IEEE international symposium on information theory

Massive multiple-input multiple-output (MIMO) is playing a crucial role in the fifth generation (5G) and beyond 5G (B5G) communication systems. Unfortunately, the complexity of massive MIMO systems is tremendously increased when a large number of antennas and radio frequency chains (RF) are utilized. Therefore, a plethora of research efforts has been conducted to find the optimal precoding algorithm with lowest complexity. The main aim of this paper is to provide insights on such precoding algorithms to a generalist of wireless communications. The added value of this paper is that the classification of massive MIMO precoding algorithms is provided with easily distinguishable classes of precoding solutions. This paper covers linear precoding algorithms starting with precoders based on approximate matrix inversion methods such as the truncated polynomial expansion (TPE), the Neumann series approximation (NSA), the Newton iteration (NI), and the Chebyshev iteration (CI) algorithms. The paper also presents the fixed-point iteration-based linear precoding algorithms such as the Gauss-Seidel (GS) algorithm, the successive over relaxation (SOR) algorithm, the conjugate gradient (CG) algorithm, and the Jacobi iteration (JI) algorithm. In addition, the paper reviews the direct matrix decomposition based linear precoding algorithms such as the QR decomposition and Cholesky decomposition (CD). The non-linear precoders are also presented which include the dirty-paper coding (DPC), Tomlinson-Harashima (TH), vector perturbation (VP), and lattice reduction aided (LR) algorithms. Due to the necessity to deal with a high consuming power by the base station (BS) with a large number of antennas in massive MIMO systems, a special subsection is included to describe the characteristics of the peak-to-average power ratio precoding (PAPR) algorithms such as the constant envelope (CE) algorithm, approximate message passing (AMP), and quantized precoding (QP) algorithms. This paper also reviews the machine learning role in precoding techniques. Although many precoding techniques are essentially proposed for a small-scale MIMO, they have been exploited in massive MIMO networks. Therefore, this paper presents the application of small-scale MIMO precoding techniques for massive MIMO. This paper demonstrates the precoding schemes in promising multiple antenna technologies such as the cell-free massive MIMO (CF-M-MIMO), beamspace massive MIMO, and intelligent reflecting surfaces (IRSs). In-depth discussion on the pros and cons, performance-complexity profile, and implementation solidity is provided. This paper also provides a discussion on the channel estimation and energy efficiency. This paper also presents potential future directions in massive MIMO precoding algorithms.

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Overview of Precoding Techniques for Massive MIMO

Improved resource allocation scheme for optimizing the performance of cell edge users in Long Term Evolution-Advanced (LTE-A) system is proposed in this paper. The proposed algorithm optimally assigns and allocates Carrier Components (CCs), Radio Blocks (RBs) and Modulation and Coding Scheme (MCS) index for the users based on the Quality of Service (QoS) provision to meet the on demand service requests. The proposed algorithm divides the cell regions into cell centre and cell edge depending on the traffic load on the network. The available RBs are allocated to meet the on demands requests of the users among these two regions. RB usage ratio for optimizing the performance of the scheduling algorithm is used during resource allocation. As the RB usage ratio reaches more than 70%, throughput and data rates of the cell may not be reached in timely and reliable manner. The proposed algorithm takes RB usage ratio into consideration during scheduling to maintain minimum QoS provisions of the users for resource allocation. Simulation result shows that, performance of the cell edge users optimally met with minimum throughput and data rates for reliable communication in the LTE-A system.

Improved resource allocation scheme for optimizing the performance of cell-edge users in LTE-A system

http://ieeexplore.ieee.org/iel5/5/31261/01455125.pdf

Orthogonal transforms for digital signal processing

In this paper, based on the block (element)-wise inverse Jacket matrix, a unified fast hybrid diagonal block-wise transform (FHDBT) algorithm is proposed. A new fast diagonal block matrix decomposition is made by the matrix product of successively lower order diagonal Jacket matrix and Hadamard matrix. Using a common lower order matrix in the form of [111-1], a fast recursive structure can be developed in the FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Since these DCT-II, DST-II, DFT, and HWT are widely used in different areas of applications, the proposed FHDBT can be applied to the heterogeneous system requiring several transforms simultaneously. Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. The proposed algorithm is also well matched to circulant channel matrix. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/DST-II compression scheme compared with the DCT-II only compression method.

/pdf/a-fast-hybrid-jacket-hadamard-matrix-based-diagonal-block-43s2zmt4ce.pdf

A fast hybrid Jacket-Hadamard matrix based diagonal block-wise transform

The block diagonalization (BD) is a linear precoding technique for multi-user multi-input multi-output (MIMO) broadcast channels, which is able to completely eliminate the multi-user interference (MUI), but it is not computationally efficient. In this paper, we propose the block diagonal Jacket matrix decomposition, which is able not only to extend the conventional block diagonal channel decomposition but also to achieve the MIMO broadcast channel capacity. We also prove that the QR algorithm achieves the same sum rate as that of the conventional BD scheme. The complexity analysis shows that our proposal is more efficient than the conventional BD method in terms of the number of the required computation.

/pdf/a-simple-block-diagonal-precoding-for-multi-user-mimo-3lbuihpqdt.pdf

A simple block diagonal precoding for multi-user MIMO broadcast channels

We consider the downlink of a multicell system comprised of base stations (BSs) and user terminals equipped with multiple antennas respectively on the condition that arbitrary BS cooperation and distance dependent propagation path loss are assumed. In this paper, we consider homogeneous networks for the rectangular coordinates and show the cell edge performance of cellular networks based on distance from their cell center, i.e., BS. We focus on the downlink capacity of edge users in the cellular networks and show that BS cooperation can improve the spectral efficiency. The BSs cooperate for their transmission to the cell edge users in order to improve their signal-to-interference-plus-noise ratio (SINR) for inter-cell interference (ICI) cancelation in downlink multicell systems. When fractional frequency reuse (FFR) is applied to the cell edge, it is conjectured that BS cooperation, or a coordinated multipoint (CoMP), will further improve the system performance. Simulation results show that the proposed scheme outperforms the reference schemes in terms of the cell edge SINR with a minimal impact on the path loss exponent in the networks.

/pdf/downlink-performance-of-cell-edge-using-cooperative-bs-for-3l9vgvz47h.pdf

Downlink performance of cell edge using cooperative BS for multicell cellular network

Recently, Lee and Hou (IEEE Signal Process Lett 13: 461-464, 2006) proposed one-dimensional and two-dimensional fast algorithms for block-wise inverse Jacket transforms (BIJTs). Their BIJTs are not real inverse Jacket transforms from mathematical point of view because their inverses do not satisfy the usual condition, i.e., the multiplication of a matrix with its inverse matrix is not equal to the identity matrix. Therefore, we mathematically propose a fast block-wise inverse Jacket transform of orders N = 2
 k
 , 3
 k
 , 5
 k
 , and 6
 k
 , where k is a positive integer. Based on the Kronecker product of the successive lower order Jacket matrices and the basis matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse and fast algorithms of Arikan polar binary and Alamouti multiple-input multiple-output (MIMO) non-binary matrices, which are obtained from BIJTs, they can be applied in areas such as 3GPP physical layer for ultra mobile broadband permutation matrices design, first-order q-ary Reed-Muller code design, diagonal channel design, diagonal subchannel decompose for interference alignment, and 4G MIMO long-term evolution Alamouti precoding design.

/pdf/arikan-and-alamouti-matrices-based-on-fast-block-wise-4q7nm6gfrj.pdf

Arikan and Alamouti matrices based on fast block-wise inverse Jacket transform

The block diagonalization (BD) precoding technique is a well-known linear transmit strategy for multiuser multi-input multi-output (MU-MIMO) systems. The MU-MIMO broadcast channel is decomposed into multiple independent parallel single user MIMO (SU-MIMO) channels and achieves the maximum diversity order at high data rates. The lattice reduction-aided decoding (LRAD) features the reduced decoding complexity in MIMO communications. The Lenstra-Lenstra-Lovasz (LLL) algorithm has been extensively used to obtain better bases of the channel matrix while the complex lattice reduction (CLR) is aimed at improving orthogonality of basis vectors and shortening them. The orthogonalization and size reduction work are left for the CLR algorithm so that a modification of the channel matrix is carried out, resulting in better precoding and detection performances. We also derive bounds for lattice decoding. Simulation results show that the bit error rate (BER) performance of our proposed algorithm is better than that of conventional ones and it reduces the complexity compared with the LLL algorithm-based schemes.

/pdf/lattice-reduction-aided-with-block-diagonalization-for-3yfnbnarwb.pdf

Lattice reduction aided with block diagonalization for multiuser MIMO systems

Block diagonalization (BD) is a linear precoding technique for multiuser multi-input multi-output (MIMO) broadcast channels such that it completely eliminates the multiuser interference We investigate the problem of multi-cell multi-user co-channel transmission, where in both inter-cell interference and inter-user interference should be well managed Interference alignment (IA) is theoretically proved to be a promising technology in managing co-channel interference In this paper, we present an efficient multi-cell coordinated linear beamforming method where IA is combined with MU-MIMO to achieve high performance multi-cell cooperative transmission We extend to a multiple-cells scenario and jointly design transmit and receiver beamforming vectors We also apply the block diagonal Jacket matrices decomposition and extend the block diagonal channel decomposition with which the MIMO broadcast channel capacity can be achieved

Hashem Ali Khan

Papers

A simple block diagonal precoding for multi-user MIMO broadcast channels

Downlink performance of cell edge using cooperative BS for multicell cellular network

Arikan and Alamouti matrices based on fast block-wise inverse Jacket transform

Lattice reduction aided with block diagonalization for multiuser MIMO systems

A block diagonal jacket matrices for MIMO broadcast channels