Signal distortion can occur when the gain or attenuation of a component changes non-linearly with frequency, which is referred to as nonlinear frequency response. Common communications components such as filters, amplifiers, and mixers can lead to nonlinear frequency responses, which can cause errors in transmitting and receiving. This article outlines the design and demonstration of a static and dynamic finite impulse response (FIR) digital equalizer circuit. Using predistortion topology with a coupled feedback loop, the adaptive Least-Mean Square (LMS) algorithm was implemented. The FIR filter was simulated in MATLAB and Vivado and then implemented onto an Eclypse Z7 Field Programmable Gate Array (FPGA) evaluation board. Simulations showed that the custom RTL module gave the same frequency response that was produced in MATLAB calculations. The filter was able to dynamically equalize the frequency responses of different nonlinear boards that were used as the devices under test (DUT). Measurements showed that the equalizer was able to compensate for system distortion from 0.2 to 0.8 Nyquist frequency. The phase response remained relatively linear across the band of interest, with a group delay flatness less than 10 ns.

This article introduces an innovative method to improve the accuracy of estimating the Direction of Arrival (DOA) by utilizing non-uniform linear arrays (NULAs) operating at harmonic frequencies. Common DOA techniques face challenges in maintaining sufficient degrees of freedom (DOFs) while minimizing the number of sensors. Our approach takes advantage of the extended array aperture of NULAs and the diverse frequencies involved in harmonics to address these challenges. We explore various NULA structures, such as nested arrays, coprime arrays, and coprime arrays with compressed inter-element spacing (CACIS), each with unique characteristics and requirements for enhancing DOFs at the third and fifth harmonics. Simulation results demonstrate a substantial increase in DOFs, emphasizing the effectiveness and adaptability of our method in improving DOA estimation across different NULA configurations. This research contributes not only to theoretical advancements in antenna array processing but also offers practical insights, showcasing the potential of our method to significantly enhance DOA estimation accuracy in complex signal environments.

This manuscript proposed an innovative digital predistortion equalizer using the LMS algorithm. In this article, we used self-made nonlinear circuit boards cascaded with an off-the-shelf RF amplifier to mimic the distorted intermediate frequency (IF) response of a wireless communication system. After applying our proposed algorithm, our prototype demonstrated adaptive equalization within 2 dB bandwidth in the 0.2 - 0.8 Nyquist frequency range (10 - 40 MHz in our case). At this range, the equalizer kept the phase response relatively linear with a group delay less than 10ns. It is foreseeable that our proposed adaptive digital equalizer can be widely used in wireless communication systems.

Nonlinear frequency responses are a common problem in radio frequency (RF) components. Specifically, in wireless communication systems, signals are often unequally amplified or attenuated across a specified frequency band. Common communications components such as filters, amplifiers, and mixers can lead to nonlinear frequency responses, which can cause errors in transmitting and receiving. This article outlines the design and demonstration of a static and dynamic finite impulse response (FIR) digital equalizer circuit. Using predistortion topology with a coupled feedback loop, the adaptive LMS algorithm was implemented. The FIR filter was simulated in MATLAB and Vivado and then implemented onto an Eclypse Z7 FPGA evaluation board with no timing errors. Simulations showed that the custom RTL module gave the same frequency response that was produced in MATLAB calculations. The filter was able to dynamically equalize the frequency responses of different nonlinear boards that were used as the devices under test (DUT). Measurements showed that the equalizer was able to compensate for system distortion from 0.2 to 0.8 Nyquist frequency. The phase response remained relatively linear across the band of interest, with a group delay flatness less than 10ns.