A Novel Combined Beamformer Based on Hypercomplex Processes

The problem of beamforming based on hypercomplex processes is considered for an airborne electromagnetic (EM) vector-sensor array. The quaternion domain facilitates modeling and processing of four-dimensional real signals (or two-dimensional complex signals). Based on the quaternion model of an airborne EM vector-sensor, a quaternion spatial matched filter (QSMF) is presented and its characteristics are analyzed. The quaternion-valued output y(n) of the QSMF consists of two complex components y₁(n) and y₂(n). The analysis in theory highlights the fact that y₂(n) includes only the interference component and noise, but doesn´t include the desired signal. By employing y₂(n) to cancel the interference component in y₁(n), we propose an interference cancellation algorithm (ICA) of the QSMF. In the presence of a strong interference, the ICA can improve the output signal-to-noise ratio (SNR). Based on the interference cancellation structure, we propose two schemes of combined QSMF and complex minimum variance distortionless response (CMVDR) beamformer (one is referred to QSMF-CMVDR and the other is referred to QSMF-DCMVDR) for an airborne EM vector-sensors array. The advantages of the proposed beamformers are that the interference can be canceled by ICA of the QSMF and the additive noise can be reduced by CMVDR beamformer. The output SNR expressions of two combined beamformers that we derive reveal that the output SNR of the QSMF-DCMVDR beamformer is superior to that of a conventional linearly constrained minimum variance (LCMV) beamformer. And in the presence of the coherent (or correlated) interferences, two combined beamformers are not subject to performance degradation. Simulation results are in agreement with our analysis.