The problem of estimating the direction-of-arrival of multiple narrowband signals impinging on an array has attracted considerable attention in the last decades.  

In particular, a variety of high-resolution algorithms which exhibit potentially excellent performance have been proposed.  

Most of these algorithms assume the array manifold is perfectly known. However, in practice, the array manifold is often affected by mutual coupling. This can seriously degrade the performance of the algorithm for high resolution. To solve this problem of array mutual coupling, many calibration algorithms have been published.  

Compared with the online calibration method which requires calibration sources, the so-called online calibration or auto-calibration is more attractive. The reason for that is it can estimate the direction-of-arrivals and the unknown mutual coupling coefficients simultaneously without any calibration sources.  

Many of the auto-calibration methods focus on uniform linear array, and more and more popular circular array in underwater acoustics is somewhat ignored. So it’s of great necessity to develop calibration techniques for circular array. 

The currently existed self-calibration algorithms for circular array can simultaneously estimate the direction-of-arrivals and coupling coefficients. Unfortunately, all of them have treated the number of nonzero coefficients in mutual coupling vector as a prior knowledge. It is usually not known exactly for a practical circular array because of the changing environment.  

More importantly, there are serious ambiguity problems during their estimation process. When the ambient conditions change, these algorithms easily fail to work. 

In order to overcome the disadvantages of previous research, a new iterative auto-calibration algorithm for uniform circular array with unknown mutual coupling has been presented by researchers from the Institute of Acoustics of the Chinese Academy of Sciences.  

This new algorithm is based on subspace theory. By performing eigen-decomposition on the array output covariance matrix, the eigenvectors can be divided into signal subspace and noise subspace.  

Since the signal spans the same space with the array manifold matrix, a cost function can be established according to the orthogonality of subspace. The unknown mutual coupling and direction of arrival can be estimated jointly by minimizing the cost function. Thus, the auto-calibration problem can be formulated as an optimization problem. 

Considering that estimating a matrix directly is not an easy task since it possesses too many parameters, they transform the mutual coupling matrix into a vector by taking advantage of its symmetric circular property. And then, the auto-calibration of mutual coupling becomes a constrained quadratic minimization problem, which can be solved by an iterative process. 

The main advantages of this new calibration algorithm lie in that it does not require any prior knowledge of the number of nonzero elements in mutual coupling vector. Besides, it is very robust without any ambiguity problems which exists in the current method.  

Researchers have conducted plenty of computer simulations to validate the performance of the new method. Simulation results show the robustness, effectiveness and higher estimated accuracy of their proposed algorithm. 

It should be noted that the proposed method has also some constraints, i.e. it is not suitable for very large mutual coupling without a proper initial value of coupling. Since in addition to the performance degradation of peak searching, the iterative process may also converge to a local optimum. 

Although the current algorithm is only validated by computer simulation, it has exhibited great potential for real-world applications. In future work, emphasis might be put on some experimental measurements to validate the algorithm further, which will make the method more applicable in practice. 

References: 

WANG Min, MA Xiaochuan, YAN Shefeng, Senior Member, IEEE, and HAO Chengpeng, Member, IEEE. An Auto-calibration Algorithm for Uniform Circular Array with Unknown Mutual Coupling. Antennas and Wireless Propagation Letters, IEEE (Vol. PP, No. 99, pp. 1, 22 April 2015 ). DOI: 10.1109/LAWP.2015.2425423 

Contact: 

WANG Min 

Institute of Acoustics, Chinese Academy of Sciences, 100190 Beijing, China 

Email: mwangcas@163.com