This paper presents a fast iterative method for the synthesis of linear and planar antenna arrays of arbitrary geometry that provides pattern reconfigurability for 5G applications. The method enables to generate wide null regions shaped according to a Gaussian distribution, which complies with recent measurements on millimeter-wave (mmWave) angular dispersion. A phase-only control approach is adopted by moving from the pattern provided by a uniformly excited array and iteratively modifying the sole phases of the excitations. This allows the simplification of the array feeding network, hence reducing the cost of realization of 5G base stations and mobile terminals. The proposed algorithm, which is based on the method of successive projections, relies on closed-form expressions for both the projectors and the null positions, thus allowing a fast computation of the excitation phases at each iteration. The effectiveness of the proposed solution is checked through numerical examples compliant with 5G mmWave scenarios and involving linear and concentric ring arrays.

By now, the expected outbreak of the 5G technology represents one of the main challenging opportunities for antenna designers, whose efforts will have to deal with several significant designs, realizations, and prototyping issues. One of the distinctive features of next-generation cellular systems will in fact consist in the adoption of the millimeter-wave (mmWave) spectrum, between 30 and 300 GHz, to satisfy the huge capacity demand that will require the implementation of the Internet of Things (IoT) and Internet of Everything (IoE) paradigms [

In this context, a basic approach to find the most suitable beamforming techniques for mmWave links may be that of considering the significant amount of algorithms that have been developed along the years and that gave outstanding solutions for a wide variety of synthesis problems. To make a preliminary effective selection, it may be also useful to properly identify the main antenna requirements that are expected to characterize the forthcoming 5G transceivers. Firstly, since mmWave systems will be designed to manage a dense environment, the spatial filtering capabilities of the antenna array will represent the main topic, to the point that many studies have assumed a significant change of perspective for the analytical characterization of the 5G performance, consisting in the translation from the so far assumed 1-4G interference-limited regime to a 5G noise-limited one [

In light of these considerations, this paper proposes a fast synthesis algorithm for linear and planar antenna arrays of arbitrary geometry that allows the reconfigurability of the pattern and the shaping of the null regions according to a Gaussian power azimuth spectrum. The algorithm takes, as starting point, a uniformly excited array, which provides a narrow beamwidth, and then iteratively modifies the sole phases of the excitations to impose wide Gaussian nulls in specified directions. Furthermore, the algorithm, which relies on the method of successive projections, is developed to obtain closed-form expressions for the projectors and analytical formulas for the positions of the nulls. This approach has the advantage of leading to a fast computation of the excitation phases, since no numerical estimations are required at each iteration. Numerical examples considering linear and concentric ring arrays are presented to assess the effectiveness of the proposed solution in a 5G interfered context, discussing, beside the performance in terms of obtained patterns, also the computational time necessary for their synthesis.

The paper is organized as follows. Section

Many phase-only null synthesis techniques for antenna arrays proposed in the recent years [

With reference to this overview, some common aspects may be highlighted. First, the phase-only requirement during the null synthesis process implies the maintenance of a unity dynamic range ratio (DRR), representing the ratio between the maximum and the minimum excitation amplitudes of the array. The problem of forming nulls while imposing an upper bound on the DRR has been discussed in detail in [

Second, many of the proposed solutions are applicable just to specific configurations [

Third, the recent channel measurements carried out at the mmWave frequencies have revealed that the angular dispersion may be often described by a Gaussian distribution [

For these reasons, in this paper, we present a phase-only control algorithm for arbitrary linear and planar arrays capable of managing Gaussian-distributed nulls. Moving from the formulation of the problem developed in the next section, the algorithm is mathematically derived in Section

With reference to a Cartesian system

Consider now a reference pattern

According to this scenario, the objective of this study is to find a pattern

The adopted synthesis strategy starts by substituting the wide null constraint in (

The localization of the nulls is performed here by a density tapering technique, which consists in finding the

Since

In order to model the synthesis problem as an intersection finding problem, first denote

It is worth noting that the iteration is stopped at a point of

The algorithm for this projector is described here following the procedure in Section V of [

The distance in (

The unknown phases are found following the single coordinate method (SCM) [

Calculating (

The algorithm for this projector has been illustrated in [

On the other hand, being

The column vector

Now that the projectors have been derived, the iterative procedure in (

In this section, two numerical examples are proposed to assess the validity of the proposed procedure. The two examples are also solved with the first method developed in [

The first numerical example refers to a phase-only synthesis problem for a linear array consisting of

First example: geometry of the linear array with

First example: linear array in Figure

The obtained pattern is represented in Figure

Magnification of the pattern synthesized in Figure

The second numerical example deals with the phase-only synthesis of a Gaussian null region using a planar array involving

Second example: geometry of the circular array with five rings of

Second example: circular array in Figure

The synthesized pattern is denoted in Figure

Magnification of the synthesized pattern in Figure

Comparison of the results.

Iteration number | CPU time (s) | Constraint ( | ||
---|---|---|---|---|

Example 1 | Proposed algorithm | 22 | 0.5 | Rigorously |

Algorithm in [ |
1000 | 992 | Approximately | |

Example 2 | Proposed algorithm | 75 | 0.7 | Rigorously |

Algorithm in [ |
1000 | 2236 | No |

An efficient technique has been proposed for the phase-only synthesis of antenna arrays with wide null regions characterized by a Gaussian shape. The synthesis algorithm has been derived by exploiting the alternating projection approach, in which all the operations are carried out in closed form. Thus, despite the iterative nature of the alternating projections, the overall synthesis procedure results extremely fast, so that the proposed algorithm can be suitable for 5G beamforming applications, where fast synthesis algorithms are recommended. Furthermore, the degrees of freedom of the problem seem to be exploited quite satisfactorily. In fact, the phase-only synthesis has been realized by moving from a uniform amplitude distribution of the array excitations, thus modifying just the phases of the element excitations. This results in a very simple feeding network, requiring only phase shifters, which are cheap and fast components. The effectiveness of the developed synthesis strategy has been verified by numerical examples involving linear and planar arrays, which have proved the low computational time required by the developed algorithm and its significant performance in terms of null region shaping and deepening.

All the data necessary to obtain the results presented in Section

The authors declare that there is no conflict of interest regarding the publication of this paper.