A novel low-complexity robust adaptive beamforming (RAB) technique is proposed in order to overcome the major drawbacks from which the recent reported RAB algorithms suffer, mainly the high computational cost and the requirement for optimization programs. The proposed algorithm estimates the array steering vector (ASV) using a closed-form formula obtained by a subspace-based method and reconstructs the interference-plus-noise (IPN) covariance matrix by utilizing a sampling progress and employing the covariance matrix taper (CMT) technique. Moreover, the proposed beamformer only requires knowledge of the antenna array geometry and prior information of the probable angular sector in which the actual ASV lies. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm and prove that this algorithm can achieve superior performance over the existing RAB methods.

Aiming at receiving a signal from a certain direction and suppressing interferences and noise, adaptive beamforming has found widespread application in many fields ranging from radar, sonar, wireless communication, and radio astronomy to medical imaging, speech processing, and so forth [

The existing RAB techniques mainly consist of diagonal loading (DL) technique [

Recently, a new approach to the design of RAB based on the interference-plus-noise (IPN) covariance matrix reconstruction has been introduced in [

To reduce the computational complexity of the RAB method in [

The rest of this paper is organized as follows. The data model of array output and some necessary backgrounds about adaptive beamformer are described in Section

Consider a uniform linear array (ULA) of

By maximizing the output SINR of the beamformer, the optimal weight vector can be obtained by

In practice, theoretical covariance matrix

The performance of standard beamformers degrades dramatically when the ASV errors exist and the DS with a high SNR is present in the training snapshots. To remove the DS from the sample covariance matrix, recently, an IPN covariance matrix reconstruction method was proposed [

In [

This method has mainly two aspects of drawbacks. Firstly, concerning the mismatch between the actual ASV and the nominal ASV, the IPN matrix may not be reconstructed accurately. Secondly, its high computational complexity restricts its practical performance [

Similar to the reconstruction of IPN covariance matrix as (

Similar to (

As mentioned above, two constraints can be imposed on

The main computational cost of the method in [

Consider the inner product of two steering vector which is written as

From the derivation above,

Denote the zeros of

Define a matrix using

In this way, the IPN covariance matrix is estimated by the sample matrix

However, when

Based on the discussions above, the proposed beamforming algorithm can be summarized by the following steps:

Construct the two subspaces

Specify the MZ taper

Substituting the reconstructed IPN covariance matrix

In the proposed algorithm, the main computational complexity lies in the eigendecomposition operation and the matrix inversion operation, both of which have complexity of

In the simulations, without loss of generality, a ULA with

The proposed beamformer is compared to the diagonal loading sample matrix inversion (LSMI) beamformer [

The look direction mismatch of the DS is assumed to be random and uniformly distributed in

Considering the influence of random look direction error on array output SINR, the performance curves versus the input SNR and the number of snapshots are drawn in Figures

The SINR performance versus the pointing error is also investigated, and the results are shown in Figure

Comparison of the normalized beam patterns in Example

Performance of the beamformers for the case of mismatch due to signal direction error. (a) Output SINR versus SNR for training data size of

Output SINR versus pointing error for training data size of

In this simulation example, the ASV of DS is assumed to be randomly distributed in an uncertainty set, which can be modeled as

Furthermore, the proposed algorithm performs almost as well as the reconstruction-based beamformer for the output SINR but enjoys a faster convergence rate because of the lower computational cost without complex integral computation. Since the ASV mismatch is comprehensive and arbitrary-type, the proposed beamformer is proved to be effective against the random error of ASV.

Deviations from the optimal SINR for training data size of

Beamformers | Deviations (dB) |
Deviations (dB) |
---|---|---|

Proposed | 1.330 | 1.347 |

LSMI | 12.277 | 57.511 |

Worst-case-based | 3.139 | 21.768 |

ESB | 2.949 | 45.948 |

SQP | 3.755 | 43.308 |

Reconstruction-based | 1.081 | 1.083 |

Beamformer in [ |
3.122 | 39.040 |

Performance of the beamformers for the case of ASV random error. (a) Output SINR versus SNR for training data size of

In this example, it is assumed that the desired signal has a time-varying ASV which can be modeled as [

In this scenario, the signal covariance matrix

Performance of the beamformers for the case of incoherent local scattering. (a) Output SINR versus SNR for training data size of

The main purpose of this example is to study the impacts of some factors on performance.

For the purpose of studying the impacts of the two factors, the model of the mismatch is set to be the same as the first example. The number of snapshots is fixed to be

Performance of the beamformers for the case of mismatch due to signal direction error. (a) Output SINR versus

In this paper, a novel low-complexity RAB method is proposed which is easier to realize in practical situations and more robust to the look direction mismatch than other existing algorithms. The ASV is estimated by a closed-form formula so as to avoid utilizing the optimization software, and the IPN covariance matrix is reconstructed by a sampling progress. The proposed beamformer only requires prior knowledge of the antenna geometry and the angular sector in which the ASV is located. Simulation results have demonstrated that the proposed beamformer can achieve superior performance over the existing state of the art RAB methods. To simplify the illustration, the influence of the element pattern, the polarization, and the mutual coupling is not considered in this paper. However, these elements will be investigated in the future study.

The authors declare that they have no competing interests.