buoys motions on sea surface

Figure2: Radiation pattern with both vertical and longitudinal corrections

In this paper, only simple corrections for the both longitudinal and the vertical movements are studied. Both corrections of movements are sequentially realized. In [2], a method has been proposed that permits to correct the swell effect in the radiation pattern. The paper of Haupt [3] showed a synthesis of aperiodic array which has the same radiation pattern as periodic array. For sea floating antennas, the inverse problem can be realized. From the data of buoys displacement, new weights of antennas are computed. Compensations can be realized by forcing the weights of each antenna in the array to correspond to the zeros of the radiation patterns of periodically spaced array.

Figure 2 introduces the results with the sequentially compensations. The sidelobe level is practically lower at -30dB except for equal to -/2 and /2: the coupling between dipoles in the array and the important deformation generated by sea movement are two explanations of this problem. In spite of movement of buoys, aperiodic arrays with sidelobe level of -30 dB can be obtained in real time, with one /2 average motion, computing new weights adapted to the displacement of the antennas in the array. The perspective in short term is to find a method which will realize the compensation including transverse displacement. A thorough study of the buoys dynamic with simple pattern can be considered.

[1] L. Sevgi, A. Ponsford, and H.C. Chan "An Integrated Maritime Surveillance System Based on HFSWR", IEEE Antennas Propagation Magazine, Aug 2001, vol. 43, No4.
[2] A. Bourges, R. Guinvarch, B. Uguen, R. Gillard, "Swell Compensation for High Frequency antenna array on buoys", APS, July 2006, Albuquerque.
[3] R. L. Haupt, "Unit Circle Representation of Aperiodic Arrays", IEEE Transaction on Antennas and Propagation, oct 1995, vol 43, No10.

 
 
2   08:50   3-D Switched Antenna Array for Angle-of-Arrival Measurements
Kwakkernaat, M.R.J.A.E.1; Herben, M.H.A.J.1; de Jong, Y.L.C.2; Bultitude, R.J.C.2
1Technische Universiteit Eindhoven, NETHERLANDS;
2Communications Research Centre, CANADA

To measure the angles-of-arrival (AoAs) of individual multipath components in the mobile radio channel, antenna array structures are usually deployed in combination with suitable high-resolution algorithms.

The uniform circular array (UCA) has drawn much attention due to its uniform performance in azimuth. When more resolution is required with the lowest performance variation and the same number of antenna elements available, Y-shaped or X-shaped geometries should be preferred. Unfortunately, all of these planar array geometries exhibit a very poor performance in low elevation angles and are incapable of distinguishing waves coming from positive and negative elevation angles, making them unsuitable for 3-D AoA estimation.

Extending the circular array geometry to a spherical or cylindrical geometry reduces the resolution performance dramatically when the same number of elements are used. Therefore, in order to obtain high-resolution properties in azimuth as well as in elevation, in this paper the idea of the Y-shaped and X-shaped geometries will be extended into the third dimension to form the 3-D tilted cross array. The antenna array, shown in Fig. 1, consists of 31 elements that are connected to a receiver in sequence by means of fast switching.

The number of antenna elements is limited to allow measurements at practical mobile speeds.

Due to its centro-symmetry and uniform element spacing the array geometry fits perfectly with a recently updated version of the multidimensional Unitary ESPRIT algorithm, allowing for low complexity high-resolution signal estimation.

A well know effect that degrades the performance of antenna arrays in general is the mutual coupling between the array elements. To limit this effect, an impedance switching technique is used that terminates the in-active elements in a complex impedance.

In order to investigate the disturbing effects of shadowing, scattering and mutual coupling on direction finding using the new array geometry, measurements were performed at the David Florida Laboratory (DFL) in Canada. The antenna array was set-up in a measurement chamber on a turn table and connected to a receiver. Measurements were performed between -20 and +20 degrees elevation and the entire azimuth range. The obtained measurement data is used as input to the Unitary ESPRIT algorithm to estimate angles-of-arrival of incident waves.

From the results presented in Fig. 2 it can be seen that the impedance switching technique reduces the angular estimation error, although some errors remain in three distinct areas, i.e. around 50, 170 and 290 degrees. These three areas coincide with regions where subsequently one of the three antenna arms is shadowed by the antenna support structure. To circumvent this problem, a selection scheme was developed that discards the erroneous data from the shadowed elements for a wave incident in these areas by analyzing the spatial frequency estimates. The results show a significant improvement in estimation.

This paper will present the design considerations and the evaluation in terms of accuracy and resolution of a novel 3- D antenna array structure for high-resolution AoA estimation. Furthermore, a method will be presented that significantly reduces the errors caused by shadowing.

 
 
3   09:10   Experiments of Closely Coupled Monopoles with Load Matching in a Random Field
Fei, Y.1; Lau, B.K.2; Johansson, A.J.2; Andersen, J.B.3
1Institute for Digital Communications, University of Edinburgh, UNITED KINGDOM;
2Department of Electroscience, Lund University, SWEDEN;
3Department of Communication Technology, Aalborg University, DENMARK

MIMO is a popular wireless communication technology due to its ability to deliver significant performance improvements over conventional, single-antenna systems [1]-[3]. However, some applications require the antenna system to be compact, which results in strong coupling among the antennas and performance degradations.

Recently, it was shown that the antenna load can play an important role in the power and correlation performance of the antenna array [4]. In fact, the load can be chosen to result in low or zero output correlation for a given random field in which the antennas reside (see Fig. 1(a)). However, it was also evident that some tradeoffs are necessary between the criteria of antenna correlation and antenna system efficiency. The existence of two maxima in received power over different load impedances (see Fig. 1(b)) was also an interesting feature for the investigated antenna arrays [4]. Nevertheless, only numerical results were presented in [4] and no experiment had been performed to confirm the observed phenomena.

In the full paper, we will present the experimental setup and compare our experimental results with the numerical results. For convenience, we consider two quarter-wavelength (lambda/4) monopole antennas with separation distance of d/lambda. Each of the antennas is directly soldered to a load impedance synthesized using transmission lines and open-circuit stubs. More details will be provided in the full paper.

References

[1] J. Winters, "On the Capacity of Radio Communication Systems with Diversity in a Rayleigh Fading Environment,"IEEE J. Select. Areas Commun., vol. SAC-5, pp.871-878, Jun. 1987.
[2] I. E. Telatar, "Capacity of multi-antenna Gaussian channels," European Trans. Telecommun., vol. 10, pp. 585-595, 1999.
[3] G. J. Foschini and M. J. Gans, "On limits of wireless communications in a fading environment when using multiple antennas," Wireless Personal Communications (Kluwer Academic Publishers), vol. 6, pp. 311-335, Mar. 1998.
[4] J. B. Andersen and B. K. Lau, "On closely coupled dipoles in a random field," IEEE Antennas and Wireless Propagat. Lett., vol. 5, no. 1, pp. 73-75, 2006.
This work was supported by VINNOVA (grant no. P24843-3) and partly conducted within the Network of Excellence NEWCOM (Network of Excellence in Communications).

 
 
4   09:30   Smart Antennas Control in Complex Scenarios through a Memory Enhanced PSO-Based Optimization Approach
Azaro, R.; Benedetti, M.; De Natale, F.; Massa, A.
University of Trento, ITALY

In the framework of control methods for adaptive phased-arrays [1], this paper proposes an innovative technique for the adaptive control of phased-arrays based on an enhanced optimization strategy for properly dealing with complex scenarios and system models. Compared to other existing approaches dealing with far-field interferences [2], such a method focus on realistic situations where the jamming sources are located either in the near-field or in the far-field of the antenna. Moreover, the effects of the mutual coupling on the array system are taken into account through a suitable network model [3]. In order to carefully address the arising issues and to effectively deal with such complex environments, an optimization approach based on an enhanced PSO-based [4] algorithm has been used.

The numerical validation, carried out by means of different array geometries and in various noisy and interference configurations, confirmed that the proposed approach presents: (a) an enhanced computational efficiency allowing an improvement of the convergence rate without increasing the computational burden of the adaptive control; (b) a robustness to both near-field and far-field interferences; (c) the capability to face with and counteract the mutual coupling effects arising in realistic models of the array architecture.
As far as the main novelties of this contribution are concerned, they can be summarized as follows: (1) the optimization approach, which has been suitably designed by introducing learning capabilities through the definition of a memory mechanism integrated in a distributed strategy for the evolution of the adaptive control; (2) the mathematical formulation of the smart array control able to model time-varying scenarios characterized by randomly located jamming sources impinging on array architectures affected by inter-element interactions.

References

[1] M. Chryssomallis, "Smart antennas," IEEE Antennas Propagat. Mag., vol. 42, no. 3, pp. 129-136, Jun. 2000.
[2] M. Donelli et al., "An innovative computational approach based on a particle swarm strategy for adaptive phased-arrays control," IEEE Trans. Antennas Propagat., vol. 54, no. 3, pp. 888-898, Mar. 2006.
[3] J. Gupta and A. A. Ksiensky, "Effect of mutual coupling on the performance of adaptive arrays," IEEE Trans. Antennas Propagat., vol. 31, no. 9, pp. 785-791, Sep. 1983.
[4] J. Robinson and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Trans. Antennas Propagat., vol. 52, no. 2, pp. 397-407, Feb. 2004.

 
 
5   09:50   Optical Beamformed Array Performance
Dalmases, F.1; Blanch, S.1; Romeu, J.1; Jofre, L.1; Vidal, B.2; Marti, J.2; McKenzie, I.3; Vez, E.4; Santamaria, J.4
1AntennaLab, Signal Theory and Communications Dept., Universitat Politecnica de Catalunya, Barcelona, SPAIN;
2Nanophotonics Technology Center, Universidad Politecnica de Valencia, Valencia, SPAIN;
3European Space Agency, European Space Research and Technology Centre, Noordwijk, NETHERLANDS;
4SENER, Aerospace Division, Tres Cantos, SPAIN

In order to support large instantaneous bandwidths, wide scanning ranges and multiple simultaneous beams, spaceborne antenna arrays require a large number of transmit/receive (T/R) modules and high resolution true-time delay lines (TDL) and become extremely complex and bulky when implemented in monolithic microwave integrated circuits (MMICs). Optical beamforming networks (OBFN) are an interesting alternative due to the highly parallel processing capabilities and the bandwidth of photonic technologies. Among the existing OBFN architectures, those based on the use of Spatial Light Modulators (SLM) to control the polarization of optical beams (see Figure 1) show great potential.

Fig. 1. Block diagram of the optical beamformed array in reception

Although in the literature several free-space OBFN techniques have been proposed and prototyped, few has been done to study the impact of this technology in the performance of a large antenna array. This paper studies different implementation aspects of photonic beamforming like insertion loss, O/E conversion, architectures and its influence on the array system.

One of the main aspects to consider are the high insertion losses (IL) introduced by the different optical components and particularly by the SLMs. In order to quantify its impact in the system performance, the OBFN has been characterized as an optical microwave link where link losses are given by the IL of the free-space components. It can be seen that the gain, noise figure (NF) and the third-order intermodulation products (IP3) of the OBFN are dominated by the losses introduced not only of the SLM stages, but also by the multiplexing of the laser-source into the optical beams.

Performance can be improved with the use of erbium-doped fiber amplifiers (EDFAs) and avalanche photodetectors (APDs). In the selection of the proper EDFA gain and APD sensitivity, the additional noise sources introduced by these devices need to be taken into account. When a proper EDFA and APD combination is found, the OBFN gain and noise figure is increased considerably. Adjustments of the other elements of the array and architectural considerations would lead to the final solution.

The use of RF phase shifters with optical TDLs further improve the array figures, since losses due to optical multiplexing are reduced. This hybrid RF and optical beamforming architecture, combined with properly chosen RF amplification, approaches to the desired performance. It also offers new tradeoffs between the number of bits of the RF phase shifter, the bits of the optical delay line and the performance of the array.

With the employment of optical and RF amplification and a proper combination of optical-TDL and RF phase shifters, it is shown that optical beamforming is a feasible technology for for future wideband spaceborne antenna arrays.

 
 
6   10:40   A SVM-Based Multi-resolution Procedure for the Estimation of the DOAs of Interfering Signals in a Communication System
Donelli, M.; Azaro, R.; Lizzi, L.; Viani, F.; Massa, A.
University of Trento, ITALY

In the last few years, there has been a growing demand for high performance devices in mobile and wireless communication systems. Several researches have been devoted to the development of methods able to detect and to track the signals coming from different and arbitrary directions. The knowledge of the directions of arrival (DOAs) of the unknown interfering and desired signals significantly improve the performances of an adaptive array for achieving high interference rejection and signal of interest enhancement. This goal can be accomplished by means of adaptive arrays by placing deep nulls in correspondence with the DOAs of the interfering signals. A number of techniques have been proposed for such a purpose [1]. For instance, the multiple signal classification (MUSIC) algorithm and the estimation of signal invariance techniques (ESPRIT). Although these approaches are able to detect signals with reduced angular separations and for low signal-to-interference-plus-noise ratios, they require high computational resources and some knowledge on the geometrical and electrical characteristics of the sensors as well as on the environment. Recently some alternative techniques based on learning-by-examples techniques [2] have been proposed. In such a framework, support vector machines (SVMs) can be efficiently used for localizing single as well as multiple signals. The SVM was introduced by Vapnik [3] and recently, it has found useful and effective in dealing with various and complex electromagnetic problems. The main features of SVM are concerned with their generalization capabilities and robustness. After the training procedure, which can be performed once and off-line, the DOAs of the signals incoming on the receiver are estimated in real time and with a limited amount of computational resources. In such a work, the estimation problem is addressed by considering an integrated strategy based on a SVM classifier and on an iterative multi-zooming procedure. A succession of approximations of a map of probability of the DOAs of the signals is defined starting from the same training set. At each step, the angular resolution is increased in a limited set of angular regions (called angular regions of interest, AROIs) defined at the previous zooming step and characterized by a greater value (with respect to the remaining part of angular investigation domain) of the probability of occurrence of the interference signals. The multi-step procedure is stopped when the required degree of accuracy in terms of angular resolution is reached in the AROIs. Summarizing, the main advantages of the proposed strategy are: (a) the favorable trade-off among computational complexity, angular resolution and the easy hardware implementation. In order to demonstrate such features, a large number of numerical experiments have been performed and a representative set of results concerned with planar arrays both in noiseless and noisy conditions will be shown and discussed.

References

[1] R. O. Schimidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propagat., vol. 34, pp. 3226-3231, 1986.
[2] A. H. El Zoogli, C. G. Christodoulou, and M. Georgiopulos, "A neural network-based smart antenna for multiple source tracking," IEEE Trans. Antennas Propagat., vol. 48, pp. 768-776, May 2000.
[3] V.Vapnik, Statistical Learning Theory. New York: Wiley, 1998.

 
 
7   11:00   Implementation of a Miniaturised Antenna Array with Predefined Orthogonal Radiation Patterns
Weber, J.; Volmer, C.; Blau, K.; Stephan, R.; Hein, M.A.
TU Ilmenau, GERMANY

This paper describes the realisation of an antenna array system consisting of three, quarter-wavelength spaced, monopoles and a passive network. This compact planar network decouples and matches the antenna array to prevent gain reduction. At the same time, the network forms orthogonal radiation patterns at the system ports, which divide the space in three different sections. The described system promises switched beam applications in small mobile platforms, where lack of space and processing power prevents the use of conventional antenna arrays.


Modern antenna arrays are expected to assume different modes of operation, to enhance the capacity and quality of communication channels. Such improvements result from a consequent exploitation of pattern diversity. An antenna consisting of p radiating elements possesses p-1 degrees of freedom to synthesise a desired radiation pattern by applying appropriate feeding currents to the antenna ports. Increasing the number of radiators not only increases the number of degrees of freedom but also the physical dimensions of the antenna. This drawback restricts the use of smart antennas in small mobile platforms. Placing individual radiators closer together aggravates the problem of mutual coupling between antenna ports: Power fed into the array ports is increasingly reflected towards the generator and thus cannot be radiated into space - the array becomes less efficient. We have demonstrated previously a method to decouple and match a miniaturised antenna array [1], [2]. Here, we present measured data of a successful implementation of an antenna system developed according to that method. The antenna array consists of three monopoles designed for 1 GHz, which are separated by one quarter of a wavelength, i.e., 75 mm. The desired system port patterns define the current transfer matrix of the network [2]. For a 3-element array, such a network contains 21 elements. By optimisation, we could eliminate the eight elements having the smallest element values, and still achieved robust operation of the network. The values of the remaining elements are between 2 pF and 11 pF for the capacitors and between 3 nH and 12 nH for the inductors. For the realisation of the network, we designed quasi-lumped network elements that were printed using a standard PCB process (figure 1d). The shunt elements were realised by stubs. The measured frequency response of the antenna system is depicted in figure 1b. The data clearly demonstrate the successful operation of the decoupling and matching network (DMN) over a bandwidth of approximately 10 MHz. The three measured system port patterns shown in figure 1c agree very well with numerical simulations. Our results prove the possibility to operate a miniaturised antenna array for switched beam applications. [1] J. Weber, et.al. ,"Miniaturisation of antenna arrays for mobile communications," in Proc. 35th European Microwave Conf. (EUMC'05), Paris, France, Oct. 2005, pp. 1173-1176.
[2] J. Weber, et.al., "Miniaturised antenna arrays using decoupling networks with realisitic elements," in IEEE Trans. Microwave Theory Tech. accepted for publication, Mar. 2006.

 
 
8   11:20   Design of a Focal Plane Array System at Cryogenic Temperatures
Simons, J.1; Bij de Vaate, J.G.1; Ivashina, M.V.1; Zuliani, M1; Natale, V.2; Roddis, N.3
1ASTRON, NETHERLANDS;
2INAF, ITALY;
3JBO, UNITED KINGDOM

This paper describes the system design and realization of a cryogenic cooled Focal Plane Array (FPA) for radio astronomy application. The system will consist of an antenna array, low noise amplifiers (LNA) and an RF beam former which are placed inside a cryostat. The antenna and the primary LNAs are cooled to 20 K, while the beam former will be at 77 K. The system design and the performance of the overall design are addressed.

This article describes the realization of a dense Focal Plane Array (FPA) system which is being developed as a European technology demonstrator project, called PHAROS [1].

FPAs are distinguished from traditional single-horn feeds by the fact that the antenna consists of an array of antenna elements. This research uses dense arrays with elements smaller than Lambda/2 [2]. Multiple beams are formed by electronically summing the signals from different groups of elements.


Figure 1: Schematic of the system inside the cryostat.

The beam properties can be optimized over a wide range of frequencies by electronically controlling element phases and amplitudes leading to high aperture efficiencies and low spillover losses of the radio telescope. The flexibility of the FPA also enables correction of surface errors of the dish and RFI mitigation. The multi beam capabilities of the FPA enable an increased Field Of View leading to a higher survey speed of the telescope.

The dense FPA concept has been demonstrated using Vivaldi elements and commercial room temperature LNAs [2-3]. This article presents a new FPA system in which the antenna array and the beam former are cryogenically cooled for low noise operation. The antenna array consists of 14 rows of 13 Vivaldi elements for each polarization. It is designed for operation on radio telescopes with F/D ratios from 0.3 to 0.5. The specific ICs in the LNAs and the beam former are also designed as part of the PHAROS project [4].

The article details the system level RF design strategy including design of the antenna array, the cryostat vacuum window, the LNAs and beam former. Interactions between these subsystems and constraints on their integration in cryostat will be discussed.


Figure 2: Preliminary cryostat design indicating the RF sections immediately behind the vacuum window.

References

[1] www.radionet-eu.org
[2] M. Ivashina, J.G. bij de Vaate, R. Braun, J. D. Bregman "Focal Plane Arrays for large Reflector Antennas: First Results of a Demonstration Project", SPIE conference Glasgow, UK, 2004
[3] M.V. Ivashina, J. Simons, J.G. Bij de Vaate "Efficiency Analysis of Focal Plane Arrays in Deep Dishes", Experimental Astronomy, Vol.17, pp.149-162, 2004.
[4] W. Ciccognani, F. Di Paolo, F. Giannini, E. Limiti, P.E. Longhi, A. Serino, "A GaAs Front-end Receiver for Radio astronomy Applications", submitted to 13th IEEE Mediterranean Electro technical Conference, Melecon 2006, Spain.

 
 
9   11:40   Optimal Uncoupled Impedance Matching for Coupled MIMO Arrays
Jensen, M.; Booth, B.
Brigham Young University, UNITED STATES

When antenna arrays for multiple-input multiple-output (MIMO) systems are adequately compact, mutual coupling between the elements can impact the system performance. Recent studies have quantified this impact for typical scenarios, including the effect of the impedance match between the antenna terminals and transmitting or receiving electronics. These results demonstrate that optimal performance can be obtained only if a coupled impedance matching network (which deliberately mixes the signals across ports) is used to compensate for the electromagnetic coupling in the array.

From a practical standpoint, however, coupled impedance matching networks are difficult to construct. While self-impedance matching has been considered in prior work, such matching is not necessarily the optimal approach for maximizing MIMO performance. Recently, a study has appeared on this topic, although the approach uses a simplistic model for the array which does not adequately include the impact of the coupling. Specifically, this prior work does not consider that the optimal uncoupled match for a coupled array depends on the transmit excitation or received field. Therefore, questions remain regarding the performance of MIMO systems with coupled antennas but uncoupled matching networks.

This paper uses a previously-developed network model for MIMO systems with coupled antennas to determine the optimal uncoupled matching network under different propagation conditions. For example, consider the case of a single plane wave impinging on a uniform linear array of coupled dipoles. If an uncoupled array termination is designed taking into account the arrival angle of the incident plane wave, this uncoupled load can perform identically to the optimal coupled load (which is excitation independent). The performance of this uncoupled match can also be significantly higher than that obtained with a more traditional self-impedance array termination, although the improvement depends on the plane wave arrival angle. The uncoupled termination can also be designed to maximize the average received power when the statistics of the incident electric field are known. In this case, the performance can be nearly as good as that obtained with the optimal coupled match, although the results are somewhat sensitive to the stochastic model assumed for the impinging field. Once again, the performance of the uncoupled match relative to that of the self-impedance match depends on the assumed wave structure.

The full paper explores the approach used for this analysis, and provides a comprehensive set of computational examples to illustrate the basic phenomena relevant to the study. Array terminations synthesized to maximize received power as well as to optimize MIMO capacity are considered as part of the analysis.

 
 
10   12:00   Shaped Single-Feed-Per-Beam Multibeam Reflector Antenna
Balling, P.1; Mangenot, C.2; Roederer, A.2
1ASC, Antenna Systems Consulting ApS, DENMARK;
2ESA ESTEC, TEC-EE, NETHERLANDS

Current Ka-band multibeam satellite antenna systems often use one feed per beam, but use many reflector antennas (four for transmit and four for receive) to realise both acceptable crossover levels and spillover losses. Developments go on to reduce the number of reflectors to one for transmit and one for receive at the cost of much complexity in the feed array and the beamforming. This paper presents a novel concept (patent pending) where a shaping of the reflector reduces both the number of feeds per beam and the number of reflectors to one. The price paid is an oversizing of the reflector making the reflector area comparable to the composite area of the four reflector solution.

The shaping procedure utilises the approximately rotational symmetric illumination of the single offset reflector by the individual feeds for long f/D ratios. The amplitude distribution is modelled by analytic distributions or imported from a reflector antenna software like TICRA's GRASP for each design frequency taking into account the feed patterns. The rotational symmetric phase distribution for the on-axis beam may be constant phases in annular zones, constant phase slopes in annular zones to avoid phase steps, or e.g. cubic splines with continuous derivatives up to the second order. An optimisation algorithm varies the phase parameters to optimise the gain over the on-axis beam coverage minimising the sidelobes over the adjacent frequency reuse beams. The symmetry ensures a fast optimisation as only a few phase variables need to be considered. The smoothness of the phase distribution and the edge taper determine the sidelobe performance. Once a satisfactory solution has been found, the reflector surface shape is output for further analysis by the reflector antenna software taking into account feed displacements, tolerance effects etc. The offset reflector geometry causes a slightly asymmetric surface shaping. For best results, the feeds should be pointed towards the central reflector point so that the amplitude distribution is similar for all beams and only the phase from the feed displacement varies.

Fig. 1 shows seven beams in one of the four frequency reuse colours for a 2.2m offset reflector with f/D=2 at 19.7 GHz (blue) and 20.2 GHz (green). Other feeds in the array provide the beams (not shown) in the three other frequency bands. The antenna boresight is close to the centre of the central beam in the upper row to illustrate the scan degradations: While the inner contour is distorted into a "bone" shape that rotates with the scan direction, the effect on the sidelobes is small. Fig. 2 superimposes pattern cuts through all seven beam centres demonstrating the well behaved sidelobes. The worst gain variation over a beam is less than 6 dB and the worst composite C/I 18.5 dB (15 dB required). Replacing the offset reflector with a sidefed offset Cassegrain reduces the gain variation to 4.8 dB and increases the C/I to 22.3 dB by essentially removing the scan degradations. The final paper will provide more results also for 0.56° beam spacing and show the wideband potential - limited by the feed - and the relative insensitivity to reflector surface errors.