Massive multiple-input-multiple-output (MIMO) systems use few hundred antennas to simultaneously serve large number of wireless broadband terminals. It has been incorporated into standards like long term evolution (LTE) and IEEE802.11 (Wi-Fi). Basically, the more the antennas, the better shall be the performance. Massive MIMO systems envision accurate beamforming and decoding with simpler and possibly linear algorithms. However, efficient signal processing techniques have to be used at both ends to overcome the signaling overhead complexity. There are few fundamental issues about massive MIMO networks that need to be better understood before their successful deployment. In this paper, we present a detailed review of massive MIMO homogeneous, and heterogeneous systems, highlighting key system components, pros, cons, and research directions. In addition, we emphasize the advantage of employing millimeter wave (mmWave) frequency in the beamforming, and precoding operations in single, and multi-tier massive MIMO systems.

https://www.mdpi.com/2079-9292/6/3/63/pdf

Massive MIMO Wireless Networks: An Overview

While achieving reduced/good peak-to-average power (PAPR) in orthogonal frequency division multiplexing (OFDM) systems is attractive, this must not be performed at the expense of the transmitted signal with over-reduced signal power, as it leads to degraded bit error ratio (BER). We introduce a uniform distribution approach to solving the PAPR reduction problem of OFDM signals and then use Lagrange multiplier (LM) optimization to minimize the number of iterations involved in an adaptive fashion. Due to the nonlinear attenuation of the PAPR reduction scheme, we compensate the output signal using a correlation factor that minimizes the error floor in the in-band distortion of the clipped signal using the minimum mean square error method so as to improve the BER performance. Three different methods are introduced each enabling PAPR reduction by clipping followed by filtering with no direct dependence on a clipping ratio parameter. We find that our approach significantly reduces the PAPR of the OFDM signals (especially with LM optimization) better than the conventional adaptive iterative clipping and filtering operating without LM optimization. Based on our proposed methods, we additionally outline two simple steps for achieving perfect PAPR reduction (i.e., 0 dB). We also evaluate the performance of the three new models over high power amplifier (HPA) for completeness; the HPA is found to induce negligible BER degradation effects on the processed signal compared with the unprocessed signal.

A New Approach to Iterative Clipping and Filtering PAPR Reduction Scheme for OFDM Systems

A type of invertible subset low density parity-check (IS-LDPC) codes was proposed to reduce the peak-to-average power ratio for orthogonal frequency-division multiplexing systems with low complexity recently, where the key idea is that each invertible subset can be independently inverted to generate other valid codewords of the LDPC code. In this paper, we firstly extend the idea of invertible subsets to quasi-cyclic LDPC (QC-LDPC) codes, and this new family of QC-LDPC codes is called as invertible subset QC-LDPC (IS-QC-LDPC) codes. Moreover, we propose two types of subset partitioning and deeply discuss the properties of IS-QC-LDPC codes with different subset partitioning. After declaring that interleaved partitioning is more appropriate for IS-QC-LDPC codes than the block partitioning, we propose a novel progressive edge graph-like algorithm to construct good IS-QC-LDPC codes with interleaved partitioning. The simulation results show that the IS-QC-LDPC codes exhibit good error-correcting performance, which is very close to that of the corresponding QC-LDPC codes of the IEEE 802.16e, for a wide range of subset number.

Invertible Subset QC-LDPC Codes for PAPR Reduction of OFDM Signals

The simple method of clipping is widely used to reduce the peak-to-average power ratio of orthogonal frequency division multiplexing (OFDM) signal prior to passing it through the high power amplifier (HPA). However, clipping is a nonlinear process that causes both in-band and out-of-band distortions. Filtering the clipped OFDM signal can eliminate the out-of-band distortion but it can lead to peak regrowth. Therefore, iterative clipping and filtering have been used to both remove the out-of-band interference and suppress the regrowth of the peak power. However, the iterative process will degrade the bit error rate performance further. In this paper, we proposed a semi-analytic scheme based on compressed sensing to reconstruct the iterative clipping noise. Moreover, the proposed scheme is also applicable for reconstructing the total nonlinear distortion of a system so that the OFDM signal passes both the clipper and HPA. Simulation results show that the proposed scheme performs well and the nonlinear distortion can be recovered effectively.

Iterative Clipping Noise Recovery of OFDM Signals Based on Compressed Sensing

In this paper, we derive new multi-component companders for reducing peak-to-average power ratio (PAPR) in orthogonal frequency-division multiplexing signals, using a constrained optimization approach. The new companders provide out-of-band power rejection performance improvements over current state-of-the art companders, while maintaining comparable demodulation performance. The newly designed companders are derived by minimally perturbing the Rayleigh signal amplitude distribution, while enforcing the constant power and probability density function constraints. The use of a multi-component approach to compander construction provides design flexibility, and expands the space of tradeoffs between demodulation performance, PAPR reduction, and out-of-band power rejection. Furthermore, the new companders provide solutions in operating regions where certain current companders fail to exist due to violation of one or more constraints; for example, solutions may be derived for cutoff amplitude values that are unobtainable using other companders. We formulate the constrained optimization problem for compander design and derive the compander and decompander forms. Through numerical simulation, we generate performance results demonstrating the capability of the new companders.

A Constrained Optimization Approach to Compander Design for OFDM PAPR Reduction

Companding is a well-known technique for the peak-to-average power ratio (PAPR) reduction of orthogonal frequency division multiplexing (OFDM) signals. However, as companding transform is an extra operation after the modulation of OFDM signals, companding schemes reduce PAPR at the expense of increasing the bit error rate (BER). In this paper, a new piecewise linear companding scheme is proposed aiming at mitigating companding distortion. In the design of the companding transform, we study the theoretical characterization of companding distortion. It demonstrates that companding larger signals with smaller amplitude increments are more favorable in reducing companding distortion. Based on the analysis results, a new piecewise linear companding transform is proposed by clipping the signals with amplitudes over a given companded peak amplitude for peak power reduction, and linearly transforming the signals with amplitudes close to the given companded peak amplitude for power compensation. With the careful design of the companded peak amplitude and the linear transform scale, the proposed transform can achieve enhanced BER and power spectral density performance, while reducing PAPR effectively.

A Piecewise Linear Companding Transform for PAPR Reduction of OFDM Signals With Companding Distortion Mitigation

Tone injection (TI) can effectively reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals without incurring data rate loss and extra side information. However, the optimal TI scheme requires an exhaustive search over all combinations of the possible perturbations of the expanded constellation over all perturbed subcarriers, which is not suitable for practical applications. To reduce the complexity while still achieving good PAPR performance, a low-complexity TI scheme based on distortion signals is proposed in this paper. Motivated by the goal of mitigating the distortions when OFDM signals pass high power amplifiers, we intuitively get the perturbation information for OFDM signals directly from the distortion signals. By exploiting the distribution of the perturbation vectors depending on the distortion signals, we design a search range limited extended constellation. Then, based on the statistical information of perturbed subcarriers, the number of the subcarriers to be perturbed is restricted. Moreover, to further reduce the complexity, we choose a proper subcarrier perturbation sequence from candidate subcarrier sets according to the mutual information between the peak sample and the distortion signals. With the selected subcarrier perturbation sequence, the original problem is decomposed into a sequential search problem, which provides a dramatic complexity reduction. Simulation results demonstrate that the proposed scheme can achieve significant complexity savings while maintaining a good PAPR performance.

A Low-Complexity Tone Injection Scheme Based on Distortion Signals for PAPR Reduction in OFDM Systems

Companding is a well-known technique for the peak-to-average-power ratio (PAPR) reduction of orthogonal frequency division multiplexing (OFDM) signals. Piecewise linear companding (PLC) scheme, compared with other companding schemes, can effectively reduce PAPR with much lower complexity, while achieving improved bit-error-rate (BER) performance. However, when the PAPR target value for companded signals is relatively small, such as 4 dB for 16-QAM or 5 dB for 64-QAM, there is a clear error floor of PLC in high SNR region for high-order QAM modulation. Focusing on this problem, we first analyze the reason for the error floor of PLC. Based on the analysis, we propose a generalized PLC scheme to reduce the distortion in decompanded signals with the relaxation of the constraint on the conservation of the average signal power. Finally, we formulate the optimization problems to obtain the parameters of the companding function in the pursuit of a preferable tradeoff between the BER and power spectral density performance under the constraint on PAPR. Simulation results verify that the proposed generalized PLC can significantly improve the BER performance while maintaining the same PAPR performance as PLC.

A Generalized Piecewise Linear Companding Transform for PAPR Reduction in OFDM Systems

In multiple-input–multiple-output broadcast channels, lattice reduction (LR) preprocessing technique can significantly improve the precoding performance. Among the existing LR algorithms, the fixed complexity Lenstra–Lenstra–Lovasz (fcLLL) algorithm applying limited number of LLL loops is suitable for the real-time communication system. However, fcLLL algorithm suffers from higher average complexity. Aiming at this problem, a computationally efficient fcLLL (CE-fcLLL) algorithm for LR-aided (LRA) precoding is developed in this study. First, the authors analyse the impact of fcLLL algorithm on the signal-to-noise ratio performance of LRA precoding by a power factor (PF) which is defined to measure the relation of reduced basis and transmit power of LRA precoding. Then, they propose a CE-fcLLL algorithm by designing a new LLL loop and introducing new early termination conditions to reduce redundant and inefficient LR operation in fcLLL algorithm. Finally, they define a PF loss factor to optimise the PF threshold and the number of LLL loops, which can lead to a performance-complexity tradeoff. Simulation results show that the proposed algorithm for LRA precoding can achieve better bit-error-rate performance than the fcLLL algorithm with remarkable complexity savings in the same upper complexity bound.

Computationally efficient fixed complexity LLL algorithm for lattice-reduction-aided multiple-input–multiple-output precoding

Eigen-beamforming is an optimal beamforming scheme for full-dimension multi-input multi-output (FD-MIMO). However, it suffers from high complexity of the singular value decomposition (SVD) of the 3D channel matrix. In this paper, we propose a low complexity dual layer beamforming scheme to exploit both the horizontal and vertical degrees of freedom. The proposed scheme first segments the channel matrix into several sub-channel matrices. Then, by selecting the vertical and horizontal beamforming from the sub-channel matrices respectively, the proposed scheme can reduce the complexity, while achieving the performance approximate to the optimal eigen-beamforming scheme. Moreover, to enable practical implementation, a hybrid codebook design is proposed which exploits the structure of the dual layer beamforming to reduce feedback overhead. According to the different correlation characteristics in horizontal and vertical direction, we design different codebooks for the horizontal and vertical beamforming. Simulation results demonstrate that the proposed scheme can effectively improve the spectral efficiency of FD-MIMO systems with limited feedback, especially for the cell edge users.

Wei Wang

Papers

A Piecewise Linear Companding Transform for PAPR Reduction of OFDM Signals With Companding Distortion Mitigation

A Low-Complexity Tone Injection Scheme Based on Distortion Signals for PAPR Reduction in OFDM Systems

A Generalized Piecewise Linear Companding Transform for PAPR Reduction in OFDM Systems

Computationally efficient fixed complexity LLL algorithm for lattice-reduction-aided multiple-input–multiple-output precoding

Dual layer beamforming with limited feedback for full-dimension MIMO systems