Frequency-domain Symbols Research Articles

Factor Graph Based Message Passing Algorithms for Joint Phase-Noise Estimation and Decoding in OFDM-IM

In order to glean benefits from orthogonal frequency division multiplexing combined with index modulation (OFDM-IM) in the presence of strong Phase-Noise (PHN), in this paper, low-complexity joint PHN estimation and decoding methods are developed in the framework of message passing on a factor graph. Both the Wiener process and the truncated discrete cosine transform (DCT) expansion model are considered for approximating the PHN variation. Then based on these a factor graph is constructed for explicitly representing the joint estimation and detection problem. Taking full account of the sparse and structured a priori information arriving from the soft-in soft-out (SISO) decoder of a turbo receiver, a modified generalized approximate message passing (GAMP) algorithm is invoked for decoupling the frequency-domain symbols. In the decoupling step, mean field (MF) approximation is employed for solving the unknown nonlinear transform matrix problem imposed by PHN. Furthermore, merged belief propagation and MF (BP-MF) methods amalgamated both with sequential and parallel message passing schedules are introduced and compared to the proposed GAMP based algorithms in terms of their bit error ratio (BER) vs. complexity. Our simulation results demonstrate the efficiency of the proposed algorithms in the presence of both perfect and imperfect channel state information.

Uplink multi‐carrier multiple access scheme LDS‐IOTA

In this study, a multiple access scheme called low density signature isotropic orthogonal transfer algorithm (LDS-IOTA) is proposed for overloading transmissions, and an analytical model for the performance limitations of this system is developed. LDS-IOTA utilises a low density signature structure for spreading the symbols in frequency domain, and applies such technique to IOTA-based filter bank multicarrier system. The input-output mutual information of LDS-IOTA is analysed for the case of finite size modulation, and LDS-IOTA is compared with OFDM as well as LDS-OFDM over multipath fadding channels.

ML-Based Iterative Approach for Blind Frequency Domain Equalization and Combination Over Sparse Channels

This letter deals with blind spatial diversity equalization and combination of sparse channels. The equalization and combination problem of multiple signals is modeled as the maximum likelihood estimation of frequency domain symbol sequence from incomplete observations, and solved by means of the expectation-maximization (EM) algorithm. Closed-form expression of the equalization output is obtained, which shows that the complicated problem of signal equalization and combination in multipath channels is converted to the weighted summation of each discrete-frequency signals, eliminating the need of complicated maximum likelihood sequence estimation (MLSE) or de-convolution demanded by time domain equalization. Simulation results show that the proposed scheme enables evident performance improvement in terms of symbol error rate especially at low signal-to-noise ratio (SNR) values and short signal lengths compared with a typical scheme.

Variational Inference-Based Frequency-Domain Equalization for Faster-Than-Nyquist Signaling in Doubly Selective Channels

This work deals with frequency-domain equalization for faster-than-Nyquist (FTN) signaling in doubly selective channels (DSCs). To handle the interference of frequency-domain symbols, the minimum mean square error (MMSE) equalizer involves high complexity in DSCs. To overcome the problem, we propose low-complexity receivers based on two variational methods, i.e., mean field (MF) and Bethe approximations. Compared with the MF method, the Bethe approximation takes into account the conditional dependencies of pairwise symbols. By only considering a small set of the frequency-domain symbols that have strong interference to each other, the complexity of the proposed algorithms increases linearly with the block length. Simulation results demonstrate that the proposed algorithms for FTN signaling are able to perform close to the MMSE equalizer in DSCs while with significantly reduced computational complexity.

A Robust and Efficient Frequency Offset Correction Algorithm With Experimental Verification for Coherent Optical OFDM System

Frequency offset correction (FOC) is essential for a coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system. In this paper, we proposed a robust and efficient FOC algorithm by designing training symbols in frequency domain. This algorithm has an advantage in overcoming imperfect frequency response induced by transmitter devices and physical channel implementations. To further improve the stability of the FOC algorithm against the optical signal-to-noise ratio degradation, a two-step iterative operation is introduced. The proposed algorithm has been utilized in a practical 100-km 16QAM-CO-OFDM transmission system to compensate the frequency offset dynamically. The efficiency and robustness of the algorithm have been validated by outstanding and stable experimental results.

Decision-aided ICI mitigation with time-domain average approximation in CO-OFDM

We introduce and investigate the feasibility of a novel iterative blind phase noise inter-carrier interference (ICI) mitigation scheme for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The ICI mitigation scheme is performed through the combination of frequency-domain symbol decision-aided estimation and the ICI phase noise time-average approximation. An additional initial decision process with suitable threshold is introduced in order to suppress the decision error symbols. Our proposed ICI mitigation scheme is proved to be effective in removing the ICI for a simulated CO-OFDM with 16-QAM modulation format. With the slightly high computational complexity, it outperforms the time-domain average blind ICI (Avg-BL-ICI) algorithm at a relatively wide laser line-width and high OSNR.

Low Complexity Discrete Hartley Transform Precoded OFDM System over Frequency-Selective Fading Channel

Orthogonal frequency-division multiplexing (OFDM) suffers from spectral nulls of frequency-selective fading channels. Linear precoded (LP-) OFDM is an effective method that guarantees symbol detectability by spreading the frequency-domain symbols over the whole spectrum. This paper proposes a computationally efficient and low-cost implementation for discrete Hartley transform (DHT) precoded OFDM systems. Compared to conventional DHT-OFDM systems, at the transmitter, both the DHT and the inverse discrete Fourier transform are replaced by a one-level butterfly structure that involves only one addition per symbol to generate the time-domain DHT-OFDM signal. At the receiver, only the DHT is required to recover the distorted signal with a single-tap equalizer in contrast to both the DHT and the DFT in the conventional DHT-OFDM. Theoretical analysis of DHT-OFDM with linear equalizers is presented and confirmed by numerical simulation. It is shown that the proposed DHT-OFDM system achieves similar performance when compared to other LP-OFDMs but exhibits a lower implementation complexity and peak-to-average power ratio.

Peak-to-average power ratio reduction using selective mapping with unequal power distribution

A new approach for peak-to-average power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems was proposed. This approach is based on assigning powers to the different subcarriers of OFDM using an unequal power distribution strategy. In addition, a reduced complexity selective mapping (RC-SLM) scheme was proposed. The proposed scheme is based on partitioning the frequency domain symbol sequence into several sub-blocks, and then each sub-block is multiplied by different phase sequences whose length is shorter than that used in the conventional SLM scheme. Then, a kind of low complexity conversions is used to replace the IFFT blocks. The performance of the proposed RC-SLM scheme along with the new approach was studied with computer simulation. The obtained results show that the proposed RC-SLM scheme is able to achieve the lowest computational complexity when compared with other low complexity schemes proposed in the literature while at the same time improves the PAPR reduction performance by about 0.3 dB.

Metric based symbol predistortion for peak power reduction of space frequency coded OFDM systems

In this paper, a metric based symbol predistortion method is introduced for Peak to Average Power Ratio (PAPR) reduction of the Space Frequency Block Coded (SFBC) Orthogonal Frequency Division Multiplexing (OFDM) systems with two transmitter antennas. In the proposed method, a metric is defined which shows the contribution of each frequency domain symbol to the time domain samples with high amplitude at both antennas. Then, the symbols with the highest metric values are chosen and predistorted such that the peak powers are reduced while the SFBC relationship between two antennas holds constant. Three variants of this method will be introduced. Then, this technique is extended to the general SFBC systems with an arbitrary number of antennas and SFBC structures. Simulation results show that the proposed methods converge when a different number of transmitter antennas and different modulation techniques are used. However, the best performance is achieved in the case of two transmitter antennas with QPSK modulation.

PAPR 감소와 효과적 채널 추정을 위한 SC-FDMA 통신 시스템의 파이럿 배치 방법

SC-FDMA(Single Carrier-Frequency Division Multiple Access) 통신 시스템에서 채널 추정을 위한 파일럿은 CAZAC 시퀀스를 이용하여 OFDM(Orthogonal Frequency Division Multiplexing) 신호의 높은 PAPR(Peak-to-Average Power Ratio)을 낮추는 방식을 사용한다. 그런데, 채널 추정을 위한 파일럿이 블록 타입으로 전송되므로, 수신단에서 파일럿 블록 사이의 여러 OFDM 심볼들은 시간 영역에서의 보간법을 시용하여 채널 추정하여야 하므로 매우 복잡하고 처리 시간이 길어질 수 있다. 또한 심한 fast fading 채널에서는 이러한 문제점이 더욱 커진다. 한편, 효과적인 고속 채널 추정을 위하여 OFDM 심벌 단위로, 주파수 영역에서 보간법을 수행하는 comb 타입의 파일럿을 사용하게 되면 OFDM 신호의 PAPR이 다시 높아지는 문제가 발생한다. 본 논문에서는 PAPR 감소와 효과적 채널 추정이 가능한 comb 타입의 파일럿을 배치 방법을 연구하였다. 이를 위하여 CAZAC 행렬 변환된 OFDM 신호에 comb 타입의 파일럿을 배치하고, 추가로 SLM 기법을 사용하였다. 그러나 기본적인 SLM(Selected Mapping) 기법은 위상 회전에 관한 부가 정보 전송이 필요하기 때문에 대역폭의 손실을 가져온다는 단점이 있다. 따라서, 본 연구에서는 파일럿은 SLM 위상 시퀀스와 곱해지지 않으며, SLM 위상 회전 시퀀스에 따라 서로 다른 파일럿을 신호에 삽입하여, 부가 정보를 사용하지 않고 대역폭의 손실이 없는 개선형 SLM 기법을 연구하였다. 시뮬레이션 결과, 4개의 위상 회전 시퀀스를 갖는 SLM을 사용하였을 때, 파일럿 삽입으로 인해 높아진 신호의 PAPR을 원래 수준과 비슷한 성능으로 감소되는 것을 알 수 있다. PAPR of the pilot symbols can be reduced down by the CAZAC sequence in the SC-FDMA communication system. However, it is very complicated and takes quite a long time to compute the interpolation between the OFDM information symbols for the channel estimation because the pilot data are trasmitted in the block type. Furthermore, situation will be much more serious in the severe fading channel. Actually the pilot insertion of the comb type is much efficient and convenient for the channel estimation since the calculation of the interpolation can be made in the frequency domain symbol by symbol. But, the PAPR will be regrown when the pilot data are inserted with the information data in the comb type. So, in this paper, we like to study the PAPR reduction and comb type pilot assignment for the efficient channel estimation. Unlike the conventional SLM(selected mapping) method requiring the side information, our improved SLM method is to use the phase rotation sequence into information data without rotating phase of pilot. We use different pilot data according to the different phase rotation sequence. From the simulation result, it can be confirmed that when SLM method of 4 phase rotation sequence is used, PAPR is almost same to the block type method without pilot.

Phase Noise Correction Based on TPS Symbols for the Chinese DTTB System

In orthogonal frequency division multiplexing (OFDM) system, phase noise (PHN) from oscillator can severely reduce the performance by causing: common phase error (CPE) and inter-carrier interference (ICI). The impact of PHN on received signal can be characterized by the circular convolution of the transmitted signal and the discrete Fourier transform (DFT) of PHN signal in frequency domain. Digital television/terrestrial multimedia broadcasting (DTMB), announced as the Chinese digital television terrestrial broadcasting (DTTB) standard, adopted the time-domain synchronous OFDM system (TDS-OFDM) system which has 36 continuous transmission parameter signaling (TPS) symbols in frequency domain which be used for PHN suppression. Based on a linearized parametric model for PHN, least squared (LS) estimation and fast Fourier transform (FFT) approaching method for PHN correction are proposed in this paper. The effects of the PHN on channel estimation in both TDS-OFDM system and conventional cyclic prefix OFDM (CP-OFDM) are also investigated. Simulations show that the proposed algorithm can effectively reduce the PHN and improve the symbol error rata (SER) of TDS-OFDM systems over both additive white Gaussian noise (AWGN) and broadcasting multipath channel. In practice, the FFT-approaching method can be applied to the DTMB receiver-chip design directly with low implementation cost.

Reduced-Complexity Iterative Equalization for Severe Time-Dispersive MIMO Channels

In this paper, a reduced-complexity soft-interference-cancellation minimum mean-square-error (SIC-MMSE) iterative equalization method for severe time-dispersive multiple-input-multiple-output (MIMO) channels is proposed. To mitigate the severe time dispersiveness of the channel, a single carrier with cyclic prefix is employed, and the equalization is performed in the frequency domain. This simplifies the challenging problem of equalization in MIMO channels due to both the intersymbol interference (ISI) and the coantenna interference (CAI). The proposed iterative algorithm works in two stages. The first stage estimates the transmitted frequency-domain symbols using a low-complexity SIC-MMSE equalizer. The second stage converts the estimated frequency-domain symbols in the time domain and finds their means and variances to incorporate in the SIC-MMSE equalizer in the next iteration. Simulation results show the bit-/symbol-error-rate performance of the SIC-MMSE equalizer, with and without coding, for various modulation schemes.

Adaptive Linear Symbol Detection for OFDM Systems in Time-Frequency-Selective Fading Channels

Time-frequency-selective, equivalently time-variant multipath, fading channels in orthogonal frequency division multiplexing (OFDM) systems introduce intercarrier interference (ICI), resulting in severe performance degradation. To suppress the effect of ICI, several symbol detection methods have been proposed, all of which are based on the observation that most of the ICI's power is distributed near the desired subcarrier. However, these methods usually ignore the channel variation in a OFDM symbol block by fixing the number of considered ICI terms. Therefore, we propose a novel frequency-domain symbol detection method with moderate complexity, which adaptively determines the number of ICI terms within each OFDM symbol block.

Low-Complexity Equalization of OFDM in Doubly Selective Channels

Orthogonal frequency division multiplexing (OFDM) systems may experience significant inter-carrier interference (ICI) when used in time- and frequency-selective, or doubly selective, channels. In such cases, the classical symbol estimation schemes, e.g., minimum mean-squared error (MMSE) and zero-forcing (ZF) estimation, require matrix inversion that is prohibitively complex for large symbol lengths. An analysis of the ICI generation mechanism leads us to propose a novel two-stage equalizer whose complexity (apart from the FFT) is linear in the OFDM symbol length. The first stage applies optimal linear preprocessing to restrict ICI support, and the second stage uses iterative MMSE estimation to estimate finite-alphabet frequency-domain symbols. Simulation results indicate that our equalizer has significant performance and complexity advantages over the classical linear MMSE estimator in doubly selective channels.

Selection of a single uniquely specifiable [formula omitted] controller in the chain-scattering framework

This paper studies the notion of central H ∞ controllers in the chain-scattering framework. Since in the chain-scattering framework the H ∞ control problem is equivalent to a factorisation problem that yields non-unique factors, it is important to somehow pin down these factors so that the resulting central controller is uniquely defined and corresponds to the central and minimum-entropy controller frequently discussed in the literature. In so doing, we devise a procedure for the selection of a single uniquely specifiable H ∞ controller in the chain-scattering framework. The chain-scattering framework is important because it has a distinct advantage over state-space based methods for some applications in that it poses and solves the H ∞ control problem entirely in an operator-theoretic setting, thereby allowing us to contemplate direct changes of the frequency domain symbols rather than changes in the corresponding state-space matrices.