Massive multiple-input multiple-output (massive-MIMO) is foreseen as a potential technology for future 5G cellular communication networks due to its substantial benefits in terms of increased spectral and energy efficiency. These advantages of massive-MIMO are a consequence of equipping the base station (BS) with quite a large number of antenna elements, thus resulting in an aggressive spatial multiplexing. In order to effectively reap the benefits of massive-MIMO, an adequate estimate of the channel impulse response (CIR) between each transmit–receive link is of utmost importance. It has been established in the literature that certain specific multipath propagation environments lead to a sparse structured CIR in spatial and/or delay domains. In this paper, implicit training and compressed sensing based CIR estimation techniques are proposed for the case of massive-MIMO sparse uplink channels. In the proposed superimposed training (SiT) based techniques, a periodic and low power training sequence is superimposed (arithmetically added) over the information sequence, thus avoiding any dedicated time/frequency slots for the training sequence. For the estimation of such massive-MIMO sparse uplink channels, two greedy pursuits based compressed sensing approaches are proposed, viz: SiT based stage-wise orthogonal matching pursuit (SiT-StOMP) and gradient pursuit (SiT-GP). In order to demonstrate the validity of proposed techniques, a performance comparison in terms of normalized mean square error (NCMSE) and bit error rate (BER) is performed with a notable SiT based least squares (SiT-LS) channel estimation technique. The effect of channels’ sparsity, training-to-information power ratio (TIR) and signal-to-noise ratio (SNR) on BER and NCMSE performance of proposed schemes is thoroughly studied. For a simulation scenario of: $4\times 64$ massive-MIMO with a channel sparsity level of $80\%$ and signal-to-noise ratio (SNR) of $10\mathrm{dB}$ , a performance gain of $18\mathrm{dB}$ and $13\mathrm{dB}$ in terms of NCMSE over SiT-LS is observed for the proposed SiT-StOMP and SiT-GP techniques, respectively. Moreover, a performance gain of about $3\mathrm{dB}$ and $2.5\mathrm{dB}$ in SNR is achieved by the proposed SiT-StOMP and SiT-GP, respectively, for a BER of ${10}^{-2}$ , as compared to SiT-LS. This performance gain NCME and BER is observed to further increase with an increase in channels’ sparsity.

Recent advances in multiple-input multiple-output (MIMO) systems have renewed the interests of researchers to further explore this area for addressing various dynamic challenges of emerging radio communication networks. Various measurement campaigns reported recently in the literature show that physical multipath MIMO channels exhibit sparse impulse response structure in various outdoor radio propagation environments. Therefore, a comprehensive physical description of sparse multipath MIMO channels is presented in first part of this paper. Superimposing a training sequence (low power, periodic) over the information sequence offers an improvement in the spectral efficiency by avoiding the use of dedicated time/frequency slots for the training sequence, which is unlike the traditional schemes. The main contribution of this paper includes three superimposed training (SiT) sequence based channel estimation techniques for sparse multipath MIMO channels. The proposed techniques exploit the compressed sensing theory and prior available knowledge of channel’s sparsity. The proposed sparse MIMO channel estimation techniques are named as, SiT based compressed channel sensing (SiT-CCS), SiT based hardlimit thresholding with CCS (SiT-ThCCS), and SiT training based match pursuit (SiT-MP). Bit error rate (BER) and normalized channel mean square error are used as metrics for the simulation analysis to gauge the performance of proposed techniques. A comparison of the proposed schemes with a notable first order statistics based SiT least squares (SiT-LS) estimation technique is presented to establish the improvements achieved by the proposed schemes. For sparse multipath time-invariant MIMO communication channels, it is observed that SiT-CCS, SiT-MP, and SiT-ThCCS can provide an improvement up to 2, 3.5, and 5.2 dB in the MSE at signal to noise ratio (SNR) of 12 dB when compared to SiT-LS, respectively. Moreover, for \(\mathrm {BER}=10^{-1.9}\), the proposed SiT-CCS, SiT-MP, and SiT-ThCCS, compared to SiT-LS, can offer a gain of about 1, 2.5, and 3.5 dB in the SNR, respectively. The performance gain in MSE and BER is observed to improve with an increase in the channel sparsity.