# Performance Analysis of ICA in Sensor Array
## 1 Introduction  
The fundamental goal of BSS is to recover the original signals from their mixtures when the mixing process is unknown. Since first considered in the biological problem of motion decoding in vertebrates by [PERSON], [PERSON] and [PERSON] [1], the BSS problem has been expanded in many multi-sensor systems: Antenna arrays in electromagnetism or acoustics, chemical sensor arrays, electrode arrays in electroencephalography, _etc._ This very wide set of possible applications is probably one reason for its success [1, 2]. Independent Component Analysis (ICA) is one of the most widely used BSS techniques for revealing hidden factors that underlie sets of random variables, measurements, or signals. The ICA of a random vector consists of searching for a linear transformation that minimizes the statistical dependence between its components [3, 4]. The power of ICA resides in the physical assumptions that different physical processes generate unrelated signals. The simple and generic nature of this assumption allows ICA to be successfully applied in a diverse range of research fields [5]. For the last three decades, ICA has received attention from varied domains, including the biomedical applications [6, 7, 8, 9, 10, 11, 12, 13] such as the single-channel electromyogram (EMG) classification with ensemble-empirical-mode-decomposition-based ICA for diagnosing neuromuscular disorders in [6], the identification of simple and complex finger flexion movements using surface electromyography (sEMG) and muscle activation strategy with Subband Decomposition ICA (SDICA)in [7] and the driver fatigue classification with ICA by Entropy Rate Bound Minimization (ICA-ERBM) in an electroencephalography (EEG)-based system in [8]; the audio source separation like the noisy speech recognition [14], the multichannel blind deconvolution and speech separation [15]; the cooperative or non-cooperative communication like the semi-blind signal extraction with possible constrains [16], the blind adaptive detection in systems like Direct Sequence Code Division Multiple Access (DS-CDMA) [17]; other applications also include those in chemical sensor arrays [18], the target decomposition (TD) in image processing [19] and the estimation of modal parameters in vibration systems [20]. There has been numerous algorithms that belong to the ICA scheme. Most representative ones are: (1) the FastICA algorithm by [PERSON] and [PERSON] [5; 21; 22], which is a fixed point algorithm that employs higher order statistics for the recovery of independent sources. FastICA uses simple estimates of negentropy based on the maximum entropy principle, which requires the use of appropriate nonlinearities for the learning rule of the neural network; (2) the Equivariant Adaptive Separation via Independence (EASI) algorithm by [PERSON] and [PERSON] [23] that is a class of adaptive algorithms for source separation implementing an adaptive version of equivariant estimation. The EASI algorithms are based on the idea of serial updating; (3) the Infomax algorithm by [PERSON] and [PERSON] [24], which belongs to a self-organizing learning algorithm maximizing the information transferred in a network of non-linear units, and is also regarded as a higher-order generalization of the principal component analysis (PCA); (4) The Joint Approximate Diagonalization of Eigenmatrices (JADE) algorithm by [PERSON] and [PERSON] [25; 26] consisting of high-order measures of independence and the class of Jacobi algorithms for their optimization. In the JADE algorithm, joint diagonalization of cumulant matrices allows the whole high-order cumulant set to be processed with computational efficiency similar to eigen-based techniques. Because of its extensive applications and attractive properties, the performance of ICA algorithms has also been studied by many researchers. Some early works mainly centered on the fundamental problem of separability, meaning whether there is the possibility for the mixtures to be separated.