[Paper Review] Directional Modulation Design Based on Crossed-Dipole Arrays for Two Signals With Orthogonal Polarisations

Bo Zhang, Wei Liu+1 more|arXiv (Cornell University)|Jan 1, 2018

Antenna Design and Optimization3 citations

TL;DR

This paper proposes a directional modulation (DM) technique using crossed-dipole arrays to transmit two orthogonal-polarization signals simultaneously in the same direction and frequency, forming a four-dimensional (4-D) composite signal. By jointly optimizing common weight coefficients across both polarizations, the method achieves a desired directional radiation pattern with phase-scrambled constellations outside the mainlobe, enhancing both physical layer security and spectral efficiency.

ABSTRACT

Directional modulation (DM) is a physical layer security technique based on antenna arrays and so far the polarisation information has not been considered in its designs. To increase the channel capacity, we consider exploiting the polarisation information and send two different signals simultaneously at the same direction, same frequency, but with different polarisations. These two signals can also be considered as one composite signal using the four dimensional (4-D) modulation scheme across the two polarisation diversity channels. In this paper, based on cross-dipole arrays, we formulate the design to find a set of common weight coefficients to achieve directional modulation for such a composite signal and examples are provided to verify the effectiveness of the proposed method.

Motivation & Objective

• To exploit polarization diversity in directional modulation to increase system spectral efficiency beyond single-signal DM.
• To address the lack of polarization utilization in existing DM designs, which typically transmit only one signal per frequency and direction.
• To develop a unified beamforming framework that jointly controls both polarization and spatial radiation patterns using crossed-dipole arrays.
• To ensure that the two orthogonally polarized signals maintain distinct, decodable constellations in the desired direction while being scrambled elsewhere.
• To validate the feasibility and performance of the proposed method through simulation examples with low sidelobe levels and robust phase scrambling.

Proposed method

• Models a crossed-dipole array with N elements, each having two orthogonal dipoles (x- and y-polarized), each excited by complex weights $ w_{n,x} $ and $ w_{n,y} $.
• Formulates the overall steering vector as a concatenation of x- and y-subarray responses, incorporating spatial steering $ \mathbf{s}_s(\theta,\phi) $ and polarization response $ \mathbf{s}_p(\theta,\phi,\gamma,\eta) $.
• Derives the beam response as $ p(\theta,\phi,\gamma,\eta) = \mathbf{w}^H \mathbf{s}(\theta,\phi,\gamma,\eta) $, where $ \mathbf{w} $ is the combined weight vector.
• Designs a common weight vector $ \mathbf{w} $ that simultaneously achieves directional modulation for both signals by aligning their phase patterns in the desired direction.
• Employs a 4-D modulation framework where the two orthogonal signals are treated as a single composite signal in a four-dimensional signal space.
• Uses standard signal processing techniques at the receiver to separate the two signals even if the receiver’s polarization alignment does not match the transmitter’s.

Experimental results

Research questions

• RQ1 Can directional modulation be extended to support two independently modulated signals with orthogonal polarizations using a single array?
• RQ2 How can a common set of weight coefficients be designed to achieve directional modulation for both orthogonal-polarization signals simultaneously?
• RQ3 What is the impact of polarization diversity on the beam pattern, sidelobe level, and constellation scrambling in directional modulation?
• RQ4 Can the proposed method maintain low cross-polarization interference and ensure reliable signal separation at the receiver despite polarization mismatch?
• RQ5 How does the 4-D signal representation via orthogonal polarizations affect the overall system capacity and security performance?

Key findings

• The proposed method successfully achieves a mainlobe with a standard phase pattern in the desired direction for both orthogonal-polarization signals.
• The beam pattern exhibits low sidelobe levels, indicating effective spatial directivity and reduced interference in unintended directions.
• The constellation mappings of both signals are scrambled in all directions except the intended one, confirming the physical layer security property of directional modulation.
• The method enables simultaneous transmission of two independent signals using the same frequency and direction, effectively doubling spectral efficiency via polarization multiplexing.
• The receiver can reliably separate the two signals using standard signal processing, even with polarization mismatch, due to the orthogonality of the signals.
• Design examples confirm the feasibility and effectiveness of the proposed 4-D directional modulation scheme using crossed-dipole arrays.