## 1 Introduction
An estimation technique for an uplink channel of massive-MIMO has been proposed in [42] that exploits the joint sparsity of the channels in a massive-MIMO system. In [43], authors have devised a Gaussian-mixture Bayesian learning based channel estimation technique for massive-MIMO. In [44], authors have devised a channel estimation technique that requires a small number of pilot sequences and exploits the sparsity and common support property of massive-MIMO communication channels. In [45], authors have exploited CS along with random linear network coding (RLNC) to devise an energy efficient scheme for vital signal telemonitoring in wireless body area networks (WBAN). By exploiting the sparsity of wireless multipath channels, SiT sequence based compressive channel sensing methods have been studied in various contexts such as single-input single-output (SISO) systems [14; 46], sparse MIMO channels [47; 48], and underwater acoustic channels [49]. In [46], a genetic algorithm (GA) based channel estimation method is proposed using an SiT sequence for SISO systems. In [14], a Dantzig selector (DS) algorithm based method is proposed for estimation of SISO sparse multipath channels using a known SiT sequence. This study is further extended in [47; 48] for the case of multiuser MIMO systems, where SiT based DS and MP algorithms are proposed. To the best of the authors' knowledge, no study has considered the use of CS based greedy algorithms in conjunction with an SiT sequence for estimation of massive-MIMO sparse uplink channels. The prime motivation for using a superimposed training based channel estimation approach is its improved spectral efficiency as compared to the conventional training based approaches. In this regard, the main contributions of this paper is to devise an SiT sequence based estimation of massive-MIMO sparse uplink channels by exploiting StOMP and GP as CS greedy algorithms. For large-scale sparse reconstruction problems, it has been established in [34] that the StOMP algorithm achieves better performance as compared to MP and OMP. Similarly, the GP algorithm enhances the performance (in terms of faster computations) of the OMP algorithm by adopting a directional gradient pursuit based approach [37]. As the CIR estimation of massive-MIMO sparse uplink channels involves a large number of channel coefficients, the choice of StOMP and GP as sparse reconstruction algorithms is more favorable for this purpose. The rest of the paper is structured as follows. In Section 2, the system model under consideration for multiuser massive-MIMO uplink communications is presented. Section 3 presents first-order statistics of the received signals along with the proposed channel estimation techniques. In Section 3.1, an SiT least squares (SiT-LS) based channel estimation technique available in literature [26] is presented. Section 3.2 presents the proposed SiT-StOMP and SiT-GP channel estimation techniques for the case of sparse uplink channels in massive-MIMO. Section 4 discusses a minimum mean square error (MMSE) equalizer for a massive-MIMO uplink communication scenario. Section 5 presents the simulation results and a performance analysis for the proposed channel estimation techniques. In Section 6, conclusions are presented. _Notations_: Matrices are denoted by boldface uppercase letters, e.g., \(\mathbf{X}\), while boldface lowercase letters are used to represent vectors, e.g., \(\mathbf{x}\). Small case letters, e.g., \(x\) are used to denote scalar quantities. Transpose and Hermitian transpose are represented by the superscripts \(T\) and \(H\), respectively. \(\Gamma^{i}\) represents the set of indices of the elements selected up to and including iteration \(i\). The matrix \(\mathbf{X}_{\Gamma^{i}}\) represents a sub-matrix of \(\mathbf{X}\) consisting of only those columns of \(\mathbf{X}\) whose indices belong to the set \(\Gamma^{i}\). The same convention is also followed for the case of vectors.