One-tap Frequency Domain Equalizer Research Articles

Widely-Linear Nyquist Criteria for DFT-Spread OFDM of Constellation-Rotated PAM Symbols

In this paper, the Nyquist criteria for ordinary linear modulation are generalized to the discrete-Fourier transform-spread (DFT-spread) orthogonal frequency-division multiplexing (OFDM) of constellation-rotated PAM symbols. Unlike the conventional Nyquist criteria with a linear receiver, the new criteria are to remove intersymbol interference in the output of a widely-linear (WL) receiver. It is shown that not only the folded spectrum, but also the shifted and reverse-folded spectrum is crucial in the criteria, where the shift offset is determined by the rotation angle. As a design example, combinations of a constellation rotation angle and a square-root raised cosine pulse are proposed. It is shown that the proposed design can achieve better performance both in spectral efficiency and in peak-to-average power ratio than the conventional DFT-spread OFDM of π/2-BPSK symbols. The optimal one-tap frequency-domain equalizer is also derived under the WL zero-forcing (ZF) constraint. It is shown that, when the rotation angle is properly chosen, the proposed one-tap WL-ZF equalizer significantly outperforms the one-tap linear ZF equalizer in output signal-to-noise ratio. The proposed equalizer also outperforms the conventional equalizer in error vector magnitude measured at the output of a nonlinear power amplifier.

Fast-convolution multicarrier based frequency division multiple access

Fast-convolution multicarrier (FCMC), the asynchronous waveform with ultra-low sidelobe, has appeared to be a promising waveform technique for future wireless communications. In this paper, we investigate the filter bank optimization as well as receiver design including low-complexity channel estimator and equalizer for FCMC based frequency division multiple access (FDMA). Starting from the conventional multi-carrier signals, we first derive a vectorized signal model as a framework to systematically design the FCMC transceiver. For nearly perfect reconstruction (NPR) filter banks design, an optimization criterion which consists of minimizing received signal segments mean square error (MSE) is proposed. From the fact that Toeplitz matrices can be asymptotically diagonalized by discrete Fourier transform (DFT) matrix, the channel equalizer can be simplified to one-tap frequency domain equalizer when DFT size is large enough. The minimum mean square error (MMSE) criterion is then applied to calculate the coefficients of one-tap frequency domain equalizer. In practice, due to the channel fading, the channel estimation has to be performed to obtain the channel state information (CSI) which is required by the channel equalization. To this end, we propose a combined cyclic prefix (CP) and cyclic suffix (CS) pilot structure which facilitates to estimate the frequency domain CSI directly in the receiver end. The proposed FCMC based FDMA features low-complexity receiver, adjustable users bandwidth and low peak-to-average power ratio. Simulation results confirm the performance of the proposed scheme.

CP-Less OFDM With Alignment Signals for Enhancing Spectral Efficiency, Reducing Latency, and Improving PHY Security of 5G Services

Although orthogonal frequency-division multiplexing (OFDM) is a widely accepted waveform in many standards and is expected to keep its dominance in future 5G systems with various types of parameterized waveforms, its performance in terms of spectral efficiency as well as transmission latency is usually degraded due to the excessive usage of cyclic prefix (CP). Particularly, in highly dispersive channels, CP rate might be very large in order to maintain the low-complex frequency-domain equalization. In this paper, we propose a novel method that can fit the low latency and high spectral efficiency requirements of future 5G wireless services by eliminating the need for inserting CP between successive OFDM symbols while keeping the whole detection process the same at the receiver side. In order to achieve that, we utilize specially designed alignment signals that can cancel the interference of one symbol on the other and add an additional signal component that makes the signal circularly convolved with the channel at the receiver side. Simulation results prove the superiority of the proposed scheme in terms of enhancing spectral and power efficiency, reducing latency, and improving physical-layer security against eavesdropping while using a low-complexity one-tap frequency-domain equalizer. These numerous, simultaneous, and desirable advantages have the potential to make the proposed technique a suitable fit for future 5G wireless services and applications including Internet of Things-based massive machine-type communication, ultra-reliable and low-latency communication, and enhanced mobile broadband.

Spectrally Precoded OFDM Without Guard Insertion

Orthogonal frequency-division multiplexing (OFDM) signaling format is commonly associated with guard subintervals to reject interblock interference (IBI) and enable simple one-tap frequency-domain equalization (FDE) at the receiver when received over dispersive channels. Despite the advantages, the insertion of guard subintervals expands the signal spectrum and thus trades off the spectral efficiency significantly. In this paper, the nonguarded OFDM (NG-OFDM) signaling format, which is exactly OFDM without inserting guard subintervals, is considered to avoid the spectrum expansion and combined with spectral precoding to further achieve high spectrum compactness. In particular, spectral precoders are designed for NG-OFDM to provide very small spectral sidelobes, and thus extremely compact signal spectrum, and associate the transmitted waveform with low peak-to-average power ratio. To reject IBI among received NG-OFDM blocks over dispersive channels, a guard subinterval in each received block is removed at the receiver, and this turns the resultant receiver as nonorthogonal over subcarrier subchannels, thus resulting in intercarrier interference (ICI). The corresponding channel capacity and linear minimum-mean-square-error (LMMSE) data estimation are analyzed. It is shown that the proposed spectrally precoded NG-OFDM (SP-NG-OFDM) system can provide channel capacity very close to nonprecoded and spectrally precoded OFDM using the cyclic prefix (CP-OFDM) when the removal guard ratio is small, and much higher channel capacity per unit bandwidth than spectrally precoded CP-OFDM conveying the same data rate provided that a small out-of-band power proportion is required. When a sufficiently small precoding rate is adopted, the SP-NG-OFDM receiver, using guard removal and LMMSE-FDE, is also shown to counteract ICI effectively and exploit frequency diversity over dispersive channels.

Design of multi-carrier transceivers based on modified discrete fourier transform filter bank

In order to improve the poor frequency selectivity and spectral leakage of traditional Orthogonal Frequency Division Multiplexing(OFDM) multi-carrier transceiver,multi-carrier transceiver based on modified Discrete Fourier Transform(DFT) filter bank was introduced. The design problem of it was formulated as nonconstrained minimized optimization of perfect reconstruction error of modulated filter banks,and the modified window method was taken to design the prototype filter in the modulated filter banks and linear optimization was used to optimize the objective function. Compared to the traditional window method,a spline function was exploited in the transition band of ideal filter of the modified window to eliminate the Gibbs effect. The simulation results show that the designed filter bank with the proposed method gives a better performance in terms of stopband attenuation,and reconstruction error,and the resulted multicarrier transceiver a better Symbol Error Rate(SER) performance in Quadrature Phase Shift Keying(QPSK) modulation and the 3GPP TS 25. 104vehicular multipath and one-tap frequency-domain equalization.

Multicarrier Systems Based on Multistage Layered IFFT Structure

This letter extends our previous work on layered inverse Fast Fourier Transform (IFFT) structure to a multistage layered IFFT structure where data symbols can input at different stages of the IFFT. We first show that part of the IFFT in the transmitter of an OFDM system can be shifted to the receiver, while a conventional one-tap frequency-domain equalizer is still applicable. We then propose two IFFT split schemes based on decimation-in-time and decimation-in-frequency IFFT algorithms to enable interference-free symbol recovery with simple linear equalizers. Applications of the proposed schemes in multiple access communications are investigated. Simulation results demonstrate the effectiveness of the proposed schemes in improving bit-error-rate performance.

Equivalent Signal-Alignment-Based Frequency-Domain Equalization for MC-CDMA Two-Way Relay Systems

In multiuser relay systems, if the relay does not have sufficient degrees of freedom to eliminate multiuser interference, the spectral efficiency gain of two-way relay (TWR) transmission may vanish. Signal alignment (SA) signaling is possible to recover this gain but may suffer from a signal power loss. To improve the spectral efficiency of multicarrier code-division multiple-access (MC-CDMA) TWR systems, we develop an equivalent SA (ESA) signaling procedure. Simply by aligning the received symbols after despreading instead of aligning the received signals as in SA signaling, ESA signaling has more feasible solutions than SA signaling, and its performance and complexity depend on the spreading sequences. This allows us to improve the system performance by optimizing ESA signaling and to reduce its complexity by designing the spreading sequences. Specifically, we develop optimal ESA signaling to maximize the signal-to-noise-ratio (SNR) under the interference-free constraint. Then, we design the spreading sequence to obtain a low-complexity ESA-based frequency-domain equalizer (FDE), i.e., ESA-based one-tap FDE, and to provide the maximal diversity gain for the one-tap FDE. Both theoretical analysis and simulation results demonstrate that ESA signaling is more spectral efficient than SA signaling for MC-CDMA TWR systems.

Dual-LP_11 mode 4x4 MIMO-OFDM transmission over a two-mode fiber

We report successful transmission of dual-LP(11) mode (LP(11a) and LP(11b)), dual polarization coherent optical orthogonal frequency-division multiplexing (CO-OFDM) signals over two-mode fibers (TMF) using all-fiber mode converters. Mode converters based on mechanically induced long-period grating with better than 20 dB extinction ratios are realized and used for interfacing single-mode fiber transmitter and receivers to the TMF. We demonstrate that by using 4×4 MIMO-OFDM processing, the random coupling of the two LP(11) spatial modes can be successfully tracked and equalized with a one-tap frequency-domain equalizer. We achieve successful transmission of 35.3 Gb/s over 26-km two-mode fiber with less than 3 dB penalty.

Frequency-Domain Block Signal Detection for Single-Carrier Transmission

One-tap frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can significantly improve the bit error rate (BER) performance of single-carrier (SC) transmission in a frequency-selective fading channel. However, a big performance gap from the theoretical lower bound still exists due to the presence of residual inter-symbol interference (ISI) after MMSE-FDE. In this paper, we point out that the frequency-domain received SC signal can be expressed using the matrix representation similar to the multiple-input multiple-output (MIMO) multiplexing and therefore, signal detection schemes developed for MIMO multiplexing, other than simple one-tap MMSE-FDE, can be applied to SC transmission. Then, for the reception of SC signals, we propose a new signal detection scheme, which combines FDE with MIMO signal detection, such as MMSE detection and Vertical-Bell Laboratories layered space-time architecture (V-BLAST) detection (we call this frequency-domain block signal detection). The achievable average BER performance using the proposed frequency-domain block signal detection is evaluated by computer simulation.

PN code-aided timing estimation, channel estimation and signal compensation in OFDM systems

In this paper, based on the correlation properties of the pseudo-random (PN) code, a scheme is proposed to achieve frame synchronization in the OFDM system. According to the estimated path delay time, the channel impulse response could be obtained with the proposed scheme. Then, based on the estimated channel response, the signal could be compensated through the one-tap frequency domain equalizer. Simulation results of the proposed frame synchronization scheme and channel estimation are presented in the paper. The miss probability of frame timing with the proposed frame synchronization scheme performs better than that with the moving average scheme and Beek's scheme. Besides, in the channel estimation, the estimator mean square error with the proposed algorithm is better than that with the algorithm using frequency domain pilots. Moreover, with the signal compensation by the estimated channel information, the frequency domain one-tap equalizer is used to improve the system performance.

Frequency-Domain Equalization for Broadband Single-Carrier Multiple Access

SUMMARY Single-carrier (SC) multiple access is a promising uplink multiple access technique because of its low peak-to-average power ratio (PAPR) property and high frequency diversity gain that is achievable through simple one-tap frequency-domain equalization (FDE) in a strong frequency-selective channel. The multiple access capability can be obtained by combining either frequency division multiple access (FDMA) or code division multiple access (CDMA) with SC transmission. In this article, we review the recent research on the SC multiple access techniques with one-tap FDE. After introducing the principle of joint FDE/antenna diversity combining, we review various SC multiple access techniques with one-tap FDE, i.e., SC-FDMA, SC-CDMA, block spread CDMA, and

Introduction of Frequency-Domain Signal Processing to Broadband Single-Carrier Transmissions in a Wireless Channel

Recently, frequency-domain equalization (FDE) has been attracting much attention as a way to improve single-carrier (SC) signal transmission in a frequency-selective wireless channel. Since the SC signal spectrum is spread over the entire signal bandwidth, FDE can take advantage of channel frequency-selectivity and achieve the frequency diversity gain. SC with FDE is a promising wireless signal transmission technique. In this article, we review the pioneering research done on SC with FDE. The principles of simple one-tap FDE, channel estimation, and residual inter-symbol interference (ISI) cancellation are presented. Multi-input/multi-output (MIMO) is an important technique to improve the transmission performance. Some of the studies on MIMO/SC with FDE are introduced.

Synchronization, Channel Estimation, and Equalization in MB-OFDM Systems

This paper addresses preamble-based low complexity synchronization, channel estimation and equalization for Zero-padded (ZP) MB-OFDM based UWB systems. The proposed synchronization method consists of sync detection, coarse timing estimation, fine timing estimation, and oscillator frequency offset estimation. The distinctive features of MB-OFDM systems and the interplay between the timing and carrier frequency hopping at the receiver are judiciously incorporated in the proposed synchronization method. In order to apply the low complexity one-tap frequency-domain equalizer, the required circular convolution property of the received signal is obtained by means of an overlap-add method after the frequency offset compensation. The proposed low complexity channel estimator for each band is developed by first averaging the over-lapadded received preamble symbols within the same band and then applying time-domain least-squares method followed by the discrete Fourier transform. We develop an MMSE equalizer and its approximate version with low complexity. We also derive the probability density functions of the UWB channel path delays, and using them we present several optimization criteria for our proposed synchronization, channel estimation, and equalization. The effectiveness of our proposed methods and optimization criteria are confirmed by computer simulation results.

Successive NBI Cancellation Using Soft Decisions for OFDM Systems

Recently, we proposed a successive narrowband interference (NBI) cancellation method for orthogonal frequency-division multiplexing (OFDM) systems, which empowers the conventional one-tap frequency-domain equalizer to gain in robustness against NBI. In this letter, we generalize such an approach by using soft (instead of hard) feedback from the decoding unit, when the digitally-modulated NBI is (possibly) improper. It is shown that, with respect to our previous work, the devised equalizers allow one to achieve a significant performance gain, with a moderate increase in computational complexity.

Modified Frequency-Domain Equalization for Channel Shortening in Reduced-CP OFDMA Systems

In orthogonal frequency-division multiple access (OFDMA) systems, the cyclic prefix (CP) length needs to be no less than the longest delay spread of the channels of many users, reducing bandwidth efficiency more significantly than in single-user orthogonal frequency division multiplexing systems. In this paper, we address OFDMA downlink data transmission when a short CP is used to mitigate the inefficient bandwidth usage. Previous time-domain equalizers (TEQs) can be used to shorten the channel; however, they tend to increase noise by introducing spectral nulls. A previous work on per-tone equalization (PTEQ) structure involves a multitap frequency-domain equalizer (FEQ) for each tone, and shows better performance than TEQ-based receiver structure. We propose a novel receiver structure with only one-tap FEQ for OFDMA systems with a reduced CP, exploiting the unused subchannels for a user. We formulate an optimization problem to set the FEQ coefficients at the unused subchannels such that the channel is shortened (approximation is involved) and noise is not enhanced at the used subchannels. With the aid of computer simulations, it is demonstrated that the proposed equalization method is superior to the conventional TEQ-based receivers, and is comparable to the previous PTEQ-based receiver in terms of the achievable SNR, error performance, and bandwidth efficiency. Although the throughput curve versus synchronization delay of the PTEQ is smoother than that of the proposed receiver, the proposed method shows proper throughput over a wider range of the delay values than PTEQ receiver when the system parameters are set so that the complexities are comparable.

Zero-forcing equalization for OFDM systems over doubly-selective fading channels using frequency domain redundancy

Rapid variations of doubly-selective fading channels lead to the loss of orthogonality among subcarriers, resulting in inter-carrier interference (ICI) in orthogonal frequency division multiplexing (OFDM) systems. In this scenario, the one-tap frequency-domain equalizer is not applicable any more. Based on an ICI analysis in both time- and frequency-domain, we propose a novel zero-forcing equalizer (ZFE) for OFDM systems over doubly-selective channels using the existing frequency domain redundancy in many OFDM standards. To deal with the zero-forcing equalizer's disadvantage of noise amplification, which causes system performance degradation when there exist deep nulls in the channel's frequency response, we also provide the MMSE-based optimization of ZFE coefficients in the presence of channel noise. We show that ZFE matrix has a sparse structure, and thus a low computational complexity. Simulation results indicate that the proposed equalizer is capable of suppressing ICI effectively with a low complexity.

Time-domain and frequency-domain per-tone equalization for OFDM over doubly selective channels

In this paper, we propose new time- and frequency-domain per-tone equalization techniques for orthogonal frequency division multiplexing (OFDM) transmission over time- and frequency-selective channels. We present one mixed time- and frequency-domain equalizer (MTFEQ) and one frequency-domain per-tone equalizer. The MTFEQ consists of a one-tap time-varying (TV) time-domain equalizer (TEQ), which converts the doubly selective channel into a purely frequency-selective channel, followed by a one-tap frequency-domain equalizer (FEQ), which then equalizes the resulting frequency-selective channel in the frequency-domain. The frequency-domain per-tone equalizer (PTEQ) is then obtained by transferring the TEQ operation to the frequency-domain. While the one-tap TEQ of the MTFEQ optimizes the performance on all subcarriers in a joint fashion, the PTEQ optimizes the performance on each subcarrier separately. This results into a significant performance improvement of the PTEQ over the MTFEQ, at the cost of a slight increase in complexity. Through computer simulations we show that the MTFEQ suffers from an early and high error floor, while the PTEQ outperforms the MMSE equalizer for OFDM over purely frequency-selective channels, it can approach the performance of the block MMSE equalizer. An important feature of the proposed techniques is that no bandwidth expansion or redundancy insertion is required except for the cyclic prefix.

Cyclic prefixed single carrier and multicarrier transmission: bit rate comparison

We consider cyclic prefixed single carrier and adaptive multicarrier transmission over a frequency selective channel. We compare the achievable bit rate for a target bit error rate. We analytically prove that the bit rate achieved with multicarrier transmission with adaptive modulation is always higher than that obtained with single carrier transmission when a one-tap frequency domain equalizer is used. We also show that the same adaptively loaded multicarrier scheme reaches the performance of single carrier transmission with a block decision-feedback equalizer.