## 2 Concept  
Figure 1a provides a conceptual overview of our envisioned hybrid optoelectronic beamforming radar system that sends LFM pulses. Due to limited memory resources, the tuning range in the electronic radar processor is restricted to hundreds of picoseconds. In contrast, optical memory buffers can provide tunable delays in the order of nanoseconds. Thus, a hybrid optoelectronic memory buffer can choose fine-tuning delay values (picoseconds) using the electronic processor and add larger delays (nanoseconds) using the optical buffer. This approach increases the tuning delay range, meeting the beamforming requirements without additional electronic memory. This paper focuses on the performance of the optical memory buffer composed of a Kerr comb and concatenated off-the-shelf chirped FBGs. The radar processor generates the RF-LFM pulse using the mathematical model:  
\[V_{in}(t)=\cos\left[2\pi f_{0}t+(\pi B/T)t^{2}\right]\cdot\text{rect}[t/T] \tag{1}\]  
where \(f_{0}\) is the RF center frequency, \(B\) is the total bandwidth of the RF signal (in Hz), and \(T\) is the pulse duration [29]. During the pulse duration \(-T/2\leq t\leq T/2\), the instantaneous frequency \(f(t)=f_{0}+(B/T)t\) linearly scans the range \(f_{0}-B/2\leq f\leq f_{0}+B/2\). In the frequency domain, the pulse is expressed as:  
\[V_{in}(f)\longrightarrow\exp\Bigl{[}-jT(f-f_{0})^{2}/2B\Bigr{]}\cdot\text{rect }[(f-f_{0})/B] \tag{2}\]  
Figure 1b shows the LFM pulse in the time and frequency domains. Figure 1c focuses on the optical memory buffer, the primary research objective of this study. The RF-LFM pulse is fed into the optical memory buffer. In the optical Mach-Zehnder modulator (MZM), the RF-LFM pulse is modulated onto optical carriers from a microresonator Kerr comb at different wavelengths (\(\lambda\)'s), creating several copies of the LFM pulse on different optical carriers. These optical copies are sent into a linearly chirped FBG (FBG1: LC-FBG), which provides a continuous wavelength-dependent group delay with added intra-channel group-delay dispersion. The added dispersion is then removed by a chirped-and-sampled FBG (FBG2: CS-FBG), compensating for the dispersion of multiple equally spaced frequency channels simultaneously. At the output of the concatenated FBGs, different copies of the input are available for detection, where each wavelength carrier corresponds to a signal  
Figure 1: **(a)** An envisioned hybrid optoelectronic beamforming radar system sending LFM pulses. Due to limited memory, the electronic radar processing unit can add only a small delay in the order of hundreds of picoseconds. In contrast, the optical memory buffer can add delays of tens of nanoseconds. **(b)** Depiction of the LFM pulse used in radar systems in the time domain and frequency domain. **(c)** The proposed optical memory buffer structure. An input RF-LFM pulse modulates optical carriers from a Kerr comb. The modulated carriers are sent through a concatenation of LC-FBG and CS-FBG. The amount of added wavelength-dependent delay is selected using a tunable optical filter, and the signal is converted to the RF domain using a photodiode. with a different delay. The signal copies are amplified, and a tunable optical filter selects the added optical delay. The output is converted back to the RF domain using a photodiode. In summary, the four essential components of the optical memory buffer system are (i) FBG1, (ii) FBG2, (iii) optical amplifier, and (iv) optical tunable filter.