The final weight vector expression for the LCMP beamformer is given by:
The LCMP beamformer can experience significant performance degradation when there is a mismatch between the presumed and actual characteristics of the source or array.
When the condition (10) is satisfied, the solution of LCMP beamformer (6) becomes:
which is an upper bound on [epsilon] so the QICLCMP beamformer is different from the LCMP beamformer.
is our sought solution to the LCMP optimization problem with a quadratic inequality constraint, which has the same form as the LCMP beamformer with a diagonal loading term [lambda]I added to [R.
Based on the analysis above, we can see that the quadratic inequality constraint can enhance the robustness of LCMP beamformer.
For comparison, the benchmark LCMP algorithm that corresponds to the ideal case when the covariance matrix is estimated by the Maximum Likelihood Estimator (MLE) and the actual steering vector is used.
Apparently, the SNRs of the QICLCMP and VLRLS-LCMP beamformer are almost closed to that of the LCMP beamformer, which are lower than that of the Ideal-LCMP beamformer.
The variation of the LCMP beamformer output SNR versus signal direction mismatch or angle mismatch is given in Fig.
The QICLCMP and QECLCMP beamformers have the same form as the LCMP beamformer with diagonal loading.
Hence, the loading level has a great impact on the SNR of the LCMP beamformer, and determines the performance improvement.
From the simulation results above, we can see that the loading level has a great impact on the performance of the LCMP beamformer, and the QECLCMP beamformer has the best pointing performance, namely, the optimal negative loading is the best.