## 1 Introduction  
Multiple-antenna techniques are well known to provide spatial diversity and multiplexing gains [1; 2; 3]. Over the last few decades, the benefits of multiple-antenna communications have been verified in both theory and practice. On the other hand, tensor-based signaling approaches that utilize several signal dimensions such as time, space, and code, are seen as good technologies for improving the information transmission rate and enhancing communication reliability [4; 5; 6]. Against this background, the problem of joint symbol and channel estimation is resolved by using tensor-based signaling approaches, and a number of semi-blind or blind receivers have been proposed for multiple-input multiple-output (MIMO) systems. A parallel factor (PARAFAC) [7] based receiver is proposed in [8] by using the Khatri-Rao space-time (KRST) coding scheme, which can achieve a flexible tradeoff between error performance and transmission efficiency. In [9], the authors extend the KRST coding scheme by using the linear constellation precoding, and then developing several semi-blind receivers. These semi-blind receivers allow a joint symbol and channel estimation without requiring pilot sequences for the instantaneous channel state information (CSI) acquisition. In [10], the authors develop a new tensor-based receiver in MIMO relay systems for channel estimation by using PARAFAC analysis. A low complexity PARAFAC-based channel estimation scheme for non-regenerative MIMO relay systems is developed in [11]. In [12], a novel semi-blind receiver is derived using a multiple KRST coding scheme for joint symbol and channel estimation. More recently, a nested PARAFAC-based receiver for cooperative MIMO communications is proposed in [13], and three-step and double two-step alternating least squares (ALS) algorithms are proposed to fit the nested PARAFAC model for estimating system parameters. For millimeter wave (mmWave) massive MIMO systems, a PARAFAC decomposition-based algorithm is developed in [14] to jointly estimate channel parameters of multiple users. In [15], the algorithm in [14] is extended to mmWave MIMO orthogonal frequency division multiplexing (MIMO-OFDM) systems for channel estimation, and Cramer-Rao bound (CRB) results for channel parameters are also derived. Considering the channel estimation issue in the presence of pilot contamination for multi-cell massive MIMO systems, a new PARAFAC-based approach is proposed in [16] to jointly estimate directions of arrival, fading coefficients, and delays. Although these works [8; 9; 10; 11; 12; 13; 14; 15; 16] consider different design approaches, their common feature is using the PARAFAC model, which needs to know the first column or row of one loading matrix to eliminate scaling ambiguity. Furthermore, the ALS algorithm used in these receivers exhibits a convergence problem when ill-conditioned factor matrices exist [17]. In contrast to the ALS algorithm, the Levenberg-Marquardt (LM) algorithm updates all the parameters to be estimated at the same time. The LM algorithm is successfully used to fit some tensor models, adapt to collinearity problems, and provide quadratic convergence [18; 19; 20]. A LM algorithm is first proposed for fitting PARAFAC model in [18]. In [19], the authors present a LM algorithm to the decomposition of the Block Component Model (BCM) in the uplink of a wideband direct-sequence code-division multiple access (DS-CDMA) systems. Recently, a LM algorithm was developed in [20] to jointly estimate information symbol and channel matrices for a generalized PARATUCK2 model. As an iterative algorithm, the LM algorithm is also sensitive to initialization. Thus, the optimization of the initial value is important to improve the performance of the LM algorithm. In [21], a tensor-based space-coding scheme using PARATUCK2 model is developed. For the PARATUCK2 model, the number of channel uses can be different from one transmitted data stream to another. In [22], a generalized PARATUCK2 model is proposed by exploiting a tensor space-time (TST) coding.