Vector OFDM Systems Research Articles

Partial intersection sphere decoding with weighted voting for sparse rotated V-OFDM systems

Vector orthogonal frequency division multiplexing (V-OFDM) is a general system that builds a bridge between OFDM and single-carrier frequency domain equalization in terms of intersymbol interference level and receiver complexity. In this paper, we focus on a rotated V-OFDM system over a broadband sparse channel owing to its large time delay spread and fewer nonzero taps. In order to collect the multipath diversity, a simple rotation matrix is designed, independent of the number of subchannels at the transmitter. For the rotated V-OFDM receiver, a partial intersection sphere decoding with weighted voting method is proposed by exploiting the sparse nature of the multipath channel. The proposed receiver chooses the transmitted vector from the set with the maximum likelihood estimation generated using the partial intersection sphere decoding method. For an extreme case, such as when a candidate set is empty, which usually occurs at a low signal-to-noise ratio (SNR), an efficient weighted voting system is used to estimate the transmitted vectors symbol-by-symbol. Simulation results indicate that the proposed receiver improves the symbol error rate performance with reduced complexity, especially for low SNR scenarios.

Achieving upper mutual information bound precoding for V‐OFDM with MMSE receiver

Traditional vector orthogonal frequency division multiplexing (V-OFDM) can obtain both multi-path diversity and outage gain by transforming an inter-symbol interference (ISI) channel into multiple ‘ISI-free’ channel vectors. To achieve full multi-path diversity and acquire better outage performance, a low-complexity precoding scheme combined with simple minimum mean square error (MMSE) equalisation for V-OFDM system is proposed in this study. First, the upper mutual information bound of the V-OFDM system is derived with channel state information at transmitter. Based on the upper bound, an optimal precoding scheme for V-OFDM is presented. Meanwhile, the closed-form and asymptotic expressions on outage probability of the proposed scheme are derived. Simulations show that this low-complexity scheme can achieve full multi-path diversity and result in lower outage probability than the traditional V-OFDM scheme. Besides, the proposed scheme in ISI fading channel is capable of approaching the upper bound with <0.1 bits/s/Hz performance gap and improving average channel capacity with 2 bits/s/Hz over the traditional V-OFDM scheme.

Space-Time and Space-Frequency Block Coded Vector OFDM Modulation

Vector orthogonal frequency division multiplexing (OFDM) is a promising modulation scheme, which allows for a flexible configuration and connects OFDM and single-carrier frequency domain equalization in a unified framework. In this letter, we design Alamouti-like space-time block coded and space-frequency block coded vector OFDM systems. Based on these schemes, we prove that, with two transmit and one receive antenna, the diversity order of the zero-forcing receiver is fixed to 2 over frequency selective fading channels, while that of the minimum mean square error receiver depends on the channel memory length, the vector block size, and the spectral efficiency.

EM-Based Phase Noise Estimation in Vector OFDM Systems Using Linear MMSE Receivers

Vector orthogonal frequency-division multiplexing (V-OFDM) for single-transmit-antenna systems is a generalization of OFDM where single-carrier frequency-domain equalization and OFDM are just two special cases. Phase noise in a V-OFDM system leads to a common vector block phase error (CVBPE) and an intervector block carrier interference effect. Severe performance degradation may occur if these two effects are not estimated and compensated well. In this paper, blind and semiblind phase noise estimation and compensation in a V-OFDM system is investigated by using the expectation-maximization (EM) algorithm. This is motivated by the fact that the conventional frequency-domain phase noise suppression schemes based on pilot-aided common phase error (CPE) or CVBPE estimation and compensation are not spectrally efficient as the vector block size is increased. Two novel schemes are proposed: One estimates the CVBPE only, and the other estimates the entire phase noise sequence in the time domain. General closed-form formulas for the maximization step of the EM algorithm for the two schemes are derived, and their computational complexity values are analyzed. The performances of the two schemes are investigated by using linear-minimum-mean-square-error (LMMSE) receivers. Simulations show that the two proposed schemes are very effective in estimating and compensating for phase noise in V-OFDM systems. It turns out that the second proposed scheme not only outperforms the traditional CPE or CVBPE schemes but is computationally efficient as well when applied to V-OFDM systems.

Analysis and Compensation of Phase Noise in Vector OFDM Systems

Vector orthogonal frequency division multiplexing (V-OFDM) for single transmit antenna systems is a generalization of OFDM where single-carrier frequency domain equalization (SC-FDE) and OFDM are just two special cases. It has been shown to be able to collect multipath diversity and thus generally outperforms OFDM. The performance of OFDM under phase noise has been extensively studied in the literature. These effects can be summarized as introducing a common phase error (CPE) and inter carrier interference (ICI) resulting in poor performance. The performance of V-OFDM under phase noise still remains uninvestigated and in this paper it is shown that phase noise in V-OFDM systems leads to a common vector block phase error (CVBPE) as well as an inter vector block carrier interference (IVBCI) effect. An expression for the signal plus interference noise ratio (SINR) for a V-OFDM system is derived and found to agree closely with simulation results. A pilot vector CVBPE based phase noise estimation technique is derived, and then combined with the maximum likelihood (ML) and the linear minimum mean square error (LMMSE) estimators to estimate the phase noise. It turns out that compared with OFDM, V-OFDM systems can perform phase noise estimation with lower complexity. The decorrelation and cancellation techniques are then used to compensate for the phase noise impairment. Numerical results for both coded and uncoded systems with perfect and practical channel estimation are provided to validate the analysis and effectiveness of the proposed phase noise estimation and compensation methods.

Response to "On Mathematical Equivalence Between Vector OFDM and Quadrature OFDMA"

In, we introduced a novel layered inverse Fast Fourier Transform (IFFT) structure based on the Divide-andConquer approach for computing the IFFT. Based on the structure we proposed asymmetric OFDM systems which bridge OFDM and single carrier systems. Its multiuser access version, Quadrature OFDMA, is developed in. In the presented form, the basic transceiver of asymmetric OFDM is mathematically similar to the vector OFDM system. We regret for not citing the vector OFDM and related work in our papers. As a response to, we argue that there are actually significant differences between our work and the vector OFDM work.

A novel Haar wavelet‐based vector BPSK–OFDM robust to channel spectral nulls and with reduced cyclic prefix length and PAPR

SUMMARYThe performance of OFDM systems may be degraded when intersymbol interference (ISI) channels have spectral nulls. The communication overhead because of the insertion of the cyclic prefix is high when ISI channels have many taps. Recently, the precoded OFDM systems and vector OFDM (VOFDM) systems were proposed to combat these two problems, respectively. This paper proposes a novel vector binary phase‐shift keying (BPSK)–OFDM system based on Haar wavelet transformation. The Haar wavelet transformation performs decomposition over the vector information symbols produced by a BPSK modulator. It shows that half of the information symbols are zero and the rest are or . Then, the vector BPSK–OFDM becomes the precoded OFDM, which inserts one or more zeros between two sets of K consecutive information symbols. This precoding scheme is able to remove the spectral nulls of an ISI channel without knowing the ISI (like conventional precoded OFDM systems), and it has the same cyclic prefix length as VOFDM systems. The proposed OFDM systems show better robustness to the spectral nulls channel, compared with the conventional VOFDM systems. Because of the insertion of (M −K) zeros between two sets of K consecutive information symbols, the conventional precoded OFDM systems have the data rate expanded and signal‐to‐noise power ratio reduced by 10 log 10(M∕K) dB compared with the proposed OFDM systems. Moreover, because half of the information symbols are zeros after Haar wavelet transformation, the proposed OFDM system can further reduce the transmitting peak‐to‐average power ratio. Finally, we compare the proposed OFDM systems with the precoded OFDM and VOFDM systems. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Minimal Euclidean distance‐inspired optimal and suboptimal modulation schemes for vector OFDM system

AbstractIn single‐input and single‐output (SISO) systems, the vector orthogonal frequency division multiplexing (VOFDM) has been proposed to reduce the cyclic prefix length, whereas the precoded OFDM has been proposed to overcome spectral‐null channels. However, VOFDM does not show robustness to spectral‐null channels, and the precoded OFDM system has expanded data rate. This work proposes the optimal and suboptimal modulation schemes in vector OFDM systems with knowledge of the channel impulse response (CIR) in order to reduce the bit error rate (BER). As the BER performance is determined by the diversity of the received vector symbols, the proposed modulation scheme mainly concerns the minimal Euclidean distance of all the possible received vector symbols. Through the analysis of the vector input and output equations, we derive the Euclidean distance of the received vector symbols. Then, we propose optimal and suboptimal modulation schemes in VOFDM system to overcome spectral‐null channels by improving the minimal Euclidean distance. Both theoretical performance analysis and simulation results are presented to show the robustness of our system. Finally, we conduct a compared performance analysis of the proposed VOFDM system, the conventional precoded OFDM system, and the conventional VOFDM system. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Modulated Coded OFDM Systems with Special Precoder

Orthogonal frequency-division multiplexing (OFDM) has been considered as a strong candidate for next-generation wireless communication systems to achieve high rate data transmission in a mobile environment. However, the performance of OFDM systems may be degraded when inter-symbol interference (ISI) channels have spectral nulls, and the data rate overhead due to the insertion of cyclic prefix is high when ISI channels have many taps. Recently, the precoded OFDM systems and vector OFDM (VOFDM) systems were proposed to combat these two problems, respectively. We propose a novel modulated coded OFDM system with special precoder that is robust to spectral nulls and with reduced cyclic prefix length. The precoder can be easily formulated by channel coding and digital modulation. This precoding scheme uses the redundancy information introduced by channel coding (such as zeros inserted in precoded OFDM system). It is able to remove the spectral nulls of an ISI channel without knowing the ISI. Simulation results show that our proposed OFDM system performance is better than precoded OFDM and VOFDM system.

Iterative decoding and demodulation for single-antenna vector OFDM systems

Vector orthogonal frequency-division multiplexing (OFDM) for single-antenna systems generalizes OFDM in that it converts an intersymbol interference (ISI) channel into multiple ISI-free vector channels and involves vector channel matrices instead of channel coefficients in its one-tap equalization (demodulation). Over frequency-selective fading channels, vector OFDM with increasing vector length implicitly offers more signal space diversity advantages over OFDM. However, the complexity of the brute force demodulator increases exponentially in terms of the vector size. In this paper, iterative demodulation and decoding for convolutionally coded vector OFDM systems are studied, and in particular, low-complexity demodulation schemes that employ linear cancellation and feature linear complexity in terms of the vector length are proposed and compared. Following the introduction of demodulators with ideal linear cancellation as benchmark, demodulators with hard and soft interference cancellation and their initialization options are studied. The demodulator with soft interference cancellation dynamically updates the symbol estimates and their instantaneous reliability measure based on the code bit probabilistic information passed from preceding iterations. It alleviates error propagation that is detrimental to the demodulator with hard interference cancellation and shows performance close to that of the brute force demodulator, with great overall complexity reduction. Extensive simulation results demonstrate how the choice among the presented schemes and the vector length affect the convergence rate and the achievable performance of the iterative receivers

Synchronization techniques and guard-band-configuration scheme for single-antenna vector-OFDM systems

Vector orthogonal frequency division multiplexing (OFDM) was proposed for single-antenna systems as a generalization of OFDM. It converts an intersymbol interference (ISI) channel into multiple "ISI-free" vector channels while involving channel matrices instead of channel coefficients in one-tap equalization. Over multipath fading channels, it benefits from signal-space diversity. This paper addresses practical issues such as guard-band configuration, timing estimation, and carrier- and sampling-frequency synchronization for vector OFDM. An equivalent structure derived for vector OFDM manifests the relation between vector OFDM and conventional OFDM so that the solutions to guard-band configuration as well as carrier- and sampling-frequency synchronization for conventional OFDM can be modified to fit into the vector-OFDM framework. It is also shown by analysis that the pre-fast Fourier transform (FFT) algorithms for timing estimation and carrier-frequency synchronization in the conventional OFDM framework can be extended straightforwardly to vector OFDM with comparable performance. Simulation results of uncoded systems are given to show the effectiveness of the proposed synchronization techniques.

Precoded and vector OFDM robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems

The performance of orthogonal frequency-division multiplexing (OFDM) systems may be degraded when intersymbol interference (ISI) channels have spectral nulls. Also, when ISI channels have many taps, the data rate overhead due to the insertion of the cyclic prefix is high. We first propose a precoded OFDM system that may improve the performance of the OFDM systems for spectral null channels. We also propose size K/spl times/x1 vector OFDM (VOFDM) systems that reduce the cyclic prefix length by K times compared to the conventional OFDM systems. The precoding scheme is simply to insert one or more zeros between each two sets of K consecutive information symbols, although it can be generalized to a general form. This precoding scheme may be able to remove the spectral nulls of an ISI channel without knowing the ISI channel. When no zero is inserted between each two sets of K consecutive information symbols and only each K consecutive symbols are blocked together, we obtain VOFDM systems. Both theoretical performance analysis and simulation results are presented. Finally, we compare the combination of the VOFDM systems and the unitary matrix modulation with the conventional OFDM systems and the phase-shift keying modulation, where both differential (noncoherent) and coherent modulations and demodulations are considered.