Nonlinear Precoding Techniques Research Articles

Reduced Complexity Precoding for One-Bit Signaling

A number of precoding methods have recently been proposed for massive MIMO scenarios that assume the use of one-bit digital-to-analog converters, or that constrain the signal to be of constant modulus. The methods that provide the best performance employ non-linear precoding techniques that require a search for a parameter vector of the same dimension as the number of antennas, which is prohibitively expensive for massive MIMO applications. In this paper, we propose a reduced complexity precoding method based on linear programming and constructive interference that exploits an initial approximate solution to significantly reduce the dimension of the search. In particular, the method uses the output of an initial quantized linear precoder and updates only those elements that do not satisfy a certain reliability condition. Simulations show that the resulting loss in performance due to the use of the simplified approach is insignificant provided that the reduced dimension is chosen to be large enough, but still much smaller than the number of antennas.

Energy Efficient Linear and Non-Linear Precoders for Massive MIMO Systems

The term Massive MIMO means, Massive multiple input multiple output also known as (large-scale antenna system, very large MIMO). Massive Multiple-Input-MultipleOutput (MIMO) is the major key technique for the future Fifth Generation (5G) of mobile wireless communication network due to its characteristics, elements and advantages. Massive MIMO will be comprised of five major elements; antennas, electronic components, network architectures, protocols and signal processing. We realize that precoding technique is a processing technique that utilizes Channel State Information Technique (CSIT) by operating on the signals before transmitting them. This technique varies base on the type of CSIT and performance criterion. Precoding technique is the last digital processing block at the transmitting side. In this paper, linear and non-linear Precoding technique was reviewed and we proposed two techniques under each that is Minimum Mean Square Error (MMSE), Block Diagonalization (BD), Tomlinson-Harashima (TH) and Dirty paper coding (DPC). Four Precoding techniques: MMSE, BD, DPC and TH were used in the studies to power consumption, energy efficiency and area throughput for single-cell and multi-cell scenarios. In comparing the proposed techniques, in terms of energy efficiency and area throughput, reuse factor (Reuse 4) performs better than other techniques when there is an imperfect CSI is used

Modified Conjugate Gradient Algorithms for Gram Matrix Inversion of Massive MIMO Downlink Linear Precoding

This paper deals with various low complexity algorithms for higher order matrix inversion involved in massive MIMO system precoder design. The performance of massive MIMO systems is optimized by the process of precoding which is divided into linear and nonlinear. Nonlinear precoding techniques are most complex precoding techniques irrespective of its performance. Hence, linear precoding is generally preferred in which the complexity is mainly contributed by matrix inversion algorithm. To solve this issue, Krylov subspace algorithm such as Conjugate Gradient (CG) was considered to be the best choice of replacement for exact matrix inversions. But CG enforces a condition that the matrix needs to be Symmetric Positive Definite (SPD). If the matrix to be inverted is asymmetric then CG fails to converge. Hence in this paper, a novel approach for the low complexity inversion of asymmetric matrices is proposed by applying two different versions of CG algorithms- Conjugate Gradient Squared (CGS) and Bi-conjugate Gradient (Bi-CG). The convergence behavior and BER performance of these two algorithms are compared with the existing CG algorithm. The results show that these two algorithms outperform CG in terms of convergence speed and relative residue.

A Novel Nonlinear and Non-iterative Precoding Technique for Single and Multi User MIMO Systems

A modification of the well known linear and iterative based precoder intended for both single and multi-user multiple-input multiple-output (MIMO) has been proposed. The proposed precoder uses the nonlinear and non-iterative processing strategies to obtain more efficient and less complexity designs. The non-linearity in the precoder is introduced by using the nonlinear constellation precoding technique based on maximum distance separable codes. Also, the computation complexity in iterative based precoder design is avoided by using a singular value decomposition method. The maximum likelihood detection for the linear MIMO channel is considered. The simulation results are provided in-terms of bit error rate versus signal-to-noise ratio to show that the proposed combined non-linear and non-iterative precoding schemes outperform the conventional linear and iterative based MIMO precoder designs.

Non-Linear and Non-Iterative Based Transceiver Design for SU-MIMO Systems

This paper considers the design of a low-complexity and high-performance precoder for multiple-input multiple-output (MIMO) systems. The precoder is designed by combining both nonlinear and non-iterative processing strategies. The proposed nonlinear precoding techniques employ a nonlinear constellation precoding technique based on maximum distance separable codes at the transmitter. We propose to reduce the computational complexity in iterative-based precoding algorithms by using less complex non-iterative singular value decomposition-based joint precoder and decoder pair design. The maximum likelihood detection for the linear MIMO channel is considered. The simulation results showed that the proposed nonlinear and non-iterative precoding schemes outperform the conventional linear MIMO precoder design, even when a reduced-complexity suboptimal strategy is adopted, considering the bit error rate performance.

Hybrid TH-VP Precoding for Multiuser MIMO

Vector perturbation (VP) is a nonlinear precoding technique that achieves near-capacity performance in multiuser multiple-input multiple-output systems at the expense of large complexity due to the search for the optimum perturbation vector. In this paper, we present the hybrid Tomlinson-Harashima VP (TH-VP) algorithm, a novel zero-forcing precoding scheme, which combines TH precoding to remove interuser interference, and VP precoding to equalize each user's multiple spatial streams. We show that the two nonlinear techniques can be integrated in a single optimization and that the proposed algorithm has lower computational requirements than any other. The performance of TH-VP is analyzed and simulation results show that TH-VP outperforms conventional zero-forcing VP and approaches the performance of dirty paper coding.

Low-Complexity SSOR-Based Precoding for Massive MIMO Systems

With the increase of the number of base station (BS) antennas in massive multiple-input multiple-output (MIMO) systems, linear precoding schemes are able to achieve the near-optimal performance, and thus are more attractive than nonlinear precoding techniques. However, conventional linear precoding schemes such as zero-forcing (ZF) precoding involve the matrix inversion of large size with high computational complexity, especially in massive MIMO systems. To reduce the complexity, in this letter, we propose a low-complexity linear precoding scheme based on the symmetric successive over relaxation (SSOR) method. Moreover, we propose a simple way to approximate the optimal relaxation parameter of the SSOR-based precoding by exploiting the channel property of asymptotical orthogonality in massive MIMO systems. We show that the proposed SSOR-based precoding can reduce the complexity of the classical ZF precoding by about one order of magnitude without performance loss, and it also outperforms the recently proposed linear approximate precoding schemes in typical fading channels.

Low-Complexity MU-MIMO Nonlinear Precoding Using Degree-2 Sparse Vector Perturbation

Multiuser multiple-input multiple-output (MU-MIMO) nonlinear precoding techniques face the problem of poor computational scalability to the size of the network. In this paper, the fundamental problem of MU-MIMO scalability is tackled through a novel signal-processing approach, which is called degree-2 vector perturbation (D2VP). Unlike the conventional VP approaches that aim at minimizing the transmit-to-receive energy ratio through searching over an $N$ -dimensional Euclidean space, D2VP shares the same target through an iterative-optimization procedure. Each iteration performs vector perturbation over two optimally selected subspaces. By this means, the computational complexity is managed to be in the cubic order of the size of MU-MIMO, and this mainly comes from the inverse of the channel matrix. In terms of the performance, it is shown that D2VP offers comparable bit-error-rate to the sphere encoding approach for the case of small MU-MIMO. For the case of medium and large MU-MIMO when the sphere encoding does not apply due to unimplementable complexity, D2VP outperforms the lattice-reduction VP by around 5–10 dB in Eb/No and 10–50 dB in normalized computational complexity.

A Novel Nonlinear Constellation Precoding for OFDM Systems with Subcarrier Grouping

This paper proposed a novel nonlinear constellation precoding (NCP) technique based on maximum distance separable (MDS) codes in orthogonal frequency-division multiplexing (OFDM) systems. The proposed method envisage to maximize both the diversity and coding gains for any number of diversity channels and desired diversity orders. The novel NCP technique combined with subcarrier groping in OFDM systems to replace the most existing linear constellation precoding (LCP) scheme. In this scheme, the full set of subcarriers are splitted into smaller groups and the codewords are constructed from $$q$$ q point constellation mapper with MDS encoder. The maximum-likelihood (ML) decoder is used in the most existing signal space diversity technique which is replaced by diversity channel selection (DCS) to reduce the decoding complexity with the cost of marginal performance loss. The effect of the Inter-carrier interference (ICI) introduced by the carrier frequency offsets (CFO) also analyzed in the proposed OFDM system. The superiority of the proposed novel NCP technique over the previously proposed designs is verified by simulation results.

Fully Pipelined Implementation of Tree-Search Algorithms for Vector Precoding

The nonlinear vector precoding (VP) technique has been proven to achieve close-to-capacity performance in multiuser multiple-input multiple-output (MIMO) downlink channels. The performance benefit with respect to its linear counterparts stems from the incorporation of a perturbation signal that reduces the power of the precoded signal. The computation of this perturbation element, which is known to belong in the class of NP-hard problems, is the main aspect that hinders the hardware implementation of VP systems. To this respect, several tree-search algorithms have been proposed for the closest-point lattice search problem in VP systems hitherto. Nevertheless, the optimality of these algorithms has been assessed mainly in terms of error-rate performance and computational complexity, leaving the hardware cost of their implementation an open issue. The parallel data-processing capabilities of field-programmable gate arrays (FPGA) and the loopless nature of the proposed tree-search algorithms have enabled an efficient hardware implementation of a VP system that provides a very high data-processing throughput.

Line Encoding for Multiuser MIMO Downlink

We investigate nonlinear precoding techniques for a multiuser multiple-input-multiple-output (MU-MIMO) downlink. When assuming full knowledge of the channel state information (CSI) at the transmitter, a vector perturbation (VP), based on sphere encoding, is a promising precoding scheme that approaches sum capacity while using a simple receiver. However, its encoding complexity can exponentially increase with the number of transmit antennas. This paper proposes a new VP scheme based on line encoding (LE), which provides very low complexity as well as competent throughput performance. For this purpose, the proposed LE scheme finds the smallest set of candidate vectors, including the optimal perturbation vector with high probability.

User-Selection Algorithms for Multiuser Precoding

A general framework for user selection in the broadcast channel with multiuser linear and nonlinear precoding techniques is investigated. Assuming full knowledge of channel-state information at the transmitter and using a minimum-mean-square-error (MMSE) criterion, we propose several user-selection algorithms based on the conventional incremental and decremental search approaches. Furthermore, a novel iterative user selection approach is introduced, offering a flexible performance-complexity tradeoff. New user grouping algorithms are also developed for orthogonal frequency-division multiple-access systems. Simulation results show that the proposed methods outperform well-known algorithms, which select users based on the users' orthogonality or sum rate bound.

Design of a Robust Multi-Channel Timing Recovery System With Imperfect Channel State Information for 10GBASE-T

The interdependence among multiple channels and the interaction between timing and equalization loops bring new challenges to the design of a multi-channel symbol timing recovery (STR) system for 10GBASE-T. In addition, the nonlinear Tomlinson-Harashima precoding (THP) technique used in the 10GBASE-T system is vulnerable to the imperfect channel state information (CSI). In this paper, we address the problem of timing inaccuracy caused by imperfect CSI and the problem of extracting correct timing information in the presence of channel-interdependence and loop-interaction for 10GBASE-T. This paper proposes a novel averaged-sampling-phase (ASP) hybrid STR scheme, which aligns the sampling clock phase of a single phase-locked loop (PLL) with an average value of the timing information provided by each wire pair so that the impact of the noisy timing information resulting from the imperfect CSI and the timing jitter of the single PLL is reduced. Moreover, a three-phase timing recovery strategy based on our architecture is also designed to correctly extract the timing information and effectively mitigate the loop-interaction. Simulation results demonstrate that the proposed multi-channel STR provides a complete loop-timed solution for 10GBASE-T and achieves a superior performance over conventional approaches in terms of robustness and timing jitter.