Time Frequency Direction Modulation Based on Nonlinear Frequency Diverse Array

Abstract

The conventional frequency diversity array (FDA) can generate arcsine form of continuous direction modulation (DM) waveforms which can automatically scan the entire space range. However, the single waveform and time varying phase of FDA cannot meet the requirements of practical security communication application scenarios. Thus, a new transmit diversity technique, called time frequency direction modulation (TFDM), is proposed to improve azimuth security. In this paper, unique timefrequency information at a given azimuth was formed by designing the beam steering term and the frequency term of each array element on the basis of the time varying characteristics of the FDA. In a transmit duration , DM can be divided into linear DM (LDM) and nonlinear DM (NDM) according to the beam shape. For LDM, for a specific observation direction, the frequency reaches the set value when the beam energy reaches the maximum value when the beam scans to this direction, but the uniqueness of time frequency information no longer exists in other directions. For NDM, the beam can pass through a given azimuth multiple times and form multiple pairs of time-frequency information, which provides a new idea for realizing multi-directional communication and solving communication rate problems. Finally, the uni-directional and multi-directional communication based on three different safe communication methods: time-direction modulation (TDM), frequency-direction modulation (FDM), and time-frequency-direction modulation (TFDM) are realized and the validity of the proposed method and the corresponding theory are verified by extensive numerical results.INDEX TERMS Frequency diversity array(FDA), frequency modulated (FM), time frequency direction modulation(TFDM), security communication.

Frequency Diverse Array Super-Resolution Design With Element Locator Polynomial Rooting Approach

“…where v q,n = v q−1,n +k 2 (q−1)−FDA v q−2,n−1 , q > 2, n > 1 with the initial conditions: v q,1 = 1 for q ≥ 1 and v 2,2 = k 2 1−FDA . The function in (17) can be expressed as a (q + 1)order polynomial:…”

“…Secondly, the detection threshold is analyzed. We consider an 11-element linear array with the following parameters: SNR 1 = 8 dB, SNR 2 = 2 dB, the number of snapshots L = 50, d = [1,2,4,6,7,9,10,12,17,20,25] T and p = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] T . Figure 2 depicts the detection threshold with respect to θ.…”

“…Although phased-array has various important applications, it has only angle-dependent focusing capability and cannot effectively control range-dependent steering. To address this disadvantage, frequency diverse array (FDA) has received much attention in mitigating range ambiguity [15], rangedependent clutter suppression [16] and range-dependent direction modulation [17].…”

Beamforming for LEO satellite communication based on FDA

“…In [10], the authors propose a method to generate direction modulation (DM) beams in the desired function form, not limited to the arcsine form. In [11], the application of DM was further explored in the physical layer of SC.…”