We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

Shape Fluctuations and Random Matrices

Orthogonal frequency division multiplexing (OFDM) is a superior technology for the high-speed data rate of wire-line and wireless communication systems. The OFDM has many advantages over other techniques such as its high capacity and immunity against multipath fading channels. However, one of the main drawbacks of the OFDM system is the high-peak-to-average power ratio (PAPR) that leads the system to produce in-band distortion and out-of-band radiation because of the non-linearity of the high-power amplifiers. Therefore, numerous techniques have been proposed to overcome the PAPR problem such as selective mapping, partial transmit sequence (PTS), clipping, and nonlinear companding. In this paper, the PTS technique was analytically reviewed as one of the important methods to reduce the high PAPR problem. The PAPR performance and the computational complexity level are discussed in terms of modifying the PTS technique in the frequency domain, time domain and modulation stage (inverse fast Fourier transform block). Moreover, the numerical statistic comparison of the current modified-PTS methods is introduced, and the criteria for selecting the suitable modified-PTS method in the OFDM system are also given. The simulation and the numerical calculations results show that the rows exchange-interleaving PTS scheme is the best method for reducing the PAPR value with low complexly in the frequency domain, and the cooperative PTS method is the best among the modulation stage methods, while the cyclic shift sequence PTS method achieves the superior performance in PAPR reduction and computational complexity for the time domain methods.

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A Review of Partial Transmit Sequence for PAPR Reduction in the OFDM Systems

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

The (inverse) discrete Fourier transform (DFT/IDFT) is often perceived as essential to orthogonal frequency-division multiplexing (OFDM) systems. In this paper, a deep complex-valued convolutional network (DCCN) is developed to recover bits from time-domain OFDM signals without relying on any explicit DFT/IDFT. The DCCN can exploit the cyclic prefix (CP) of OFDM waveform for increased SNR by replacing DFT with a learned linear transform, and has the advantage of combining CP-exploitation, channel estimation, and intersymbol interference (ISI) mitigation, with a complexity of $\mathcal{O}(N^2)$. Numerical tests show that the DCCN receiver can outperform the legacy channel estimators based on ideal and approximate linear minimum mean square error (LMMSE) estimation and a conventional CP-enhanced technique in Rayleigh fading channels with various delay spreads and mobility. The proposed approach benefits from the expressive nature of complex-valued neural networks, which, however, currently lack support from popular deep learning platforms. In response, guidelines of exact and approximate implementations of a complex-valued convolutional layer are provided for the design and analysis of convolutional networks for wireless PHY. Furthermore, a suite of novel training techniques are developed to improve the convergence and generalizability of the trained model in fading channels. This work demonstrates the capability of deep neural networks in processing OFDM waveforms and the results suggest that the FFT processor in OFDM receivers can be replaced by a hardware AI accelerator.

Deep-Waveform: A Learned OFDM Receiver Based on Deep Complex-valued Convolutional Networks

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

Orthogonal frequency division multiplexing (OFDM) is a multi-carrier modulation technique for transmitting large volumes of digital data but suffers high peak-to-average power ratio (PAPR) at the transmitter. In this paper, we propose a PAPR reduction technique based on the combination of a low complexity transform-Fast Walsh–Hadamard and Fourier transform (FWFT) and the parameter-adjustable piecewise exponential companding (PEC). To reduce algorithm complexity, FWFT uses a fast orthonormal unitary transform to calculate both the Walsh–Hadamard transform (WHT) and the discrete Fourier transform (DFT). In FWFT, WHT realizes precoding to OFDM signals and as a result the PAPR is reduced first. Moreover, the parameter-adjustable PEC transform is adopted to further reduce PAPR by transforming the statistics of the companded signal into exponential distribution with adjustable parameters. Simulation results show that the hybrid method achieves significant PAPR reduction and improves the BER performance of OFDM systems when used in multipath fading channels.

A Low Complexity PAPR Reduction Method Based on FWFT and PEC for OFDM Systems

High peak-to-average power ratio (PAPR) is a major drawback of orthogonal frequency division multiplexing (OFDM) systems. A new companding scheme is proposed to reduce PAPR by transforming the statistics of the companded signal into exponential distribution with adjustable parameters. The proposed scheme can enhance the bit error rate (BER) performance significantly by minimising the companding distortion in the reduction of PAPR. Moreover, with the introduction of an inflexion point and transform parameters, the proposed scheme can offer more flexibility in the PAPR reduction, and therefore achieves a better tradeoff among the PAPR reduction, BER and power spectral density (PSD) performance. With a theoretical analysis presented, the parameter selection criteria are derived. Simulation results verify that the proposed scheme can significantly improve the BER and PSD performance while reducing PAPR effectively.

Parameter-adjustable piecewise exponential companding scheme for peak-to-average power ratio reduction in orthogonal frequency division multiplexing 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.

Meixia Hu

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 Low Complexity PAPR Reduction Method Based on FWFT and PEC for OFDM Systems

Parameter-adjustable piecewise exponential companding scheme for peak-to-average power ratio reduction in orthogonal frequency division multiplexing systems

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