Communications systems and other high-frequency electronic systems are now leveraging multiple-element antenna arrays rather than single antennas and advanced computer-modeling techniques to fine-tune physical designs. On that front, a group of researchers from China’s Wuhan University applied mathematical modeling and modern sensing and sampling methods to optimize beamforming under various array element conditions. Beamforming is an important part of array signal processing in many applications, including radar, sonar, and satellite-communications (satcom) systems.
The researchers employed convex constrained optimization and compressed-sensing beamforming (CCOB-CS) models and an orthogonal matching pursuit (OMP) approach to achieve high mainlobe gain and low sidelobes with the aid of MATLAB mathematical-based computer modeling software from MathWorks.
Conventional beamforming (CBF) methods provide good directional resolution and rejection of interference under stationary conditions. When spatial signals are constantly changing, however, the steering vector of the desired signal will deviate, leading to signal error problems. Some of the limitations of CBF methods have been confronted by adaptive beamforming methods using neural networks to dynamically steer the main beam towards the desired signal. But the approach is relatively slow and requires a large amount of processing power, with compromises in beamforming gain.
The new beamforming optimization approach involves using an analog-to-digital converter (ADC) in the direction of moving signals to take a few samples for analysis. By using a small number of low-dimensional snapshots to accurately reconstruct the original signal, the approach can provide suitable gain without requiring a large amount of digital processing power.
In a scenario with little change, an ADC can capture a statistically valid number of samples to construct a good covariance matrix. But when changes become more frequent, the number of samples required to reconstruct the sampled signals increases dramatically, requiring gigasample-per-second sampling rates. For an array assumed to be a linear array, the direction of arrival (DOA) will change when the linear array is moving in a circular fashion as well as changing in angular velocity.
The research team focused their beamforming improvements on satellite signals, specifically on the Global Navigation Satellite System (GNSS), hoping to protect desired signals from loss and interference. To overcome estimated errors in the DOA of the satellite signals, the steering vector is estimated by the multiple-signal-classification (MUSIC) principle. Using an optimization equation, it is possible to obtain the best estimated value of the steering vector for the desired signal.
See “A Novel Beamforming Technique,” IEEE Antennas & Propagation Magazine, Vol. 58, No. 4, August, 2016, p. 48.