Evaluation of multi‐user multiple‐input multiple‐output digital beamforming algorithms in B5G/6G low Earth orbit satellite systems

Satellite Communication (SatCom) systems will be a key component of 5G and 6G networks to achieve the goal of providing unlimited and ubiquitous communications and deploying smart and sustainable networks. To meet the ever-increasing demand for higher throughput in 5G and beyond, aggressive frequency reuse schemes (i.e., full frequency reuse), combined with digital beamforming techniques to cope with the massive co-channel interference, are recognized as a key solution. Aimed at (i) eliminating the joint optimization problem among the beamforming vectors of all users, (ii) splitting it into distinct ones, and (iii) finding a closed-form solution, we propose a beamforming algorithm based on maximizing the users’ Signal-to-Leakage-and-Noise Ratio (SLNR) served by a Low Earth Orbit (LEO) satellite. We investigate and assess the performance of several beamforming algorithms, including both those based on Channel State Information (CSI) at the transmitter, i.e., Minimum Mean Square Error (MMSE) and Zero-Forcing (ZF), and those only requiring the users’ locations, i.e., Switchable Multi-Beam (MB). Through a detailed numerical analysis, we provide a thorough comparison of the performance in terms of per-user achievable spectral efficiency of the aforementioned beamforming schemes, and we show that the proposed SLNR beamforming technique is able to outperform both MMSE and ZF schemes in the presented SatCom scenario.

With the increasing rate of wireless devices and high bandwidth operations, wireless networking and communications are becoming over crowded. To cope with such crowded and messy situation, massive MIMO is designed to work with hundreds of low-cost serving antennas at a time as well as improve the spectral efficiency at the same time. Time Division Duplexing (TDD) has been used for gaining beamforming which is a major part of massive MIMO, to gain its best improvement to transmit and receive pilot sequences. All the benefits are only possible if the channel state information or channel estimation is gained properly. Least Square (LS), Minimum Mean Square Error (MMSE) and Linear Minimum Mean Square Error (LMMSE) are the estimators commonly used for estimating channel matrices. We have optimized these methods using genetic algorithm to minimize the mean squared error and finding the best channel matrix from existing algorithms with less computational complexity. Our simulation result has shown that the use of Genetic Algorithm (GA) worked well on existing algorithms in a Rayleigh slow fading channel and existence of Additive White Gaussian Noise. We found that the GA optimized LS is better than existing algorithms. GA provides optimal result in some few iterations in terms of Mean Square Error (MSE) with respect to SNRand computational complexity.

Wavelet-Based Identification of Linear Discrete-Time Systems

Multiple transmit antennas can be employed in a downlink channel to serve multiple users under the assumption of perfect channel state information (CSI) of all users at the base station. In practice, however, the channel knowledge available at the base station is not perfect. For instance, in case of a time division duplex (TDD) system, the transmit CSI is the estimated uplink channel. On the other hand, in a frequency division duplex (FDD) system, feedback from the users is required to obtain transmit CSI. In this case, we assume the transmit CSI consists of a quantized version of the normalized estimated channel vector and the statistics of the channel norm of each user. In this work we consider the transceiver design of the downlink of a multiuser MISO system based on the minimum mean square error (MMSE) criterion with imperfect CSI as discussed above.

Interference alignment (IA) is a multi-user wireless communication strategy that enables several transmitters simultaneous communicate with their paired receivers without interfering each other. IA is a multiplexing gain optimal strategy at the expense of requiring the global channel state information (CSI) at the transmitters. Most previous works assume the availability of perfect CSI which is not possible in practice. The performance of IA algorithms based on perfect CSI drop dramatically in circumstance where CSI errors exist. In this paper we propose a robust minimum mean square error (MMSE) IA algorithm with imperfect CSI. Based on a Gaussian statistic channel error model, we give the mean square error objective function with per transmitter power constraint. The objective function is not joint convex in precoders and decoders, but convex in precoders with fixed decoders and vice versa. We convert the problem to two convex sub problems and iteratively find the solutions. Numerical results are presented to validate the effectiveness of proposed algorithm when CSI errors exist.

In this paper, a group pre-coding scheme is proposed for multimedia broadcast multicast service (MBMS) downlink transmission in distributed multiple input multiple output (D-MIMO) antenna system. The ideal channel state information (CSI) is assumed to know at both transmitters and receivers. In order to evaluate the performance of the group pre-coding, the average symbol error rate (SER) of the Block Diagonalization - Minimum Mean Square Error (BD-MMSE) and Block Diagonalization - Zero forcing (BD-ZF) algorithms with group pre-coding in both D-MIMO and centralized MIMO (C-MIMO) system are investigated through Monte Carlo simulation. The SER performance of conventional pre-coding schemes with BD-MMSE is also given for comparison. The simulation results show that the degradation in SER performance of group pre-coding proposed is slightly comparing with that of the conventional pre-coding scheme, but the computational complexity of group pre-coding scheme is reduced significantly.

In this paper, we propose a relay selection method in an amplify-and-forward (AF) scenario considering complete outdated channel state information (CSI) of all links. Differing from the methods in the literatures considering only outdated CSI over the link from the relay to the destination, another type of outdated CSI, i.e., the outdated CSI over the link from the source to the relay, is also considered in the relay selection. In order to overcome the effect of these outdated CSIs due to feedback delay, we use minimum mean square error (MMSE) estimation to predict the SNRs of the source-to-relay links and the relay-to-destination links at the forwarding instant. Along with the relay selection, an effective power allocation method is proposed to optimize the power allocation between the source and the relays. Moreover, the expression of the system outage probability is derived. The simulation results show that the proposed method, along with the power allocation, improves the outage performance of the system.

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, the authors propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, the authors compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. The authors show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.

We address the problem of transmit beamforming under channel uncertainty for a multiuser (MU), single carrier frequency domain equalization multiple input multiple output (SC-FDE-MIMO) system. SC-FDE-MIMO scheme is effective solution with relative low complexity to combat inter -symbol interference (ISI) whilst exploiting multi antennas diversity gain. In our system, the signal to leakage ratio (SLR) criterion is used to design the transmit beamformer and the minimum mean square error (MMSE) criterion is employed for the receiver equalization and combining. Non-robust beamforming techniques require perfect channel state information (CSI) knowledge which is not available in practice. In this paper, we propose a robust transmit beamformer which can successfully tolerate CSI imperfection. Diagonal loading is employed to introduce robustness to channel state information errors. The novelty of this work, however, is the application of the robust beamforming in the context of downlink MU-SC transmission. Average bit error (BER) simulations are presented to verify the efficiency of the proposed method.

A novel interference alignment (IA) scheme based on the errors-in-variables (EIV) mathematic model has been proposed to overcome the channel state information (CSI) estimation error for the MIMO interference channels. By solving an equivalently unconstrained optimization problem, the proposed IA scheme employing a weighted total least squares (WTLS) algorithm can obtain the solution to a constrained optimization problem for transmit precoding (TPC) matrices and minimizes the distortion caused by imperfect CSI according to the EIV model. It is shown that the design of TPC matrices can be realized through an efficient iterative algorithm. The convergence of the proposed scheme is presented as well. Simulation results show that the proposed IA scheme is robust over MIMO interference channels with imperfect CSI, which yields significantly better sum rate performance than the existing IA schemes such as distributed iterative IA, maximum signal-to-interference-plus-noise ratio (Max SINR), and minimum mean square error (MMSE) schemes.

Multi input multi output (MIMO) system with the multiple antennas at both the transmitter and receiver is the emerging technology in the modern wireless system. MIMO systems are well adopted due to its high spectral efficiency and high data rates. For the detection of MIMO systems, a powerful technique called Lattice Reduction (LR) algorithm are used to obtain the better orthogonality in the channel matrices and is aided with the linear and low complexity detectors such as Zero forcing(ZF) and Minimum mean square error (MMSE) for the reduction in complexity. In this paper we propose a new algorithm called Enhanced lattice reduction algorithm to improve the error performance for the linear detectors with the lesser complexity and also it is aided with the non linear precoding called Tomlinson-Harashima precoding (THP) in the presence of channel state information (CSI). Lattice reduction aided with THP improves the performance linearly. BER performance of the proposed algorithm is determined and it is compared with the other LR aided algorithms in the literature.

In this paper, we design a zero-forcing (ZF) Tomlinson-Harashima precoding (THP) and a minimum mean square error (MMSE) THP for multiuser MIMO relay system with direct link. Based on these precoding structures, we propose the optimal combining weights of the ZF THP and the MMSE THP in half duplex relay system, and the sub-optimal weights of MMSE THP to reduce feedback channel state information (CSI). Through the Monte Carlo simulation, we verify that the optimal weights combining method outperforms the constant weights combining method. In addition, we confirm that the performance of the sub-optimal weights combining method is close to the optimal method, while reducing the feedback CSI simultaneously.

Two numerical approaches, the Robust-Generalized Iterative Approach (R-GIA) and the Robust-Transmit Covariance Optimization Approach (R-TCOA), are proposed for jointly designing the minimum mean square error (MMSE) precoders and decoders of uplink multiuser multiple-input-multiple-output (MIMO) systems with arbitrary linear equality power constraints and possibly imperfect channel state information (CSI). The R-TCOA always gives optimum solutions but is only applicable when the rank constraints on the precoders are relaxed, the spatial correlation matrix for the transmit antennas of each user is an identity matrix, and there exists a scalar such that squaring the source covariance matrices is the same as multiplying them by it. The statistics of the CSI error also need to be the same for all users if the power constraints of the users are interdependent. The R-GIA, on the other hand, has no such restrictions. But whenever the R-TCOA is applicable, both approaches converge, and all the transmit covariance matrices are full rank, the two solutions are actually equivalent (i.e. the R-GIA is also optimum)! Numerical results show that these two robust approaches, for the most part, outperform their non-robust counterparts in various different channel correlation scenarios.

Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI

In this paper, we consider a cooperative system based on relay selection in a scenario where the available channel state information (CSI) is subject to delays. In order to exploit the selection diversity gains of the system while providing robustness against CSI inaccuracy, we propose a robust relay selection strategy based on a minimum mean square error (MMSE) Bayesian estimator. As shown in the paper, the proposed robust strategy provides significant gains in scenarios with different levels of CSI inaccuracy.