## 1 Introduction
To reap the benefits of massive-MIMO, adequate knowledge of the CIR between each transmit-receive link is required. In a typical massive-MIMO system, the BS is equipped with a large number of antennas. Therefore, a large number of channels needs to be estimated. Thus, CIR estimation in massive-MIMO systems is quite a challenging task due to high dimensionality of massive-MIMO channels. Several CIR estimation techniques have been proposed in literature for the case of MIMO systems that can be broadly categorized into blind, e.g., [20,21], semiblind, e.g., [22,23], training/pilot based, e.g., [24,25], and superimposed training (SiT), e.g., [14,26], based techniques. For the training based channel estimation techniques, a known training sequence, also known as a pilot sequence, is transmitted along with a block of transmit symbols. At the receiver side, the channel is estimated by using the received training sequence and the known training sequence. The drawback of training based channel estimation techniques is that a significant portion of the channel capacity is consumed by the training sequence. On the other hand, blind channel estimation schemes use the statistical parameters of the received signal to estimate the CIR. However, blind estimation techniquesare computationally complex and have slow convergence rate. Semi-blind methods use some training symbols along with the statistics of received signal to estimate the CIR. Semi-blind channel estimation techniques share the benefits and trade-offs of the blind and training based estimation techniques. Recently, SiT based techniques have gained significant attention for the purpose of channel estimation. In an SiT based technique, a low power and periodic training sequence is superimposed over the information sequence and transmitted. Consequently, SiT based techniques avoid the allocation of any dedicated time/frequency slots for the training sequence. Over the past few years, compressed sensing (CS) has emerged as a new paradigm for the recovery of sparse signals. The authors in [27; 28] have established the fact that a finite-dimensional sparse signal can be exactly reconstructed from fewer, linear and nonadaptive measurements. The CS approach has been established as an efficient solution to estimate sparse multipath channels--see e.g., [14; 29]. Computing the sparse solution requires solving a \(\ell_{0}\)-minimization problem, which is computationally non-deterministic polynomial-time (\(NP\)) hard. An alternative approach is to relax the \(\ell_{0}\)-minimization to \(\ell_{1}\)-minimization and solve the problem for a sparse solution. This approach is termed as Basis Pursuits (BP) [30]. A BP based approach achieves more accurate solutions but requires higher computational complexity. Another approach used to find the sparse solution of an underdetermined system of linear equations is that of greedy algorithms, which iteratively approximate the sparse signal by suitably choosing the columns from the sparse measurement matrix. In literature, a wide variety of the greedy algorithms have been proposed to solve the CS problem such as matching pursuit (MP) [31], orthogonal matching pursuit (OMP) [32], regularized orthogonal matching pursuit (ROMP) [33], stagewise orthogonal matching pursuit (StOMP) [34], orthogonal complementary matching pursuit (OCMP) [35], compressive sampling matching pursuit (CoSaMP) [36], and gradient pursuit (GP) [37]. Several massive-MIMO channel estimation techniques have been proposed in the literature--see e.g., [23; 38] and references therein. In order to estimate CIR in massive-MIMO systems, linear minimum mean-squared error (LMMSE) estimation techniques are usually used. Several CS based techniques have also been proposed to estimate the CIR in massive-MIMO (see e.g., [39; 40]). In [41], authors have proposed a low complexity polynomial channel estimation based on Bayesian channel estimators to estimate CIR in massive-MIMO.