Cubic Metric Research Articles

Low Cubic Metric Reed-Muller Sequence Design for Pilot-Less Transmission

A versatile sequence set design with both low cubic metric (CM) and low maximum-absolute-crosscorrelation is proposed for pilot-less sequence-based transmission as a solution to current pilot/symbol-based 5G design in coverage-limited scenarios. Based on generalized second-order Reed-Muller sequences that provide already sequence length flexibility and good correlation properties, a modified construction is introduced to achieve a very low CM for any resource allocation. New sequences inherently incorporate a symbol spreading pattern matching the signal bandwidth, leading to a windowing effect that limits the time-domain signal variations. Simulation results show that the proposed design effectively improves CMs and outperforms error rates of current 5G NR uplink control signals.

Cubic metric reduction for repetitive CAZAC sequences in frequency domain

In NR-based Access to Unlicensed Spectrum (NR-U) of 5G system, to satisfy the rules of Occupied Channel Bandwidth (OCB) of unlicensed spectrum, the channels of PRACH and PUCCH have to use some sequence repetition mechanisms in frequency domain. These repetition mechanisms will cause serious cubic metric(CM) problems for these channels, although these two types of channels are composed of Constant Amplitude Zero Auto-correlation(CAZAC) sequences.. Based on the characteristics of CAZAC sequences, which are used for PRACH and PUCCH (refer to PUCCH format 0 and format 1) in 5G NR, in this paper, we propose some new mechanisms of CM reduction for these two types of channels considering the design principles to ensure the sequence performance of the auto-correlation and cross-correlation. Then the proposed CM schemes are evaluated and the optimized parameters are further provided considering CM performance and the complexity.

OFDM PAPR Reduction via Time-Domain Scattered Sampling and Hybrid Batch Training of Synchronous Neural Networks

Peak-to-average power ratio (PAPR) reduction in multiplexed signals in orthogonal frequency division multiplexing (OFDM) systems has been a long-standing critical issue. Clipping and filtering (CF) techniques offer good performance in terms of PAPR reduction at the expense of a relatively high computational cost that is inherent in the repeated application of fast Fourier transform (FFT) operations. The ever-increasing demand for low-latency operation calls for the development of low-complexity novel solutions to the PAPR problem. To address this issue while providing an enhanced PAPR reduction performance, we propose a synchronous neural network (NN)-based solution to achieve PAPR reduction performance exceeding the limits of conventional CF schemes with lower computational complexity. The proposed scheme trains a neural network module using hybrid collections of samples from multiple OFDM symbols to arrive at a signal mapping with desirable characteristics. The benchmark NN-based approach provides a comparable performance to conventional CF. However, it can underfit or overfit due to its asynchronous nature which leads to increased out-of-band (OoB) radiations, and deteriorating bit error rate (BER) performance for high-order modulations. Simulations’ results demonstrate the effectiveness of the proposed scheme in terms of the achieved cubic metric (CM), BER, and OoB emissions.

Optimizing cubic metric in orthogonal frequency division multiplexing systems using chaotic differential search algorithm

Cubic metric (CM) is a more precise measure to compute the large envelope fluctuations of orthogonal frequency division multiplexing signals. In this study, we use the partial transmit sequence method to reduce the high CM of signals. Despite the dramatic CM reduction ability of the partial transmit sequence method, its computational complexity is very high because of an exhaustive search over all possible combinations of phase factors. In order to overcome the search complexity of the partial transmit sequence method, we introduce an effective and fast convergence optimizer called a chaotic differential search algorithm (CDSA). The CDSA is a population based optimization method to solve the complex, large-scale and non-linear problems. Simulation results show the superiority of the proposed CDSA compared with several counterpart algorithms in terms of search complexity and CM mitigation performance.

DFT-s-OFDM With Enhanced Time-Domain Spreading for B-IFDMA

Enhanced time-domain spreading is proposed for block-interleaved frequency division multiple access (B-IFDMA) with discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM). By repeating each consecutive modulation symbol prior to the spreading, we show that the DFT of the spreading sequence becomes a window function, which compared to the existing method of repeating the whole block of modulation symbols, offers a signal with both lower cubic metric (CM) and block error rate (BLER). Modulation symbol-specific spreading sequences are further shown to improve the BLER. The new transmission scheme is supported by both time- and frequency domain despreaders, as well as by two channel estimation methods for B-IFDMA.

A New SLM-UFMC Model for Universal Filtered Multi-Carrier to Reduce Cubic Metric and Peak to Average Power Ratio in 5G Technology

The new generation of wireless communication systems has adopted different waveforms. The universal filtered multicarrier is one of the adopted candidates that has symmetry with various numerology designs. However, the high peak to average power ratio is one of the major limitations faced by universal filter multicarrier (UFMC) designers. Moreover, recent studies utilize cubic metric along with the peak to average power ratio (PAPR) to show the power back-off effect of the signal in which the PAPR metric identifies the maximum peak and the cubic metric (CM) identifies the Out of Band emission and In-Band distortion. Most of the current solutions, such as amplitude clipping, tone reservation, and active constellation extension, decrease the PAPR but cause degradation to the bit error rate. Selected mapping is one of the promising techniques that is recently used to solve the PAPR and CM problems without causing bit error rate (BER) degradation. In this paper, the selected mapping (SLM) is integrated with UFMC to reduce the PAPR and CM without affecting the BER of 5G networks. The SLM-UFMC solution model is simulated by MATLAB and the results show that the SLM-UFMC model presents better PAPR and CM performance without BER degradation. The PAPR has been decreased to 1.5 dB with respect to eight-phase rotation vectors and the CM decreased to 1.25 dB compared to the conventional UFMC.

An improved backtracking search optimization algorithm for cubic metric reduction of OFDM signals

Abstract The large amplitude variations of OFDM signals generate in-band distortion and out-of-band radiation. In recent years, cubic metric (CM) has been verified as a more accurate metric to measure the amplitude variations. In this paper, the PTS technique is used to decrease the CM of OFDM signals. To overcome the search complexity of an exhaustive search based PTS technique, we introduce an improved backtracking search (IBS) optimization algorithm. Simulations are conducted to show the advantages of the proposed IBS based PTS approach compared with the conventional OFDM, and several state-of-the-art methods in terms of search complexity and CM reduction performance.

DCO-OFDM Signals with Derated Power for Visible Light Communications Using an Optimized Adaptive Network-Based Fuzzy Inference System (ANFIS)

Direct current-biased optical orthogonal frequency division multiplexing (DCO-OFDM) signals used in visible light communications suffer from high peak-to-average-power ratio (PAPR) or cubic metric (CM). It strongly degrades the performance due to the great back-off necessary to avoid the clipping effect in the light-emitting diode. Thus, PAPR and CM reduction techniques become crucial to improve the system performance. In this paper, an adaptive network-based fuzzy inference system (ANFIS) is used to obtain efficient DCO-OFDM signals with a low power envelope profile. First, signals specially designed for DCO-OFDM with very low CM, as the ones obtained from the raw cubic metric (RCM)–active constellation extension method, are used to train the fuzzy systems in time and frequency domains. Second, after the off-line training, the ANFIS can generate a real-valued signal in a one-shot way with 8.9 dB of RCM reduction from the original real-valued signal, which involves a gain in the input power back off larger than 2.8 dB, an illumination-to-communication conversion efficiency gain of more than 35% and considerable improvements in bit error rate.

Minimizing the Error Vector Magnitude With Constrained Cubic Metric and Spectral Sidelobe in NC-OFDM-Based Cognitive Radio Systems

In this paper, we propose a minimized error vector magnitude (M-EVM) scheme to simultaneously reduce the cubic metric (CM) and spectral sidelobe in noncontiguous orthogonal frequency-division multiplexing (NC-OFDM)-based cognitive radio (CR) systems by modifying the constellations on the secondary user (SU) subcarriers and adding canceling symbols on the primary user (PU) subcarriers. The proposed M-EVM scheme formulates an optimization problem, which minimizes the EVM with constraints of the CM and spectral sidelobe. Furthermore, we propose an iterative approximation algorithm to solve the optimization problem. Simulation results show that the M-EVM scheme offers significant reductions of the CM and spectral sidelobe.

Evaluating and Reducing the Envelope Fluctuations of OFDM Signals Based on Distortion Prediction

Abstract Orthogonal frequency division multiplexing (OFDM) signals with large envelope fluctuations are prone to be affected by power amplifier (PA), resulting in degradation of system performance. Peak-to-average power ratio (PAPR) and cubic metric (CM) are commonly used as the reduction criteria of envelope fluctuations of OFDM signals. However, our analysis shows that minimizing the PAPR or CM does not necessarily mean the optimization of system performance, since both metrics are inadequate to quantify the distortion in nonlinear OFDM transmission. In this paper, we fully discuss the effects of PA nonlinearity on OFDM signals and propose a new metric called distortion component metric (DCM), which is closely related to the nonlinear distortion caused by the PA. We compare the system performance when several metrics are respectively used as the reduction criterion for the selective mapping scheme. It is shown that in the presence of memoryless or memory PA, the usage of DCM can provide better inband and out-of-band performance than PAPR and CM.

On the Properties of Cubic Metric for OFDM Signals

As a metric for amplitude fluctuation of orthogonal frequency division multiplexing (OFDM) signal, cubic metric (CM) has received an increasing attention because it is more closely related to the distortion induced by nonlinear devices than the well-known peak-to-average power ratio (PAPR). In this paper, the properties of CM of OFDM signal is investigated. First, asymptotic distribution of CM is derived. Second, it is verified that 1.7 times oversampling rate is good enough to capture the CM of continuous OFDM signals in terms of mean square error, which is also practically meaningful because the fast Fourier transform size is typically 1.7 times larger than the nominal bandwidth in the long-term evolution (LTE) of cellular communication systems.

Neural Network Based Simplified Clipping and Filtering Technique for PAPR Reduction of OFDM Signals

Many iterative clipping and filtering (ICF) based techniques have been proposed that achieve similar peak-to-average power ratio (PAPR) reduction of orthogonal frequency division multiplexing (OFDM) signals as the original ICF, but with lower complexity, such as the simplified clipping and filtering (SCF) technique. However, these low complexity methods require numerous complex fast Fourier transform (FFT) operations and parameter calculations. In this letter, we introduce a novel ICF method that uses an optimized mapper based on artificial neural network and SCF techniques. Compared to the conventional ICF based methods, the proposed scheme offers desirable cubic metric (CM) and bit error rate (BER) simulation results with significantly reduced computational complexity.

A High-Accuracy Metric for Predicting the Power De-Rating of RF Power Amplifiers

Cubic metric (CM) is being recognized as a better alternative to determine the power de-rating of radio frequency power amplifiers (PAs) than peak-to-average power ratio (PAPR). However, in this letter our analysis shows that actually the CM is still inaccurate to predict the required PA power de-rating that satisfies the out-of-band radiation (OBR) requirement of a communication system. Further, by investigating the effect of the third-order nonlinearity of PA on the OBR, we propose a novel metric. Compared with PAPR and CM, the proposed metric has a strong correlation with the OBR, and thus it provides much higher accuracy in determining the required power de-rating of PAs, which is verified by extensive experimental results.

Cubic Metric Reduction for DCO-OFDM Visible Light Communication Systems

Visible light communication (VLC) systems with a direct current-biased optical orthogonal frequency division multiplexing (DCO-OFDM) architecture suffers from the well-known problem of high peak-to-average power ratio (PAPR). A DCO-OFDM signal at the input of the light emitting diode (LED) with high PAPR can experience clipping due to its limited dynamic-range. This causes distortion and degradation of the signal quality, forcing a large power back-off, and so leading to an inefficient use of the LEDs. In order to resolve this problem, we propose to apply a power derating reduction technique at the VLC transmitter based on a modification of the active constellation extension (ACE) method with two important changes: a better predictor of the power derating than the PAPR, the cubic metric (CM), and a more effective clipping stage. With the proposed method, we achieve a significant CM reduction as large as 7.1 dB, which contributes to a noticeable gain in the input power back-off of 2.5 dB or an important reduction of signal distortion, and a greater illumination to communication efficiency (ICE), higher than $30\%$ .

On Minimizing the Cubic Metric of OFDM Signals Using Convex Optimization

A main disadvantage of orthogonal frequency division multiplexing (OFDM) signals is the large envelope fluctuation that limits transmitter power efficiency. Peak-to-average power ratio and cubic metric (CM) are two metrics commonly used to quantify this envelope fluctuation, and now the latter is attracting increasing attention as it can more accurately predict the power de-rating of power amplifier. In this paper, convex optimization is introduced to minimize CM, subject to the constraints on error vector magnitude (EVM) and spectral mask. To solve the formulated optimization problem, a customized interior-point method (IPM) is developed. Simulation results verify the high efficiency of the proposed IPM. For an 802.11a compliant OFDM system, subject to the maximum allowed EVM=5%, 10%, 15% and spectral mask constraints, after three iterations the performance gaps between our IPM and the optimal solution are less than 0.2dB for 99.9% of the symbols.

A New Metric for the Envelope of OFDM Signals Based on Memory Power Amplifier

Orthogonal frequency division multiplexing (OFDM) signals with large envelope variations usually requires power de-rating operation on the power amplifier (PA) to meet the requirement of adjacent channel leakage ratio of systems. Peak-to-average power ratio (PAPR) and cubic metric (CM) are two metrics commonly used to characterize the envelope of OFDM signals. And the amount of power de-rating is determined by their values. However, both PAPR and CM do not take the memory effects (MEs) of PA into account. Actually, for wideband system such as OFDM, the inherent MEs in PA can not be ignored any more. In this paper, we study the behavioral model of PA with memory and sufficiently analyze the impacts of memory PA on OFDM signals. Based on our analysis, a new metric for the envelope characteristics of OFDM signals is proposed. The simulation results show that the proposed metric provides much more accurate prediction on required power de-rating of PA than both PAPR and CM. So the new metric is a better choice for the envelope characteristics of OFDM signals.

Descendent clipping and filtering for cubic metric reduction in OFDM systems

The cubic metric (CM) is being regarded as a more accurate metric for envelope fluctuations of orthogonal frequency division multiplexing (OFDM) signals than peak-to-average power ratio (PAPR). Iterative clipping and filtering (ICF) is a simple and efficient technique for PAPR reduction. However, analysis shows that it cannot achieve sufficient CM reduction due to the difference between the two metrics. Proposed is a new technique called descendent clipping and filtering (DCF) for CM reduction. Unlike ICF, DCF introduces a new parameter termed descent factor to improve its performance. Simulation results show that DCF can achieve better performance with only one iteration than ICF with multiple iterations

Improved power efficiency for DVB-SH transmitters

Power efficiency is an important criterion for modern communications systems. It is well known that due to its high Peak-to-Average Power Ratio (PAPR) the Orthogonal Frequency Division Multiplexing (OFDM) modulation scheme presents serious power efficiency problems related to the High Power Amplifier (HPA) of the transmitter that are critical in satellite systems like Digital Video Broadcasting Satellite to Handheld (DVB-SH). In order to improve the power efficiency we propose to apply to DVB-SH the Active Constellation Extension (ACE) algorithm as a PAPR reduction method. Additionally we also present a new ACE optimization criterion: the reduction of the cubic metric (CM). The minimization of both metrics provides an important improvement of the out of band distortion and the Output Back Off (OBO) of the amplifiers, and consequently an increase of the HPA power efficiency.

Comparative Study of Open-Loop Transmit Diversity Schemes for DFT-Precoded OFDMA in Frequency-Selective Fading Channels

This paper presents comprehensive comparisons based on the block error rate (BLER) of open-loop (OL) transmit diversity schemes considering a cubic metric (CM) for single-carrier (SC)-Frequency Division Multiple Access (FDMA) using discrete Fourier transform (DFT)-precoded OFDMA in uplink frequency-selective fading channels. The OL transmit diversity schemes assumed in the paper are space-time block code (STBC), space-frequency block code (SFBC), single-carrier (SC) - SFBC, cyclic delay diversity (CDD), and frequency switched transmit diversity (FSTD) for two antennas and a combination of STBC, SFBC, SC-SFBC and selection transmit diversity including time switched transmit diversity (TSTD) or FSTD for four antennas. We derive the most appropriate OL transmit diversity scheme for SC-FDMA using a frequency domain equalizer (FDE) with QPSK and 16QAM modulations and with various channel coding rates employing turbo coding. We investigate the best OL transmit diversity scheme under various propagation channel conditions including the fading maximum Doppler frequency and root mean square (r.m.s.) delay spread, and the fading correlation between transmitter/receiver antennas.

On Cubic Metric Reduction in OFDM Systems by Tone Reservation

One of the major drawbacks of multicarrier modulation is the large envelope fluctuations which either requires an inefficient use of high power amplifiers (HPAs) or decreases the system performance. Peak-to-average power ratio (PAPR) is the best known measure of the envelope fluctuations and is widely employed to design multicarrier systems. However, recently, another metric known as cubic metric (CM), is being considered in several multicarrier systems since it can predict HPA power de-rating more accurately. In this paper tone reservation (TR) technique, originally used for PAPR-reduction, is reformulated to reduce CM. We first simplify CM to define the objective function, denoted as objective CM (OCM). Then we demonstrate that OCM is convex and formulate TR for CM-reduction as an unconstrained convex optimization problem. The solution to this problem is found by means of an iterative algorithm which approaches the optimal solution with few steps. In this paper a low-complexity suboptimal algorithm capable of approaching the optimum with sufficient accuracy is also proposed. Simulation results show that for similar computational complexity, the performance of CM-reduction is superior to that of PAPR-reduction both in terms of bit error rate and out-of-band leakage.