Large antenna arrays have very important applications in many fields. Instead of using a single large antenna to receive signals, a number of smaller antennas are used in concert to enhance multiple received signals with weak signal-to-noise ratio (SNR). One of the proven approaches is signal combining, whose main task is to find a set of combining weight and achieve the maximum output SNR.
Traditional signal combining algorithm, such as SUMPLE, tends to be unstable with a weak SNR because of the phase wandering. By contrast, eigen-based methods are stable and effective. Using SNR, combined output power (COP), and autocorrelation coefficient (AC) as the objective functions, these algorithms are called SNR EIGEN, COP EIGEN, and AC EIGEN, respectively.
The major problem for eigen-based methods is the heavy computational burden. Their calculation involves forming signal correlation matrix and solving an eigenvector problem.
To reduce the computational cost, WANG Leiou and his team from the Institute of Acoustics of the Chinese Academy of Sciences (IACAS) proposed a signum polarization (SP) method, where the complicated floating point multiplications of signal correlation matrices can be replaced by simple increase (or decrease) 1 operations, with a Collatz–Wielandt (CW) iteration method to solve the eigenvector problem.
Based on the relationship between the cross correlation function and the polarization cross correlation function, researchers proposed a SP mathematical model and obtained an estimation of polarization cross correlation function. To reduce computation, the estimation of the cross correlation function can be calculated by using Chebyshev polynomials.
On the other hand, CW is an efficient method to find the dominant eigenvector, and the computational cost can be further reduced by using this iteration method, especially for a large array.
Simulation results indicated that the proposed fast algorithm SP+CW can be flexibly applied to COP or AC EIGEN, and significantly reduce the computational cost while providing good combining performance.
The paper entitled “A Signum Polarization Fast Eigen-Based Signal Combining Algorithm” was published on IEEE Transactions on Aerospace and Electronic Systems .
WANG Leiou, WANG Donghui, HAO Chengpeng. A Signum Polarization Fast Eigen-Based Signal Combining Algorithm. IEEE Transactions on Aerospace and Electronic Systems (Early Access 2018). DOI: 10.1109/TAES.2018.2801379.
Institute of Acoustics, Chinese Academy of Sciences, 100190, Beijing, China