Carrier mode shift keying (CMSK) is a recently proposed waveform-domain index modulation scheme that improves the spectral efficiency (SE) of hybrid carrier (HC) communication systems. This innovative scheme simultaneously transmits information bits mapped to the traditional constellation symbols as well as information bits mapped to the index of the weighted-type fractional Fourier transform (WFRFT) parameter. In this paper, we propose an enhanced version of CMSK (E-CMSK) that introduces a subblock precoding module at the transmitter side. Compared with CMSK, E-CMSK conveys index information through subblock-level parameter mapping, thereby further improving the SE. Furthermore, E-CMSK provides enhanced system flexibility, enabling trade-offs among the SE, reliability and detection complexity through subblock size adjustment. To address the prohibitive complexity of the maximum likelihood (ML) detector, a low-complexity sequential detector based on linear frequency domain equalization (FDE) is developed, which reduces the computational complexity from exponential to linear. Furthermore, to compensate for the performance loss inherent in linear equalization, an enhanced iterative block decision feedback equalization (IB-DFE) detector is proposed. This iterative scheme effectively suppresses residual interference, enabling the system to approach the global ML performance. An analytical expression for the average overall bit error rate (BER) is derived to provide theoretical performance insights. While this expression reveals the impact of key parameters like Euclidean distance, its complexity makes it intractable for direct optimization. Therefore, we directly analyze the Euclidean distance distribution of the E-CMSK constellation as an intuitive yet effective tool for system design. This analysis guides the design of a Gray-coded bit-parameter mapping scheme and an equally spaced WFRFT parameter selection strategy, which aims to improve the overall BER performance. Simulation results demonstrate that the proposed E-CMSK scheme outperforms the conventional HC system in multi-path fading channels, particularly at high SNRs.

The rapid evolution of reconfigurable intelligent surfaces (RISs) has opened new frontiers in channel impairment mitigation, particularly through passive beamforming. However, when integrated with waveforms under doubly selective channels, a fundamental timescale mismatch exists: the existing RIS designs typically employ a single static phase configuration per frame due to hardware constraints, whereas the channel is time-varying. To address this issue, we propose a novel RIS-aided orthogonal time frequency space (OTFS) system integrated with index modulation (IM). IM serves as a generalized framework encompassing conventional modulation, enhancing the spectral efficiency (SE) and transmission flexibility. By analyzing the structure and energy distribution of time-varying channels in the delay-Doppler (DD) domain, we develop a diagonal phase alignment (DPA) strategy that aligns the RIS-reflected paths with the direct path, maximizing the achievable rate with negligible computational overhead. Unlike existing works, we explicitly consider the impact of imperfect biorthogonality in rectangular pulse-shaping waveforms, which alters the structure of the equivalent channel matrix. This paper provides detailed mathematical system models and RIS deployment scenarios. Furthermore, the closed-form upper bound of bit error rate (BER) is derived for Rician fading channels. Simulation results validate the theoretical analysis and demonstrate promising performance in terms of the achievable rate and BER.

With tens of thousands of low earth orbit (LEO) satellites to be launched in the near future, phased array antennas are envisioned as attractive candidates for future satellite ground stations due to their ability to generate multiple beams via beamforming network, thus supporting multiple satellites simultaneously. Multi-satellite tracking is of great importance for ensuring link quality in satellite communications. However, it is challenging to simultaneously tracking multiple satellites due to orbital perturbations and interference from other satellite signals. In this paper, we propose a multi-satellite tracking scheme for multibeam phased array ground station communication with LEO satellites, which employs direction of arrival (DOA) measurements of satellite signals to aid the satellite dynamics. First, we establish a tracking model that incorporates the relationship between satellite dynamics and measurement angles. Then, we develop a data fusion-based method for multiple LEO satellites by exploiting the DOA measurements of satellite signals using a phased array antenna. The measured DOA data are associated with the target satellite state and processed using an extended Kalman filter (EKF) to enhance tracking accuracy. The updated satellite position is further integrated into a dynamics model to predict angular information, leading to accurate satellite tracking during measurement gaps. Simulation results demonstrate that the proposed tracking scheme achieves a tracking accuracy of within 0.1 degrees in multi-satellite scenarios, significantly improving the tracking accuracy compared to other methods.

The thriving of satellite communication (SatCom), particularly the expansion of constellation size, offers significant opportunities for cooperative multi-satellite transmission (MST). MST leverages the diversity of fading channels arising from the spatial separation of satellites through novel waveform schemes, such as delay-Doppler (DD) domain-based orthogonal time frequency space (OTFS) and chirp domain-based affine Fourier division multiplexing (AFDM). This paper demonstrates that MST can achieve substantial synergistic gain by combining signal-to-noise ratio (SNR) gain and diversity gain with proper waveform design. We prove that OTFS/AFDM avoids the loss of diversity distinguishability compared to current orthogonal frequency division multiplexing (OFDM) and single-carrier (SC) systems, thereby maximizing the synergistic gain of MST. Furthermore, our simulation results indicate that, although the maximum likelihood (ML) receiver can theoretically achieve the SNR gain of MST under weak small-scale fading channels, the MMSE equalizer fails to do so. Overall, the results suggest that MST is more suitable for severe fading channels and highlight a challenge for future receiver designs to achieve SNR gain under weak fading channels.

In this work, we propose a non-orthogonal chirp multi-carrier system termed as truncated orthogonal chirp division multiplexing (TOCDM), which uses time-domain truncation to reduce the number of transmitted samples, thereby enhancing spectral efficiency. Compared with the existing truncated orthogonal frequency division multiplexing (TOFDM), TOCDM is more resistant to interference caused by truncation due to the use of chirp. A comprehensive description of the TOCDM system model is given, along with an analysis of inter-carrier interference (ICI) caused by truncation. Simulations demonstrate the superiority of the TOCDM over existing TOFDM in both spectral efficiency and transmission performance.

A fundamental prerequisite for implementing distributed satellite cooperative beamforming (DSCBF) is achieving accurate time, phase, and frequency synchronization. However, existing synchronization techniques often fall short of the accuracy required for DSCBF applications. Moreover, many of these techniques rely on external references, such as GPS, to coordinate electrical states, thereby limiting their applicability in environments where external references are unavailable. Furthermore, many synchronization techniques fail to rigorously account for the impacts of platform motion, thereby constraining their applicability in distributed satellite systems (DSS). In this paper, we first analyze the impacts of timing offset, frequency offset, and phase shift on cooperative beamforming gain, thereby establishing the synchronization requirements for DSS. Subsequently, the waveform-based synchronization algorithm is proposed in this paper that enables high-precision frequency offset estimation without additional hardware or external references while effectively compensating for Doppler frequency shifts induced by relative motion. Simulation results demonstrate that the proposed algorithm significantly enhances the performance of beamforming in mobile DSS.

This paper proposes the integration of the Multiple Signal Classification (MUSIC) algorithm with Affine Frequency Division Multiplexing (AFDM)-based Integrated Sensing and Communications (ISAC) system, enabling high-accuracy joint range-velocity estimation for multiple targets. To address the high computational complexity of conventional MUSIC, we propose a low-complexity iterative MUSIC (LCI-MUSIC) variant that employs cyclic spectral peak search instead of uniform grid scanning. This innovation achieves an exponential reduction in computational complexity while maintaining detection accuracy. In addition, the LCI-MUSIC enables trade-offs between complexity and estimation accuracy. Simulations demonstrate that compared to conventional MUSIC, the LCI-MUSIC algorithm achieves higher estimation accuracy at the same computational complexity.

Orthogonal Time Frequency Space (OTFS) is a promising modulation technique in high-mobility scenarios. By leveraging the sparsity of the channel in the delay-Doppler domain and achieving full diversity gain, message passing (MP)-based detectors are considered highly promising nonlinear detectors for OTFS. However, these detectors typically use empirically-driven constant damping factors to control the convergence of the algorithm, which significantly limits the stability of algorithm performance. In this paper, we innovatively propose the Functional Damping Factor-Message Passing (FD-MP) algorithm. This algorithm achieves dynamic optimization of the damping factor by establishing a function model with the value of the probability mass function as the independent variable. By constructing multiple evaluation methods for the function model, we have verified that the proposed scheme, with a fixed functional damping factor, can achieve a better bit error rate (BER) performance than the MP algorithm under different channel conditions while maintaining the same computational complexity. This innovation significantly enhances OTFS detection performance and environmental adaptability, providing support for the practical implementation of OTFS systems.

In the rapidly evolving field of wireless communication, Extremely Large-Scale Multiple-Input Multiple-Output (XL-MIMO) has emerged as a key technology for 6G communication. Due to the complex nature of XL-MIMO channels, which exhibit hybrid-field characteristics, there is a pressing need for advanced channel estimation techniques to ensure accurate signal transmission. In this paper, we propose an Adaptive Weighted-Orthogonal Matching Pursuit (AW-OMP) algorithm, which dynamically adjusts the matching process through a data-driven approach to enhance the accuracy and robustness of channel estimation. Furthermore, to ensure the computational efficiency of residual updates in the algorithm, we introduce a residual orthogonal projection matrix to directly correct residuals, providing a novel method for residual updates. The simulation results demonstrate that the proposed algorithm significantly outperforms several existing hybrid-field channel estimation algorithms.

Existing distributed antenna system (DAS) synchronization methods typically only focus on scenarios involving multiple time or frequency offsets and use independent detection methods, which results in poor real-time performance. In this paper, we propose a lightweight detection method based on CAZAC sequences (LDCS) for joint time-frequency offset estimation in DAS. Meanwhile, due to the influence of fading channel, we develop a two-step synchronization strategy-based peak detection algorithm to identify effective antennas. Based on the detection results, we can estimate the time offsets and integer frequency offsets (IFOs) between different effective transmit-receive antenna pairs. Furthermore, we utilize cyclic correlation operations to complete the estimation of fractional frequency offsets (FFOs). This is a multi-parameter estimation method based on time-domain signal processing, which has higher real-time performance and lower computational complexity. The simulation results verify the effectiveness of the proposed scheme in estimating time-frequency offsets for synchronization.

Forward-looking sonar (FLS) image segmentation can help reduce the amount of raw data that needs to be transmitted in underwater communication systems, making it a crucial technique for next-generation communication systems and the Internet of Things (IoT). However, its effectiveness is often hindered by weak semantic information, blurry edges and low resolution, which pose challenges for current segmentation algorithms. In this study, we propose a multimodal feature-enhanced Unet for FLS image segmentation (MFEUnet), built upon the Unet framework. The multimodal features considered primarily include spatial and frequency features. For spatial features, recognizing Unet’s strength in local feature extraction, we integrate a transformer to enhance its ability to capture global features. Frequency features are utilized to capture different details of FLS images, with a dual-branch wavelet transformation employed to decompose images into low-frequency and high-frequency components, facilitating the enhancement of these features. And a preprocessing reconstruction module is integrated to reduce the noise of FLS images. Furthermore, to address class imbalance in FLS datasets, we design a specialized segmentation loss function. Experimental results show that MFEUnet significantly outperforms state-of-the-art segmentation methods, demonstrating its effectiveness in overcoming the unique challenges of underwater sonar imaging.

We present a 2-bit coding array that features high beam-pointing accuracy and side-lobe-level (SLL) performance for wide-angle beam scanning. By symmetrically exciting a circular ring patch antenna and integrating a 90° phase shifter into the feeding line, a 2-bit characteristic is obtained. Four positive-intrinsic-negative (PIN) diodes are deployed in each antenna element and are controlled by a field-programmable gate array (FPGA) for switching the states of PINs. The 2-bit circular ring patch element is subsequently used for building a$1\times 12$array. Apart from introducing a set of initial phases, we add initial amplitudes to the array for the first time to further improve the array performance. Both initial phases and amplitudes are obtained from the invasive weed optimization (IWO) algorithm by setting the goals of desired beam pointing accuracy and SLL performance. In addition, the active element pattern (AEP) that accounts for the mutual coupling between elements is used in the optimization process to provide an accurate array response. The simulated and measured results agree well, and both show that the proposed array can achieve a scanning range of ±50° with a beam pointing error (BPE) within ±1°, yet the simulated maximum SLL (MSLL), 9.2 dB, deteriorates to 8.3 dB in the measurement. The measured peak aperture efficiency is 43.2% with a peak gain as 13.2 dBi. The proposed array, which features low cost, low profile, and low power consumption, is well suited for intelligent Internet of Things (IoT) applications where space and power are limited.

With constrained resources, the industrial Internet of Things (IIoT) craves for lightweight and robust access authentication protocols to secure the network. Existing physical unclonable functions (PUFs)-based cryptographic protocols face privacy threats from wireless environments and semitrusted participants, while physical-layer authentication (PLA) is costly as a complementary protocol to upper layer. Therefore, in this article we propose a cross-layer mutual authentication with the key agreement protocol based on PUFs for IIoT. The proposed protocol integrates PUFs’ challenge-response pairs (CRPs) into low-complexity cryptographic primitives and signal phases of subcarriers, employs a newly designed authentication decision methodology, and achieves excellent authentication performance while reducing protocol redundancy. Our protocol also provides device anonymity, dynamic updates, and storage-free CRPs to defend against potential insider threats. The security of the proposed protocol has been formally and informally verified. The performance analysis results show that our protocol provides better security and privacy performance with low computation and communication cost. The simulation results show the protocol can obtain great authentication performance in the indoor factory (InF) wireless scenario of the 3GPP TR 38.901 standard.

The integration of orthogonal time frequency space (OTFS) and index modulation (IM) is an attractive innovation, which can meet both high throughput and low energy consumption in highly mobile scenarios. This paper presents a novel dual frequency index modulation (DFIM) scheme for OTFS to improve spectral efficiency (SE). Exploring the internal relationship between indices, the proposed scheme, termed OTFS-DFIM, turns the classic index mapping process into a cascaded procedure involving partial index mapping and index updating. The differential information between grid points in the delay-Doppler domain and the time-frequency information are utilized to jointly determine the active grid points, which enables the OTFS frame to remain sparse and results in promising bit error rate (BER) performance. We also propose three distribution modes of IM subblocks in the two-dimensional grid and analyze their impact on receiver structure and system performance. The tight closed-form expressions of BER are derived. Additionally, we evaluate existing linear/non-linear equalization algorithms in OTFS and adapt them to the OTFS-IM/OTFS-DFIM system, offering a comprehensive insight on the tradeoffs between complexity and BER performance. Numerical simulations validate the superior performance of the OTFS-DFIM scheme in both SE and BER.

A novel two-antenna hybrid carrier system combining Alamouti space-time block coding is proposed, in which two information symbol vectors are transmitted in single carrier (SC) and multi-carrier (MC) schemes, respectively, from different antennas at the same time. The Weighted Fractional Fourier Transform (WFRFT) is involved at the transmitter. And a new mathematical transformation termed the Weighted Fractional Negative Fourier Transform (WFRNFT) is defined for demodulation. The simulation results show that the cross-modulation system has better bit error rate (BER) performance than the existing SC and MC Alamouti systems.

The weighted-type fractional Fourier transform (WFRFT)-based hybrid carrier (HC) system has been proposed to bridge the gap between orthogonal frequency division multiplexing (OFDM) system and single-carrier system with frequency domain equalization (SC-FDE). In this paper, we propose a novel HC system based on efficient fast-convolution (FC) without a cyclic prefix to meet the requirements of complex scenarios towards future communications. The proposed system can achieve flexible optimization of system performance, such as minimizing out-of-band emission (OOBE), peak to average power ratio (PAPR) and bit error rate (BER). This efficient FC based hybrid carrier (FCHC) system is among the most competitive waveforms. The closed-form BER expressions are derived and analyzed over additive white Gaussian noise (AWGN) and frequency-selective fading channels. A modified equalizer over frequency-selective channels is also provided to resist the inter-block interference (IBI). Moreover, the banded minimum mean-square error (MMSE) equalization based on FC can be embedded in the proposed system over doubly-selective channels, and then the interference caused by fading channels can be further suppressed through the combination of FC and HC. The simulation results demonstrate the superiority of the proposed system over the conventional HC system in terms of OOBE, PAPR and BER. The significant flexibility and combined performance advantages make the proposed system a potential scheme for future communications.

In this paper, we propose an adaptive multi-attributes based physical layer authentication framework for enhanced authenticity provisioning. Instead of optimizing the "threshold" for a preset PHY-layer signature, this paper resort to exploiting and selecting multiple historical better performed PHY-layer attributes for authentication enhancement. In particular, the authenticator of the proposed scheme is designed to be capable of recording the historically performance of each potential attribute. Based on which, the most effective PHY-layer attributes (MEA) would be chosen to improve the reliability of the PHY-layer authentication. This paper experimentally proves that the dimension extension on PHY-layer signature attributes effectively enhances authenticator's capability in signal discrimination. However, with more attribute to observe, it also complicates the predicting and authenticating procedure. Therefore, a learning-based search algorithm is then formulated to facilitate the MEA selection procedure. Both theoretical analysis and experiment results are given to demonstrate the efficiency and superiority of the proposed scheme.

Cyclic prefix (CP) insertion is the most common way for inter-symbol interference (ISI) suppression, however, detrimental to the high-speed data transmission demand for its waste of spectrum resources. To solve this problem, a CP-free hybrid-carrier(HC) scheme is proposed in this paper. In the proposed scheme, the inherently relational process between circular convolution and Fourier transformation is utilized through zero-padding and interval extraction to maintain the cyclic characteristic of the received data block instead of the conventional CP insertion. Both analytical and simulation results are provided to demonstrate the practicability and the superiority of the proposed scheme, in term of bit error rate(BER) performance. Moreover, the proposed CP-free HC-FDE is also proved to be more spectral effective compared to the conventional FDE schemes.

Wireless communication in substation scenarios can be seriously degraded by impulsive noise. In this paper, we aim to investigate and mitigate the impact of impulsive noise for substation communications. Specifically, symmetric alpha-stable (SaS) distribution is used to model the impulsive noise and channel in substation scenario is modeled as a frequency selective fading channel with additive impulsive noise. Based on weighted fractional Fourier transform (WFRFT), a hybrid carrier (HC) scheme that is compatible with both conventional single carrier (SC) and multi-carrier (MC) schemes is introduced. Further, the WFRFT-based HC system combined with Alamouti scheme, referred as to HC-Alamouti, is proposed to mitigate the adverse effects of impulsive noise and frequency selective fading in substation scenarios. The impulsive noise mitigation mechanism of the proposed HC-Alamouti scheme is analyzed. Moreover, simulation results are given to show the superiority of the proposed HC-Alamouti system in terms of bit error rate (BER).

With the high mobility, flexibility and manoeuvrability, unmanned aerial vehicles (UAVs)‐enabled mobile edge computing (MEC) plays an important role in many applications that lack of available terrestrial infrastructures, such as disaster response, emergency relief and military scenarios. However, the high mobility of UAVs may severely degrade the implementation of UAV‐enabled MEC in computation‐intensive or delay‐sensitive scenarios from a physical layer signalling perspective, e.g. frequency selective fading effect caused by the low altitude and low elevation angle routes of UAVs. In this study, a generalised weighted‐type fractional Fourier transform (GWFRFT) based signal energy‐spreading transmission (EST) scheme is proposed for signalling and quality of service (QoS) provisioning for UAV‐enabled MEC. In the proposed scheme, the communication signal energy is redistributed evenly at the time‐frequency plane to enhance the robustness of UAV communications against the severe fading channels. The signalling provisioning mechanism of the GWFRFT‐EST scheme is analysed and simulated under poor air‐to‐ground channels with low Rician K ‐factor. Simulation results show that the proposed method greatly improves the bit error rate performance with a negligible computational complexity increase.

In systems that aim to mitigate the inter-carrier interference (ICI) caused by doubly selective (DS) channels, the partial Fast Fourier Transform (PFFT) has emerged as an interesting alternative to the conventional FFT. In this letter, we propose a novel PFFT demodulation scheme based on fast convolution (FC) structure. The proposed scheme uses the overlap-save operation of FC to further suppress the residual interference (RI) to improve performance over DS channels, including in terms of bit error rate (BER), while, at the same time, allowing for an improvement in spectral efficiency by avoiding the use of a cyclic prefix (CP). We provide a theoretical analysis of RI and numerical simulations to demonstrate the superiority of the proposed scheme in terms of BER performance.

The major drawback of orthogonal frequency division multiplexing (OFDM) systems is the high peak-to-average power ratio (PAPR) problem. Some PAPR reduction methods have been proposed in the literature, and clipping and filtering (CAF) has been recognized as the simplest one. However, the CAF method introduces in-band distortion. In this paper, weighted fractional Fourier transform (WFRFT) is utilized to enhance the CAF method to improve the PAPR performance and mitigate the in-band distortion, which is called WFRFT-CAF method. The proposed WFRFT-CAF method is compared with existing PAPR reduction methods, based on computation complexity, PAPR reduction capacity, power spectral density (PSD), and bit error rate (BER) performance. Through simulations, it is validated that the WFRFT-CAF method can obtain better PAPR and BER performance than existing PAPR reduction methods considering the transmit power gain and path loss.

The long term evolution-advanced (LTE-A) and worldwide interoperability for microwave access (WiMAX) standards are the two main contenders in the 4th generation (4G) wireless systems, which adopt the single carrier-frequency division multiplexing access (SC-FDMA) and orthogonal frequency division multiplexing access (OFDMA) schemes in the uplink, respectively. However, these two schemes have certain advantages and disadvantages. As the weighted fractional Fourier transform (WFRFT)-based system can merge the SC- FDMA scheme with the OFDMA scheme, it inherits these two schemes' characteristics and has the potential to obtain better performance. For enhancing the bit error rate (BER) performance of the future uplink communication, in this paper, we propose a new order selection method for the WFRFT- based system to obtain better BER performance than the existing conventional uplink SC-FDMA or OFDMA scheme concerning the peak-to-average power ratio (PAPR) and the uplink power control (UPC) parameter under frequency selective fading channels.

Non-orthogonal multiple access (NOMA) has been recognized as a promising technique for future radio access. In this paper, different from [3], it is proposed that the cyclic prefix (CP) is used in the asynchronous uplink NOMA transmission for mitigating asynchronous effects. Through analyzing the inter-user interference (IUI) and residual interference, it is shown that the asynchronism can degrade the uplink NOMA users' bit error rate (BER) performance severely for the conventional-successive interference cancellation (Conv-SIC) technique. By applying the SIC-phase compensation (SIC-PC) technique and CP, the asynchronous effects can be mitigated. The BER performance of near and far users can be improved substantially, compared with other existing successive interference cancellation (SIC) techniques.

In this paper, the performance of hybrid carrier (HC) systems based on weighted fractional Fourier transform (WFRFT) is investigated in an uplink non‐orthogonal multiple access (NOMA) scenario. NOMA is a promising technology to improve the system capacity, in which two users (far‐user and near‐user relative to a base station) are allocated to use the same time‐frequency resources, and the successive interference cancellation (SIC) technique is implemented to decode signals at the receiver. Considering the actual error decoding in the SIC process (i.e. imperfect SIC), NOMA cannot avoid the inter‐user interference (IUI) and residual interference (or error propagation). Therefore, firstly IUI and residual interference are analysed, and signal to interference plus noise ratio (SINR) of the far‐user is expressed mathematically considering the residual interference. Then, based on the analysis of IUI, considering different WFRFT orders, a near‐user BER expression over additive white Gaussian noise (AWGN) channels is derived. Furthermore, the optimal WFRFT order selection to minimise the interference influence in the uplink is formulated and solved efficiently. Simulation results have verified the mathematical expression of SINR, the near‐user theoretical BER expression, and the proposed optimal WFRFT order selection to obtain the maximum sum spectral efficiency.

A weighted fractional Fourier transform (WFRFT) scheme is proposed for the orthogonal frequency division multiplexing (OFDM) system to combat impulsive noise (IN) in substation communications. According to the central limit theorem, the analytic expression of the real-valued IN probability density function (PDF) after WFRFT is derived and for ease of calculation, the closed form expression of the approximate PDF is also put forward. The PDF of IN shows that WFRFT makes IN more concentrated to the small amplitudes in the fractional Fourier transform domain than in the frequency domain at the receiver. As a result, the WFRFT scheme achieves a better bit error rate (BER) performance than the conventional OFDM system. In addition, the proposed scheme is also compatible with other existing IN mitigation techniques, such as dynamic peak-based threshold estimation-lookup table (DPTE-LUT) blanking. Simulation results have verified that the derived analytic and closed form PDF expressions of IN after WFRFT and the advantage of the proposed scheme over the counterpart OFDM system in the IN channels at high SNR with and without the DPTE-LUT blanking.

Generalised frequency division multiplexing (GFDM) as a non‐orthogonal waveform candidate is posed to reduce the high out of band radiation of orthogonal frequency division multiplexing system via pulse shaping. In this study, an analytical model of introduced interference from neighbouring subcarriers caused by pulse shaping is firstly proposed. Signal‐to‐interference‐plus‐noise ratio (SINR) is calculated according to related GFDM models with different weighted‐type fractional Fourier transform (WFRFT) precoding orders. Approximated bit error rate (BER) expressions are derived for the low complexity GFDM system over additive white Gaussian noise and fading channels based on the analysis of SINR. Particularly, the BER superiority of WFRFT precoding is highlighted over the fading channels. Furthermore, peak‐to‐average power ratio and out of band power suppression performances are simulated at different WFRFT orders to illustrate the advantages of WFRFT precoding.

This paper presents a generalized frequency division multiplexing (GFDM) communication scheme based on 4-weighted fractional Fourier transform (WFRFT) precoding. The proposed scheme as well as its low complexity version achieves flexible multi-object optimization of system performance such as bit error rate (BER) and peak to average power ratio (PAPR). Compared to traditional GFDM scheme, the improved system based on weighted parameter selection brings about combined performance advantages.