Peak-to-average Power Ratio Constraint Research Articles

Integrated sensing and communication waveform design in the Internet of Vehicles

We design an integrated sensing and communication (ISAC) transmission waveform with total transmission power, waveform similarity, and peak-to-average power ratio (PAPR) constraints in the Internet of Vehicles (IoV). The integrated waveform can complete radar target detection while communicating with downlink cellular users. The design of IoV with ISAC can not only improve the spectrum efficiency, but also further promote the integration of communication and sensing equipment. In this paper, the IoV with ISAC is formally modeled from the communication view and sensing view respectively. On this basis, taking the joint optimization of multi-user interference (MUI) total energy and Cramér Rao Bound (CRB) as the objective function, the transmission waveforms are designed with total transmission power, waveform similarity, and PAPR constraints respectively. To obtain the global optimal solution, we adopt a low complexity algorithm to solve the optimization problem under the total transmit power constraint and the optimization problem based on waveform similarity and PAPR constraints is further transformed into a nonconvex quadratically constrained quadratic programming (QCQP) problem, which is solved by using the semidefinite relaxation (SDR) technique. By ranking one approximation of the constrained optimization problem, it can be transformed into the solution of semidefinite programming (SDP) problems. The numerical results show that the designed ISAC transmission waveform can achieve an efficient tradeoff between sensing and communication performance, and each KPI is superior to one of the only communication and only sensing waveform design schemes. And it can improve the real-time information interaction ability of the IoV.

Beam Domain MIMO-OFDM Optical Wireless Communications With PAPR Reduction

Multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM), confirmed as an efficient technique, has been applied in optical wireless communications (OWCs) to improve the transmission rate. However, the disadvantage of high peak-to-average power ratio (PAPR) also brings into the OWC systems, especially for multi-user communications, resulting in low power efficiency. This paper proposes beam domain MIMO-OFDM OWCs with PAPR reduction. We describe the MIMO-OFDM OWC system architecture and derive the achievable sum rate and PAPR for multi-user OFDM systems, which are dominated by the precoding vectors. To reduce the PAPR, we design the precoding vectors to maximize the sum rate under the PAPR constraint. We propose an iterative process to obtain a candidate optimal solution by the sequential parametric convex approximation (SPCA) method. Furthermore, we prove that the PAPR increases with the number of users and propose a low complexity beam scheduling and power allocation algorithm. Numerical results validate that the proposed schemes can efficiently improve the transmission rate and reduce the PAPR.

Interference optimized dual-functional radar-communication waveform design with low PAPR and range sidelobe

Dual-functional radar-communication system integrates the radar and communication functions into one system with a shared dual-functional waveform. In this paper, we focus on the problem of dual-functional waveform design under the peak-to-average power ratio (PAPR) constraint and low range sidelobe requirement. When the conventional schemes aim to minimize the multi-user interference (MUI) energy and maximize the similarity to the reference radar waveform, in our proposed method, a weighted summation objective function incorporated with the PAPR constraint and optimized MUI is constructed for the waveform design. Specifically, MUI is classified into destructive interference and constructive interference, while the latter is exploited as a free power for communication and is constrained to guarantee the communication quality-of-service (QoS). To tackle the resulting high order nonconvex problem, we develop an iteration algorithm based on the alternating direction method of multipliers (ADMM) procedure, which involves two quadratic programming subproblems in each iteration and is easy to solve with the current solver. Moreover, by taking the imperfect channel state information (CSI) into consideration, we further investigate the robust dual-functional waveform design problem with the bounded uncertainty of the CSI. Numerical simulations validate the effectiveness of the proposed method.

EVM Mitigation With PAPR and ACLR Constraints in Large-Scale MIMO-OFDM Using TOP-ADMM

Although signal distortion-based peak-to-average power ratio (PAPR) reduction is a feasible candidate for orthogonal frequency division multiplexing (OFDM) to meet standard/regulatory requirements, the error vector magnitude (EVM) stemming from the PAPR reduction has a deleterious impact on the performance of high data-rate achieving multiple-input multiple-output (MIMO) systems. Moreover, these systems must constrain the adjacent channel leakage ratio (ACLR) to comply with regulatory requirements. Several recent works have investigated the mitigation of the EVM seen at the receivers by capitalizing on the excess spatial dimensions inherent in the large-scale MIMO that assume the availability of perfect channel state information (CSI) with spatially uncorrelated wireless channels. Unfortunately, practical systems operate with erroneous CSI and spatially correlated channels. Additionally, most standards support user-specific/CSI-aware beamformed and cell-specific/non-CSI-aware broadcasting channels. Hence, we formulate a robust EVM mitigation problem under channel uncertainty with nonconvex PAPR and ACLR constraints catering to beamforming/broadcasting. To solve this formidable problem, we develop an efficient scheme using our recently proposed three-operator alternating direction method of multipliers (TOP-ADMM) algorithm and benchmark it against two three-operator algorithms previously presented for machine learning purposes. Numerical results show the efficacy of the proposed algorithm under imperfect CSI and spatially correlated channels.

Maximal-Minimum hybrid approach with decomposed SLM technique for 5G UFMC system PAPR reduction

The Universal Filtered Multi-carrier (UFMC) system's low latency, minimal out-of-band, and low frequency offset support high spectral efficiency and impact 5 G cellular networks. Due to its high peak-to-average power ratio (PAPR), the system's performance is severely degraded. This paper proposes a hybrid Maximal-Minimum approach with decomposed selective mapping to minimize PAPR constraints for 5 G UFMC systems. The complex signal is decomposed into real and imaginary branches, allowing the inverse fast Fourier transform (IFFT) operation. In each branch, different phase vectors are mixed with real and imaginary terms. The FIR response is based on individually optimized PAPR values, which are then copied for transmission. Simulations showed that the proposed method reduced PAPR by optimizing the weighting factor within the Out of Band (OoB) range. It is superior in Bit Error rate (BER)-wise, reduction as compared with selective mapping (SLM) and decomposed-UFMC-SLM.

Low-Complexity PAPR Minimization for Symbol Level Precoded Multi-User MISO-OFDM System

This letter proposes a method exploiting constructive interference (CI) to reduce the transmit signal’s peak-to-average power ratio (PAPR), while keeping the total transmission power as low as possible. An optimization problem that jointly performs power minimization and PAPR reduction is formulated, which is however difficult to solve directly due to the non-convex PAPR constraint. To obtain a feasible solution in low complexity, by using the vectorization method and introducing a regularization factor, we relax the PAPR constraint. The original optimization problem is transformed into a convex problem that can be solved with an improved fast iterative shrinkage-thresholding algorithm (FISTA). Numerical results are presented to show 1dB savings in terms of transmission power and 52% savings in terms of PAPR compared with state-of-the-art PAPR minimization techniques.

Design of Complete Complementary Sequences for Ambiguity Functions Optimization With a PAR Constraint

Complete complementary sequence (CCS) design has become an important topic in recent years due to its theoretically ideal zero sidelobe performance. However, the main obstacle for the widespread use of the CCS is its sensitivity to the Doppler shift. In this letter, a method for constructing the CCS with the desired matrix-valued ambiguity functions under a peak-to-average-power ratio (PAR) and an energy constraint is proposed. A gradient-based nonlinear iterative algorithm is used to solve the constrained sequence design problem. Numerical results are presented to show that, compared with the state-of-the-art methods, the proposed method can produce CCS with better correlation properties and the Doppler tolerance. Finally, indoor experiments are conducted to verify the superior performance of the designed CCS, and a peak sidelobe level under −45 dB is realized on the hardware system.

PAPR Reduction Using Iterative Clipping/Filtering and ADMM Approaches for OFDM-Based Mixed-Numerology Systems

Mixed-numerology transmission is proposed to support a variety of communication scenarios with diverse requirements. However, as the orthogonal frequency division multiplexing (OFDM) remains as the basic waveform, the peak-to average power ratio (PAPR) problem is still cumbersome. In this paper, based on the iterative clipping and filtering (ICF) and optimization methods, we investigate the PAPR reduction in the mixed-numerology systems. We first illustrate that the direct extension of classical ICF brings about the accumulation of inter-numerology interference (INI) due to the repeated execution. By exploiting the clipping noise rather than the clipped signal, the noise-shaped ICF (NS-ICF) method is then proposed without increasing the INI. Next, we address the in-band distortion minimization problem subject to the PAPR constraint. By reformulation, the resulting model is separable in both the objective function and the constraints, and well suited for the alternating direction method of multipliers (ADMM) approach. The ADMM-based algorithms are then developed to split the original problem into several subproblems which can be easily solved with closed-form solutions. Furthermore, the applications of the proposed PAPR reduction methods combined with filtering and windowing techniques are also shown to be effective.

Spectrally Compatible Waveform Design for MIMO Radar With ISL and PAPR Constraints

This paper deals with the waveform design to ensure the spectrum co-existence between multiple-input multiple-output (MIMO) radar and communication systems. The transmit waveform energy of MIMO radar in the prescribed spatial-frequency domain is minimized to reduce the mutual interference induced by the overlaid communication services. Additionally, the integrated sidelobes level (ISL) and peak-to-average power ratio (PAPR) constraints are forced on the probing waveform. To tackle the resulting NP-hard problem, we first introduce several auxiliary variables to convert the fourth-order ISL constraint and the PAPR constraint into several quadratic constraints. Then, the recast problem is formulated into a new alternating direction method of multipliers (ADMM) form, with small-sized tractable subproblems solved sufficiently. Numerical simulations verify that the proposed algorithm outperforms another competitive method in terms of the convergence performance and also demonstrate that the designed waveform can achieve spatial-frequency nulling under the ISL and PAPR constraints.

Transmit beamformer design with a PAPR constraint to trade-off between beampattern shape and power efficiency

This study examines the effect of peak-to-average power ratio (PAPR) constraint on the transmit beamformer design problem with the goal of establishing a trade-off between the power efficiency (maximizing the average transmitted power) and other metrics such as the power level fluctuation in mainlobe, peak-sidelobe level (PSL), etc. Typically, unimodular weights are utilized in transmit beamforming to maximize the average transmitted power. Yet, unimodular weights maximize the power efficiency at the expense of other performance metrics. It is shown that even a slight relaxation of the design problem from the unimodular condition (PAPR=1), say setting PAPR⩽1.1, results in a significant improvement in other performance metrics at a negligible loss of power efficiency. To achieve the trade-off between the metrics, an alternating direction method of multipliers (ADMM) based solution to the transmit beamformer design is given. The suggested solution is applicable to both narrowband and wideband beamformers and also to some other related problems such as the unimodular radar waveform design (code design) problem.

MIMO Radar Waveform Design for Quasi-Equiripple Transmit Beampattern Synthesis via Weighted $l_p$-Minimization

In this paper, under the peak-to-average power ratio (PAR) and energy constraints on the transmit waveforms, a new efficient weighted ℓp-norm metric (with p ≥ 2) is introduced for colocated wideband/narrowband multiple-input multiple-output radar transmit beampattern matching design. The proposed metric can achieve quasi-equiripple beampattern, which is desirable to improve the robustness of radar systems with imprecise direction information of targets and reduce radar clutter. In addition, mainlobe ripple control, peak sidelobe suppression, and deep null/notch formation can be obtained. On the other hand, the PAR and energy constraints cause the radar waveform losing the degree of freedom to match arbitrary pattern shape, and the desired pattern usually lies in matching an appropriately scaled version of the shape. Thus, a scaling factor is introduced into the proposed metric to tackle the scaling ambiguity problem. The resultant optimization problems are difficult to solve due to the higher order polynomial objective function with coupled scaling factor and waveform matrix, and also the nonconvex PAR constraint. To develop a fast and efficient algorithm, by utilizing the majorization-minimization technique, we decouple the scaling factor and radar waveform matrix variables by a majorization step, derive a new quadratic majorizer to tackle the quadratic function with the matrix variable, and surrogate the nonsmooth nonconvex functions by convex functions. Numerical examples show that the devised approach can synthesize beampattern with lower peak sidelobe level and more flat mainlobe compared to the existing algorithms.

Weighted Sum Rate Maximization Under the Given PAPR Constraints for a Multi-user OFDM System

Orthogonal frequency division multiplexing (OFDM) is proved to be the best candidate to support the colossal increase in mobile users and their required high rate of transmission in frequency selective fading environments, where the inter-symbol interference is at highest. In an OFDM system, when the sinusoidal signals of the subcarriers are added constructively, the peak to average power ratio (PAPR) becomes very large causing major drawbacks for multicarrier signaling. Earlier efforts to address this problem have been mainly concentrated on the reduction of signal PAPR and various methods of achieving linear and efficient power amplification. However, all the deployed techniques suffer from different ambiguities such as high distortion, complexity, computational time, memory requirements, and above all, the data rate loss. This manuscript is mainly aimed at solving a convex optimization problem in which power and radio resources in an OFDM system are allocated among different subcarriers and users in order to, maximize the weighted sum rate for different users considering total power and PAPR limitations.

An Enhanced Iterative Clipping and Filtering Method Using Time-Domain Kernel Matrix for PAPR Reduction in OFDM Systems

Iterative clipping and filtering (ICF) is a straight-forward method for reducing the peak-to-average power ratio (PAPR) of signals in orthogonal frequency-division multiplexing (OFDM) system. Recently, convex optimization has been used to find the optimal filter coefficients that minimize the error vector magnitude (EVM) and meet the PAPR constraint. However, high-computation complexity may be incurred when solving the convex optimization problem. Therefore, we develop an efficient PAPR reduction method that uses the time-domain kernel matrix to generate the PAPR-reduction signal. Besides, we relax the assumption that the clipping noise is a series of uncorrelated parabolic pulses and apply the proposed method to more general cases. Based on the instantaneous observation of clipping noise, the proposed method constructs a simple time-domain kernel matrix and employs the curve fitting approach to optimize the corresponding scaling factors. The simulation results show that the proposed method can achieve very close performance to that using convex optimization in terms of both the PAPR reduction and EVM while the computational cost is reduced greatly. In addition, due to the decrease of iteration numbers and computational complexity, the proposed method is more efficient than some existing clipping and filtering methods.

Real-Time Uncompressed Video Transmission Over Wireless Channels Using Unequal Power Allocation

Uncompressed video transmission has recently attracted research attentions since it ensures ultra-low latency, high video quality, and low complexity. In this paper, we propose a real-time uncompressed video transmission system, where unequal power allocation (UPA) strategies are adopted to maximize the peak signal-to-noise ratio (PSNR) while considering the peak-to-average power ratio (PAPR) reduction. Specifically, the relationship between the bit error rate (BER) and the mean square error (MSE) of this system is established. Based on the relationship, a group of optimization problems are formulated and UPA schemes are proposed through solving these problems. Among all strategies, UPA with an adaptive Hadamard switch is finally adopted in the proposed system, because it outperforms other schemes in PSNR performance under both the total power constraint and the PAPR constraint. Simulation results show that the PSNR of the reconstructed video is improved largely compared with reference methods.

Distributed Precoding for BER Minimization With PAPR Constraint in Uplink Massive MIMO Systems

Precoding can effectively reduce the peak-to-average power ratio (PAPR) of the transmitted waveform but will usually degrade the bit error rate (BER) performance. In this paper, we investigate the PAPR-guaranteed BER minimization problem through precoding in uplink massive multiple input–multiple output (MIMO) systems. First, we formulate an optimization problem to minimize the BER via precoding design and derive the necessary condition of the optimal precoding matrix. Second, we discuss the BER minimization with PAPR constraint and propose a two-step distributed precoder to deal with this problem. Simulation results verify the effectiveness of the proposed precoding. Particularly, it is efficient for massive MIMO systems in terms of energy efficiency.

Cognitive Radar-Based Sequence Design via SINR Maximization

The ambiguity function plays an important role in radar systems. In fact, many radar design problems can be interpreted from the perspective of persuing desired ambiguity functions to adapt to various application scenes. In this paper, we consider designing a radar sequence, subject to a peak-to-average power ratio (PAR) constraint, to maximize the signal-to-interference plus noise ratio, which can also be interpreted as designing a sequence with a desired ambiguity function. From an optimization point of view, this is equivalent to optimizing a complex quartic function with the PAR constraint. An efficient algorithm based on the general majorization–minimization (MM) method is developed to solve this problem with guaranteed convergence to a stationary point under some mild conditions. In addition, the unit-modulus constraint, as a special case, is considered and another algorithm is proposed, which is the combination of the general MM and the coordinate descent method. Numerical experiments show that the proposed algorithms can shape a desired ambiguity function based on the prior information, and the performance is much better compared with the existing methods.

PAPR Constrained Power Allocation for Multicarrier Transmission in Multiuser SIMO Communications

Peak-to-average power ratio (PAPR) constrained power allocation for multicarrier transmission in multiuser single-input multiple-output (SIMO) communications is considered in this paper. Reducing the PAPR in any transmission system is beneficial because it allows the use of inexpensive energy-efficient power amplifiers. In this paper, we formulate a power allocation problem for single-carrier (SC) frequency division multiple access (FDMA) and orthogonal FDMA (OFDMA) transmission with instantaneous PAPR constraints. Moreover, a statistical approach is considered in which the power variance of the transmitted waveform is controlled. The constraints for the optimization problems are derived as a function of transmit power allocation and two successive convex approximations (SCAs) are derived for each of the constraints based on a change of variables (COV) and geometric programming (GP). In addition, the optimization problem is constrained by a user-specific quality of service (QoS) constraint. Hence, the proposed power allocation strategy jointly takes into account the channel quality and the PAPR characteristics of the power amplifier. The numerical results show that the proposed power allocation strategy can significantly improve the transmission efficiency of power-limited users. Therefore, it is especially beneficial for improving the performance for cell edge users.

Design of PAR-Constrained Sequences for MIMO Channel Estimation via Majorization–Minimization

PAR-constrained sequences are widely used in communication systems and radars due to various practical needs; specifically, sequences are required to be unimodular or of low peak-to-average power ratio (PAR). For unimodular sequence design, plenty of efforts have been devoted to obtaining good correlation properties. Regarding channel estimation, however, sequences of such properties do not necessarily help produce optimal estimates. Tailored unimodular sequences for the specific criterion concerned are desirable especially when the prior knowledge of the channel is taken into account as well. In this paper, we formulate the problem of optimal unimodular sequence design for minimum mean square error estimation of the channel impulse response and conditional mutual information maximization, respectively. Efficient algorithms based on the majorization-minimization framework are proposed for both problems with guaranteed convergence. As the unimodular constraint is a special case of the low PAR constraint, optimal sequences of low PAR are also considered. Numerical examples are provided to show the performance of the proposed training sequences, with the efficiency of the derived algorithms demonstrated.

Asymmetrically Reconstructed Optical OFDM for Visible Light Communications

In conventional optical orthogonal frequency-division multiplexing (OOFDM) systems, such as pulse-amplitude-modulated discrete multitone (PAM-DMT) and asymmetrically clipped optical OFDM (ACO-OFDM), half of the time-domain transmitted signals carry meaningful information, while the other half are set at zero after asymmetric clipping. By specifically exploiting the asymmetric structure of OOFDM such as PAM-DMT and ACO-OFDM, we present a new framework for implementing OOFDM with enhanced performance in terms of both bit error rate (BER) and peak-to-average power ratio (PAPR). The proposed scheme introduces asymmetric signal reconstruction, instead of direct clipping, in the time domain before transmission. The designed asymmetric reconstruction refines the time-domain statistics of the OOFDM signals by constructively exploiting zero-padded signal positions in conventional OOFDMs. This way, the PAPR of the reconstructed OOFDM signals is effectively reduced. For receivers, to recover the received signals precisely, we further develop an optimal maximum a posteriori detection method, along with an efficient simplified method. Simulation results validate that the proposed scheme enhances the BER performance compared with conventional OOFDMs under both an ideal and a dispersive visible light communication (VLC) channel via our prototype. Specifically, under an ideal additive white Gaussian noise channel, an approximately 4-dB gain is achieved at the BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , along with a 2.5-dB lower PAPR constraint. While under the real dispersive channel, our test shows about 6-dB gain in BER performance.

PAPR Reduction of SC-FDMA Signals Using Optimized Additive Pre-distortion

One challenge of employing high-order modulations in single carrier frequency division multiple access (SC-FDMA) systems is the resultant high peak-to-average power ratio (PAPR). We propose a novel PAPR reduction scheme by jointly considering the PAPR reduction and the incurred bit error rate (BER) degradation for SC-FDMA systems with high-order modulations. In the proposed scheme, an additive pre-distortion vector is introduced to modify the few modulated symbols causing the peak of the SC-FDMA signal. This pre-distortion vector is optimized to minimize the in-band distortion under the expected PAPR constraint. Simulation results demonstrate that our proposed scheme can achieve the desired PAPR reduction with negligible BER performance degradation.