The crosstalk error is widely used to evaluate the performance of blind source separation. However, it needs to know the global separation matrix in advance, and it is not robust. In order to solve these problems, a new adaptive algorithm for calculating crosstalk error is presented, which calculates the crosstalk error by a cost function of least squares criterion, and the robustness of the crosstalk error is improved by introducing the position information of the maximum value in the global separation matrix. Finally, the method is compared with the conventional RLS algorithms in terms of performance, robustness and convergence rate. Furthermore, its validity is verified by simulation experiments and real world signals experiments.

Blind signal separation (BSS) technology originated from the famous “cocktail party” problem (Choi and Cichocki,

The crosstalk error represents the approximate degree between the global separation matrix

In response to the above problems, a fully adaptive crosstalk error estimation model based on the recursive least square (RLS) algorithm is presented in this paper. This new approach consists of sifting the impact of step size on the estimation of crosstalk error. Furthermore, the robustness of the crosstalk error is improved by introducing the position information of the maximum value of each row in the global separation matrix

The paper is organized as follows. In Section

Suppose that an antenna array is made up of

In order to simplify the problem of BSS and reduce the computational complexity, it is generally necessary to pre-whiten the signal, and the signal after whitening is

In practice, the blind source separation algorithms can only make

In matrices

Therefore, the maximum value of all the rows in the

For overcoming the shortcomings of the original crosstalk error, firstly a model for estimating the mixed matrix

In this subsection, an estimation method based on recursive least-squares (RLS) is proposed to estimate the global separation matrix in real time. According to formula (

The gradient of

Let

Let

It can be seen from the first section that some isolated signals may be the same signal, if the maximum value of the corresponding rows share the same column. Therefore, an improved crosstalk error definition is proposed here to eliminate the wrong decision caused by positions of optimal values in the same column, which is defined as

Crosstalk errors given in (

Pseudo code of the proposed algorithm

In this section, the proposed algorithm is evaluated by two methods, which are simulation experiment and real world experiment.

The new proposed crosstalk error definition defined by formula (

Comparison of the estimation of

In order to verify the robustness of the new proposed calculation method for evaluating BSS, two simulation examples for comparison are presented. First, we use the natural gradient RLS algorithm mentioned in literature (Zhu and Zhang,

According to the initial conditions, the initial values of the estimated and theoretical values are 0.8669 and 0.8412, respectively. From Fig.

The source signals.

The estimation of source signals.

Figure

The former experiment was established under positive definite conditions. In this case, we evaluate the algorithm in over-determined conditions, and the source signal vector becomes:

Average performance index in an over-determined model.

Average performance index of the proposed algorithm and the conventional algorithm.

In order to indicate the advantage of our proposed algorithm in terms of convergence rate, we apply to the conventional algorithm proposed by Zhang

In the real word signals experiments, a set of actual signals are used to test the proposed algorithm. The experimental environment is shown in Fig.

The experiment setup.

In the test, the signal generator generates single-frequency signals that are transmitted through the transmitting antennas, and then the signal receiver receives the mixed signals using the four-element antenna array. The sampling frequency is set to 62 MHz. We select 16,000 sampling points to compute the crosstalk error. The experimental result is shown in Fig.

Average performance index of the proposed algorithm and the conventional algorithm in a real world experiment.

From the above experiments, we can know that the proposed algorithm for calculating the crosstalk error not only improves the robustness and the convergence rate of the crosstalk error greatly, but also deduces the crosstalk error to practical applications.

At present, the crosstalk error is widely used to verify the validity and stability of the BSS algorithms in the simulation conditions. However, in the real application environment, it is impossible to know the global separation matrix of the signal in advance. Therefore, this criterion cannot be used in practice. In this paper, the crosstalk error calculation model is established based on the RLS algorithm, and the calculation method of the crosstalk error is deduced as an adaptive algorithm without prior knowledge by using real-time estimating of the global separation matrix. It can greatly extend the use scope of the crosstalk error. At the same time, a new crosstalk error definition is proposed to improve the robustness and convergence rate of the original crosstalk error. Finally, the experimental results show that the method proposed in this paper can predict the convergence trend of the crosstalk error well, which indicates the validity and robustness of the method proposed in this paper.

The authors would like to thank the editor and the referees for their helpful comments and suggestions that have improved the presentation.