Frequency diverse arrays

How an antenna array focuses spherical waves

The same M-element array, shown at the same moment as a phased array, a linear FDA and a permuted FDA. M, f_c and Δf apply to all three screens.

About

Draft manuscript · 2026

Working title of the draft manuscript

Beamfocusing Beyond the Near Field: Frequency Diverse Arrays for OFDM-ISAC Systems

This MATLAB code studies frequency diverse arrays (FDAs): antenna arrays in which each element transmits on a slightly different carrier frequency, so the beam can focus at a chosen distance as well as a direction, even far from the array, where an ordinary phased array cannot. It models a 128-element array at 28 GHz whose offsets fit the OFDM subcarrier grid, and compares phased arrays and FDAs on beam focus, single-user degrees of freedom and multiuser data rate.

The simulation on this page uses the same field model as the paper code, with exaggerated frequency offsets so the range structure fits on screen.

Code and website: Arda Akyazı, METU Electrical and Electronics Engineering
Supervisor: Dr. Abdulkadir Çelik
Co-authors: Ahmed Hussain and Dr. Asma Abdallah
Project: Research internship, School of Electronics and Computer Science, University of Southampton, Summer 2026

What the simulation computes

FDA beamforming

Each element radiates a spherical wave at its own frequency. Each screen shows their sum, seen from above.

Element frequency

f_{m} = f_{c} + k_{m} Δ f

Array field

S (r, θ, t) = \sum_{m = 0}^{M - 1} \frac{1}{R_{m}} \exp {j [2 π Δ f_{m} t - \frac{2 π f_{m} R_{m}}{c} + ψ_{m}]}

Focusing phase

ψ_{m} = \frac{2 π f_{m} R_{m} (F)}{c}

Intensity

I = {| S |}^{2}

Symbols

$M, m$: Number of elements and element index.
$f_{c}, Δ f$: Carrier frequency and offset step.
$k_{m}$: Offset index of element $m$ .
$R_{m}$: Distance from element $m$ to the point on the screen.
$F$: Focus point. At $t = 0$ every element is in phase there.

Three offset rules

Phased array (PA)

$k_{m} = 0$

One carrier. The beam steers in angle, and focuses in range only close to the array.
Linear FDA

$k_{m} = m$

Each element runs Δf above the one below it. The beam becomes a range–angle ridge that sweeps outward at c.
Permuted FDA

$k_{m}$ shuffled

The same offsets in random order. The ridge collapses to one spot, focused in range and angle, that moves outward at c.

MATLAB code

16 files · 2,130 lines · MATLAB R2026a

The array model, the beam and rate metrics, the figure scripts and the plot styling of the paper. To run them, keep the files in one folder and run a figure script such as figure2_beampattern in MATLAB. No toolboxes are needed.