This paper proposes a manifold optimization-based tensor recovery algorithm for channel estimation (MO-TRACE) in reconfigurable intelligent surface (RIS)-assisted millimeter wave (mmWave) MIMO-OFDM systems. Specifically, considering the inherent sparse scattering characteristics of mmWave channels, the multidimensional cascaded channel in the angular-delay domain is represented by a sparse and low-rank tensor, and we formulate the channel estimation problem as a sparse and low-rank tensor recovery problem. Then, we use the canonical polyadic (CP) decomposition technique to decompose the tensor into multiple factor matrices, where the factor matrices are related to the channel parameters. To account for the sparse factor matrices, we add the sparse regularization terms of the factor matrices to the optimization objective, which can also reduce the number of nonzero columns in factor matrices, i.e., the rank of the tensor. As the concatenation of multiple factor matrices can be seen as a point on a product manifold, we apply MO algorithms to search for the optimal sparse point with enhanced convergence speed. The proposed MO-TRACE algorithm provides a more precise description of channels and ensures that the iteration point always remains within the feasible domain, thereby enhancing solution accuracy. Simulation results validate the superiority of the proposed MO-TRACE in terms of estimation accuracy.

In this study, the authors investigate the joint design problem of interference alignment (IA) and power splitting (PS) in simultaneous wireless information and power transfer (SWIPT) networks. The existing joint design method is generally divided into two steps. First, IA is performed, and then the PS ratio is optimised. To obtain IA and SWIPT, a new joint design multi‐objective alternating optimisation (MOAO) algorithm is proposed. Different from the existing joint design method, the proposed MOAO algorithm not only maximises the sum harvested power after PS, but also maximises the sum signal‐to‐intereference‐plus‐noise ratio (SINR) by jointly designing the transmitting precoding matrices, the receiving interference suppression matrices, and the PS ratio. For this multi‐objective optimisation problem, a weighted optimisation method is proposed, which compromises between maximising the sum harvested power and maximising the sum SINR. Simulation validates that the sum achievable rate and sum harvested power of the proposed MOAO algorithm are significantly superior to those of the current scheme under the reasonable weighting coefficients.

The decode‐and‐forward multi‐relay system with the presence of an eavesdropper is researched in this study. Two widely used transmission schemes are considered, namely, the best‐relay selection scheme and the all‐relay‐based beamforming scheme. To be specific, the former scheme adopts only the single best relay among all the candidate relays that have succeeded in decoding the source signal to assist the transmission, whereas the all‐relay‐based beamforming scheme allows all the candidates to assist the source simultaneously in a beamforming manner. The authors reveal that in both schemes, if the total transmit power of the two hops is constrained, contradiction exists between the two means of improving physical‐layer security: (i) letting more relays succeed in decoding the source signal; (ii) increasing the transmit power of the selected relay(s). The authors thus analyse the secrecy outage behaviour of the two schemes and derive expressions of secrecy outage probability (SOP), based on which, the optimal power allocation solutions are obtained. It is demonstrated that in both schemes, the analysis results match well with the simulation results. Moreover, the proposed power allocation solutions surpass the conventional average power solution in SOP in both schemes.

This paper studies the asymptotic capacity of large MIMO amplify-and-forward (AF) relay networks with one source-destination pair equipped with M antennas and K single-antenna relays. In contrast to prior works, we consider not only the multipath fading but also the path loss effect. By using random matrix theory, we first derive the asymptotic eigenvalue distribution (A.E.D.) of the channel covariance matrix between the source and the destination as M and K approach infinity while their ratio remains constant. Based on the resulting A.E.D., the system capacity is then obtained. More specifically, a linear relay distribution is considered to evaluate the asymptotic capacity, which can realistically model the large MIMO AF relay networks. Both theoretical analysis and Mont-Carlo simulations have consistently shown the impact of path loss parameters on the asymptotic capacity.

In this paper, we propose a joint relay and destination optimization design for two-way half-duplex amplify-and-forward (AF) relay systems with multiple relays, each with multiple antennas. By using the sum mean-squared error (MSE) criterion and Wiener filtering principle, the joint relay and destination design is formulated as an optimization problem of the relay precoding matrix under the constraint of total relay transmit power. Then, constructing a virtual point to point MIMO channel and using the singular-value-decomposition (SVD), the optimization problem is simplified to a convex minimization of an upper bound of the sum MSE through a diagonalization process. Finally, a suboptimum scheme is proposed to solve the simplified convex optimization problem. Monte-Carlo simulation shows that the proposed suboptimal scheme gives a better MSE performance than the existing gradient descent algorithm does, and moreover, our method becomes more advantageous when the number of relays or the number of relay antennas increases.

This paper presents a joint linear processing scheme for two-hop and half-duplex distributed amplify-and-forward (AF) relaying networks with one source, one destination and multiple relays, each having multiple antennas. Under the perfect CSI (channel state information) assumption, a joint relay and destination design is proposed to minimize the mean-square error (MSE) of the output signal at the destination. By the Wiener filter principle, it is formulated as an optimization problem with respect to the relay precoding matrix under the constraint of a total relay transmit power. And then, the constrained optimization with an objective to design the relaying block-diagonal matrix is simplified to an equivalent problem with scalar optimization variables. Moreover, it is revealed that the scalar-version optimization is convex when the total relay power or the second-hop SNR (signal to noise ratio) is above a certain threshold. The underlying optimization problem, which is non-convex in general, is solved by the complementary geometric programming (CGP). Simulation results show that the proposed scheme outperforms the existing relaying method in the case of relatively large second-hop SNR.

This paper presents a relay precoding scheme under the imperfect channel state information (CSI)assumption for two-hop amplify-and-forward based MIMO relay networks with one source, one destination and multiple relays. The forward channel mean and covariance available at the relays is assumed to be for the robust design of the linear relay precoder. By using the average mutual information criterion along with a total relay transmitting power constraint, an optimization problem is formulated by assuming the imperfect CSIT(CSI at the transmitter) at the relays. We first derive the approximation of the average mutual information rate, and then simplify the constrained optimization problem into the equivalent problem involving scalar optimization variables. Through an in-depth study of the problem formulation, it is revealed that the objective function is convex only when each optimization variable is larger than a certain threshold, which can be determined mainly by the system configurations and the channel condition. The effectiveness of the proposed relay precoder is validated by Monte-Carlo simulations with comparison to that under perfect CSI assumption.

By employing the amplify-and-forward relaying strategy, a relay selection method with simplified precoding is proposed for two-hop multi-relay channels. The proposed method consists of two parts. In the first part, the authors present an optimal beamforming scheme with full channel state information (CSI) and derive a simplified and analytic expression for the output SNR through each relay, thereby selecting the best relay. The second part considers the transmiit precoding problem with the CSI known to the receiver only and provide a selection strategy with Grassmannian beamforming. The new algorithm chooses only one relay based on the maximal received SNR to assist in transmission. It can significantly reduce the system consumption, achieve excellent bit-error-rate and average throughput and maintain full diversity order. Simulation results demonstrate that the performance of the proposed schemes with low complexity approaches towards the optimal iteration method. For practical situations with a distance attenuation factor, the performance gain of the authors schemes is also evident.

In this paper, we first derive an optimal precoder for amplify-and-forward (AF) multiple-antenna relay systems with single-antenna source and destination terminals by maximizing the output signal-to-noise ratio (SNR). Then, the resulting maximum SNR expression and its approximation at high transmission SNR are analyzed to obtain their statistical properties for independently identically distributed (i.i.d.) Rayleigh fading channels. Based on the properties of the approximate maximum SNR, the average symbol error probability (ASEP) is investigated, leading to an explicit diversity order and array gain. The ergodic achievable rate is also studied, giving a tight closed-form upper bound. The theoretical analysis is finally validated by Monte Carlo simulations.

This paper presents an optimal relay precoding scheme for two-hop amplify-and-forward based MIMO relay networks with one source, one destination and multiple relays. A constrained optimization problem for relay precoder is formulated by using the mutual information criterion along with a total relay transmitting power constraint. It is shown that due to the block-diagonal structure of the precoding matrix, the optimization problem can not be solved directly by the existing methods. We then simplify it into an equivalent problem involving scalar optimization variables only. Through an in-depth study of the problem formulation, it is revealed that the objective function is convex only when the relay power is larger than a certain threshold, which can be determined mainly by the system configurations and the channel condition. Finally, under the convex condition, the simplified problem is solved by a convex optimization method. The effectiveness of the proposed precoder is validated by Monte-Carlo simulations with comparison to some of the existing methods.