In this paper, we study the channel estimation problem in microwave correlated massive multiple-input-multiple-output systems with reduced number of radio-frequency chains. We exploit the knowledge of the transmit and receive correlation between the antennas. Leveraging the fact that the channel entries are uncorrelated in its eigen-domain, we seek to estimate the channel in this domain. Due to reduced number of radio-frequency chains, channel estimation is performed in multiple time slots. Under a total energy budget, we aim to optimally design the hybrid precoder and combiner in each training time slot, in order to estimate the channel using the minimum mean squared error criterion. We show that the optimal precoder and combiner in each time slot are aligned to transmitter and receiver eigen-directions, respectively. The energy allocation of each eigen-direction determines the significance of each eigen-direction; more energy is allocated to the stronger eigen-directions. At low training energy budget, only significant part of the channel needs to be estimated. At high training energy budget, the energy is equally distributed among all eigen-directions. Simulation results show that the proposed channel estimation scheme can efficiently estimate correlated massive multiple-input-multiple-output channels within a few training time slots.

The availability of accurate channel state information (CSI) is essential in multiuser massive multiple-input multiple-output (MIMO) systems. However, most published works focus on frequency-flat channel estimation which requires that the estimation must be repeated for every frequency slot, e.g., subcarrier, in a broadband system. Since the channels in the frequency-domain are the Fourier transform of a small set of time-domain channel coefficients, the time-domain channel estimation requires that fewer parameters be estimated. In this paper, we propose a semi-blind, time-domain, channel estimation technique for frequency-selective massive MIMO systems. Our solution depends on the subspace spanned by the signal eigenvectors of the received signal covariance matrix. Importantly, since the receiver samples at the symbol rate, time-domain-based estimation inherently has available enough samples for an accurate matrix estimate. To avoid asymptotic assumptions, we express each channel vector as a linear combination of the signal eigenvectors. We estimate the linear combination using a set of training symbols. Given the many samples of the received signal in the time-domain, we obtain a better channel estimate compared to conventional subcarrier-wise frequency-domain channel estimation. Unlike the previous published results, in this paper, we do not assume orthogonality of users' channels or knowledge of large-scale fading coefficients. In addition, our estimation procedure does not require orthogonality between the training symbols of the users in all cells.

Channel state information (CSI) is essential in massive multiple-input mulitple-output (MIMO) systems. However, most of the literature focuses on frequency-flat channel estimation; in a realistic broadband setting this implies that the estimation must be repeated for each subcarrier. In this paper, we propose a new channel estimation technique for frequency-selective channels in the time-domain. Time-domain CSI acquisition requires the estimation of fewer parameters. Importantly, since the receiver samples at the symbol rate, time-domain based estimation yields many samples of the received signal. Our approach depends on the estimation of the subspace spanned by users' channels, requiring a large number of antennas to ensure that the required rank constraints are met. Unlike previous published results, in this paper, we do not make any assumption on orthogonality of users' channel vectors or knowledge of large-scale fading coefficients. Additionally, our channel estimation, does not require orthogonality between the training symbols of the users in all cells.

In this study, the authors consider two multiple‐antenna transceivers exchanging information through a relay‐assisted network using a single‐carrier communication scheme. The authors assume that the propagation delay in different relaying path is negligible and the relay nodes are synchronous. As a result, the end‐to‐end multipath channel is not frequency‐selective (time‐dispersive) and hence, the successive arriving signals at the transceivers do not interfere with each other. Otherwise, inter‐symbol‐interference (ISI) will be inevitable and cyclic insertion and removal matrices will be required to combat ISI. In such a two‐way network, the relay nodes harvest energy from the surrounding environment and utilise this energy to forward their received messages using a harvest‐then‐forward protocol. For different receiver diversity combining techniques, the authors design an optimal relay beamforming to maximise the quality of the received signals at the transceivers subject to the energy casualty constraint at the relay nodes (the energy consumed for transmission of each block cannot exceed the accumulative harvested energy). For each diversity combining technique, a closed‐form solution is obtained for the optimal signal‐to‐noise ratio (SNR) that shows how adjusting the data transmission rate of the transceivers and the amount of energy harvested at the relays affects the received SNR.

In this work, a bi-directional network is considered where two single-antenna transceivers communicate with each other through multiple energy harvesting relay nodes. This communication is accomplished using a single-carrier scheme by exchanging the signal blocks between the transceivers. Since the distances between the transceivers through different relaying paths are not the same, the propagation delay of each path is different than the others. As a result, at sufficiently high data rates, the end-to-end multi-path channel is time-dispersive (frequency-selective) and inter-symbol-interference (ISI) is not avoidable at the both transceivers (in our single-carrier scheme the received signal blocks experience inter-block-interference (IBI)). A relay selection scheme is proposed to combat such an IBI by switching on the relay nodes that contribute to a single tap of the end-to-end channel and turning off the remaining relays. For each tap of the channel, an optimal relay beamformer is designed in order to maximize the transmission rate when the energy consumed by the relays to transmit a signal block is restricted to the harvested energy so far and a minimum desired signal-to-noise ratio (SNR) at the both transceivers is guaranteed. The performance of such an energy harvesting network design is illustrated by presenting the simulation results.

We study the problem of obtaining achievable signal-to-noise ratio (SNR) region and the corresponding rate region for an asynchronous bidirectional multi-carrier relay network which consists of two transceivers and multiple relays. We assume that each relaying path, corresponding to each relay, causes a delay in the signal transmitted by one of the transceivers when this signal goes through that relay and arrives at the other transceiver. This delay depends on the distance traveled by the signal. Hence, different relaying paths incur different delays in the signal time of arrival at each of the two transceivers. In our data model, we take into account that these delays are different for different relaying paths. Assuming distributed beamforming at the relays and power control at the transceivers, we characterize the achievable SNR region and the corresponding rate region for this network. Such a characterization is performed when each subcarrier is used to enable bidirectional communication between several outer transceivers. To do so, we present our optimization framework and examine its structure, thereby showing how it can be solved. We prove that for the case where the rates over different subcarriers at each transceiver are constrained to be equal, our approach leads to semi-closed-form solutions for the relay beamforming weights and transceivers' subcarrier powers and for the boundaries of the SNR region.

In this letter, we study the problem of joint power allocation and channel design for an active link which conveys information from a source to a destination through multiple orthogonal subchannels. In such a link, the power can be injected into the channel not only at the source but also at each subchannel. For such a parallel channel, we study the problem of sum-rate maximization under the assumption that the source power as well as the total power of the active channel are limited. Although this problem is not convex, we present an efficient solution to this sum-rate maximization. An interesting aspect of this solution is that it requires only a subset of the subchannels to be active and the remaining subchannels should be turned off. This is in contrast with passive parallel channels with equal subchannel signal-to-noise-ratios (SNRs), where water-filling solution to the sum-rate maximization under a source total power constraint leads to an equal power allocation among all subchannels. Furthermore, we prove that the number of active subchannels depends on the product of the source and channel powers. We also prove that if the total power available to the source and to the channel is limited, then in order to maximize the sum-rate via optimal power allocation to the source and to the active channel, half of the total available power should be allocated to the source and the remaining half should be allocated to the active channel.