To achieve the extreme high data rate and extreme coverage extension requirements of 6G wireless communication, new spectrum in sub-THz (100-300GHz) and non-terrestrial network (NTN) are two of the macro trends of 6G candidate technologies, respectively. However, non-linearity of power amplifiers (PA) is a critical challenge for both sub-THz and NTN. Therefore, high power efficiency (PE) or low peak to average power ratio (PAPR) waveform design becomes one of the most significant 6G research topics. Meanwhile, high spectral efficiency (SE) and low out-of-band emission (OOBE) are still important key performance indicators (KPIs) for 6G waveform design. Single-carrier waveform discrete Fourier transform spreading orthogonal frequency division multiplexing (DFT-s-OFDM) has achieved many research interests due to its high PE, and it has been supported in 5G New Radio (NR) when uplink coverage is limited. So DFT-s-OFDM can be regarded as a candidate waveform for 6G. Many enhancement schemes based on DFT-s-OFDM have been proposed, including null cyclic prefix (NCP)/unique word (UW), frequency-domain spectral shaping (FDSS), and time-domain compression and expansion (TD-CE), etc. However, there is no unified framework to be compatible with all the enhancement schemes. This paper firstly provides a general description of the 6G candidate waveforms based on DFT-s-OFDM enhancement. Secondly, the more flexible TD-CE supporting methods for unified non-orthogonal waveform (uNOW) are proposed and discussed. Thirdly, a unified waveform framework based on DFT-s-OFDM structure is proposed. By designing the pre-processing and post-processing modules before and after DFT in the unified waveform framework, the three technical methods (NCP/UW, FDSS, and TD-CE) can be integrated to improve three KPIs of DFT-s-OFDM simultaneously with high flexibility. Then the implementation complexity of the 6G candidate waveforms are analyzed and compared. Performance of different DFT-s-OFDM enhancement schemes is investigated by link level simulation, which reveals that uNOW can achieve the best PAPR performance among all the 6G candidate waveforms. When considering PA back-off, uNOW can achieve 124% throughput gain compared to traditional DFT-s-OFDM.

Coprime (pair of) DFT filter banks (coprime DFTFB), which process signals like a spectral analyzer in time domain, divides the power spectrum equally into MN bands by employing two DFT filter banks (DFTFBs) of size only M and N respectively, where M and N are coprime integers. With coprime DFTFB, frequencies in wide sense stationary (WSS) signals can be effectively estimated with a much lower sampling rates than the Nyquist rates. However, the imperfection of practical FIR filter and the correlation based detection mode give rise to two kinds of spurious peaks in power spectrum estimation, that greatly limit the application of coprime DFTFB. Through detailed analysis of the spurious peaks, this paper proposes a modified spectral analyzer based on dual coprime DFTFBs and sub-decimation, which not only depresses the spurious peaks, but also improves the frequency estimation accuracy. The mathematical principle proof of the proposed spectral analyzer is also provided. In discussion of simultaneous signals detection, an O-extended MN-band coprime DFTFB (OExt M-N coprime DFTFB) structure is naturally deduced, where M, N, and O are coprime with each other. The original MN-band coprime DFTFB (M-N coprime DFTFB) can be seen a special case of the OExt M-N coprime DFTFB with extending factor O equals ‘1’. In the numerical simulation section, BPSK signals with random carrier frequencies are employed to test the proposed spectral analyzer. The results of detection probability versus SNR curves through 1000 Monte Carlo experiments verify the effectiveness of the proposed spectrum analyzer.

This paper presents the average block error rate (BLER) performance of circular 32QAM and 64QAM schemes employing a frequency domain equalizer (FDE) for discrete Fourier transform (DFT)-precoded orthogonal frequency division multiplexing (OFDM) in multipath Rayleigh fading channels. The circular QAM scheme has an advantageous feature in that the fluctuation in the amplitude component is smaller than that for the cross or rectangular QAM scheme. Hence, focusing on the actual received signal-to-noise power ratio (SNR) taking into account a realistic peak-to-average power ratio (PAPR) measure called the cubic metric (CM), we compare the average BLER of the circular 32QAM and 64QAM schemes with those of cross 32QAM and rectangular 64QAM schemes, respectively. We investigate the theoretical throughput of various circular 32QAM and 64QAM schemes based on mutual information from the viewpoint of the minimum Euclidean distance. Link-level simulation results show that the circular 32QAM and 64QAM schemes with independent bit mapping for the phase and amplitude modulations achieves a lower required average received SNR considering the CM than that with the minimum Euclidean distance but with composite mapping of the phase and amplitude modulations. Through extensive link-level simulations, we show the potential benefit of the circular 32QAM and 64QAM schemes in terms of reducing the required average received SNR considering the CM that satisfies the target average BLER compared to the cross 32QAM or rectangular 64QAM scheme.

Expectation propagation (EP) decoding is proposed for sparse superposition coding in orthogonal frequency division multiplexing (OFDM) systems. When a randomized discrete Fourier transform (DFT) dictionary matrix is used, the EP decoding has the same complexity as approximate message-passing (AMP) decoding, which is a low-complexity and powerful decoding algorithm for the additive white Gaussian noise (AWGN) channel. Numerical simulations show that the EP decoding achieves comparable performance to AMP decoding for the AWGN channel. For OFDM systems, on the other hand, the EP decoding is much superior to the AMP decoding while the AMP decoding has an error-floor in high signal-to-noise ratio regime.

The spreading technique can improve system performance since it mitigates the influence of deeply faded subcarrier channels. Proposals for implementing orthogonal frequency division multiplexing (OFDM) systems include frequency symbol spreading (FSS) based on the Walsh-Hadamard transform (WHT) and the discrete Fourier transform (DFT). In a single carrier frequency division multiplexing (SC-FDMA), good performance is obtained by the interleaved subcarrier allocation. Moreover, in a multiple-input multiple-output (MIMO), interleaving the operation of the different transmit antennas is also effective. By combining these techniques, in this paper, we propose the different antenna interleaved allocation with the full and divided WHT/DFT spreading for a high time resolution carrier interferometry (HTRCI) MIMO-OFDM.

The conventional universal filtered-DFT-spread-OFDM (UF-DFTs-OFDM) can drastically improve the out-of-band emission (OOBE) caused by the discontinuity between symbols in the conventional cyclic prefix-based DFTs-OFDM (CP-DFTs-OFDM). However, the UF-DFTs-OFDM degrades the communication quality in a long-delay multipath fading environment due to the frequency-domain ripple derived from the long transition time of the low pass filter (LPF) corresponding to the guard interval (GI). In this paper, we propose an enhanced UF-DFTs-OFDM (eUF-DFTs-OFDM) that achieves significantly low OOBE and high communication quality even in a long-delay multipath fading environment. The eUF-DFTs-OFDM applies an LPF with quite short length in combination with the zero padding (ZP) or the CP process. Then, the characteristics of the OOBE, peak-to-average power ratio (PAPR), and block error rate (BLER) are evaluated by computer simulation with the LTE uplink parameters. The result confirms that the eUF-DFTs-OFDM can improve the OOBE by 22.5dB at the channel-edge compared to the CP-DFTs-OFDM, and also improve the ES/N0 to achieve BLER =10-3 by about 2.5dB for QPSK and 16QAM compared to the UF-DFTs-OFDM. For 64QAM, the proposed eUF-DFTs-ODFDM can eliminate the error floor of the UF-DFTs-OFDM. These results indicate that the proposed eUF-DFTs-OFDM can significantly reduce the OOBE while maintaining the same level of communication quality as the CP-DFTs-OFDM even in long-delay multipath environment.

The windowed interpolation DFT methods have been utilized to estimate the parameters of a single frequency and multi-frequency signal. Nevertheless, they do not work well for the real-valued sinusoids with closely spaced positive- and negative- frequency. In this paper, we describe a novel three-point windowed interpolation DFT method for frequency measurement of real-valued sinusoid signal. The exact representation of the windowed DFT with maximum sidelobe decay window (MSDW) is constructed. The spectral superposition of positive- and negative-frequency is considered and calculated to improve the estimation performance. The simulation results match with the theoretical values well. In addition, computer simulations demonstrate that the proposed algorithm provides high estimation accuracy and good noise suppression capability.

The sliding discrete Fourier transform (DFT) is a well-known algorithm for obtaining a few frequency components of the DFT spectrum with a low computational cost. However, the conventional sliding DFT cannot be applied to practical conditions, e.g., using the sine window and the zero-padding DFT, with preserving the computational efficiency. This paper discusses the extension of the sliding DFT to such cases. Expressing the window function by complex sinusoids, a recursive algorithm for computing a frequency component of the DFT spectrum using an arbitrary sinusoidal window function is derived. The algorithm can be easily extended to the zero-padding DFT. Computer simulations using very long signals show the validity of our algorithm.

In this paper, we propose a texture descriptor based on amplitude distribution and phase distribution of the discrete Fourier transform (DFT) of an image. One dimensional DFT is applied to all the rows and columns of an image. Histograms of the amplitudes and gradients of the phases between adjacent rows/columns are computed as the feature descriptor, which is called aggregated DFT (ADFT). ADFT can be easily combined with completed local binary pattern (CLBP). The combined feature captures both global and local information of the texture. ADFT is designed for isotropic textures and demonstrated to be effective for roughness classification of castings. Experimental results show that the amplitude part of ADFT is also discriminative in describing anisotropic textures and it can be used as a complementary descriptor of local texture descriptors such as CLBP.

The proposed stimulus design for linearity test is embedded in a differential successive approximation register analog-to-digital converter (SAR ADC), i.e. a design for testability (DFT). The proposed DFT is compatible to the pattern generator (PG) and output response analyzer (ORA) with the cost of 12.4-% area of the SAR ADC. The 10-bit SAR ADC prototype is verified in a 0.18-µm CMOS technology and the measured differential nonlinearity (DNL) error is between -0.386 and 0.281 LSB at 1-MS/s.

This paper presents frequency diversity effects of localized transmission, clustered transmission, and intra-subframe frequency hopping (FH) using a frequency domain equalizer (FDE) for discrete Fourier transform (DFT)-precoded Orthogonal Frequency Division Multiple Access (OFDMA). In the evaluations, we employ the normalized frequency mean square covariance (NFMSV) as a measure of the frequency diversity effect, i.e., randomization level of the frequency domain interleaving associated with turbo coding. Link-level computer simulation results show that frequency diversity is very effective in decreasing the required average received signal-to-noise power ratio (SNR) at the target average block error rate (BLER) using a linear minimum mean-square error (LMMSE) based FDE according to the increase in the entire transmission bandwidth for DFT-precoded OFDMA. Moreover, we show that the NFMSV is an accurate measure of the frequency diversity effect for the 3 transmission schemes for DFT-precoded OFDMA. We also clarify the frequency diversity effects of the 3 transmission schemes from the viewpoint of the required average received SNR satisfying the target average BLER for the various key radio parameters for DFT-precoded OFDMA in frequency-selective Rayleigh fading channels.

This paper investigates the average block error rate (BLER) performance of star 16QAM schemes considering the effective peak-to-average power ratio (PAPR) criterion called a cubic metric (CM) for uplink discrete Fourier transform (DFT)-precoded orthogonal frequency division multiple access (OFDMA). We clarify the best ring amplitude ratio for the (4, 12) and (8, 8) star 16QAM schemes from the viewpoint of the required average signal-to-noise power ratio (SNR) that satisfy the target average BLER based on link-level simulations. We also validate the agreement of the best ring amplitude ratios with those maximizing the mutual information based throughput. Then, employing the best ring amplitude ratios for the respective coding rates of the turbo code, we show that (8, 8) star 16QAM achieves better average BLER performance compared to that for (4, 12) star 16QAM. Moreover, we show the effectiveness of the (8, 8) star 16QAM scheme compared to square 16QAM in terms of the required average received SNR considering the CM when the coding rate is low such as 1/3 for uplink DFT-precoded OFDMA.

This paper proposes an improved discrete Fourier transform (DFT)-based channel estimation technique for time domain synchronous orthogonal frequency division multiplexing (TDS-OFDM) communication systems. The proposed technique, based on the concept of significant channel tap detector (SCTD) scheme, can effectively improve the system performance of TDS-OFDM systems. The correlation of two successive preambles is employed to estimate the average noise power as the threshold for obtaining the SCTD threshold estimation error and loss path information in large delay spread channel environments. The proposed estimation scheme roughly predicts the noise power in order to choose the significant channel taps to estimate the channel impulse response. Some comparative simulations are given to show that the proposed technique has the potential to achieve bit error rate performance superior to that of the conventional least squares channel estimation.

The wideband noise controlling performance of the delayless subband adaptive filtering technique is affected by the group delay and in-band aliasing distortion of analysis filter banks. A method of recursive second-order cone programming is proposed to design the uniform DFT modulated analysis filter banks, with a small in-band aliasing error and low group delay. Simulation results show that the noise controlling performance is improved with small residual noise power spectra, a high noise attenuation level and fast convergence rate.

In this paper, we constructed a class of low correlation zone sequence sets derived from the interleaved technique and DFT matrices. When p is a prime such that p > 3, p-ary LCZ sequence sets with parameters LCZ(pn-1,pm-1,(pn-1)/(pm-1),1) are constructed based on a DFT matrix with order pp, which is optimal with respect to the Tang-Fan-Matsufuji bound. When p is a prime such that p ≥ 2, pk-ary LCZ sequence sets with parameters LCZ(pn-1,pk-1,(pn-1)/(pk-1),1) are constructed based on a DFT matrix with order pkpk, which is also optimal. These sequence sets are useful in certain quasi-synchronous code-division mutiple access (QS-CDMA) communication systems.

A simple DFT-based noise variance estimator for orthogonal frequency division multiplexing access (OFDMA) systems is proposed. The conventional DFT-based estimator differentiates the channel impulse response and noise in the time domain. However, for partial frequency response, its time domain signal will leak to all taps due to the windowing effect. The noise and channel leakage power become mixed. In order to accurately derive the noise power, we propose a novel symmetric extension method to reduce the channel leakage power. This method is based on the improved signal continuity at the boundaries introduced by symmetric extension. Numerical results show that the normalized mean square error (NMSE) of our proposed method is significantly lower than that of the conventional DFT method.

We propose an iterative frequency estimation method for accuracy improvement of discrete Fourier transform (DFT) phase-based methods. It iterates frequency estimation and phase calculation based on the DFT phase-based methods, which maximizes the signal-to-noise floor ratio at the frequency estimation position. We apply it to three methods, the phase difference estimation, the derivative estimation, and the arctan estimation, which are known to be among the best DFT phase-based methods. Experimental results show that the proposed method shows meaningful reductions of the frequency estimation error compared to the conventional methods especially at low signal-to-noise ratio.

In this letter, a novel resource allocation method is proposed for Discrete Fourier Transform Spread Orthogonal Frequency Division Multiple Access (DFT-s-OFDMA) systems in Long Term Evolution (LTE). The proposed method is developed based on a minimal metric loss criterion and performs better than the commonly used Recursive Maximum Expansion (RME) method.

In this letter, an area-efficient architecture for the hardware implementation of the real-time prime factor Fourier transform (PFFT) is presented. In the proposed architecture, a prime length DFT module with the one-point-per-cycle (OPPC) property is implemented by the parallel distributed arithmetic (DA), and a cyclic convolution feature is exploited to simplify the structure of the DA cells. Based on the proposed architecture, a real-time 65-point PFFT processor is designed, and the synthesis results show that it saves over 8% gates compared to the existing real-time 64-point DFT designs.

A new transmission scheme for OFDM systems that uses the odd discrete Fourier transform to provide frequency diversity gain is proposed. Odd DFT allows the transmission of data subcarriers in frequencies that are centred between those employed by the traditional DFT. This fact is exploited to transmit data subcarriers on the group of frequencies that gives better performance using either traditional DFT or odd DFT. As an example, by using this approach a diversity gain up to 5.3 dB at a BER of 10-4 in a typical indoor channel model can be achieved.