Orthogonal time frequency space (OTFS) modulation has been proposed to achieve outstanding performances over delay-Doppler channels in comparison with orthogonal frequency division multiplexing (OFDM) systems. Particularly, transmitter and receiver structures of OTFS are same as those of asymmetric OFDM (A-OFDM) waveforms, and OTFS is simplified as A-OFDM over static multipath channels. In this paper, we propose an integrated waveform framework based on weighted-type fractional Fourier transform (WFRFT) with two-dimensional adjustable parameters and strong scalability, called as WFRFT-OTFS, which can be reduced to OTFS, A-OFDM, hybrid carrier (HC), OFDM and other waveforms. Basically, theoretical BER expressions of integrated WFRFT-OTFS framework over multipath channels with zero forcing (ZF) and minimum mean square error (MMSE) receivers are derived through fusing different waveform components and verified by simulation results.

In this paper, we investigate bit error rate (BER) performances of weighted-type fractional Fourier transform (WFRFT) precoded orthogonal frequency-division multiplexing (OFDM) and generalized frequency-division multiplexing (GFDM) waveforms with an integer time offset (TO) over additive white Gaussian noise and fading channels. First of all, theoretical BER expressions of hybrid carrier systems with TO are derived according to the linear combination characteristic of WFRFT. In addition, the fusion mechanism is also employed to calculate noise enhancement factor (NEF) of WFRFT precoded GFDM waveforms, and then analytical BER expressions are derived, including the cases with TO. Basically, analytical BER expressions of WFRFT precoded OFDM and GFDM waveforms are under the same framework, and BER of the latter could be simplified to the former when GFDM systems are reduced to OFDM systems. Through WFRFT precoding, the BER performance of GFDM waveforms could be improved by about 2 dB over fading channels with timing errors. Furthermore, using derived NEF of WFRFT precoded GFDM waveforms, theoretical BER expressions could be easily extended to space-time coded systems. Finally, when interblock interference and intercarrier interference are generated due to insufficient cyclic prefix and timing errors, BER performances of WFRFT precoded OFDM and GFDM waveforms also surpass their two special cases, i.e., nonprecoded and discrete Fourier transform precoded ones.

From the points of spectral efficiency, low latency and massive connectivity, novel modulation and multiple access schemes have been proposed in fifth generation (5G) wireless networks. However, the combinations of multiplexing and multiple access techniques have not been widely investigated in most literatures. Therefore, we joint generalized frequency division multiplexing (GFDM) waveforms and power-domain non-orthogonal multiple access (NOMA) systems together in order to further extend the framework of multi-carrier NOMA, and also achieve performance evaluations for NOMA networks with one base station and two users. Basically, theoretical BER expressions of downlink and uplink GFDM assisted NOMA schemes are mathematically derived and then verified by simulation results. In addition, combined performance advantages, including higher achievable sum rate, lower peak-to-average power ratio (PAPR) and out of band power (OOBP) radiation, can be obtained in GFDM assisted NOMA networks.

Orthogonal Time Frequency Space (OTFS) has attracted the attention of researchers due to its excellent BER performance in high-speed mobile scenarios. In this paper, a low complexity Minimum Mean Square Error Serial Interference Cancellation (MMSE-SIC) receiver is proposed, which replaces the computationally intensive matrix inversion calculations in the symbol decision process with two low complexity algorithms. Firstly, a low complexity LDLH decomposition algorithm is proposed based on the properties of the equivalent channel matrix. Secondly, a low complexity algorithm is put forward for the inversion of lower triangular matrices. Finally, the concept of adjustable parameter is introduced to achieve dynamic adjustment of complexity. Simulation results demonstrate that the proposed algorithm achieves significant performance gains compared to the linear equalization algorithm and similar BER performance as the traditional SIC algorithm with reduced complexity.

Orthogonal time frequency space (OTFS) modulation has been put forward to achieve better performances over delay-Doppler channels in comparison with orthogonal frequency division multiplexing (OFDM) systems. In this paper, a nonlinear corrective active constellation expansion (NC-ACE) method is firstly proposed in OTFS waveform to achieve precise control of peak-to-average power ratio (PAPR) and BER performances due to its nonlinear compression characteristics. Compared to linear constraint of clipping and filtering process in traditional active constellation expansion (ACE) and bounded distortion ACE (BD-ACE) strategies, nonlinear compressed clipping noise is considered with a flexible curvature control coefficient. According to flexible features of NC-ACE, a bridge between optimal suppression and no reduction of PAPR performances is established in OTFS systems, where tradeoff between PAPR and BER performances can be further obtained.